NISTIR 7327 

Design, Measurements and Performance Predictions 

for a Micromolded Refrigerant Expansion Device 

David A. Yashar 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

National Institute of Standards and Technology 

Technology Administration 

United States Department of Commerce 
NISTIR 7327 

Design, Measurements and Performance Predictions 

for a Micromolded Refrigerant Expansion Device 

David A. Yashar 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

April 2006 

U.S. DEPARTMENT OF COMMERCE 

Carlos M. Gutierrez, Secretary 

TECHNOLOGY ADMINISTRATION 

Michelle O’Neill, Acting Under Secretary of Commerce for Technology 

National Institute of Standards and Technology 

William Jeffrey, Director

ii
ABSTRACT 

The design, fabrication and testing of a thermopneumatic microfabricated valve for 

controlling refrigerant mass flow rate during expansion is presented in this report. This device 

was fabricated through nickel electroplating within very thick SU8 molds, thereby realizing 

expansion devices useful for small vapor compression systems through an inexpensive modified 

Ultraviolet-LIGA (German acronym for lithography, electrodeposition and molding) process. 

This work begins with process development to create meso-scale nickel pieces through 

electroplating into SU8 molds. Two test benches were constructed and used to benchmark the 

performance of a prototype with compressed air and R134a. Three dimensional numerical 

simulations were performed on the flowfield within the device to predict its ability to control 

compressed air. A code was also developed to predict the device’s temporal response and 

relationship between actuation level and power input. 

The prototype was able to reduce the mass flow rate of the compressed air by 22 % at the 

conditions used in the analysis. The performance was then demonstrated in a 1.5 kW to 2 kW

R134a vapor compression system to characterize both steady state and transient response. 

Steady state data showed that the mass flow rate of refrigerant could be controlled using the 

valve. The level of refrigerant subcooling defined the magnitude of the response. Steady state 

data taken at 750 kPa inlet pressure shows the mass flow rate was reduced by 4.2 % at 1 oC 

subcooling and up to 10.8 % at 5 oC subcooling for a given level of actuation. Transient system

response was characterized using cyclic actuation of the device. The change in capacity was 

approximately 5 %, at the conditions used during these tests. 

Keywords: HVAC&R, MEMS, Microfabrication, Refrigerant Expansion, SU8

iii
ACKNOWLEDGEMENTS 

I would like to thank Dr. Piotr Domanski, Dr. W. Vance Payne II, Dr. Mark Kedzierski, Dr. 

David Didion and Mr. John Wamsley of the National Institute of Standards and Technology 

(NIST) for their technical and laboratory support during this project. 

I would also like to thank my dissertation advisor, Dr. Don DeVoe, Associate Professor at the 

University of Maryland, for his direction and assistance during this project. Also, I would like to 

extend gratitude to the members of my advisory committee at the University of Maryland, Dr. 

Amr Baz, Dr. Inderjit Chopra, Dr. Kenneth Kiger, and Dr. Reinhard Radermacher for their 

guidance, assistance, and cooperation. 

I would also like to thank the Cornell Nanoscale Science and Technology Facility (CNF) for the 

use of their cleanroom during the fabrication of the DRIE prototype produced during this effort. 

iv
PREAMBLE 

This report is essentially the dissertation of David Anthony Yashar which was submitted to the 

University of Maryland in partial fulfillment of his Doctor of Philosophy requirements. 

v
DISCLAIMER 

Certain trade names and company products are mentioned in the text or identified in an 

illustration in order to adequately specify the experimental procedure and equipment used. In no 

case does such an identification imply recommendation or endorsement by the National Institute 

of Standards and Technology, nor does it imply that the products are necessarily the best 

available for the purpose. 

 

vi
Table of Contents 

Abstract...................................................................................................... iii 

Acknowledgements.................................................................................... iv 

Preamble ......................................................................................................v 

Disclaimer.................................................................................................. vi 

Table of Contents...................................................................................... vii 

List of Tables ............................................................................................. ix 

List of Figures..............................................................................................x 

Nomenclature........................................................................................... xiii 

Nomenclature: Greek and other Symbols.............................................. xiv 

1: Introduction..............................................................................................1 

 1.1 Expansion Devices.............................................................................1 

 1.2 Applications.......................................................................................4 

 1.3 Existing MEMS Fluidic Valves.........................................................6 

 1.4 Fabrication Options............................................................................9 

 1.4.1 Wet Etching ..............................................................................9 

 1.4.2 Dry Etching...............................................................................9 

 1.4.3 LIGA Based Methods.............................................................10 

2: Design Concept......................................................................................12 

 2.1 Design ..............................................................................................12 

 2.2 Simulation........................................................................................14 

 2.2.1 Stresses on Diaphragm............................................................14 

 2.2.2 Oil Coefficient of Thermal Expansion....................................15 

 2.2.3 Relationship Between Oil Temperature and Piston Motion ...16 

3: Performance Measurement Methodology..............................................17 

 3.1 Compressed Air Test Apparatus......................................................17 

 3.2 Breadboard Vapor Compression Test Apparatus ............................18 

4: DRIE Silicon Prototype .........................................................................23 

 4.1 Design and Fabrication ....................................................................24 

 4.1.1 Masks......................................................................................24 

 4.1.2 Device Fabrication..................................................................26 

 4.2 Assembly..........................................................................................27 

 4.3 Characterization ...............................................................................29 

 4.4 Attempted Testing in an R134a System...........................................31 

 4.5 Conclusions Drawn from Silicon Prototype ....................................32 

5: Thick SU8-Nickel Micromolding Process.............................................34 

6: SU8 Nickel Micromolded Device..........................................................45 

 6.1 New Design .....................................................................................45 

 6.2 Fabrication ......................................................................................47 

 6.3 Feature Characterization ..................................................................53 

 6.3.1 Piston/Diaphragm Piece..........................................................53 

 6.3.2 Flow Channel Piece ................................................................56 

 6.3.3 Flow Channel Cap Piece.........................................................58 

 6.4 Assembly..........................................................................................59 

 6.5 Measured Piston Actuation..............................................................62 

7: Temporal Response Analysis.................................................................64 

vii
 7.1 Overview .........................................................................................64 

 7.2 Derivation of Nodal Equations .......................................................65 

 7.3 Nodal Spacing and Code Structure .................................................73 

 7.4 Transient Response Experiments ....................................................76 

 7.5 Summary .........................................................................................80 

8: Numerical Simulations ..........................................................................81 

 8.1 Initial Simulations ...........................................................................81 

 8.2 Verification of Initial Simulation ....................................................84 

 8.2 Flow Control Prediction Curve .......................................................89 

9: Gas Flow Measurements........................................................................92 

 9.1 Flow Control Measurement ............................................................92 

 9.2 Comparison to CFD Simulations.....................................................93 

10: R134a Vapor Compression Test Results and Discussion....................95 

 10.1 Steady State Operation ..................................................................95 

 10.2 Quasi-Transient Operation.............................................................96 

 10.3 Discussion......................................................................................99 

 10.3.1 Subcooling Influence ..........................................................101 

 10.3.2 Inlet Pressure Influence.......................................................101 

 10.3.3 Temporal Response.............................................................102 

 10.4 Summary......................................................................................103 

11: Summary and Future Work................................................................105 

 11.1 Summary .....................................................................................105 

 11.2 Significant Contributions.............................................................106 

 11.3 Future Work.................................................................................106 

References................................................................................................108 

Appendix A: Raw Code for Transient Analysis.....................................113 

Appendix B: Air Flow Measurement Data and Uncertainty ..................119 

 B.1 Raw Data .................................................................................119 

 B.2 Uncertainty Analysis for Gas Flow Measurements.................120 

Appendix C: Test Data and Uncertainty for Refrigerant Flow 

 Control Measurements.....................................................122 

 C.1 Uncertainty Analysis...............................................................122 

 C.2 Steady State Data – No Actuation...........................................CD 

 C.3 Steady State Data – With Actuation........................................CD 

 C.4 System Response Data ............................................................CD 

viii
List of Tables 

2.1 Volume Measurements for PAG..........................................................15 

6.1 Measurements of Diaphragm Thickness..............................................56 

6.2 Measurements for Flow Channel Piece ...............................................57 

6.3 Measurements for Flow Channel Cap Piece .......................................59 

7.1 Curve fit Parameters for Device’s Time Response .............................80 

8.1 Initial Conditions used for Preliminary Simulations ..........................83 

8.2 Test Matrix for Simulations ................................................................90 

ix
List of Figures 

1.1 Vapor Compression Cycle ....................................................................1 

1.2 Short Tube Restrictor.............................................................................2 

1.3 Thermostatic Expansion Valve ..............................................................3 

1.4 Air Conditioner Efficiency Relative to Refrigerant Charge 

 for Systems with Short Tubes and TXV’s ..........................................4 

1.5 Multipath Evaporator without (a) and with (b) Smart Distributor ........5 

1.6 Results of Smart Distributor study at NIST ..........................................6 

1.7 Fluidic Valve by Redwood Microsystems – basic 

 normally-open design ............................................................................7 

1.8 Fluidic Valve by Redwood Microsystems for Refrigerant 

 Control ..................................................................................................7 

1.9 Bubble-Actuated Planar Microvalve by Papavasiliou ..........................8 

1.10 SU8 Molecule ...................................................................................10 

1.11 Cationic Polymerization Process ......................................................11 

2.1 Conceptual Sketch of Refrigerant Expansion Device .........................12 

2.2 Sketch of Piston/Diaphragm ...............................................................12 

2.3 Sketch of Cover-plate Chip .................................................................13 

2.4 Actuator Assembly ..............................................................................13 

2.5 Final Assembly of Refrigerant Expansion Device Components ........13 

3.1 Schematic of Gas Flow Test Apparatus ..............................................17 

3.2 Refrigerant Flow Loop for Vapor Compression Test Apparatus ........19 

3.3 Condenser HTF Flow Loop for Vapor Compression Test 

 Apparatus ............................................................................................20 

3.4 Evaporator HTF Flow Loop for Vapor Compression test 

 Apparatus .............................................................................................21 

4.1 Process Flow used to Produce the Piston/Diaphragm Chip ................23 

4.2 Process Flow used to Produce the Coverplate Chip ...........................23 

4.3 Masks used for Piston/Diaphragm Chip .............................................25 

4.4 Masks used for Coverplate Chip .........................................................25 

4.5 SOI Wafer after the Fabrication of Pistons and Diaphragms .............26 

4.6 a) Coverplate Device ...........................................................................27 

 b) Piston/Diaphragm Device ................................................................27 

4.7 Assembled Device ..............................................................................28 

4.8 Specifications of Brass Capsule ..........................................................28 

4.9 Specifications of Brass Capsule Cap ..................................................28 

4.10 Heater and Cap Assembly .................................................................29 

4.11 Final Assembly of Actuator ..............................................................29 

4.12 Performance Simulation for Displacement of Piston ........................30 

4.13 Characterization of Piston Displacement ..........................................31 

5.1 Basic Fabrication Process Goal for SU8 .............................................35 

5.2 Buckling Mechanism for Multiple SU8 Layer Stacks ........................36 

5.3 Geometrical Constraint for Nickel Device .........................................38 

5.4 Fill Process for SU8 Overhangs or Channels .....................................38 

5.5 Mask Process for SU8 Overhangs or Channels ..................................39 

5.6 Lamination Process for SU8 Overhangs or Channels .........................39 

x
5.7 Typical Thick Layer SU8 Edge Bead Distortion ................................41 

5.8 Process Steps to Eliminate Edge Bead ................................................42 

5.9 Process Steps to Eliminate Edge Bead Continued ..............................43 

5.10 Typical Thick Layer SU8 Deposition Using Additional Fabrication 

 Steps ...................................................................................................44 

6.1 Sketch of Piston/Diaphragm Piece ......................................................45 

6.2 Sketch of Flow Channel Piece ............................................................46 

6.3 Sketch of Flow Channel Cap Piece .....................................................46 

6.4 Assembly of the Micromolded Pieces ................................................47 

6.5 Masks used to Fabricate Molds for Piston/Diaphragm Piece .............48 

6.6 Masks used to Fabricate Molds for Flow Channel Piece ....................48 

6.7 Masks used to Fabricate Molds for Flow Channel Cap Piece ............49 

6.8 Process Flow for Fabrication of Piston/Diaphragm Molding .............51 

6.9 Electroplating Apparatus ....................................................................52 

6.10 Characterization Photograph: Top of Piston ....................................53 

6.11 Side Profile of Piston .........................................................................54 

6.12 Locations of Characterization Measurements for 

 Piston/Diaphragm Piece ....................................................................54 

6.13 a) Portion of Mask #2 .......................................................................55 

 b) Resulting Curvature of Ridges .....................................................55 

6.14 Locations of Characterization Measurements for Flow 

 Channel Piece ....................................................................................56 

6.15 a) Photograph of Channel Wall .........................................................57 

 b) Photograph of Channel Through Hole ..........................................57 

6.16 Piston and Port Assembly .................................................................58 

6.17 Locations of Characterization Measurements for Flow 

 Channel Cap Piece ............................................................................59 

6.18 a)Top portion of oil capsule ..........................................................60 

 b) Bottom portion of oil capsule ...................................................60 

6.19 Oil Capsule Top Connected to Flow Restrictor ................................61 

6.20 Bottom Portion of the Oil Capsule, Including Heater .......................61 

6.21 Predicted Displacement of Piston .....................................................62 

6.22 Characterization of Piston Displacement for Nickel Micromolded 

 Prototype ..........................................................................................63 

7.1 Sketch of Capsule ...............................................................................64 

7.2 Nodal Network for Horizontal Medium Change .................................66 

7.3 Nodal Network for Vertical Medium Change .....................................67 

7.4 Nodal Network for Upper-Corner Medium Change............................69 

7.5 Nodal Network for Lower-Corner Medium Change ...........................70 

7.6 Nodal Network for Nodes Along Centerline .......................................71 

7.7 Nodal Network for Nodes Along Centerline with Medium Change ...72 

7.8 Flowchart for Code Execution.............................................................74 

7.9 Steady State Temperature Distribution................................................75 

7.10 Time Elapsed Temperature Distribution at 1 Watt of Heat 

 Generation.........................................................................................77 

7.11 Transient Thermal Response of Device to Heat Input.......................78 

xi
7.12 Immediate Response to Heat Input....................................................79 

8.1 Portion of Device used for Initial CFD Simulations ...........................82 

8.2 Comparison of Mach Number ............................................................87 

8.3 Comparison of Velocity ......................................................................87 

8.4 Comparison of Pressure ......................................................................88 

8.5 Comparison of Temperature ...............................................................88 

8.6 Geometry used for CFD Analysis .......................................................89 

8.7 Close-Up of Flow Obstruction Geometry ...........................................89 

8.8 Results from CFD Simulations............................................................91 

9.1 Results of Air Flow Measurements .....................................................92 

9.2 Comparison Between Gas Flow Measurements and CFD Analysis....93 

10.1 Steady State Refrigerant Mass Flow Rate for Two Levels of 

 Actuation ...........................................................................................96 

10.2 System Response – Normalized Piston Position, 

 Condensing Pressure, and Subcooling ..............................................97 

10.3 System Response – Normalized Piston Position, 

 Refrigerant Mass Flow Rate, and System Capacity...........................97 

10.4 System Response – Evaporator Exit Superheat and Normalized 

 Piston Position ...................................................................................98 

10.5 System Capacity in Response to Device Operation ..........................99 

10.6 Mass Flow Rate vs. Inlet Pressure for Constant Subcooling...........102 

xii
Nomenclature

Parameter ..............................................................................................Units 

Acs Cross Sectional Area.........................................................m

2

C Speed of Sound ................................................................m/s 

Cp Specific Heat Capacity................................................J/kg·K 

Dh Hydraulic Diameter...........................................................m

2

E Young’s Modulus..........................................................N/m

2

f Friction Factor.................................................dimensionless 

Gr Grashof Number..............................................dimensionless 

h Enthalpy ........................................................................kJ/kg 

hp Height of Piston ................................................................. m 

k Thermal Conductivity ................................................W/m·K 

Lc Critical Length ................................................................... m 

M Mach Number .................................................dimensionless 

m Nodal Variable ................................................dimensionless 

m& Mass Flow Rate...............................................................kg/s 

n Nodal Variable ................................................dimensionless 

P Pressure.........................................................................N/m

2

Po Stagnation Pressure.......................................................N/m

2

P* Choking Pressure for Fanno Flow ................................N/m

2

R Universal Gas Constant............................................. m

2

/s2·K

R2 Residual Squared Error for Best Fit Curve .....dimensionless 

Re Reynolds Number ...........................................dimensionless 

r Radius of Diaphragm......................................................... m 

rp Radius of Piston ................................................................. m 

s Entropy........................................................................J/kg·K 

t Diaphragm Thickness........................................................ m 

T Temperature ........................................................................K 

Tss Steady State Temperature ...................................................K 

To Stagnation Temperature ......................................................K 

Ux x-Component of Velocity ................................................m/s 

Uy y-Component of Velocity ................................................m/s 

Uz z-Component of Velocity.................................................m/s 

V Shear Force ...................................................................N/m2

w Pressure Differential Across Diaphragm ......................N/m2 

xiii
Nomenclature: Greek and other Symbols 

Parameter ..............................................................................................Units 

α Thermal Diffusivity ....................................................... m2/s 

β Coefficient of Thermal Expansion...................................1/K 

γ Ratio of Specific Heats...................................dimensionless 

δ Piston Deflection................................................................ m 

ε Time Lag.............................................................................s 

φ Parameter used for Deflection Analysis Integration.......... m 

ν Poisson’s Ratio...............................................................none 

ρ Density .........................................................................kg/m3

σ Stress.............................................................................N/m

2

σy Yield Stress...................................................................N/m2

τ Time Constant......................................................................s 

τs Shear Stress...................................................................N/m2

Θ Steady State Temperature ...................................................K 

∀ Volume .............................................................................m3

xiv
CHAPTER I 

Introduction

The vapor compression cycle is used to move energy from a low temperature reservoir to 

a high temperature reservoir. There are four major mechanical components of the vapor 

compression cycle which are necessary to implement this cycle. The four basic cycle 

components and the process which the refrigerant undergoes are shown below in Figure 1.1. 

Figure 1.1 Vapor Compression Cycle and Required Mechanical Components 

25 50 75 100 125 150 175 200 225 250 275 300

102

103

104

h [kJ/kg]

P [kPa]

 8°C

 43.38°C

 30°C

 3°C

 0.2 0.4 0.6 0.8

R134a

Condenser 

The compressor takes low pressure vapor and compresses it into a hot, high pressure 

vapor. 

The condenser is a heat exchanger that takes the hot, high pressure vapor from the 

compressor and allows it to reject heat. While doing so, the fluid undergoes phase change and 

condenses into a liquid. 

The expansion device is a flow constricting device; its purpose is to establish a pressure 

differential between the components on either side. Also, the expansion device is tasked with 

controlling the mass flow of the refrigerant through the cycle. As the refrigerant from the 

condenser passes through the expansion device, it undergoes substantial pressure drop. This 

pressure drop occurs without energy addition to the fluid; therefore, the temperature of the fluid 

is lowered through this process. Generally, the expansion device receives refrigerant that is near 

saturated liquid conditions, and it lowers the refrigerant’s pressure to the point where it 

undergoes a partial change of phase and becomes a liquid-vapor mixture. 

The evaporator is a heat exchanger that takes the low temperature liquid-vapor and 

allows it to absorb heat from an outside source. This causes the remaining liquid refrigerant to 

boil at a low temperature, producing a cooling effect. 

1.1 Expansion Devices 

Most of the smaller vapor compression systems use a simple, fixed area flow restrictor as 

the expansion device. Their simple design and low cost make them well suited for many 

applications. The most common of these devices are the capillary tube and the short tube 

restrictor. 

The capillary tube is the device of choice for the smallest systems, such as household 

refrigerating appliances [1]. The capillary tube is a small gage section of pipe which induces a 

drop in pressure through friction. Typical sizes for capillary tubes range between 1 m and 6 m in 

Compressor

Evaporator

Expansion 

Device 

1
length, with a diameter between 0.5 mm and 2 mm. The exact diameter and length of a capillary 

tube must be selected based on the designed operating conditions and the specifications of the 

compressor. 

Short tube restrictors are commonly used for many residential air conditioning and heat 

pump applications. They are also frequently used in automotive air conditioning systems. A 

short tube is a slug of metal, typically between 5 mm and 40 mm in length, with a small hole 

bored through its length. The short tube diameter typically ranges between 0.5 mm and 2 mm. 

A sketch of a short tube is shown below in Figure 1.2. 

Figure 1.2 Short Tube Restrictor 

Unlike the capillary tube, which induces pressure drop through friction, the short tube 

mainly induces pressure drop through abrupt changes in flow area. As the refrigerant enters one 

side of the short tube, the area contraction causes the refrigerant’s pressure to drop, 

isenthalpically, until it begins to undergo phase change. At this point, the flow is termed

“approximately” choked because it seems to be relatively insensitive to the downstream 

conditions [2, 3]. This is one of the most difficult problems in fluid mechanics to analyze 

because it involves metastable multiphase flow with the vapor phase traveling near its sonic 

velocity. Like the capillary tube, the short tube, is also a fixed area expansion device and must 

be sized according to its application. 

A major disadvantage of these devices is that they must be designed for a unique 

operating condition. Therefore, a system operating with a fixed area expansion device loses 

efficiency when operating away from its design point, which often occurs through changes in the 

heating or cooling load. Also, a refrigerant working in the system is at a much higher pressure 

than atmospheric and therefore tends to leak out of a system over time if not perfectly sealed. 

When a system leaks refrigerant the cycle efficiency declines, and the impact is very large for a 

fixed area expansion. 

Improved operational efficiency can be realized if the expansion device has the ability to 

control the mass flow rate of the refrigerant so that the demands of the application are aptly met 

[4]. There are a few types of expansion devices designed to control the mass flow rate of 

refrigerant based on information that is sensed during operation. The most common of which is 

the thermostatic expansion valve (TXV). The TXV is shown below in Figure 1.3 [5]. 

2
Figure 1.3 Thermostatic Expansion Valve 

The TXV is controlled by a small bulb that is in thermal contact with the exit of the 

evaporator heat exchanger. The bulb’s temperature is very close to the temperature of the 

refrigerant exiting the evaporator. The bulb is filled with liquid and vapor refrigerant, therefore 

the pressure in the bulb will vary according to the temperature of the refrigerant. A membrane 

on the upper portion of the expansion valve flexes in response to the changes in the pressure of 

the bulb, and thereby controls the movement of a plug inside the valve. 

The operation is easily understood by example. If the refrigerant flow rate through the 

evaporator is too low, then the refrigerant would be exiting the evaporator at a warmer than 

desired temperature. This causes the temperature in the bulb to rise, thereby raising the pressure 

of the refrigerant in the bulb. The increased pressure in the bulb causes the membrane in the 

valve to flex downward (as shown in figure 1.3). Since the membrane is rigidly connected to the 

plug in the valve, the plug also moves downward which opens the flow passage for the 

refrigerant. This allows more refrigerant to flow through the valve into the evaporator. 

TXV’s are mainly used in moderate sized refrigeration systems and residential heat 

pumping and air conditioning applications. Obviously, they are much more expensive than the 

constant area devices; therefore, they are not typically used unless the cost can be offset by the 

improvement in operational efficiency. The benefits seen from employing TXV’s over a fixed 

area expansion device can be quite substantial, particularly when the cycle must operate over 

varying conditions [6]. Figure 1.4, taken from Proctor [7], demonstrates the decline in 

residential air conditioner efficiency with off-design refrigerant charge. This occurs in

approximately 2/3 of all residential systems at any moment in time [8]. 

3
Figure 1.4 Air Conditioner Efficiency Relative to Refrigerant Charge for Systems with Short 

Tubes and TXV’s (Proctor [7]) 

The obstacle for using a TXV over a constant area device is cost. If variable restriction 

expansion devices could be produced cheaply, they could be used in many different applications 

where they are currently uneconomical. 

1.2 Applications 

One application which would greatly benefit from an inexpensive, small, variable 

expansion device is that of automotive air conditioning systems. These systems are all oversized 

for their application out of necessity because such a system must be able to quickly reduce the 

temperature in the car when first started. Also, the compressors receive power directly from the 

crankshaft; therefore, these systems can not be hermetically sealed and consequently, they leak 

refrigerant over time. 

According to the National Renewable Energy Laboratory [9], the average car in the 

United States has a fuel economy of 9.4 kilometers per liter. This reduces to 7.7 km/L while the 

air conditioner is operating. This means that a 15 % to 30 % increase in automotive AC 

efficiency, which is a reasonable expectation for a variable flow restrictor replacing its fixed area 

expansion device, will result in a 0.3 km/L to 0.5 km/L improvement in the fuel economy. The 

cost of using a variable expansion device for automotive air conditioning is substantially larger

than the savings in fuel consumption; therefore, they are rarely used in automotive AC systems. 

Given the current global concerns of rising fuel costs and CO2 emissions, this will likely get 

more attention; but it will not become common unless one can be produced inexpensively. 

Another excellent application for an inexpensive controllable expansion device is in the 

concept of a smart distributor [10]. Most residential air conditioning systems use a multiple 

circuit evaporator. By dividing the refrigerant flow between parallel circuits in the evaporator, 

the penalties associated with the refrigerant’s pressure drop in the evaporator are reduced. 

Currently, the refrigerant’s pressure is reduced by the expansion device, and then divided 

amongst the circuits in the evaporator using a distributor. After the refrigerant passes through a 

circuit and exits the evaporator, it is reconnected to the other circuits and the refrigerant goes on 

to the compressor, see Figure 1.5a. If a TXV is used, the sensing bulb is located at a point after 

the circuits are merged to ensure that no liquid droplets are passed to the compressor. Nonuniform air flow or partial frosting of the evaporator can significantly impact the uniformity of 

4
the heat transfer from circuit to circuit. If the refrigerant exiting one of the circuits is not 

completely vaporized, the TXV will sense that there is not enough superheat in the suction line 

and the total mass flow rate to all of the circuits will be reduced. 

The concept of a smart distributor works in a slightly different manner. Here, the 

distributor precedes the expansion process and the refrigerant to each circuit can be throttled 

individually based on the demands of that circuit, see Figure 1.5b. Therefore, if the refrigerant in 

one circuit does not completely vaporize, only the mass flow rate through that circuit will be 

reduced. As a consequence, the refrigerant will be rerouted through circuits that can 

accommodate greater mass flow. 

Figure 1.5 Multipath Evaporator without (a) and with (b) Smart Distributor 

The benefits of a smart distributor were demonstrated at the National Institute for 

Standards and Technology through a series of tests [10]. For these tests, the capacity of a three 

circuit evaporator was measured under conditions of uniform air flow. Next, a non-uniform air 

flow pattern was imposed on the evaporator, with one half of the evaporator receiving more air 

than the other. A reduction in the evaporator capacity resulted. Finally, the individual expansion 

valves for each circuit were adjusted so that the exit conditions for each circuit were identical 

under non-uniform air flow conditions. Figure 1.6 shows the results of this study. In this figure, 

the blue diamonds depict the degraded performance of the evaporator under non-uniform air 

flow and uniform refrigerant distribution, the pink squares depict the capacity of the evaporator 

with non-uniform air flow and individually optimized expansion. It was found that the 

performance of this evaporator was severely reduced as the air flow became more non-uniform, 

and with a smart distributor, nearly all of the lost capacity could be recuperated. 

5
0.5

0.6

0.7

0.8

0.9

1

1.1

1 1.522.5 3 3.5 4 4.5

Air Velocity Ratio (bottom/top)

Capacity Relative t

o Baseline

Optimized refrigerant mass flow rate

Uniform refrigerant mass flow rate

Figure 1.6 Degradation of Evaporator Capacity with Uniform and Optimized Refrigerant 

Distribution [10] 

These are just two applications which would benefit greatly from a small, inexpensive, 

variable expansion device. In addition, there are a number of small HVAC&R systems that 

would benefit if their fixed area expansion device were replaced by such a device. Other 

applications include window-style air conditioners and household refrigerating appliances. 

1.3 Existing MEMS Fluidic Valves

Fabrication technologies developed for MicroElectroMechanical Systems (MEMS) 

processes have been widely explored as a means to develop fluidic valves. Batch fabrication 

processes offer potential for satisfying the demands of refrigerant expansion at a market 

acceptable cost. Several groups have developed microfabricated valves that may be applicable 

for refrigerant expansion. Microstaq [11] has fabricated a valve for which refrigerant expansion 

is named as a possible application. Their valve is made from a three layer stack of silicon, 

fabricated using reactive ion etching (RIE), deep reactive ion etching (DRIE), and wet etching. 

The valve operation is based on the principle of thermal actuation controlling a sliding plate 

which alters the dimensions of an orifice. At the present time, Microstaq has not begun 

production, nor have they publicly disclosed any test data for refrigerant expansion. 

Redwood Microsystems [12-15] has developed a boss-and-valve seat type valve which 

was demonstrated as a refrigerant expansion control device with flow rates of up to 3 g/s and 

differential pressures of up to 1 MPa. This device was designed and fabricated using 

inexpensive wet etching techniques. It uses thermal expansion of a liquid to seal a valve seat 

with a membrane. A schematic of their basic normally-open device is shown below in 

Figure 1.7. This device is comprised of three layers in a stack. The bottom and middle layers 

are made out of silicon and formed by anisotropic wet etching. The bottom layer is the orifice 

layer and serves as a connection point for the manifold; the middle layer contains a thin 

membrane. The top layer is made out of Pyrex, it has a metal resistive heaters patterned onto the 

6
lower side and two contact holes drilled through it ultrasonically. In between the Pyrex layer and 

the membrane layer is a reservoir liquid, shown in blue. 

Figure 1.7 Fluidic Valve by Redwood Microsystems – basic normally-open design 

The fluid being controlled flows upwards through the inlet port at the center of the stack 

and leaves through the exit port shown on the right hand side of the device. When the heaters are 

powered on, the liquid is warmed and it expands, pushing the membrane downwards. The 

membrane acts as a valve seat, partially or completely sealing off the inlet port to the device. 

For the operation of the basic design, the liquid must undergo very large temperature 

changes. Although the magnitude of this temperature increase was not directly disclosed in any 

of their publications, it could be easily calculated from their work as being between 120 °C to 

350 °C depending on the design parameters studied in their published works. 

Since the basic design inherently provides a high degree of heat transfer between the 

liquid and the fluid passing through the device, Redwood Microsystems changed the design so 

that it could be used for refrigerant control. This design incorporates a fourth layer into the stack, 

as seen below in Figure 1.8, which greatly reduced the amount of heat transfer imparted onto the 

fluid. 

Figure 1.8 Fluidic Valve by Redwood Microsystems for Refrigerant Control 

The additional layer is a Pyrex layer which sits between the membrane layer and the 

heater layer. This layer adds a considerable amount of volume to the liquid reservoir, thereby 

requiring a smaller temperature change to push the membrane onto the valve seat. Also, this 

Pyrex layer provides a mechanical stop for the membrane under conditions of rapid cool down. 

This device was demonstrated with refrigerant HFC134a, controlling flow rates between 0 g/s 

and 3 g/s with differential pressures of up to 1 MPa. Redwood Microsystems’ devices have not 

received much acceptance in the HVAC&R market to date, mainly due to the refrigerant path 

inherent to its design. 

In order for a fluid to flow through this device, it must travel up through the inlet port, be 

impinged on the membrane, turn 90° towards the outer edge of the device, and turn another 90° 

before leaving through the exit port. Furthermore, the fully-open gap between the membrane and 

the valve seat is typically on the order of 50 μm.

7
Real HVAC systems are made of copper, brass, and steel components which must be 

brazed or soldered together; therefore, there are always particulates entrained in the refrigerant. 

With the flow pattern dictated by the Redwood Microsystem design, it is inevitable that this 

device will become clogged with particulates. Some HVAC&R systems use filters in the 

refrigerant lines to catch these particulates; however, filters that can reliably remove particulates 

to the level required for this device can cause substantial pressure drop within the system. 

Therefore this device is acceptable for laboratory work, but HVAC&R systems manufacturers 

are skeptical. It is more desirable to ensure an open flow path on the order of 500 μm.

There are literally hundreds of other designs of devices being developed at numerous 

research institutions worldwide for the purpose of fluid control. The common concern is the 

ability to completely stop flow with very little leakage. In order to accomplish this, the concept 

of a boss and valve seat, as shown in the Redwood Microsystems design, is the focus of nearly 

all research. The problem with this is type of design is that current fabrication processes make it 

difficult to scale up such a design so that the fluidic path can pass particulates entrained in the 

flow. Nguyen and Wereley [16], Gad-El-Hak [17], Cui [18], and Kovacs [19] present good 

overviews for the types of device concepts that have been developed for fluid control. 

One device which works on a fundamentally different basis than boss and valve seat is 

that of Papavasiliou [20-21], shown in Figure 1.9. This device works by opening and closing a 

gate across a fluidic channel, which thereby decreases or increases the resistance to the flow in 

the channel. 

Figure 1.9 Bubble-Actuated Planar Microvalve by Papavasiliou 

The Papavasiliou device works on the basis of bubble actuation. The slider is pushed 

back and forth by the formation of bubbles in the bubble actuation chambers. The actuation 

mechanism takes advantage of the relative importance of surface tension at the micro scale, 

8
using it to hold the gate in position. The flow channel for this device is 75 μm tall and 100 μm 

in width. 

What sets the Papavasiliou device apart from other microfabricated fluid controllers is 

that the motion of the slider and that of the fluid are in the same plane. Therefore, it can disturb 

the flow without forcing it through an obscure path. Although this device is too small for the 

application of refrigerant expansion, and it would be difficult to scale it up because of the 

actuation mechanism, this concept of planar impingement on the flow channel is attractive 

because it allows for a wide-open fluid passage when the device is not interfering with the fluid 

flow. 

1.4 Fabrication Options

The feature sizes necessary to fabricate a device capable of being used for the expansion 

of refrigerants are on the order of 100 μm to 1 000 μm. This leaves very few options for the 

processes that can be used to build them, because this is on the larger side of available 

microfabrication processes. At the present time, there are three different types of processes 

which can be used to produce features of this magnitude [22]: wet chemical etching, deep 

reactive ion etching, and LIGA (including LIGA-like derivatives). 

1.4.1 Wet Etching

Wet chemical etching processes are the most common processes used to fabricate 

microfluidic structures. This is because wet etching is generally very inexpensive and can make 

features that are large enough to facilitate fluid flow. The reserve is that the possible geometries 

formed with wet etching are limited. Wet etching can be isotropic or anisotropic. 

Anisotropic wet etching works on the basis that, in crystal form, certain silicon atoms are 

more readily etched based on their orientation. Specifically, the {111} crystal planes are etched 

considerably slower than the {110} and the {100} planes. This allows the ability to etch Vshaped grooves, inverted pyramidal shapes, and vertical channel walls into single crystal silicon. 

Curved features or complex geometries, however, cannot be made with wet etching. 

1.4.2 Dry Etching

Reactive Ion Etching, or RIE, refers to a dry etching technique in which large quantities 

of material may be removed from a substrate. An RIE chamber consists of two parallel plates, 

with a large voltage difference between them. The chamber is filled with an inert gas at low 

pressure which undergoes electrical breakdown when the electrons are accelerated in the existing 

field and transfer an amount of kinetic energy greater than the ionization potential to the inert 

gas’ neutrals. Collisions generate free electrons and ions which reenergize, and a current begins 

to flow between the anode and cathode. 

To use this as an etching mechanism, a wafer is placed between the parallel plates and in 

contact with the cathode. The energized electrons and ions bombard the surface of the wafer and 

remove material by reacting chemically with the substrate. A typical chemical reaction that 

takes place for reactive ion etching of silicon is . - 4+

4 4F +Si → SiF

Deep Reactive Ion Etching (DRIE) refers to a slightly more complicated mechanism in 

which the RIE process can be manipulated to preferentially etch in one direction, specifically in 

the direction along the path from the anode to the cathode, perpendicular to the surface of the 

wafer. DRIE involves an iterated sequence of etching and passivation steps. The etching step is 

similar to the RIE process, but only lasts for a few seconds. The passivation step involves 

9
depositing a thin polymer layer on the wafer to protect the sidewalls that were created during the 

etching process. The momentum in the ions during the subsequent etch step is not sufficient to 

remove the polymer coating on the side walls, but it is sufficient to remove the polymer that is 

facing the anode. The result is that the silicon is etched straight downward, regardless of crystal 

orientation. 

The flexibility provided by this process allows the creation of shapes that would 

otherwise be impossible to produce in silicon such as curved or complicated features. The 

drawback is that DRIE is a somewhat expensive process. The use of DRIE will be explored for 

prototyping purposes, but it is probably too expensive to be used for a real device. 

1.4.3 LIGA Based Methods

LIGA (German acronym for Lithographie, Galvanoformung, Abformung or lithography, 

electrodeposition, molding) is a process where a thick layer of polymethylmethacrylate (PMMA) 

is patterned using X-ray lithography and the resulting structures are used as a mold for 

electroplating. X-ray lithography offers many benefits in terms of fabrication tolerances and 

attainable thicknesses; however, it is very expensive. Low cost LIGA-like methods are currently 

being explored at numerous research institutions with promising results. Some researchers have

worked with dry film photoresists, but these materials often lack the adhesive properties and 

chemical resistance that are necessary to make very tall structures [23, 24]. At the forefront are 

methods based on SU8, a negative tone, UV sensitive, epoxy based photoresist. 

The SU8 molecule contains 8 epoxy groups which enable polymerization [25]. The SU8 

molecule is shown below in Figure 1.10. In this figure, carbon atoms are denoted in black and 

oxygen atoms are red. 

Figure 1.10 SU8 Molecule 

Included with the SU8 is a photoacid generator, which forms a weak acid in the presence 

of ultraviolet light. This acid reacts with the epoxy groups on the SU8 molecules and enables 

them to cross link with other molecules, forming a rigid polymer structure. The cationic 

polymerization process is shown below in Figure 1.11. An epoxy group (a) becomes ionically 

bonded to a hydrogen atom (b). Next, the epoxy ring is opened by cross linking with an epoxy 

10
ring from another SU8 molecule (c) and a hydrogen atom is freed (d) to react with another epoxy 

group. 

(a) (b) (c) (d) 

Figure 1.11 Cationic Polymerization Process 

Afterwards, the polymerized structures are rigid and resilient towards most chemicals;

therefore, unpolymerized SU8 may be selectively etched with a solvent. This process is used to 

produce tall, rigid polymer structures with ultraviolet light, at very low cost. 

There are many drawbacks involved with using SU8 as a material for a LIGA-based 

process. First, it is not possible to attain the same resolution with ultraviolet light as that 

attainable with X-ray lithography. This is simply a result of X-rays having a much smaller 

wavelength than UV light. Therefore, the effects of scattering are more pronounced with UV 

lithography. The resolution attainable with UV lithography, however, is suitable for many 

applications. Also, ultraviolet light, unlike X-rays, is absorbed by SU8. Because of this material 

property, there exists a theoretical upper limit to the thickness of a single layer of SU8 that can 

be patterned with UV light, approximately 2 mm. 

Another issue which needs to be addressed is that SU8 is a relatively new material; 

therefore, the process parameters are not optimized for many feature sizes. A lot of information 

exists on SU8 application for 1 μm to 250 μm layers, but little information exists for thicker 

layers. In fact, there is currently conflicting information regarding these parameters. 

During the polymerization process, SU8 molecules become highly tangled, which 

induces very large stresses within the material. With thicker and thicker films, this stress can 

cause SU8 to lose adhesion to the substrate on which it is deposited or approach the ultimate 

stress of the cross-linked material causing the SU8 to shatter. Therefore, there are a lot of 

stability problems involved with thick SU8. 

Finally, once cross linked, SU8 is very resilient towards most chemicals. Therefore, it is 

not easy to remove SU8 at the end of a process. For this reason, SU8 is often used as a 

permanent structure. Removal of SU8 has been accomplished by various methods for different 

applications. Methods for removing SU8 are generally application specific because most of the 

devised methods will attack and/or affect other materials present in the fabrication sequence. 

Thus, any application involving SU8 removal must involve a unique plan for that fabrication 

sequence. 

11
CHAPTER 2 

Design Concept

The basic concept of the refrigerant expansion device presented in this report is rather

simple. The operation of this device involves a small flow restrictor combined with a 

microfabricated actuator that is capable of moving an obstruction into and out of the refrigerant 

flow. Therefore, when the device is not actuated, the flow passage is similar in nature to a 

common short tube restrictor. When the device is actuated, the flow passage is partially blocked 

by an obstruction fixed to one of the boundaries. Inserting a flow obstruction into the short tube 

introduces a boundary discontinuity and reduces the cross sectional area of the passage, thereby 

producing a more restrictive tube. 

2.1 Design 

A sketch of this mechanism is shown in Figure 2.1, note that the flow path of the 

refrigerant is between the semi-circular tube and the flat wall in the direction perpendicular to 

this page. 

 (a) Unactuated (b) Actuated 

Figure 2.1 Conceptual Sketch of Refrigerant Expansion Device 

The actuator consists of two parts, bonded together. The first of the two pieces consists 

of a thin membrane, with a piston fixed to it. A sketch of this is shown below in Figure 2.2. 

Figure 2.2 Sketch of Piston/Diaphragm 

The second piece is a device containing a port slightly larger than the diameter of the 

piston. The port allows the piston to pass through and interact with fluid on the opposite side of 

this piece. Also, one of the pieces must have a rigid lip that maintains a small gap between the 

two pieces. A sketch of the coverplate device is shown below in Figure 2.3. In this figure, the 

spacer is shown as a circular divot removed from the device. 

12
Figure 2.3 Sketch of Cover-plate Chip 

 The pieces are then assembled to produce the structure shown below in Figure 2.4. 

Figure 2.4 Actuator Assembly 

The device’s principle of operation is based on thermal expansion of a liquid in order to 

produce the necessary forces for actuation. Once the fabrication and assembly of the actuator 

has been completed, it is to be inserted between the short tube refrigerant flow restrictor and a 

reservoir filled with the actuating fluid; in this case an oil. Included in the oil reservoir is a small 

electric resistance heater. As thermal energy is added into the oil reservoir from the heater, the 

oil gets warmer and its density decreases. This expanding oil exerts pressure on the thin flexible 

membrane, which results in the membrane flexing outward. This movement pushes the flow 

obstruction into the short tube refrigerant passage. The final assembly and device actuation is 

shown in Figure 2.5. Note that the direction of the refrigerant flow is perpendicular to this page. 

OIL 

 (a) Unactuated (b) Actuated 

Figure 2.5 Final Assembly of Refrigerant Expansion Device Components 

RESERVOIR 

(COOL) 

OIL 

RESERVOIR 

(WARM) 

13
2.2 Simulation

2.2.1 Stresses on the Diaphragm

The membrane is the only moving part in the system. The walls of the oil cavity are 

much thicker than the membrane and will not flex. The membrane is exposed to the oil reservoir 

by a circular area. When the oil is heated, the circular area of the diaphragm will flex outward. 

Centered on top of the membrane is a post. When the diaphragm is flexed, the post is pushed 

into the refrigerant flow passage, thereby obstructing the refrigerant’s flow. 

The properties that are required to simulate the stresses on the diaphragm are Young’s 

modulus, the yield strength, and Poisson’s ratio. A design spreadsheet was generated to 

calculate the necessary dimensions of the device’s features, based on the material properties and 

the expected movement. 

The input to the design spreadsheet includes the following parameters: 

• The desired deflection δ

• The thickness of the diaphragm, t

• The radius of the diaphragm, r

• The radius of the piston, rp

• The height of the piston, hp

The first parameter calculated from this input is the required pressure differential, w, 

across the diaphragm to make the center flex upward by a distance δ. For a circular diaphragm,

these parameters are linearly related by the following formulas [16, 26]: 

( )

3

2 4

16

3 1

E t

w

r

δ

ν

⋅ ⋅ ⋅ = − ⋅

Once the required pressure differential is known, the maximum stress in the membrane 

due to the flexure is calculated as: 

2

max, 2

3

4 flex

w r

t

σ ⋅ ⋅ = ⋅

Next, there exists a stress on the diaphragm at the point where it is attached to the post. 

This stress is due to the force exerted by the refrigerant’s interaction with the top of the post. In 

order to calculate the stress induced on the diaphragm an assumption was made that the worst 

case scenario would occur if the entire pressure differential between the evaporator and 

condenser were held at the tip of the post. This pressure difference was based on an air 

conditioning cycle using R134a, operating with a condensing pressure of 1.3 MPa (Tcond = 50 °C) 

and an evaporating pressure of 200 kPa (Tevap = -10 °C), representing a pressure difference of 

1.1 MPa [27]. 

This pressure difference is multiplied by the cross sectional area of the flow channel that 

is blocked by the piston to obtain the shear force on the piston, V. The maximum stress on the 

diaphragm due to this shear force is [28]: 

14
,max 2 3

4

p

s r

V

π

τ =

This stress is added to the stress resulting from the diaphragm flexure by superposition to 

obtain the total maximum stress on the diaphragm. This is then compared to the yield stress of 

the material to obtain a factor of safety. 

Using this design spreadsheet, the device material could be easily changed by inserting 

the appropriate values for Young’s modulus and the yield strength. The thickness and radius of 

the diaphragm, as well as the dimensions of the post and the desired flexure could easily be 

manipulated while monitoring their effect on the maximum stress. 

2.2.2 Oil Coefficient of Thermal Expansion

It was necessary to measure the coefficient of thermal expansion of the oil used in the 

reservoir, so that its interaction with the membrane could be predicted. The particular oil that 

was selected for this application was polyalkalene glycol (PAG), a common lubricant for use 

with hydrofluorocarbon (HFC) refrigerants. In order to measure the coefficient of thermal 

expansion, a known amount of PAG was placed in a graduated cylinder and the volume of the oil 

in the cylinder was monitored as the temperature varied. 

A 500 mL graduated cylinder was used for this experiment. A fixed mass of PAG was 

placed into the cylinder along with a thermocouple probe. The cylinder was then placed in a 

refrigerated environment for a period of time and allowed to cool. Heat was added to the 

cylinder by placing in quiescent air, then in a warm bath, during which time the temperature and 

volume was recorded. The following data was taken for a mass of 387 g: 

Table 2.1 Volume Measurements for PAG 

T (K) ∀ (m3) ρ (kg/m3

) 

280 0.000399 ± 0.000001 969.9 ± 2.4 

285 0.000399 ± 0.000001 969.9 ± 2.4 

290 0.000400 ± 0.000001 967.5 ± 2.4 

295 0.000400 ± 0.000001 967.5 ± 2.4 

300 0.000401 ± 0.000001 965.1 ± 2.4 

305 0.000403 ± 0.000001 960.3 ± 2.4 

310 0.000403 ± 0.000001 960.3 ± 2.4 

315 0.000404 ± 0.000001 957.9 ± 2.4 

320 0.000405 ± 0.000001 955.6 ± 2.4 

325 0.000405 ± 0.000001 955.6 ± 2.4 

330 0.000406 ± 0.000001 953.2 ± 2.3 

The density data points were then fitted with the best fit straight line: 

ρ (kg/m3) = 1073.46-0.3652*T (K). 

The coefficient of thermal expansion (β) at 295 K was calculated as a reference: 

0.0003755 1 ⎟ = ⎠

⎞ ⎜

⎝

⎛

∂

∂ = − T P

ρ

ρ

β

15
2.2.3 Relationship Between Oil Temperature and Piston Motion

Once the dimensions of the diaphragm and piston were deduced, and the thermal 

expansion properties of the oil were measured, the volume of additional space in the oil cavity 

due to the flexure was calculated. To calculate this volume, the shape of the flexed diaphragm is 

taken from [16]. 

( )( )2 2 2

3

2

16

3 1 φ ν − − = r

Et

w

y

Therefore, the volume of additional space underneath the diaphragm is calculated from

the 2-dimensional axisymmetric integral underneath this curve as shown below: 

( )( ) φ φ ν πφ φ πφ − ∂ − ∀ = ∂ = ∫ ∫

r

r

Et

w

y

0

2 2 2

3

2

16

3 1 2 2

( ) 6

3

2

16

1

r

Et

πw −ν ∀ =

Substituting the relationship for the pressure differential, w, the volume reduces to: 

3

2 πδr ∀ =

Another spreadsheet was generated to construct a relationship between the oil 

temperature and the displacement of the piston. In order to generate this relationship, all of the 

relevant parameters were calculated as a function of the displacement in the following manner. 

The pressure differential, w, was calculated from the displacement, δ, and the material 

properties. Next, the additional volume of oil was calculated from the relationship derived 

above, which then corresponds to the additional volume that the oil needs to occupy in order to 

push the diaphragm outward by the distance δ. 

The initial volume of the oil placed behind the diaphragm and its temperature during 

assembly is used in conjunction with its thermal expansion coefficient to calculate the

temperature that the oil must be in order to fill this additional volume. By working with these 

equations in a spreadsheet form, the required oil temperature was calculated for every 10 μm of 

vertical displacement of the piston. Once these calculations were tabulated, the results were fit 

with a curve. This curve can then be used to predict the displacement as a function of the oil 

temperature. 

16
CHAPTER 3 

Performance Measurement Methodology 

Two separate test beds were constructed to validate the performance of the device. A 

breadboard HVAC system capable of delivering a large range of operating conditions was 

constructed as the primary test apparatus. After the first design of the device was fabricated and 

assembled, measurement of its performance in this system was attempted. Based on the findings 

of the first prototype, a second test bed was constructed to test the device’s ability to control the 

flow of compressed air. 

There are two reasons for this second test apparatus. The first reason is that it is not 

possible to analytically or numerically predict the flow of flashing refrigerant through the 

geometry presented by this device. The only methods of mass flow prediction currently 

available rely on empirical data based on present day expansion devices. By using a single phase 

fluid, it is possible to predict the performance with numerical methods; thereby, providing a basis 

to compare with measurements. The second reason for constructing the compressed air test 

apparatus is that it provides a testing environment that can be operated at significantly lower 

pressures, without excessive vibration, and is therefore more likely to allow proper operation of 

the device during the developmental process. 

3.1 Compressed Air Test Apparatus 

A simple test apparatus was constructed to measure the flow of air through the device. A 

supply of compressed air is connected to the device. A manual valve is located between the 

apparatus and the compressed air supply to control the inlet pressure to the device. A pressure

transducer is located upstream and downstream of the device. A manually adjustable needle 

valve is located downstream of the device to adjust the back pressure. A hose is connected to the 

outlet of the device and discharges into a basin full of water. As air is discharged into the basin, 

it is collected in an inverted container which is initially full of water. This container is delimited 

with markings that read up to 8 L. A schematic of this apparatus is shown below in Figure 3.1. 

Figure 3.1 Schematic of Gas Flow Test Apparatus 

17
With this apparatus, the air passing through the device over a period of time can be 

collected with the graduated cylinder and this could then be used to determine the mass flow rate 

of air through the device. 

Initially, the manual valve to the compressed air supply is closed and the discharge hose 

is left outside the water basin. During this time, the ambient pressure is recorded. Next, the 

valve is opened and adjusted until the desired supply pressure is stable. Simultaneously, the 

downstream needle valve is adjusted to fix the back pressure. The hose is then placed 

underneath the container and a stopwatch is used to monitor the time to fill the container. Once 

the container is filled to a level near the 8 L mark, the time is logged and the discharge hose is 

moved so that it no longer sends air to the container. 

The container is then held so that the water level inside is even with the water level 

outside so that the pressure of the air in the cylinder is equal to the atmospheric pressure. The 

volume of air in the cylinder is recorded. A thermocouple probe is then placed inside the 

container and the temperature of the air is recorded. The mass of the air collected inside the 

container is calculated from the volume, the ambient pressure and the air temperature. The mass 

is then divided by the amount of time to fill the container to obtain the mass flow rate. 

The upstream pressure transducer was calibrated using a standard dead weight tester with 

5 points in the range of 100 kPa to 275 kPa with an uncertainty of 0.15 % with 95 % confidence. 

The uncertainty of the thermocouple was 0.15 oC with 95 % confidence and was calibrated 

between 10 oC and 50 oC using a thermistor. Temperatures and pressures are recorded through a 

virtual instrument interfacing with a data acquisition system. This virtual instrument 

communicates with three channels of a 20 channel relay card on the data acquisition system, one 

channel for the pressure transducer and one for each thermocouple. 

3.2 Breadboard Vapor Compression Test Apparatus 

A vapor compression system was constructed and outfitted with instrumentation to test 

the device’s ability to control the expansion of a refrigerant. The test loop was designed so that 

the operating parameters could be easily manipulated and a large range of operating conditions 

could be obtained. The test rig consists of three major flow loops: (1) a refrigerant flow loop 

which contains a detachable test section, (2) a cold water-glycol (heat transfer fluid, HTF) flow 

loop used to exchange heat with the refrigerant flow loop’s evaporators, and (3) a warm HTF 

flow loop used to exchange heat with the refrigerant flow loop’s condenser. 

A schematic of the main loop of the experimental setup is shown in Figure 3.2. An opendrive compressor is used to pump the refrigerant through the loop. This compressor is capable of 

pumping 1.35 m3

/h to 10.8 m3/h of refrigerant over its acceptable input drive of 500 RPM to 4 

000 RPM. The drive shaft for this compressor is controlled by 3 700 W motor capable of 

delivering up to 1 745 RPM at 60 Hz input; therefore, the maximum pumping capability of the 

compressor is 4.71 m3

/h. The motor speed is controlled by a variable frequency AC inverter. An 

oil separator was placed near the compressor discharge so that the oil concentration in the 

circulating refrigerant would be minimized. 

18
Figure 3.2 Refrigerant Flow Loop for Vapor Compression Test Apparatus 

Condenser 

Bypass 

Evaporator 

Needle 

valve 

Compressor 

Oil Separator 

Test 

Evaporator 

TEST SECTION 

After the oil separator, the refrigerant changes phase into a liquid and is subcooled by 

exchanging heat with the condenser HTF flow loop. Next, the liquid line splits into two circuits. 

The test circuit directs refrigerant through the test section where its pressure is reduced 

and it flashes to two phase. The test section consists of two manual shut off valves with the flow 

restriction device between. This allows for easy removal and change of flow restrictors. After 

passing through the test section, the refrigerant enters a brazed plate heat exchanger, where it 

absorbs energy from the evaporator HTF flow loop. After exiting the evaporator, the refrigerant 

passes through a vapor turbine meter to measure its flow rate. 

Constructed in parallel to the test section and test evaporator is a bypass evaporator with 

a manually controlled needle valve. The bypass loop also contains a bonnet valve which can 

close this circuit completely. This loop allows refrigerant to bypass the test section and test 

evaporator. The outlet of this bypass evaporator connects to the exit of the test evaporator and 

the refrigerant from both circuits returns to the compressor. 

Temperatures are monitored using copper-constantan (type-T) thermocouples placed at 

the compressor discharge, the condenser inlet, and the condenser exit. Additionally, five 

thermocouples are placed at the test section inlet, test section exit, test evaporator outlet, bypass 

evaporator inlet, and bypass evaporator outlet. Five thermocouples are used at these locations so 

that these temperatures can be measured with higher confidence. Pressure measurements are 

recorded with transducers located at the compressor exit, the test section inlet, test section exit, 

and the test evaporator exit. 

19
The condenser HTF flow loop is shown in Figure 3.3. It is circulated by a single speed 

pump which draws a 50/50 mix of Dowtherm SR-1 and water from a 230 - liter container. A 

bypass valve is located in parallel with the pump so that the flow rate of HTF can be reduced 

from the maximum output of the pump. After the pump, the HTF passes through a heat 

exchanger where it is cooled by chilled water. Next, an electrical resistance heater, capable of 

delivering between 0.0 kW and 1.5 kW, is used to set the temperature of the HTF before it enters 

the condenser. 

Figure 3.3 Condenser HTF Flow Loop for Vapor Compression Test Apparatus 

Condenser HTF 

After the HTF passes over the heater, it enters the condenser where it removes energy 

from the refrigerant loop. Upon leaving the condenser, the HTF returns to the 230 - liter 

container. 

A thermocouple is located at the inlet to the condenser. Also, 10 junction thermopiles are 

used to monitor the temperature change that the HTF undergoes as it passes through the chilled 

water heat exchanger, the electrical resistance heater and the condenser. The flow rate of HTF is 

estimated by dividing the heat addition from the electric heater by the temperature change and 

the specific heat of the HTF. 

The evaporator HTF loop is shown in Figure 3.4. The evaporator HTF is also drawn 

from a 230 - liter container containing a 50/50 mix of Dowtherm SR-1. It is circulated by a 

single speed pump and the flow rate is controlled by a manual bypass valve located in parallel 

with the pump. Down stream from the pump, the mass flow rate of HTF is measured by a 

Coriolis effect mass flow meter. Next, the temperature of the HTF is set by two electrical 

Condenser 

Heater

Reservoir 

Bypass Valve 

Chilled water 

Circulating Pump 

20
resistance heaters which are capable of adding up to a total of 3 kW of heat transferred into the 

flow. 

The flow is then split into two parallel circuits each controllable with a manual ball valve 

so that all of the HTF can be routed through either circuit or split between them. Each circuit 

passes through an evaporator to exchange heat with the refrigerant loop. A turbine meter is 

located prior to the entrance of the bypass evaporator and the flow through each circuit is 

deduced by subtracting this reading from that of the Coriolis mass flow meter located after the 

pump. It would be more desirable to place the turbine meter in the opposite circuit, so that the 

HTF flow into the test section could be measured directly; however, the physical constraints of 

the test system would not allow this. Also, the bypass evaporator was completely shut off during 

the test measurements, therefore there was no HTF flow through it and the test evaporator HTF 

flow was read directly from the coriolis flow meter. 

After exiting the evaporators, the HTF then enters another heat exchanger where it is 

cooled by chilled water. The chilled water supply is a single speed system; therefore, ball valves 

are located upstream of and in parallel with the chilled water heat exchanger so that the flow of 

HTF may partially or entirely bypass the chiller. The HTF returns to the 230 - liter reservoir 

after passing this station. 

Five type-T thermocouples are located and the entry and exit point of each evaporator. 

The temperature rise seen by the HTF as it passes the electrical resistance heaters is monitored 

with a 10 junction thermopile. Also, the temperature of the HTF is monitored with a 

thermocouple at the point where the flow splits between the two circuits. 

Figure 3.4 Evaporator HTF Flow Loop for Vapor Compression test Apparatus 

Evaporator HTF 

Reservoir 

Ball Valves 

Turbine Meter

Chilled Water

Bypass Valve 

Heaters 

Mass Flow

Circulating Pump 

21
All measurement devices are connected to a data acquisition and control unit. This 

system interfaces with a personal computer through a GPIB connection. A virtual instrument 

was scripted to monitor the system’s pressures, temperatures and flow rates and to compute the 

enthalpy, entropy, subcooling, saturation properties, evaporator inlet quality and evaporator 

capacity. The evaporator HTF loop flow rates and temperatures are also monitored and the HTFside evaporator capacity is calculated from these parameters and compared to the refrigerant-side

capacity. All of the heaters in all three loops are also controlled by the virtual instrument. 

All thermocouples used in this experimental setup were calibrated to within 0.15 oC at 

95 % confidence, all pressure transducers to within 0.2 % reading at 95 % confidence, and all 

flow rate measurement devices were calibrated to within 0.3 % reading at 95 % confidence. 

22
CHAPTER 4 

DRIE Silicon Prototype

The first method of prototyping this device was Deep Reactive Ion Etching (DRIE) of a 

Silicon-on-Insulator (SOI) wafer. An SOI wafer is a composite of three layers, consisting of two 

layers of silicon, with a layer of SiO2 sandwiched between them. The reason that SOI wafers are 

useful is that DRIE will etch silicon approximately 200 times faster than SiO2. SiO2 therefore 

provides a good etch stop for the DRIE process. The flexibility provided by DRIE on a SOI 

wafer is ideal for fabricating a prototype of the device in this study. 

It is very common for the two silicon layers to have very different thicknesses; the thicker 

of the two is called the base and the thinner is called the handle. In order to fabricate the first 

device from an SOI wafer using DRIE, the simplest method is using the handle of the SOI as the 

diaphragm and etching the base in such a way as to leave the piston attached to the center of the 

diaphragm. For the second device, it is desirable to use the thin handle layer as the cover plate 

with a pass through for the piston while using the thick base layer to provide a space between the 

two chips in the assembly. Figure 4.1 describes the process flow used to produce the 

piston/diaphragm device and Figure 4.2 describes the process flow used to produce the 

coverplate device. 

Front-Side DRIE through base 

removing all material except for piston 

SOI wafer 

Figure 4.1 Process Flow used to Produce the Piston/Diaphragm Chip 

Back-Side DRIE through 

handle

Figure 4.2 Process Flow used to Produce the Coverplate Chip 

SOI 

Front-Side DRIE through 

base 

Remove SiO2 to open passage

through chip

23
4.1 Design and Fabrication 

For this fabrication run, 100 mm diameter SOI wafers were obtained. The base layers of 

these wafers were polished to a thickness of 450 μm, the handle was polished to a thickness of 

75 μm, and the silicon dioxide layer between them was 1 μm thick. 

The dimensions for this design are somewhat dictated by the specifications of the SOI 

wafers. In this case, the wafer dictates the diaphragm thickness of 75 μm and the space between 

the two pieces as well as the piston height is fixed to 450 μm. These specifications, incidentally, 

force the design to be slightly different than explained in the last section. This is because the 

piston height should be equal to the diaphragm thickness plus the gap spacing; therefore, the 

devices resulting from this fabrication run will be assembled such that the piston will be recessed 

75 μm from the top of the coverplate when the diaphragm is not flexed. This could have been 

remedied by polishing one of the wafers by an additional 75 μm thereby reducing the gap to 

375 μm. For the first fabrication run, however, this is acceptable because the actuation can still 

be demonstrated and the additional cost of polishing further is not warranted. 

Given the constraints imposed by the specifications of the wafer, the dimensions of the 

features were calculated so that a safety factor of approximately 2 was maintained during 

operation. Since the material properties of single crystal silicon are directional, the following 

material properties were selected so as to result in the greatest stress on the diaphragm and they 

were input to the design spreadsheet [22]: 

E = 186.5 GPa 

σy = 1.8 GPa 

ν = 0.21 

In addition, the desired deflection was 200 μm, which in this case would move the tip of 

the piston 125 μm beyond the coverplate. The piston diameter was 1 000 μm. With these 

parameters, the diaphragm diameter was found to be 8 800 μm, which results in a safety factor of

1.8 relative to diaphragm failure. 

4.1.1 Masks

The first step was to create the photolithography masks for the fabrication run. A 

computer aided drafting software package was used to generate the drawings needed for the 

masks. A total of 5 masks were needed for this fabrication run, which included one mask for 

each of the three DRIE etches outlined in the previous section and one mask for each etch to 

outline the borders of the devices on the wafers. These borders are necessary because they 

provide a line through which the wafer may be cut later to obtain the devices. On each of the 

five masks, an array of 25 (5 X 5) devices were drawn. 

Mask # 1 outlined the borders for the piston/diaphragm devices. For this mask, the 

pattern consisted of a 5 X 5 array of square dark field boxes with a side of dimension 16 950 μm. 

The light fields of the masks were the lines that separated the squares; the widths of these lines 

were 100 μm. 

Mask # 2 outlined the pattern for the second etch on the piston/diaphragm device. This 

pattern consists of a dark field circle, centered inside of a light field square. The circle has a 

diameter of 1 000 μm, as was the desired piston diameter. The square has a dimension of 

12 000 μm on a side, which once fabricated will be wide enough to fit the coverplate device. 

24
The squares on the array of devices were separated by a dark field of 4 950 μm. A drawing of 

the patterns on the masks used for the piston/diaphragm devices (Mask # 1 and Mask # 2) are 

shown in Figure 4.3 

. 

Mask #1 Mask #2

Borders for piston/diaphragm Piston and diaphragm

Figure 4.3 Masks used for Piston/Diaphragm Chip 

Mask # 3 outlined the borders on the coverplate device. This mask is very similar in 

pattern to mask #1, however the dimensions are slightly different. For this mask, the sides of the 

dark field squares were 11 800 μm, and the light field lines were 5 150 μm thick. The dimension 

of these features are slightly smaller than that of Mask # 2 because the features produced with 

this mask will fit into the ones produced with Mask # 2. 

The pattern on Mask # 4 is used to etch the hole through which the piston will move. 

This pattern was transferred to the handle side of the coverplate wafer. These holes are 

1 100 μm in diameter, which is 100 μm larger than the piston. 

The last mask, Mask # 5, was transferred onto the base side of the coverplate device. 

This pattern produces a large diameter hole (8 800 μm) which will provide a gap between the 

two devices after they are assembled. Figure 4.4 shows the patterns on the masks used for the 

coverplate device. 

Mask #3 Mask #4 Mask #5

Borders for coverplate Backside hole on coverplate Spacer hole on coverplate

Figure 4.4 Masks used for Coverplate Chip 

25
Once all of the mask patterns were drawn using the CAD package, the patterns were 

transferred onto blank masks with an Optical Pattern Generator. The fabricated masks were 

125 mm X 125 mm glass chromium masks with a resolution of 0.6 μm. 

4.1.2 Device Fabrication

Once the masks were produced they were used to transfer patterns onto the SOI wafers. 

The piston/diaphragm device was fabricated by spinning 1.6 μm of photoresist onto the base side 

of a wafer. Mask # 1 was used to expose the border pattern onto this photoresist using a contact 

aligner with a dose of 12.6 mW/cm2

 of UV light at 280 nm. Since this was the first pattern 

exposed, the mask was aligned to the primary flat. The photoresist was developed in MIF 300 

for 60 s with high agitation. 

The wafer was then placed inside of a DRIE chamber, and etched for a period of 60 s. 

The photoresist was dissolved in acetone and the wafer was cleaned. The depth of this etch was 

measured with a profilometer to be 3.5 μm. Regardless of the depth; however, this etch was 

clearly visible and could serve as a mark along which the wafer could be diced; which was the 

purpose of this feature. 

The next step was to prepare the wafer for the deep etch. A different photoresist was 

used, which is much more viscous than the photoresist used for the first step. It was spun on at a 

speed of 2 000 RPM to leave a layer of 11.5 μm. Mask # 2 was aligned to the features left from

the first DRIE with the MA6, and this photoresist was administered a dose of 390 mW/cm

2

, then 

it was developed for 80 s in MIF 319. 

The pattern from Mask#2 was ready to be etched into the wafer by the DRIE chamber. 

According to the tool’s logbook, its selectivity had been repeatedly characterized to show that it 

etches silicon approximately 150 times faster than silicon dioxide and approximately 55 times 

faster than photoresist. The thickness of the photoresist was measured with the profilometer and 

was found as 11 μm; which is adequate since the desired etch depth was 450 μm. 

The wafer was etched until silicon dioxide could be seen at the bottom of all etch pits, 

which took slightly longer than 3 hours (3:02:12). The end product can be seen below in 

Figure 4.5. 

Figure 4.5 SOI Wafer after the Fabrication of Pistons and Diaphragms

26
The coverplate devices were fabricated next. A 1.6 μm layer of photoresist was spun 

onto the base side of the coverplate wafer, in the same manner as was done for the 

piston/diaphragm wafer. This photoresist was exposed with the contact aligner, using Mask # 3 

and a dose of 12.6 mW/cm2

. It was then developed and etched in the DRIE chamber for a period 

of one minute. 

The wafer was then cleaned and a layer of the same photoresist was spun onto the handle 

side. This layer was exposed using a back side contact aligner. This exposure system uses 

optical imaging to allow alignment with features on the back side of the wafer. With this tool, 

Mask # 4 was aligned to the features left from Mask # 3 on the opposite side of the wafer. The 

photoresist was exposed, developed, and etched in the DRIE chamber until the layer of buried 

silicon dioxide was exposed (20:08). 

The wafer was then cleaned and an 11 μm layer of STR 1075 was spun onto the base 

side. It was exposed using the contact aligner with Mask # 5 and a dose of 390 mW/cm

2

. The 

photoresist was developed and the wafer was etched in the DRIE chamber until the silicon 

dioxide was exposed in the bottom of the etch pit. 

Once the fabrication of both wafers was complete, they were disassembled into the 

components. The wafers were diced by coating them with a very thick layer (approximately 

1 mm thick from the deepest etched trenches) of photoresist. The photoresist provided an easily 

removable, thick, flexible layer which damped the vibrations that resulted from cutting the 

wafers. The wafers were then cut along the borders between the devices with a diamond-tip saw 

blade. After cutting the devices free from the wafers, they were soaked in acetone to remove the 

photoresist. Figure 4.6 shows photographs of the two chips after they have been cut from the 

wafers. 

 Figure 4.6a Coverplate Device Figure 4.6b Piston/Diaphragm Device 

The final fabrication step was to open the pass through hole in the coverplate device. The 

hole was blocked by a 1 μm thick layer of silicon dioxide. This layer of silicon dioxide was 

removed by dipping the device in a solution containing hydrofluoric acid (HF) for a few seconds 

until the SiO2 was dissolved. 

4.2 Assembly 

At this point, one of each of the pieces was assembled into the first prototype. To do this, 

the two pieces were set together with an epoxy. This particular epoxy was formulated to work 

with refrigerants and was rated at pressures of up to 27.5 MPa. Figure 4.7 shows a photograph 

of the assembled devices. 

27
Figure 4.7 Assembled Device 

Next, two small brass pieces were machined on a lathe. These pieces make up the small 

chamber that encapsulates the oil used to flex the membrane. The brass pieces were machined 

according to the specifications shown on Figures 4.8 and 4.9. 

30 mm

Figure 4.8 Specifications of Brass Capsule 

Figure 4.9 Specifications of Brass Capsule Cap 

The devices were then mounted onto the brass capsule and secured with epoxy. A small 

13.1 Ω electrical resistance heater was placed inside the capsule by running its wires through the 

cap and sealing the cap to the capsule. 

8.75 mm

Rear Front 19.5 mm 15 mm 

23 mm

3 mm

4 mm

19.5 mm

15.2 mm 

45°

9 mm 

3 mm

28
Figure 4.10 Heater and Cap Assembly

ext, the capsule was filled with polyalkalene glycol (PAG) 118 using a syringe. The 

capsule

le

N

was filled with oil through the hole in the rear of the cap using 4.0 cm3

 of oil at a fill 

temperature of 22 °C. When the capsule was completely filled with oil, a type-T thermocoup

probe was inserted through the hole and the capsule was sealed with epoxy. A picture of the 

final assembly is shown in Figure 4.11 below. 

Figure 4.11 Final Assembly of Actuator 

.3 Characterization 

g the movement of the piston, calculations were performed to estimate 

the disp

s the

4

Before measurin

lacement based on the oil temperature. This was done using the spreadsheet described 

earlier. The dimensions of the silicon pieces and brass oil reservoir were inserted into the 

spreadsheet along with the information regarding the oil in the capsule. Figure 4.12 depict

prediction of the vertical movement of the piston in response to a changing oil temperature. 

29
y = 132.75x - 2950.9

R2

 = 1

0

100

200

300

400

500

600

22 23 24 25 26 27

Temperature (degrees C)

Predicted Deflection (microns)

Point of mechanical failure

Design point

Pre

dicted Deflection (

μm)

Temperature (oC)

y = 132.75x - 2950.9

R2

 = 1

0

100

200

300

400

500

600

22 23 24 25 26 27

Temperature (degrees C)

Predicted Deflection (microns)

Point of mechanical failure

Design point

Pre

dicted Deflection (

μm)

Temperature (oC)

Figure 4.12 Performance Simulation for Displacement of Piston 

The magnitude of the movement predicted by this model seems to be a little dangerous 

from a reliability point of view. The prediction is that, for a relatively small change in 

temperature (4.1 °C), the piston would move beyond its entire range of motion and the 

diaphragm would rupture. 

There is, however, a major shortfall of the simulation model in that the epoxy holding the 

diaphragm to the oil reservoir has quite a bit of flexibility. As the pressure in the capsule 

increases, the epoxy will stretch and thus some of the additional volume in the capsule will be 

realized. There is, however, no means by which this amount may be accounted; therefore, it was 

left out of the simulations. This factor is helpful because it works to suppress the motion of the 

piston. If the motion is not as strong of a function of the oil temperature as predicted, the device 

will require a greater range of temperature to undergo this much motion; thereby making it easier

to control. This is not an accident. The initial volume of the oil reservoir was determined 

through trial and error by noticing the effects of the epoxy and using a larger reservoir to attain 

the desired displacement. 

The movement of the piston was then measured and correlated to the temperature of the 

oil in the capsule. For this measurement, the first step was to devise a method of measuring a 

small displacement that was perpendicular to the plane in which it may be viewed. The method 

used was to examine the device on a microscope, and focus the scope on a point on the piston. 

As the piston moved vertically, the focal point was tracked using the focus adjustment knob. 

The focus adjustment knob on the microscope was divided by 100 tick marks per 

rotation. To obtain a conversion from these tick marks to actual distances, a calibration was 

performed. The profilometer measurements that were done on the piston/diaphragm chip 

verified that the distance from the top of the piston to the base was 450 μm; therefore, this chip 

was used as a reference for the calibration of the tick marks. Measurements from the bottom to 

30
the top of the piston resulted in a conversion factor of 0.996 ticks/μm. This optical method can 

be used to distinguish features to within ± 10 μm.

The assembled device was then placed on the microscope stage. The heater wires were 

connected to a variable power source connected in parallel to a handheld multimeter. This 

allowed the voltage input to the heater to be controlled and monitored. The thermocouple which 

monitors the oil temperature was connected to a handheld thermocouple reader. 

The position of the piston was recorded, along with temperature and voltage information, 

as heat was added to the capsule through the variable power source. The voltage was increased 

in small discrete increments with a minimum of 1 minute between readings. This allowed a 

range of data to be covered without capturing any transient effects. The temperature range that 

was used to collect data spanned the range between the ambient temperature in the laboratory 

and 32.2 °C. 

Measurements were taken on three separate days; therefore, the starting point was not 

identical for each measurement. The position was recorded for each measurement and plotted as 

a position relative that at 23.9 °C. Figure 4.13 below shows the data taken on three separate 

occasions. 

-50

0

50

100

150

200

22 23 24 25 26 27 28 29 30 31 32

Oil Temperature (°C)

V

ertical Displace

m ent (

μm )

Measurement #3

Measurement #2

Measurement #1

Figure 4.13 Characterization of Piston Displacement 

This data demonstrated that the displacement of the piston was both linear and repeatable. 

The slope of a best fit line through all of the data points showed that the piston moved 

20.98 μm/°C. This is much smaller of a slope that the 132.75 μm/°C predicted in the 

simulations; however, this is a reasonable expectation considering the effects of the epoxy’s 

flexibility. 

4.4 Attempted Testing in an R134a System 

After the motion of the piston was characterized, installation and testing in the 

breadboard HVAC system was attempted. The device was mounted along a cut away section of 

a small gage tube and installed between the evaporator and condenser heat exchangers as the 

main pressure drop device in an R134a vapor compression cycle test apparatus. 

 A set of conditions were imposed on the cycle to represent the operating conditions of a 

household refrigerator. The temperature of the oil in the capsule was held at 23.9 °C while the 

31
system parameters stabilized. Once steady state operation was achieved, the temperature of the 

oil in the capsule was elevated and the refrigeration cycle parameters were monitored. As heat 

was added into the capsule, it was expected that the piston would begin to obstruct the refrigerant 

flow path which would cause the mass flow to decrease, the liquid line pressure and temperature 

to increase, the evaporating temperature and pressure to decrease, and the capacity to decrease. 

None of this, unfortunately, occurred. 

Once the oil temperature was raised to 29.4 °C, within the range of device 

characterization, the oil temperature began to decline very rapidly. A rapid decline in the oil 

temperature seemed to be the result of a ruptured diaphragm, which would allow refrigerant to 

mix directly with the oil in the capsule. This could occur if the piston was slightly misaligned 

with the tube to which it was mounted, and that the attempted actuation may have forced the 

piston into the tube wall. This would result in the piston being restrained, and eventually the 

rupturing of the diaphragm before any obstruction was introduced into the capillary tube. The 

device was removed from the system and examined. It was positioned with the tube in a vertical 

position, and oil droplets began to drip from the tube, indicating that the diaphragm had in fact 

ruptured. 

4.5 Conclusions Drawn from Silicon Prototype 

As this device was assembled from the last surviving set of silicon pieces, it was not 

possible to assemble and test another specimen. However, a lot of information was obtained 

through these tests, which is valuable for the second generation of such devices. The most 

important piece of information yielded from this experience is that such a device was possible to 

construct. Also, much of the knowledge gained through this fabrication and assembly may be 

carried over to the next generation of devices. 

The first recommendation for design changes to the second generation of devices is to use 

a different material. The devices produced in this fabrication run were made out of silicon, 

which is a brittle material. This device can be made from silicon; however, at this stage of

development it would be better to work with a more ductile material. Also, expensive processes 

and specialized wafers were needed to fabricate the features on these devices. Although the cost 

of fabrication of these parts may be feasible in large scale production, less expensive alternatives 

are possible if different materials are used. 

The second recommendation is to change the design of the device so that the refrigerant 

flow path is fabricated as part of the device itself. This will eliminate any problems associated 

with trying to align the actuator to the refrigerant flow path, which is what ultimately caused the 

test specimen to fail in the HVAC system. 

The third change is that the range of motion attainable by the piston should be larger and 

a higher factor of safety should be used. The features for this prototype were calculated based on 

the diaphragm experiencing a maximum stress equal to half of the yield stress when subject to a 

200 μm extension and a large pressure differential occurring at its top. For the second 

generation, the minimum factor of safety will be doubled. Also, with the fabrication of the flow 

channel being part of the system, the range of motion of the piston will extend to the top of the 

flow channel. This will allow the device to completely stop the flow, rather than merely 

inducing more flow resistance. 

Next, a different method of fixing the diaphragm to the oil reservoir is recommended. 

The epoxy used to hold the pieces together worked, but it had a large dampening effect on the 

32
movement attainable by the piston due to its flexure. More importantly, a lot of difficulty was 

experienced with the epoxy in terms of containing the oil in the capsule. 

Finally, an alternative method of benchmarking the performance of the device’s ability to 

control fluid flow is desired. The reasons for this are explained in Chapter 3. 

33
CHAPTER 5 

Thick SU8-Nickel Micromolding Process 

The second generation of the refrigerant expansion device is based on electroplating 

nickel into SU8 molds. There are many difficulties involved with working with SU8 in layers 

greater than 1 mm [29], the thickness necessitated by this design. In order to make this a viable 

option, extensive work was done to determine process parameters and tricks that would allow the 

formation of SU8 molds in excess of 1 mm. 

The biggest problem that occurs in thick layer SU8 processing is that the material’s stress 

becomes very large when it is cross linked [30-32]. This often causes the SU8 layer to buckle, 

shatter, or lose adhesion and detach from the substrate. As SU8 is deposited in thicker and 

thicker layers, the stresses generated during cross linkage become more pronounced and the 

likelihood of failure increases. 

The available processing information from the manufacturer [33] gives detailed steps that 

instruct the user on how to build structures as tall as 260 μm. A manual [34] outlines a 

procedure for up to 430 μm tall SU8 layers. There is also a lot of information on the internet 

dedicated to the sharing of processing information of SU8 [35]. Many journal articles also share 

a lot of processing tips that help improve SU8 deposition [36-48]. These manuals and web sites 

often report conflicting information, but the suggestions provided were a good starting point. 

Very little, however, has been reported for thicker deposition of SU8. Researchers in 

Switzerland have successfully deposited and patterned SU8 in excess of 1200 μm [49, 50], and 

Sandia National Laboratory has published work showing deposition of up to 950 μm [51]; 

however, the recipes that they developed are proprietary and could not be obtained. 

As an example, the process flow for 260 μm tall SU8-2100 features from the 

manufacturer’s manual is described as follows: 

1) Wafer pretreat: Whenever possible, the substrate should be undergo a piranha etch/clean 

(H2SO4 + H2O2); or at minimum a soak in isopropanol. Afterwards, a dehydration step is 

necessary, which typically consists of 5 min on a hot plate at 200 °C. 

2) Coat: Liquid SU8 can easily be applied to a wafer through normal spin coating. 

However, SU8 is a very thick liquid (the kinematic viscosity of SU8-2100 at room temperature is 

0.045 m2

/s, one order of magnitude greater than that of honey) and can be difficult to dispense. 

Therefore, it is typically poured directly onto the wafer rather than dispensed from a pipette. A 

spin rate of 1000 RPM will leave a layer of 260 μm on the wafer. 

3) Soft bake: After the SU8 has been applied to the wafer; it must be heated to evaporate 

the solvent and solidify the SU8. Most photoresists achieve best results with this step performed 

in an oven, it has been widely reported that a hot plate soft bake is better for SU8. This is 

because an oven bake tends to form a crust on the SU8 surface, which will hinder the mass 

transfer of solvent out of the SU8. The wafer should be slowly ramped up and down from the 

soft bake temperature. The manufacturer states that the soft bake for a 260 μm layer requires 

60 min on a hot plate at 95 °C, although other resources claim that as much as 5 h is necessary. 

4) Exposure: A weak acid is formed when exposed to UV illumination. This acid reacts

with the SU8 molecules and causes them to cross link and form a rigid polymer. Because of this 

mechanism, SU8 is relatively insensitive to overexposure. The exposure dose reported by 

manufacturer for a 260 μm layer is 400 mJ/cm2

, although other sources recommend a minimum 

of twice this dose and it has been reported the increasing the dose will typically result in better 

adhesion to the substrate. 

34
5) Post Expose Bake: To promote the chemical reaction of the SU8 molecules cross 

linking, a post exposure bake is necessary. The manufacturer recommends a post exposure bake 

of 15 minutes on a 95 °C hot plate for a 260 μm layer. This can be a very tricky step because the 

SU8 begins to forms a high stress solid with a very large coefficient of thermal expansion once 

the molecules begin to cross link. The recommendation is to slowly ramp the temperature up 

and down to minimize the thermal gradients within the SU8, thereby reducing the stress caused 

by these thermal gradients. 

6) Develop: SU8 is developed in a solution of PGMEA (propylene glycol methyl ether 

acetate). The developer dissolves SU8 that is not cross linked. It also seems to cause a high 

degree of stress in the SU8. For very thick layers, this is a very delicate step because the stress 

caused during the development can easily cause the SU8 to shatter. If this occurs, it will take 

place the instant that the very first drop of PGMEA comes into contact with the SU8; if there are 

no problems getting the wafer into the developer, catastrophic failure is not likely. The

manufacturer recommends an agitated bath of PGMEA for 20 min to develop a layer of 260 μm 

thick. 

7) Rinse: After the layer is developed, it should be rinsed in isopropanol. This also helps to 

determine if the development step is complete because undeveloped SU8 will form a milky 

residue if it comes into contact with isopropanol; therefore if this is present, it should be returned 

to the developer. 

With the basic process steps outlined, substantial effort was put forth to fine tune this 

process so that it could be used in a process flow similar to LIGA. The basic process involves 

depositing and patterning SU8, and then filling in the cavities by electroplating a metal into it. 

Afterwards, the SU8 is removed and the metal structure is free. Figure 5.1 outlines the basic 

process flow. 

Figure 5.1 Basic Fabrication Process Goal for SU8 

(i)

(v) 

(ii) 

(vi) (iii) 

(iv) (vii)

We begin with a clean substrate (i). Then it is coated with a layer of metal to be used as 

an electrical conductor for a plating base (ii). A thick layer of photoresist is deposited on top 

(iii), and then exposed and developed to leave the desired pattern (iv). Next, the substrate is 

submersed in an electrolyte solution with a mass of the plating metal. An electrical power source 

is connected to the plating metal (anode) and the plating base on the substrate (cathode) such that 

the plating metal undergoes oxidation: 

35
n Metal Metal ne → ++ −

And metal is deposited on the cathode through reduction (iv): 

n Metal ne Metal + − + →

As the metal deposits, it will eventually grow out of the mold (vi). At this point, it may 

be polished to a desired level if required. Finally, the photoresist and the substrate are removed 

(vii) from the metal piece or pieces. 

To build upon this basic process, there are a few obstacles to overcome. First, in order to 

fabricate the components that are required for this device, multiple layers must be deposited and 

patterned. With traditional LIGA, this is not a difficult task. The solution is simply to polish the 

deposited metal layer to the appropriate level, then repeat the process steps with a different 

pattern. This is not possible with thick SU8 photoresist because it has such a high stress and it 

does not have very good adhesion with metals, i.e. the subsequent layer of SU8 will not stick to 

the electroplated metal and will ultimately detach from the substrate entirely. 

Also, if a thick (>500 μm) layer of SU8 is deposited onto a metal layer, it will often lose 

adhesion during electroplating. This doesn’t seem to be much of a problem when a thin layer of 

SU8 is used; but the adhesion cannot overcome the stress associated with thick layers. 

Therefore, the SU8 can not be deposited on top of the plating base. 

Another issue is that once a thick layer of SU8 is developed it is difficult, if not 

impossible, to deposit a second thick layer of SU8 on top. See Figure 5.2. The main reason for 

this is that SU8 contracts slightly when developed, which is a source of a great amount of tensile 

stress. The magnitude of this stress can be inferred from the curvature that is introduced to the 

substrate [52]. For SU8 layer thicknesses in the range of 1 mm, these stresses are on the order of 

25 MPa to 30 MPa, which is close to the maximum stress for SU8 of 34 MPa [53]. If another 

thick layer is deposited on top of one which is already developed, then it is unlikely that the stack 

of SU8 will survive. 

Figure 5.2 Buckling Mechanism for Multiple SU8 Layer Stacks. (i) Bare wafer. (ii) SU8 

deposited on surface. (iii) SU8 developed. (iv) Second layer of SU8 deposited. (v) Second 

layer of SU8 developed. 

(i) 

(iv)

(ii) 

(v) (iii) 

A third issue is that SU8, when cured, is very resilient to chemicals. This makes it an 

excellent material for many applications where it is a permanent structure. However, removing 

36
SU8 has proven to be very difficult. Recently, some researchers [54-56] have reported that SU8 

can be etched by certain plasma or reactive ion etch (RIE) recipes; however, the results have 

shown etch rates between (1 and 4) μm per minute. With layer thicknesses of greater that 1 mm, 

these etch procedures would take an exceedingly long time and result in very expensive 

equipment usage. Similar etch rates have been found with wet etching techniques [57], and 

selectivity is an issue. 

Given these constraints, modifications to the recipe were developed to fabricate 

devices > 1 mm out of nickel. First, the SU8 must be deposited onto bare silicon, instead of a 

metallic plating base as is common for traditional LIGA based processes. The adhesion between 

SU8 and silicon dioxide or metals is not as good as with silicon. It can be deposited onto many 

different materials, however, when the stresses become large, it will detach. SU8 adheres best to 

silicon; therefore, this offers the most protection against separation. For this reason, it is also 

necessary that the wafer be soaked in HF to remove any silicon dioxide. 

Secondly, it is necessary to use either a thick wafer or multiple wafers bonded together. 

The large stresses cause significant wafer bowing. Using a thick wafer drastically reduces the 

amount of bowing, because the radius of curvature of the wafer is proportional to the square of 

the thickness. It has been found that a 100 mm diameter, 900 μm thick silicon wafer can 

withstand the stress induced by the deposition of 1200 μm of SU8 unlike a standard 500 μm 

wafer of this diameter. 

Third, most of the stress occurs when SU8 reacts with PGMEA; therefore, all layers of 

SU8 must be developed in one single shot. Once thick layers of SU8 are deposited and 

developed, they are too unstable to undergo further processing (at least processes which 

introduce large stresses such as additional SU8 deposition). By developing all of the layers at

once, the interstitial stresses between layers will be minimized. 

In order to construct tall molds with varying features at different depths, the process steps 

2-4 outlined in the beginning of this chapter (coat, pre-expose bake, expose) may be iterated. It 

is unnecessary to perform a post exposure bake (step 5) until after the final layer has been 

exposed. This is because each pre-expose bake for a subsequent layer will have the same effect. 

Also, it is not desirable to superfluously undergo additional thermal cycling. 

In order to satisfy the single development rule, the geometry of the device itself is 

limited. The geometry must be constrained so that split-level features cannot include any 

overhangs. See Figure 5.3. 

37
Figure 5.3 Geometrical Constraint for Nickel Device. 

Possible Not possible 

The reason for this constraint is that the SU8 molds must be made in such a way that 

every layer has a wider open area than the layer beneath it. This is because SU8 is a negative 

photoresist and it becomes a permanent structure when exposed to UV light. If a layer of SU8 is 

exposed, all layers directly beneath it will also receive UV radiation. Therefore, it is only 

possible to expose areas that lie directly on top of other exposed areas. 

Researchers at the Swiss Federal Institute [58, 59] have developed three methods of 

forming overhangs and enclosed channels with SU8. Brief process flows are shown in 

Figures 5.4 - 5.6. 

Figure 5.4 Fill Process for SU8 Overhangs or Channels 

(i) (iv) 

(vii) 

(ii) (v) 

(viii) 

(iii) (vi) 

For the fill process, SU8 is deposited onto a substrate, patterned, and developed (i-v). 

Next, a sacrificial layer of dissolvable material is used to fill the trenches of the SU8 structures 

(vi). Another layer of SU8 is deposited on top of the stack, then it is exposed and developed, and 

the filler material is dissolved (vi-vii). This is not a feasible option for very thick layers because 

it involves multiple development steps. 

38
Figure 5.5 Mask Process for SU8 Overhangs or Channels 

(i)

(vi) 

(ii) (iv) 

(iii) (v) (vii) 

For the mask process, SU8 is deposited onto a substrate and patterned, but not developed 

(i-iv). Next, a layer of metal is deposited and patterned on top of the SU8 (v). This metal layer 

blocks the UV light from reacting with the unexposed SU8 beneath. Another layer of SU8 is 

deposited on top of the stack, and then exposed and all layers are developed (vi-vii). This is not 

a feasible option for very thick layers either because the high stress SU8 will not adhere to the 

metal layer. 

Figure 5.6 Lamination Process for SU8 Overhangs or Channels 

(i) 

(ii) (iv) (vi)

(iii) (v) 

(vii) 

For the lamination process, SU8 is deposited onto a substrate, patterned, and developed 

(i-v). Next, a layer of film laminate photoresist is deposited on top of the SU8 (vi). The 

laminate film is exposed and developed so that it forms the top portion of the structure or the 

overhangs (viii). Therefore, the structures are not completely made of SU8. This is a very useful 

process flow for fabricating microfluidic structures, but it has limitations for micromolding. The 

major limitation is that laminate photoresists have poor chemical resistance to electrolyte 

solutions, which are needed for electroplating. Therefore, the lamination process is not a feasible 

option either. 

In order to deposit a metal with an electroplating process, a conductive layer must be 

present. Since SU8 cannot be deposited onto a metal, the metal must be deposited on top of the 

SU8 mold. Of the available methods for metal deposition, the process must have very good step 

39
coverage to coat within the trenches of the molding. The simplest way to achieve the required 

metal deposition is by sputtering. 

Finally, the last step requires that the metal devices are somehow freed from the SU8 

molding. The easiest way to remove SU8 is to take advantage of SU8’s instability and the fact 

that it does not exhibit the best adhesion to metal. The simplest method of pushing this material 

beyond its limit is to rapidly raise its temperature. This thermal shock causes the SU8 to lose 

adhesion to the metal, thus it can be easily removed. It has been found through experience that if 

the substrate is placed on a 500 °C hotplate, the metal will be ejected from the SU8 within 5 s to 

10 s while it is still cold to touch. The SU8 is destroyed during this process, but the silicon wafer 

is left in tact. This is quite beneficial because the wafer may be polished, cleaned, and used 

again. 

In order to use this method, an additional layer of SU8 is needed to completely cover the 

substrate. This sacrificial layer of SU8 is required so that the metal is fixed only to SU8 and not 

to the substrate. Therefore the metal is not restrained to the wafer while the SU8 is attempting to 

eject it. 

All of the rules outlined thus far are necessary to successfully deposit layers of SU8 in 

excess of 1 mm total thickness. However, following these steps alone does not result in a good 

pattern transfer, and additional fabrication steps are necessary to deposit a thick layer of SU8 

with good uniformity. This is because the edge bead resulting from the fabrication process 

outlined is extraordinarily large. It is impossible to accurately measure the magnitude of this 

problem because no good tool for this measurement exists. 

In order to gauge the magnitude of the problem, a layer of 500 μm of SU8 was deposited 

onto a wafer prepared using the method outlined thus far. Calipers were used to measure the 

thickness of a layer of SU8 and wafer in a few locations, although it was impossible to reach to 

the center of the wafer with the calipers. In general, using the 500 μm recipe would result in an 

outer ridge-edge bead thickness of approximately 500 μm. However, this ridge is generally 2 cm 

to 3 cm wide, and the thickness of the SU8 inside the bead is much smaller; typically 100 μm to

150 μm. A typical pattern is shown below in Figure 5.7. 

40
Figure 5.7 Typical Thick Layer SU8 Edge Bead Distortion 

This is quite problematic not only because any resulting structure height is greatly 

altered; but because light passing through a mask placed on top of this will scatter terribly, 

resulting in a very poor pattern transfer. Furthermore, any subsequent fabrication steps will be 

distorted because this layer will be uneven. 

Eliminating this edge bead, and the problems caused by it, is a rather challenging task. 

Conventional edge bead removal is generally performed by treating the photoresist near the edge 

with a solvent. This will not work with SU8 because it is a negative photoresist. Grinding the 

SU8 edge bead to the correct thickness is not a feasible option either because in order to do this, 

the SU8 layer must be developed and it was found that, once developed, thick SU8 cannot 

withstand further processing. 

After trying a few different options, a procedural modification was devised which 

resulted in much more uniform SU8 deposition. The additional fabrication steps to deposit one 

layer of thick SU8 are outlined in Figures 5.8 and 5.9. 

Initially, the SU8 is deposited onto a wafer using the guidelines set forth thus far. The 

bare wafer 5.8 (a) is cleaned, then SU8 is spun onto the wafer according to the spin-spread rates 

at a given temperature and the wafer undergoes a soft bake to drive off the solvents. This results 

in a deposition pattern similar to that shown in Figure 5.8 (b). After the soft bake, a mask is 

placed over the wafer and held in contact. A region that is not in contact with the mask is clearly 

visible through the mask at this point 5.8 (c). Once the mask and the wafer are secured together, 

an opaque layer of black electrical tape is used to cover all parts of the mask that lie directly 

41
above areas that are not in contact with the SU8 5.8 (d). Next, the SU8 is exposed through the 

mask/black tape assembly. 

(a)

(d)

(b) (c)

(e)

(a)

(d)

(b) (c)

(e)

Figure 5.8 Process Steps to Eliminate Edge Bead 

At this point, the form of the SU8 that remains on the wafer is that of an exposed ridge, 

of appropriate thickness, with a thin, unexposed area in the middle, 5.9 (a). Next, a small puddle 

of SU8 in a less viscous formulation, SU8-2025, is placed in the center of this area 5.9 (b). It is 

important that no air bubbles are entrained in the SU8-2025 in this step. Next, this puddle is 

spread out evenly over the surface of the wafer, using a glass plate or another object that is 

smooth and long enough to span across the entire wafer 5.9 (c). At this point, the exposed SU8 

is in the shape of a dish which contains a puddle of liquid, low viscosity SU8-2025. The wafer is 

then placed flat in an oven at a low baking temperature for a long period of time to allow the 

solvents to be expelled from the SU8-2025; 75 oC for a period of 15 h to 16 h works well. 

When it is removed from the oven, the thickness of the SU8 is fairly constant across the 

surface of the wafer. At this point, the remaining portions of the SU8 need to be exposed to a 

dose of UV radiation. The mask is realigned to the pattern left from the first exposure, except 

42
this time there is no black tape on the mask. The SU8 is given a dose of UV radiation, 

Figure 5.9 (e), and then undergoes its post expose bake. 

(a) (b) (c)

(d) (e) (f)

(a) (b) (c)

(d) (e) (f)

Figure 5.9. Process Steps to Eliminate Edge Bead Continued 

Altogether, these additional process steps roughly double the total amount of bake time

needed to process a wafer, but the resulting pattern transfer and the yield are far superior to those 

fabricated without these additional steps. A typical product of thick layer SU8 deposition using 

these additional fabrication steps is shown below in Figure 5.10. 

43
Figure 5.10 Typical Thick Layer SU8 Deposition Using Additional Fabrication Steps

44
CHAPTER 6 

SU8 Nickel Micromolded Device 

In the previous chapters, processes have been developed that will allow the fabrication of

the refrigerant expansion device out of a metal using SU8 micromolds. Based on the findings of 

the device fabricated with DRIE and the limitations of SU8 micromolding, a number of changes 

were incorporated into this new design. 

6.1 New Design

Nickel was selected as a new material because it is an easy metal to use for thick layer 

electroplating and it is substantially more ductile than silicon, which lowers the risk of 

catastrophic failure in a harsh environment. The electrodeposition method used to deposit nickel 

in this manner is also much less expensive than the fabrication techniques required to construct 

similar features from silicon. The most significant change to the design of the device is that the 

refrigerant flow passage is now incorporated directly into the device. This change eliminates 

many of the problems that occur during device assembly. 

As a consequence of the design and fabrication process changes, the new design must be 

fabricated in three pieces, the diaphragm/piston section, the flow channel section, and the flow 

channel cap section. 

The diaphragm/piston section is comprised of a thin circular membrane with a cylindrical 

piston located in its center and a ring on its perimeter to add stability. A sketch of this piece is 

shown in Figure 6.1. 

Figure 6.1 Sketch of Piston/Diaphragm Piece 

Next, the flow channel section is comprised of a flat, circular mass of material with a pass 

through hole in the center. On one side of this piece are two vertical walls, separated by a gap 

such that they lie on either side of the pass through hole. These walls and the portion of the disk 

that lies between them make up the bottom and sides of the refrigerant flow passage. The flow 

passage extends a short distance beyond the perimeter of the circular disk so that connections to 

fluidic conduits may be made later. A sketch of the flow channel section piece is shown in 

Figure 6.2. 

45
Figure 6.2 Sketch of Flow Channel Piece 

The third piece is the flow channel cap section which is simply a piece of material that 

seals the top of the refrigerant flow channel. This piece is comprised of a section which spans 

the length of the flow channel and contains a wall on either side to clasp onto the channel. A 

sketch of this piece is shown in Figure 6.3. 

Figure 6.3 Sketch of Flow Channel Cap Piece 

The three pieces are assembled as shown in Figure 6.4. 

46
Figure 6.4 Assembly of the Micromolded Pieces 

The first step to fabricating these pieces is to calculate the dimensions that are required to 

allow the device to operate through its desired range of motion. The flow channel was designed 

to be of rectangular cross section with a height of 500 μm and a width of 1 000 μm. In order to 

close off this channel, the piston must have a 500 μm range of motion. 

A spreadsheet, similar to that generated for the silicon prototype, was created to calculate 

the required dimensions of the nickel pieces. The mechanical properties of electroplated nickel 

were acquired from [60]. Young’s modulus and the yield strength of electroplated nickel were 

found to be substantially different from cast nickel, and these properties are also affected by the 

current density used during the electrodeposition. The properties used for this analysis 

corresponded to a current density of 12.7 mA/cm2

, which is equivalent to a current of 1 A over 

the surface area of a 100 mm diameter wafer. The value of Poisson’s ratio was taken to be 0.31 

[61]. The values used for this analysis are: 

E = 18.8 GPa 

σy = 770 MPa 

The calculations detailed in section 5 of this report were repeated with these material 

properties. The radius of the diaphragm was chosen to be 6 200 μm and the selected thickness 

was 150 μm. The required deflection of 500 μm was held constant on this spreadsheet, as this 

was the minimum acceptable height of the refrigerant flow channel, and it is desired to ultimately

close this channel with the piston. These dimensions result in a factor of safety of 3.5. 

6.2 Fabrication

The three pieces which make up the device were fabricated using the nickel 

micromolding procedure. A total of 7 photolithography masks were created for the three pieces. 

The masks used for this work were produced by high resolution (5 080 dpi) printing of the mask 

layers onto transparency film. 

The diaphragm/piston piece was fabricated in the following manner. This device has

three distinct layers; therefore, it required a three-mask process. The first mask defines the top 

half of the piston; the second mask defines the bottom half of the piston and the ring attached to 

the perimeter of the diaphragm; and the third mask defines the diaphragm. Since SU8 is a 

47
negative tone photoresist, the final pieces that are to be formed of metal were drawn as dark 

fields on the photolithography masks. An array of 31 identical devices was able to fit onto each 

mask, given the dimensions of the features. Drawings of the three masks used to fabricate the 

molds for this piece are shown in Figure 6.5. 

Figure 6.5 Masks used to Fabricate Molds for Piston/Diaphragm Piece 

Mask # 1 Mask # 2 Mask # 3 

The flow channel piece and the flow channel cap piece each contain two distinct layers; 

therefore, a two-mask process is required to fabricate these molds. The masks for the flow 

channel piece are shown in Figure 6.6. Using this arrangement an array of 31 devices was able 

to fit on each mask. The mask designated Mask # 4 defines the area which sits atop the 

diaphragm/piston piece, with a small opening in the center to define the pass through. Mask # 5 

defines the area which will make up the side walls of the refrigerant flow passage. 

Figure 6.6 Masks used to Fabricate Molds for Flow Channel Piece 

Mask # 4 Mask # 5

The masks needed to fabricate the flow channel cap piece are shown Figure 6.7. The area 

needed to fabricate this piece is significantly less than the other pieces; therefore, more of them

48
can be made during a process run. Using this arrangement an array of 47 devices was able to fit 

on each mask. The mask designated Mask # 6 defines the walls of the flow channel cap. 

Mask # 7 defines the area which will seal the top of the refrigerant flow passage. 

Figure 6.7 Masks used to Fabricate Molds for Flow Channel Cap Piece 

Mask # 6 Mask # 7 

In the following recipes, all liquid SU8 was brought to a temperature of 25 oC prior to 

dispensing onto the wafers. Also, all temperature changes imposed on the wafer (baking rampup and cool-down) were done at a rate of 0.2 oC/s or less to avoid problems with rapid 

temperature change. The process flow for this device began with soaking 900 μm thick silicon 

wafers in hydrofluoric acid for 10 min to remove any silicon dioxide. The wafers were then 

rinsed with de-ionized water and allowed to dehydrate on a hot plate for 30 min at 120 °C. 

Figure 6.8 depicts the process flow for fabricating the molding for the piston/diaphragm pieces. 

A 40 μm thick layer of SU8-2025 was spun onto the wafer at 2 000 RPM, soft baked for 10 min 

on a level hot plate at 95 oC, and flood exposed with 1.77 J/cm2

 of UV radiation with no 

mask (i). This step coated the entire wafer with a 40 μm thick layer of cross linked SU8 so that 

the metal layers (to be deposited later) will not contact the silicon and can be easily removed. 

After the “sacrificial” layer of SU8 was deposited, a layer of SU8-2100 was spun onto the 

wafer at 1 000 RPM, and soft baked (soft bake # 2) at 95 oC for 1 h, to deposit a 250 μm thick 

ridge of SU8 onto the wafer. After soft bake # 2, the spin on process (SU8-2100 at 1000 RPM) 

was repeated, and the wafer was soft baked again (soft bake # 3) at 95 oC for 1 h. 

At this point, the wafer was covered with an exposed 40 μm layer of SU8. On top of this 

was an unexposed layer of SU8, with a thickness of 500 μm near the outer edge and much 

thinner near the center (ii). The wafer was sandwiched between Mask # 1 and a glass plate. The 

two glass plates were held in together using 8 binder clips along their outer edge. Upon securing 

the clips, a clearly visible distinction could be made between SU8 in contact with the mask and 

the areas where SU8 was not in contact with the mask (iii). Opaque, black electrical tape was 

placed over the areas where the SU8 was not in contact with the mask, so that only the thicker, 

outer edge of the SU8 could be seen through the mask (iv). A dose of 5.4 J/cm2

 was 

administered to the SU8 on the wafer (v). Next, the mask was removed and a puddle of low 

viscosity SU8-2025 was placed in the center of the wafer (vi). The SU8-2025 was then 

smoothed into place using a glass plate (vii) and placed into a low temperature oven at 75 oC for 

49
18 h. Upon removing the wafer from the oven, it could be seen that the resulting layer of SU8 

was level. The wafer was once again sandwiched between Mask # 1 and a glass plate, using 8 

binder clips. This time, the Mask # 1 was aligned to the previous exposure, and no black tape 

was necessary because all of the SU8 was seen to be in contact with the mask. The wafer was 

then given a 5.4 J/cm2

 dose of ultraviolet radiation (viii). This completed the patterning of the 

first 500 μm thick layer of the micromold (ix). 

Next, fabrication steps (ii) through (viii) were repeated using Mask # 2 (x). This time, 

Mask # 2 was aligned to the features left by Mask # 1 for the first exposure (with black tape), 

and to the features left by itself for the second exposure. This completed the patterning of the 

second 500 μm thick layer of the micromold. 

Finally, a layer of SU8-2100 was spun onto the wafer at 1 850 RPM, corresponding to a 

thickness of 150 μm. The wafer was then soft baked at 95 oC for 35 min. Following the soft 

bake, the wafer was sandwiched between Mask # 3 and a glass plate, black tape was placed over 

the non-contact areas, and the wafer was given a dose of 3.3 J/cm2

. The wafer was then filled in 

with SU8-2025 in the same manner and placed in an oven overnight for 24 h at 75 oC. The wafer 

was then realigned to Mask # 3 and administered the same dose of 3.3 J/cm2

 (xi), and placed 

back into the oven at 75 oC for 19 h. This completed the final lithography step for the mold 

fabrication. 

The wafer was then developed in PGMEA. Development of molds this tall is a very slow 

process as well. The wafers were submerged in PGMEA and agitated. The progress was 

periodically checked with isopropyl alcohol and the developer solution was changed every 

20 min. During this process run, development took approximately 1 h and 20 min (xii). 

50
(i) (ii) (iii)

(iv) (v) (vi)

(vii) (viii) (ix)

(x) (xi) (xii)

(i) (ii) (iii)

(iv) (v) (vi)

(vii) (viii) (ix)

(x) (xi) (xii)

Figure 6.8 Process Flow for Fabrication of Piston/Diaphragm Molding 

51
The same process was used to fabricate the flow channel pieces and the flow channel cap 

pieces with the exception that the top layer (step xi) was not needed for these devices as they are 

two-layer devices. The other difference is that these two wafers were given a slightly longer post 

exposure bake of 24.5 h. 

Once the molding was completed, a 4800 layer of gold was sputtered over the entire 

surface of the cross linked SU8. Gold was selected for this purpose because it is a good 

electrical conductor and its deposition rate through sputtering is very fast in comparison to other 

metals (approximately 500 /min). Also, it has been noted that gold has the worst adhesion to 

SU8; therefore, it will make it easier to eject the fabricated parts from the SU8 molds. 

o

A

o

A

The next step was to deposit nickel into the molding. A large beaker containing a 

solution of 51 % nickel sulfamate was warmed to 65 °C on a hot plate. The wafer containing the 

molding was placed in the beaker along with a 100 mm X 150 mm X 3 mm strip of alloy 200 

nickel (>99.5 % Ni). Electrical wires were secured to the nickel strip and to the gold layer with 

alligator clips. These wires were connected to a DC power supply as shown in Figure 6.9. 

Figure 6.9 Electroplating Apparatus 

1.0 A + -

A steady DC current of 1.0 A was held between the base plate and wafer. An estimate of 

the time required to fill the molds was calculated at this current for the piston/diaphragm piece. 

The estimate was based on assumptions that the volume of nickel transferred from the anode to 

the cathode was equivalent to 1 150 μm in thickness over the entire surface of the wafer, that 2 

electrons were transferred through the power source in order to deposit each atom of nickel, and 

the atomic packing density of nickel (face centered cubic) is 74 %. The resulting estimate 

showed it would take 73.5 h of electroplating to fill the molds; therefore, the electroplating 

process was run for 91 h to ensure that enough nickel had been deposited. Similarly, estimated 

electroplating times were calculated for the flow channel piece and the flow channel cap piece 

based on a 1 000 μm thick layer deposition. It was estimated that these devices would take 

52
approximately 64 h to electroplate at a current of 1 A; therefore, the process was performed for 

80 h. 

After the molds had been filled, the nickel was polished down until SU8 was exposed. At 

this point, the nickel devices were removed from the mold by placing the wafer on a 500 °C hot 

plate for 10 s. This thermal shock caused the SU8 to fracture and eject the nickel pieces. 

6.3 Feature Characterization

The features of the micromolded pieces were measured and compared to expectations. A 

general observation about the SU8 molding is that the effects of edge beading were vastly 

improved by the additional fabrication steps. For this fabrication run, the yield of usable product 

was generally around 70 %. The exact tolerances of the best pieces were generally good; the 

main hindrance to better pattern transfer was the number of exposure alignments. This can, 

however, be improved by using proper alignment equipment in the future; although, it may not 

be necessary for many applications. 

Since this fabrication process is experimental, each piece is inherently unique. Therefore 

for the sake of brevity, a full characterization of only one of each of the pieces that were 

assembled to form the device will be presented in this section. Obviously the best devices on 

each wafer were used for the assembly; therefore, this section does not represent the 

characterization of the average device on the wafer. The features fabricated during this process 

run are larger than what can be measured using a profilometer; therefore, although less accurate, 

a micrometer was used to measure most of the results. The accuracy of the micrometer was 

+/- 3 μm. Features that are not measurable with a micrometer due to their geometry or 

orientation were characterized using the microscope focus dial method. 

6.3.1 Piston/Diaphragm Piece

Figure 6.10 shows a photograph of the top of a piston. The intended geometry of the 

piston was to be that of a cylinder 1 000 μm tall, with a diameter of 950 μm. The diameter at the 

top of the post measured 900 μm and 913 μm along two different chords. The red circle shown 

on this figure outlines the intended feature geometry. 

Figure 6.10 Characterization Photograph: Top of Piston 

53
It can be seen from this photograph that the opening in the SU8 mold was slightly larger 

than intended. This is because SU8 is a negative type photoresist, and any misalignment or 

scattering will result in areas near the dark fields receiving some UV radiation. Also, there is 

some difficulty developing the SU8 near the bottom of the trenches, which correspond to 

features at the top of the piston. Since the edges at the bottom of the SU8 trenches are sharp 

internal corners, it is difficult to dissolve and remove all of the unexposed SU8. This results in 

rounded edges near the top of the micromolded features. Figure 6.11 is a photograph of the 

piston, taken from an angle to show the profile. 

Figure 6.11 Side Profile of Piston 

The figure shows that the top of the piston is slightly thinner than the bottom, and that the 

edges are rounder near the top of the piston. Notice that the orthogonal geometry near the 

bottom of the piston gives way to a smooth section near the top. 

The next feature of this device to be analyzed is the ridge which stabilizes the perimeter 

of the diaphragm. The ridge was intended to be 500 μm in width and 500 μm tall. 

Measurements were taken around the ridge at the locations shown in Figure 6.12. 

Figure 6.12 Locations of Characterization Measurements for Piston/Diaphragm Piece 

width 

A

B

C

D

54
The width of the ridge was measured with a micrometer to be 500 μm, 520 μm, 500 μm, 

and 540 μm in locations A, B, C, and D, respectively. The reason why this feature is wider than 

intended in some locations is because of the photolithography masks. The pattern transfer was 

quite good here, but the method used to make the masks has some limitations. 

The layouts for the masks were drawn using a commercially available CAD package and 

then exported as encapsulated postscript files. Next, these postscript files were then printed on 

transparency film at a resolution of 5 080 dpi. The limitations of postscript format are such that 

it cannot comprehend smooth curves and they are consequently represented as a series of 

triangles. Therefore, some of the smoothness of the curves is lost. Figure 6.13a is a magnified 

clipping from the postscript file used to make Mask # 2. It is apparent from this file that images 

of smooth curves will not be transferred as such. The resulting image transfer is illustrated by 

Figure 6.13b, which shows a portion of one of the ridges. 

 Figure 6.13 a) Portion of Mask #2 b) Resulting Curvature of Ridges 

This affected every non-rectilinear feature, although it is most pronounced in the example 

shown above. For the purposes of this device, however, this is quite acceptable. There is no 

reason why this would affect the performance of the device, but it is necessary to document for 

the purpose of SU8 micromolding procedure development. 

The next feature that was examined was the thickness of the membrane. This could not 

be measured directly; therefore, it was calculated as the difference between the ridge height on 

the inner and outer edges. The height of the outer edge was measured with a micrometer. The 

height of the inner edge was measured using the microscope adjustment dial. The measurements 

at locations shown in Figure 6.12 are tabulated in Table 6.1 below. 

55
Table 6.1 Measurements of Diaphragm Thickness 

Location Outer Ridge Height 

(μm)

Inner Ridge Height 

(μm)

Diaphragm Thickness 

(μm)

A 655 495 160

B 650 500 150

C 645 505 140

D 648 497 151

The value of the diaphragm’s thickness varied a little bit from location to location. This 

is mainly because the diaphragm was manually polished to its final thickness. The average of 

the thickness measurements is 150.25 μm, and this is very close to the intended value of 150 μm. 

The height of this piston was also very close to the intended height. This is because a 

significant amount of the fabrication effort was centered around zeroing in on the parameters that 

would yield the appropriate SU8 thickness. The piston height was measured by subtracting the 

diaphragm thickness from the overall height of the piston and diaphragm, measured with a 

micrometer. The piston height plus diaphragm thickness is 1 143 μm, therefore the piston itself 

is 993 μm tall. 

 

6.3.2 Flow Channel Piece

The features of the flow channel piece were measured in locations indicated by the points 

in Figure 6.14. For this device, all features were measured using a micrometer. 

Figure 6.14 Locations of Characterization Measurements for Flow Channel Piece 

E

F

J G K

H 

I 

The measurements of plate thickness, wall height, and wall width at these locations are 

tabulated in Table 6.2. The target value for each of these features was 500 μm. The target value 

for the channel width was 1 000 μm. 

56
Table 6.2 Measurements for Flow Channel Piece 

Location Plate Left Wall Right Wall 

Thickness 

(μm)

Channel 

Width 

(μm)

Height 

(μm)

Width 

(μm)

Height 

(μm)

Width 

(μm)

E 450 1050 400 400 375 300

F 450 1080 400 400 375 300

G NA 1100 300 300 300 300

H 360 1080 390 300 400 300

I 320 1100 400 300 400 300

J 500

K 500

The measured plate thickness was slightly thinner than the target thickness of 500 μm 

near one of the edges. This is again because the back ends of these devices were polished 

manually, and there is a degree of difficulty in keeping the wafer perfectly parallel to the sand 

paper. This should not affect the performance of the device, since the affected area is merely a 

point of connection to the tubing that supplies the flow through the device. 

Figure 6.15a shows a photograph of one of the channel walls. It can be seen from this 

photograph that the walls have a slight trapezoidal shape to them where the top of the flow 

channel wall is thinner than the bottom. This is likely the result of the same factors explained for 

the piston being too narrow. Distortion of the channel walls for this piece, and also those on the 

flow channel cap piece, will not affect the performance of the device. This is because these 

pieces are used to establish a gap between the top and bottom of the flow channel. As long as a 

500 μm gap can be maintained on each end of the channel, the flow channel itself will be

500 μm tall, regardless of the lengthwise profile of the walls. 

Figure 6.15b is a picture of the center hole of this piece. The opening of this hole, 

measured with a micrometer, is 1 092 μm in the direction perpendicular to the channel walls and 

1 078 μm in the direction parallel to the walls. The intended shape was to be a circular opening 

with a diameter of 1 000 μm. The main cause of this slight distortion is due to the pattern on the 

photolithography mask. This is inferred from the shape of the hole. The edge looks more like a 

series of straight lines than a continuous curve. 

 Figure 6.15 a) Photograph of Channel Wall b) Photograph of Channel Through Hole 

57
Figure 6.16 is a photograph of the top of the piston from the piston/diaphragm piece assembled 

to the through port on the flow channel piece. As detailed earlier, the target diameter for the 

piston was 950 μm and that of the port was 1 000 μm; while the diameters as fabricated are 

between 900 μm and 913 μm for the piston and between 1 078 μm and 1 092 μm for the port. 

Figure 6.16 Piston and Port Assembly 

In all instances, the distortion that occurs with SU8 would not prevent the device from 

functioning. This is because SU8 is a negative photoresist, therefore any errors due to alignment 

or scattering will cause cured SU8 to be present where it is not wanted. Also, any problems due 

to underdevelopment will also leave SU8 where it is not wanted. Ultimately, any imperfections

in the pattern transfer will result in the nickel pieces having structures that are thinner than 

desired and open areas being wider than desired. If this were not the case, then a less than 

perfect pattern transfer could result in nickel pieces that would not properly assemble. In the 

case shown above in Figure 6.16, the gap left between the piston and the edges of the port is 

between 82.5 μm and 96 μm, depending on location; the desired gap is 25 μm uniformly around 

the piston. Therefore, the piston will still be able to enter the flow passage, but it will not have 

the ability to completely seal it off.

6.3.3 Flow Channel Cap Piece

The features of the flow channel cap piece were measured in locations indicated by the 

points in Figure 6.17. For this device, all features were measured using a micrometer. 

58
Figure 6.17 Locations of Characterization Measurements for Flow Channel Cap Piece 

L

M

N

The measurements of wall height and thickness at these locations are tabulated in 

Table 6.3. The target value for each of these features is 500 μm.

Table 6.3 Measurements for Flow Channel Cap Piece 

Location Left Wall Right Wall 

Height 

(μm)

Width 

(μm)

Height 

(μm)

Width 

(μm)

L 440 300 500 350

M 500 300 500 350

N 500 300 500 350

The features on this piece showed similar distortions as the channel walls on the flow 

channel piece, which is to be expected. Again, these distortions should not affect the 

performance of the device, since the walls merely serve as a spacer. 

6.4 Assembly

Many different options were examined before a method of assembling this prototype was 

devised. The assembly procedure used for the silicon prototype proved undesirable because it 

was difficult to seal the oil cavity with epoxy. Also, once a working prototype was assembled, 

the epoxy that held the silicon pieces to the oil cavity proved to be quite flexible which 

substantially degraded the motion of the piston. Ultimately, such a device would most likely be 

assembled using a technique similar to [62], but an alternative method must be used for this 

device due to the mask layouts. 

Soldering the pieces to each other and to the oil cavity was an attractive option; however, 

this presented obstacles which needed to be overcome. Soldering offers a great deal of comfort 

in terms of creating a seal between the pieces that can withstand high pressure. The difficulty of 

soldering these pieces together lies in keeping molten solder from flowing into the thin flow 

channel. The flow channel is a conduit that is approximately 500 μm tall by 1 000 μm wide, 

which makes it a good conduit for capillary forces to draw molten solder. 

Using a laser to weld the pieces together offers the benefits of superior seals between the 

pieces and to the capsule. The drawbacks associated with this method are the start up time and 

59
cost associated with devising a good method of guiding the laser around the perimeter to create a 

quality, uniform seal. For this reason, energy and time was focused towards solving the 

difficulties of soldering these pieces.

Rather than machining an oil capsule for this prototype, commercially available fittings 

were used. This allows for the possibility of disassembly and repair should the oil leak from the 

cavity. The cavity was made from two Swagelok fittings; the top portion is a 9.5 mm to 9.5 mm 

tube to female NPT fitting and the bottom portion is a 1.6 mm tube to 6.3 mm male NPT fitting. 

The top portion of the oil capsule is shown below in Figure 6.18a. The left hand side of 

this fitting is a 9.5 mm compression fitting, which has an outer diameter of 12,700 μm. The size 

of the piston/diaphragm molded piece was designed to fit on top of this opening. The bottom

portion of the capsule is shown in Figure 6.18b. The left hand side of this fitting fits into the 

other fitting. The right hand side allows a connection to a 1.6 mm tube, which will be used for a 

thermocouple probe. When these two pieces are assembled, a void of approximately 2.0 mL to 

2.5 mL is left between them, which will be filled with oil when the assembly is complete. 

 Figure 6.18 a) Top Portion of Oil Capsule b) Bottom Portion of Oil Capsule 

In order to properly solder these pieces together and to the top of the oil capsule, they had 

to be held together, therefore they were spot welded. Welding does not work very well between 

nickel and brass due to conflicting material properties. Also it is not possible to form a seal that 

would withstand high pressure in the manner; however, this did work well enough to hold the 

pieces together so that the assembly could be soldered. 

The capsule and pieces were soldered together using a hot plate. Soldering flux was 

carefully painted into the crevices where solder was desired using a thin wire. Ground up chards 

of silver solder was then placed on and around the soldering flux and the assembly was placed 

onto the hot plate. The assembly was monitored while it heated towards the melting point of the 

solder. Once the solder melted, it was drawn into the crevices and the assembly was quickly 

removed from the hot plate. 

Visual inspection showed that this method formed a continuous seal in all areas. The 

capsule top was then pressure tested by connecting 1 MPa of compressed air to the back end and 

submersing the assembly in water. No bubbles were present, indicating that the 

diaphragm/piston piece was well connected to the capsule. This portion of the assembly is 

shown below in Figure 6.19. 

60
Figure 6.19 Oil Capsule Top Connected to Flow Restrictor 

For the next step, a 14.4 Ω electric resistance heating element was placed into the bottom 

portion of the oil capsule and its wires were fed through a 1.5 mm diameter hole that was drilled 

through the rear of the fitting. The heater wires were secured into the hole with refrigerant 

epoxy. The bottom portion of the oil capsule is shown below in Figure 6.20. 

Figure 6.20 Bottom Portion of the Oil Capsule, Including Heater 

Next, the two portions of the capsule were fixed together. The reservoir was then filled 

with 2.1 mL of polyalkalene glycol at a temperature of 24.3 °C, through the compression fitting 

hole. A thermocouple, calibrated to an uncertainty of 0.1 °C with 95 % confidence, was then 

secured into this hole. 

The measurements taken from the device characterization and the amount and initial 

temperature of oil were used in a prediction of performance spreadsheet. Figure 6.21 shows the 

predicted displacement of the piston in this assembly. 

61
y = 32.791x - 800.72

R2 = 0.9999

-100

0

100

200

300

400

500

20 22 24 26 28 30 32 34 36 38 40

Temperature (degrees C)

Pre

dicted Deflection (microns)

Temperature (oC)

Predicted Deflectio

n (μm)

y = 32.791x - 800.72

R2 = 0.9999

-100

0

100

200

300

400

500

20 22 24 26 28 30 32 34 36 38 40

Temperature (degrees C)

Pre

dicted Deflection (microns)

Temperature (oC)

Predicted Deflectio

n (μm)

Figure 6.21 Predicted Displacement of Piston 

According to the prediction curve, the tip of the piston should reach the top of the flow 

channel when the oil reservoir temperature is 39.6 °C. There should be some flexibility in the 

other components surrounding the oil reservoir, but not nearly to the extent that was seen while 

testing the silicon prototype, since this prototype was soldered together. In the interest of 

avoiding problems with the piston pushing against the top of the channel, it is not desired to test 

the device far beyond this point. 

6.5 Measured Piston Actuation

Figure 6.21 served as a tool to estimate the motion of the piston while testing the 

prototype’s ability to control flow. In order to truly know the position of the piston, it is 

necessary to have a measured curve of the relationship between oil temperature and piston 

position. However, this could only be found through destructive testing. Therefore, after all of 

the flow experiments were carried out with this device, the flow channel cap piece was cut from

the prototype and measurements were taken using the microscope method described in Chapter 4 

of this report. Figure 6.22 shows the results of these measurements. 

62
-50

0

50

100

150

200

250

300

25 27 29 31 33 35 37 39 41 43 45

Oil Temperature (degrees C)

V

ertical Displacement (

micro

n

s)

R

elative t

o chan

n

el flo

or

Temperature (oC)

Vertical Dis

placement (μm)

Relati

ve to Cha

n

nel Floor

Figure 6.22 Characterization of Piston Displacement for Nickel Micromolded Prototype 

There are a few useful bits of information that came from these measurements. First, the 

results of these measurements show that the piston does not exhibit significant motion until the 

oil temperature is warmed past approximately 30 oC. The most logical explanation for this is that

a small air bubble is likely present within the capsule, and that the expanding oil must first 

collapse this bubble before a significant amount of pressure can be applied to the diaphragm. 

The second piece of information is the relationship between oil temperature and 

displacement. Once the piston begins to move with changes in the oil temperature the 

relationship is linear, as was expected, but the slope of the curve is different than the predicted 

slope. The measured slope was determined from a best fit straight line through the points above 

30 oC oil temperature. The slope of this line is 20.19 μm /oC, which is about 2/3 of the predicted 

slope. 

The third piece of information is that, when unactuated, the top of the piston lies 

approximately 20 μm to 25 μm below the surface of the channel floor. This gap is likely due to 

the space occupied by the solder between the diaphragm piece and the flow channel piece. 

63
CHAPTER 7 

Temporal Response Analysis 

The speed at which the device actuates is a rather complicated feature to analyze. It is 

dependent on the properties of the oil in the reservoir, the properties of the materials making up 

the capsule, the mass of these materials, the geometry of the capsule, the heater input, and the 

ambient conditions outside of the capsule. 

There are many tradeoffs that must be considered when designing the capsule. As an 

example, if the amount of oil contained within the capsule is decreased, the thermal mass of this 

system decreases which tends to speed up the device’s response time. Concurrently, the 

temperature change which must be realized to flex the diaphragm increases, which typically 

slows down the device’s response time. All in all, most design parameters influence the 

response time in more than one way, and every aspect must be taken into account. 

From an initial design and testing point of view, there exists a tradeoff between 

controllability and response. At this stage of development, controllability is far more important. 

Although a fast responding device may ultimately be desired, this may be counterproductive to 

the initial design and testing phase because the user must be able to react faster than the device. 

Therefore, at this stage of design, the device was designed and assembled in such a way that the 

oil reservoir and chamber have a large thermal capacitance; i.e., the device will respond slowly 

to heat input. 

What follows in this chapter is an analysis to predict the response time of the device as it 

was designed. Ultimately, this type of analysis would be used as a design tool which would 

enable an engineer to speed up the device’s response. 

7.1 Overview

Since this device is made up of multiple materials, has multiple boundary conditions, and 

a complex geometry, an analytical solution is impossible to determine. Therefore, a numerical 

approach is used to determine how fast the oil in the reservoir will change temperature in 

response to a change in the heater output. Before this can be determined, it is necessary to 

ascertain the physics of this situation. A sketch of the capsule is shown below in Figure 7.1 

Figure 7.1 Sketch of Capsule 

Thin Nickel 

Layer 

Oil 

Reservoir 

Heater 

Brass

z 

r 

64
The capsule is approximated by a cylindrical vessel and it is assumed that there are no 

rotational effects; therefore, a 2-dimensional analysis is adequate. The capsule containing the oil 

consists of a brass piece that makes up the bottom and sides, and a thin nickel membrane at the 

top. A heater is located near the center of the capsule. The outer edge of the brass part of the 

capsule is exposed to ambient conditions. The top of the membrane is exposed to the fluid that is 

passing through the device. 

As the heater is powered up, heat is dissipated into the oil reservoir. This raises the 

temperature of the oil, which changes its density and flexes the membrane outward. As the 

temperature of the oil is raised, it dissipates heat to the ambient through the brass portion and to 

the fluid in the channel through the nickel membrane. At some point, the temperature will 

stabilize; i.e. the energy input from the heater will balance with the dissipation through the brass 

and nickel sides of the capsule. 

The first step is to identify the mode of heat transfer that is occurring within the capsule. 

The oil inside the capsule is a liquid and there are no forced currents; therefore, the initial 

assumption is that energy is being transferred through natural convection. Certain 

thermodynamic properties of this particular oil are not known; therefore, they are approximated 

by the properties of glycerin [63]. 

kgK

J 2261

mK

W 0.282

s

m 0.00831

2

=

=

=

Cp

k

ν

The Grashof number is calculated in order to verify or reject the occurrence of natural 

convection in the capsule. The oil capsule has dimensions of 12.6 mm in diameter and 24 mm in 

height. The characteristic length is found by the ratio of the capsule volume to that of the 

internal surface area, or one quarter of the diameter, Lc=3.15 mm. The temperature differences 

within this capsule are typically 10 K to 20 K; cautiously estimating the Grashof number based 

on a temperature difference of 100 K results in: 

( )( )

4

2 2

3

2

2

3

1.7 10

s

m 0.00831

100K 0.00315m

K

1 0.0003775

s

m 9.8

Gr − = ×

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎠

⎞ ⎜

⎝

⎛

⎟

⎠

⎞ ⎜

⎝

⎛

= ∆ = ν

gβ TLc

Natural convection can be neglected for Gr <104

 [64]. Since this situation represents 

eight orders of magnitude below this limit, it is safe to assume that the energy is transferred 

through the oil solely through conduction. 

7.2 Derivation of Nodal Equations 

The heat conduction equation in 2-dimensional radial coordinates without heat generation 

is shown below for points within a single, continuous medium: 

65
t

T C

z

T k

r z

T kr

r r p ∂

∂ ⎟ =

⎠

⎞ ⎜

⎝

⎛

∂

∂

∂

∂ ⎟ +

⎠

⎞ ⎜

⎝

⎛

∂

∂

∂

∂

ρ

1

By assuming that the material properties do not change within the limits of a medium

(oil, brass, or nickel), this equation becomes: 

t

T

z

T

r

T

r

r

T

r ∂

∂ = ∂∂

+⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+

∂

∂

α

1 1

2

2

2

2

Next, the coordinates are discretized (r z, ) → ∆ (m r,n∆z) and the equation can be written in 

the form: 

( ) ( ) ( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )( ( ) ( ) ) 1, , 1, 1, , , 1 , 1 ,

2 2 , ,

1 m n m n m n m n 2 2 m n m n m n m n 1 m n m n t t t

T T T T T T T T m r T T m r m r r z α t

+ + − + −

+∆

⎛ ⎞ − + − ⎛ + − ⎞ ⎜ ⎟ + ⋅∆ + ⎜ ⎟ = − ⋅ ∆ ⎜ ⎟ ⋅ ∆ ∆ ∆ ⎜ ⎟ ∆ ⎝ ⎠ ⎝ ⎠

Or more apt for computer calculations: 

( ) ( )

( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( ) ( ) m n m n m n m n m n m n m n m n t m n t t m n T T T

z

t T T m T T T

a r

t T T 1, 1, , 2 1, 1, ,

2

, , 2 1, , 2 + − 2

∆

∆ − + + − + ⋅∆

∆ = + + + − + − +∆α α

This is the general form that can be used to calculate the temperature distribution as time

is marched forward. In addition to the relationship derived above, special relationships must be 

derived for nodes that are aligned to a change in medium, i.e., the oil-brass interface, oil-nickel 

interface, and the brass-nickel interface. 

For medium changes that occur along a horizontal line, the relationship is derived as 

follows, where A and B represent the two media: 

Figure 7.2 Nodal Network for Horizontal Medium Change 

(m,n+1)

The energy transferred into and out of the node in the radial direction is: 

( ) ( ) ( ) ( ) ( ) 1, , ( ) ( ) , ( 1, )

1 1 1 1 1 1

2 2 2 2 A B m n m n A B m n m n k k m r z T T k k m r z T T

r r − +

⎧ ⎫ ⎛ ⎞ ⎧⎛ ⎞ ⎫

+ − ⎨ ⎬ ∆ ∆Θ∆ − − + + ⎨ ∆ ∆Θ∆ ⎬ − ⎜ ⎟ ⎜ ⎟ ⎩ ⎭ ⎝ ⎠ ∆ ∆ ⎩⎝ ⎠ ⎭

which is simplified to: 

( )( ) ( ) ( ) 1, ( , ) ( ) ( ) , ( 1, )

1 1

2 2 2

A B

m n m n m n m n

k k

r z m T T m T T

r − +

+ ⎧ ⎫ ⎛ ⎞ ⎛ ⎞ ∆ ∆Θ∆ ⎨ ⎬ − − − + − ⎜ ⎟ ⎜ ⎟ ∆ ⎩ ⎭ ⎝ ⎠ ⎝ ⎠ . 

The energy transferred into and out of the node in the vertical direction is: 

(m-1,n) (m,n) (m+1,n)

(m,n-1)

Material A

Material B

66
( ) ( ( ) ( ) ) ( ) , 1 , ( ( ) , ( , 1) ) 1 1 B A m n m n m n m n k m r r T T k m r r T T

z z − + ∆ ∆Θ∆ − − ∆ ∆Θ∆ − ∆ ∆

which is simplified to: 

( )( )2 { B A ( ( ) m n, 1 (m,n) ) ( ( ) m n, (m n, 1) )} m r

r z k T T k T T

z − +

∆ ∆ ∆Θ∆ − − − ∆ . 

The energy stored in the node is: 

( )( )( ) ( ) ( ) ( ( ) , , ( ) )

2 A B

m n m n t t t

P P A P B P

T T T T m r C C m r r z r z C C

t t

ρ ρ ρ ρ +∆

− ∆ ∆ ⎧ ⎫ ∆ ∀ = ∆ ∆Θ ∆ ∆ = ∆ ∆Θ∆ ⎨ ⎬ +

∆ ∆ ⎩ ⎭ ∆t

Canceling similar terms and assembling these terms results in the following relationship: 

( ) ( ( ) ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) { } ( ) ( ) ( ) ( ) ( ) ( )

, ,

1, , , 1,

2 , 1 , , , 1

1 1

2 2 2 A B

m n m n t t t A B

A P B P m n m n m n m n

B A m n m n m n m n

T T

m r k k

C C m T T m T T

t r

m r k T T k T T

z

ρ ρ +∆

− +

− +

− +

2

⎧ ⎫ ∆ ⎧⎛ ⎞ ⎛ ⎞ ⎫ ⎨ ⎬ + = ⎨ − − − + ⎜ ⎟ ⎜ ⎟ ⎩ ⎭ ∆ ∆ ⎩ ⎭ ⎝ ⎠ ⎝ ⎠

∆

+ − − − ∆

− ⎬

which can then be rewritten as: 

( ) ( )

( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( )( ) ( ) ( ) ( ) ( ) ( ) { } ( ) 2 , 1 , , , 1

, , 2 1, , , 1,

2

2

1

2

1

− +

− + +∆

− − − + ∆

∆

+

⎭

⎬

⎫

⎩

⎨

⎧ ⎟ − ⎠

⎞ ⎜

⎝

⎛ ⎟ − − + ⎠⎞ ⎜

⎝

⎛ − ∆ +

+ ∆ = +

B m n m n A m n m n

A p B p

m n m n m n m n

A p B p

A B

t m n t t m n

k T T k T T

C C z

t

m T T m T T

m r C C

k k t T T

A B

A B

ρ ρ

ρ ρ

This relationship can then be used to calculate the temperature distribution along a change of 

medium that takes place in the horizontal direction. 

Similarly, a relationship is needed to calculate the heat transfer along a set of points that 

correspond to a change of medium in the vertical direction. 

Figure 7.3 Nodal Network for Vertical Medium Change 

(m,n+1) 

The energy transferred into and out of the node in the radial direction is: 

(m-1,n) (m,n) (m+1,n) 

(m,n-1)

Medium A Medium B

67
( ) ( ) 1, ( , ) ( ) , ( 1, ) ) 2 2 A B m n m n m n m n r r ⎢ ⎥ ⎜ ⎟ − ⎢⎜ ⎟ ⎥ +

⎣ ⎦ ⎝ ⎠ ∆ ∆ ⎣⎝ ⎠ ⎦

hich is simplified to: 

( 1 1 1 1 k m r z T T k m r z T T ⎡ ⎤ ⎛ ⎞ ⎡⎛ ⎞ ⎤ − ∆ ∆Θ∆ − − + ∆ ∆Θ∆ −

w

( ) ( ( ) 1, ( , ) ) ( ) ( ) , ( 1, )

1

2 2

B

m n m n m n m n

k T T m T T

r r − +

1 ⎤ ⎡ ⎤⎫ A k

r z m

⎧⎪ ⎡ ⎛ ⎞ ⎪ ⎨ ⎬ − − + − ⎢ ⎥ ⎜ ⎟ ⎢⎜ ⎟ ⎥ ⎪ ⎪ ⎩ ⎭ ∆ ⎣ ⎦ ⎝ ⎠ ∆ ⎣⎝ ⎠ ⎦ . 

The energy transferred into and out of the node in the vertical direction is: 

⎛ ⎞ ∆ ∆Θ∆ −

( )( ) ( ( ) ( ) ) ( )( ) , 1 , ( ( ) , ( , 1) ) 2 2 A B m n m n A B m n m n z z − + ∆ ∆

which is simplified to: 

1 1 1 1 k k + ∆m r∆Θ∆r T − T − k + k m∆r∆Θ∆r T −T

( )

( ) ( )( ( ) ( ) ( )

m kA B k r

r z

+ ∆

2 ∆ ∆Θ∆ , 1 , 1 2 , ) 2 m n m n m n T T T

z − + + − ∆ . 

The energy stored in the node is: 

( ) ( ) ( ( ) , , ( ) )

2 A B

m n m n t t t

P A P B P

T T T m r C r z C C

t t

ρ ρ ρ +∆

− ∆ ∆ ⎧ ⎫ ∀ = ∆ ∆Θ∆ ⎨ ⎬ +

∆ ∆ ⎩ ⎭

Canceling similar terms and assembling these terms results in the following relationship: 

( ) ( ( ) ( ) ) ( ) ( ) ( ) ( ) ( ) ( )

( )

( ) ( ) ( ) ( ) ( )

, ,

1, , , 1,

2 , 1 , 1 ,

1 1

2 2

2

2

A B

m n m n t t t A B

A P B P m n m n m n m n

A B

m n m n m n

2

C C m T T m T T

t r r

m k k r

T T T z

ρ ρ +∆

− +

− +

T T

m r k k − ⎧ ⎫ ∆ ⎧⎪ ⎡⎛ ⎞ ⎤ ⎡⎛ ⎞ ⎤⎫⎪ ⎨ ⎬ + = ⎨ ⎢⎜ ⎟ − − ⎥ ⎢ − ⎜ + ⎟ − ⎥⎬ ⎩ ⎭ ∆ ∆⎩ ⎭ ⎪ ⎣⎝ ⎠ ⎦ ⎣ ∆ ⎝ ⎠ ⎦⎪

+ ∆

+ + − ∆

Which is rewritten as: 

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( )

( )( ) ( ) ( ) ( ) ( ) m n m n m n

A p B p

A B

A m n m n B m n m n

A p B p

t m n t t m n

T T T

C C z

k k t

k m T T k m T T

m r C C

t T T

A B

A B

2 , 1 , 1 ,

, , 2 1, , , 1,

2

2

1

2

2 1

+ − + ∆

+ ∆

+

⎭

⎬

⎫

⎩

⎨

⎧

⎥

⎦

⎤ ⎢

⎣

⎡ ⎟ − ⎠

⎞ ⎜

⎝

⎛ − + ⎥

⎦

⎤ ⎢

⎣

⎡ ⎟ − ⎠

⎞ ⎜

⎝

⎛ − ∆ +

∆ = +

− +

− + +∆

ρ ρ

ρ ρ

This relationship can then be used to calculate the temperature distribution along a 

change

rst of

of medium that takes place in the vertical direction. Within the geometry shown in

Figure 7.1, there also exists two points where a change of medium occurs in corners. The fi

these points is shown below in Figure 7.4 

68
Figure 7.4 Nodal Network for Upper-Corner Medium Change 

(m,n+1) 

For this situation the energy transferred into and out of the node in the radial direction is: 

( ) ( ) ( ) 1, ( , ) ( ) ( ) , ( 1, )

1 1 1 1 1

2 2 2 A B m n m n B m n m n k k m r z T T k m r z T T

r r − +

⎡ ⎤ ⎛ ⎞ ⎡⎛ ⎞ ⎤

+ − ∆ ∆Θ∆ − − + ∆ ∆Θ∆ − ⎢ ⎥ ⎜ ⎟ ⎢⎜ ⎟ ⎥ ⎣ ⎦ ⎝ ⎠ ∆ ∆ ⎣⎝ ⎠ ⎦

which is simplified to: 

( ) ( ) ( ) ( ) 1, ( , ) ( ) ( ) , ( 1, )

1 1

2 2 2

A B B

m n m n m n m n

k k k

r z m T T m T T

r r − +

⎧ ⎫ ⎪ ⎪ + ⎡ ⎤ ⎛ ⎞ ⎡⎛ ⎞ ∆ ∆Θ∆ ⎨ ⎬ − − − + − ⎢ ⎥ ⎜ ⎟ ⎢⎜ ⎟ ⎪ ⎪ ⎩ ⎭ ∆ ∆ ⎣ ⎦ ⎝ ⎠ ⎣⎝ ⎠

⎤

⎥

⎦ . 

The energy transferred into and out of the node in the vertical direction is: 

( )( ) ( ( ) ( ) ) ( ) , 1 , ( ( ) , ( , 1) ) 1 1 1

2 A B m n m n B m n m n k k m r r T T k m r r T T

z z − + + ∆ ∆Θ∆ − − ∆ ∆Θ∆ − ∆ ∆

which is simplified to: 

( ) ( ) ( ) 2 ( ) ( ) , 1 ( , ) ( ) ( ) , ( , 1) 2

A B

m n m n B m n m n

m r k k

r z T T k T T

z − +

∆ ⎧ + ⎪ ⎪ ∆ ∆Θ∆ ⎨ ⎬ − − − ∆ ⎪ ⎪ ⎩ ⎭

⎫

. 

The energy stored in the node is: 

( ) ( ) ( ( ) , , ( ) ) 3

4 A B

m n m n t t t

P A P B P

T T T m r C r z C C

t t

ρ ρ ρ +∆

− ∆ ∆ ⎧ ⎫ ∀ = ∆ ∆Θ∆ ⎨ ⎬ +

∆ ∆ ⎩ ⎭

Canceling similar terms and assembling these terms results in the following relationship: 

( ) ( ( ) ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( )

( )( ) ( ) ( ) ( ) ( ) ( )

, ,

1, , , 1,

2 , 1 , , , 1

1 1 3

4 2 2

2

A B

m n m n t t t A B B

A P B P m n m n m n m n

A B

m n m n B m n m n

T T m r k k k C C m T T m T T

t r r

m r k k

T T k T T z

ρ ρ +∆

− +

− +

− ⎧ ⎫ +

2

⎧ ⎫ ∆ ⎪ ⎪ ⎡⎛ ⎞ ⎤ ⎡⎛ ⎞ ⎤ ⎨ ⎬ + = ⎨ − − − + ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎢ − ⎥⎬ ⎩ ⎭ ∆ ∆ ⎪ ⎪ ⎩ ⎭ ⎣⎝ ⎠ ⎦ ⎣ ∆ ⎝ ⎠ ⎦

∆ ⎧ + ⎪ ⎪⎫

+ − ⎨ ⎬ − − ∆ ⎪ ⎪ ⎩ ⎭

which is rewritten as: 

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

( )( )

( )( ) ( ) ( ) ( ) ( ) ( )

, , 2 1, , , 1,

2 , 1 , , , 1

4 1 1

3 2 2 2

4

3 2

A B

A B

A B

m n m n m n m n B m n m n t t t A P B P

A B

m n m n B m n m n

A P B P

t k k

T T m T T k m T T m r C C

t k k

T T k T T

C C z

ρ ρ

ρ ρ

− + +∆

− +

∆ ⎪ ⎪ ⎧ ⎫ + ⎡⎛ ⎞ ⎤ ⎡⎛ ⎞ ⎤

= + ⎨ ⎬ − − − + − ⎢⎜ ⎟ ⎥ ⎢⎜ ⎟ ⎥ ∆ + ⎪⎩ ⎭ ⎣⎝ ⎠ ⎦ ⎣⎝ ⎠ ⎦⎪

∆ ⎧ + ⎪ ⎪⎫

+ − ⎨ ⎬ − − + ∆ ⎪ ⎪ ⎩ ⎭

(m-1,n) (m,n) (m+1,n) 

(m,n-1)

Medium A Medium B

69
This relationship can then be used to calculate the temperature distribution when a 

change of medium takes place in an upper internal corner. The relationship for the lower internal 

corner is derived next, Figure 7.5 shows this situation. 

Figure 7.5 Nodal Network for Lower-Corner Medium Change 

For this situation the energy transferred into and out of the node in the radial direction is the 

same as the previous case: 

( ) ( ) ( ) ( ) 1, ( , ) ( ) ( ) , ( 1, )

1 1

2 2 2

A B B

m n m n m n m n

k k k

r z m T T m T T

r r − +

⎧ ⎫ ⎪ ⎪ + ⎡ ⎤ ⎛ ⎞ ⎡⎛ ⎞ ∆ ∆Θ∆ ⎨ ⎬ − − − + − ⎢ ⎥ ⎜ ⎟ ⎢⎜ ⎟ ⎪ ⎪ ⎩ ⎭ ∆ ∆ ⎣ ⎦ ⎝ ⎠ ⎣⎝ ⎠

⎤

⎥

⎦

The energy transferred into and out of the node in the vertical direction is: 

( ) ( ) ( ) ( )

( )

( ) , 1 , ( ) ( ) , ( , 1)

1 1

2

A B

B m n m n m n m n

k k

k m r r T T m r r T T

z z − +

+

∆ ∆Θ∆ − − ∆ ∆Θ∆ − ∆ ∆

which is simplified to: 

( ) ( ) ( ) ( ) ( )

( ) 2 , 1 , ( ) ( ) , ( , 1) 2

A B

B m n m n m n m n

m r k k

r z k T T T T

z − +

∆ ⎧ + ⎪ ⎪ ∆ ∆Θ∆ ⎨ ⎬ − − − ∆ ⎪ ⎪ ⎩ ⎭

⎫

. 

The energy stored in the node is again: 

( ) ( ) ( ( ) , , ( ) ) 3

4 A B

m n m n t t t

P A P B P

T T T m r C r z C C

t t

ρ ρ ρ +∆

− ∆ ∆ ⎧ ⎫ ∀ = ∆ ∆Θ∆ ⎨ ⎬ +

∆ ∆ ⎩ ⎭ . 

Canceling similar terms and assembling these terms results in the following relationship: 

( ) ( ( ) ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

( )( ) ( ) ( )

, ,

1, , , 1,

2 , 1 , , , 1

1 1 3

4 2 2

2

B B

m n m n t t t A B B

A P B P m n m n m n m n

A B

B m n m n m n m n

T T m r k k k C C m T T m T T

t r r

m r k k

k T T T T z

ρ ρ +∆

− +

− +

− ⎧ ⎫ +

2

⎧ ⎫ ∆ ⎪ ⎪ ⎡⎛ ⎞ ⎤ ⎡⎛ ⎞ ⎤ ⎨ ⎬ + = ⎨ − − − + ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎢ − ⎥⎬ ⎩ ⎭ ∆ ∆ ⎪ ⎪ ⎩ ⎭ ⎣⎝ ⎠ ⎦ ⎣ ∆ ⎝ ⎠ ⎦

∆ ⎧ + ⎪ ⎪⎫

+ − ⎨ ⎬ − − ∆ ⎪ ⎪ ⎩ ⎭

(m-1,n) (m,n) (m+1,n) 

(m,n+1)

(m,n-1)

Medium A Medium B 

70
which can be rewritten as: 

( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

( )( ) ( ) ( ) ( )

( )( ) ( ) ( )

, , 2 1, , , 1,

2 , 1 , , , 1

4 1 1

3 2 2 2

4

3 2

B B

B B

A B

m n m n m n m n B m n m n t t t A P B P

A B

B m n m n m n m n

A P B P

t k k

T T m T T k m T T m r C C

t k k

k T T T T

C C z

ρ ρ

ρ ρ

− + +∆

− +

∆ ⎧ ⎫ ⎪ ⎪ + ⎡⎛ ⎞ ⎤ ⎡⎛ ⎞ ⎤

= + ⎨ ⎬ − − − + − ⎢⎜ ⎟ ⎥ ⎢⎜ ⎟ ⎥ ∆ + ⎪⎩ ⎭ ⎣⎝ ⎠ ⎦ ⎣⎝ ⎠ ⎦⎪

∆ ⎧ + ⎪ ⎪⎫

+ − ⎨ ⎬ − − + ∆ ⎪ ⎪ ⎩ ⎭

This relationship can then be used to calculate the temperature distribution when a change of 

medium takes place in a lower internal corner. 

Next, the nodes along the centerline (r = 0) require a special derivation. For this case, a 

heat generation term is also included because it is assumed that the heater will reside along the 

centerline (see Figure 7.6 below). In this analysis, a simplification was used that assumes the 

heat generation occurs wholly within the centerline nodes. This is not completely accurate, but it 

is good for modeling purposes. Inaccuracies derived from this assumption are due to the 

resulting heat generating nodes which form a heater that is smaller than the actual heater. This 

will result in a warmer centerline temperature in the oil because the modeled heat flux must be 

greater than the actual heat flux to result in the same output. 

Figure 7.6 Nodal Network for Nodes Along Centerline 

For this situation, symmetry dictates that there is no energy transferred into or out of the 

cells from the left hand side; therefore, the energy transferred in the radial direction is simply: 

( ) ( ) 2, (1, )

1

2 n n

r k z T T

r

⎛ ⎞ ∆ ∆Θ∆ − ⎜ ⎟ ⎝ ⎠ ∆

The energy transferred into and out of the node in the vertical direction is: 

( ) ( ) ( ) ( ) ( ) 1, 1 1, ( ) ( ) 1, (1, 1)

1 1

8 8 n n n n

r r k r T T k r T T

z z − +

⎛ ⎞ ∆ ∆ ∆Θ∆ − − ∆Θ∆ − ⎜ ⎟ ⎝ ⎠ ∆ ∆

which is simplified to: 

( ) ( ) 2 ( ( ) 1, 1 (1, 1) 2 (1, ) ) 8 n n

k r

r z T T T

z − +

∆ ∆ ∆Θ∆ + − ∆ n . 

The energy input to the node through the heater is simply: 

(1,n)

(2,n)

(1,n+1)

CL

(1,n-1)

71
''' ''' ( ) 8 gen

r

q q q r z • ⎛ ⎞ ∆ = ∀ = ⎜ ⎟ ∆ ∆Θ∆ ⎝ ⎠ . 

The energy stored in the node is again: 

( )( ( ) , , ( ) )

8

m n m n t t t

P P

T T T r C C r z

t t

ρ ρ +∆

− ∆ ∆⎛ ⎞ ∀ = ⎜ ⎟ ∆ ∆Θ∆

∆ ∆ ⎝ ⎠ . 

Canceling similar terms and assembling these terms results in the following

relationship:

( ( ) ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

, ,

2, 1, 2 1, 1 1, 1 1,

1 2 ''' 8 2 8

m n m n t t t

n n n n n

T T

r r T T T T T q

α t r z

+∆

− +

− ⎛ ⎞ ∆ ∆ ⎛ = − + + − +

8

r

k

∆ ⎞ ⎜ ⎟ ∆ ∆ ∆ ⎝ ⎠ ⎜ ⎟ ⎝ ⎠ , 

can be rewritten as: 

( ) ( ) ( ) ( ) ( ) ( ) ( ) , , 2 2 2, 1, ( ) ( ) 1, 1 (1, 1) (1, )

4 2 ''' m n m n n n n n n t t tt t T T T T T T T q

r z k

α α − + +∆∆ ∆ ⎛ ⎞ = + − + + − + ⎜ ⎟ ∆ ∆ ⎝ ⎠α∆t

This relationship can then be used to calculate the temperature distribution along the 

centerline with heat generation. 

Finally, relationship for the last case of a change of medium along the centerline is 

analyzed. For this case, the heat generation term is left out because the heater in the capsule 

resides only in the oil. See Figure 7.7 below. 

Figure 7.7 Nodal Network for Nodes Along Centerline with Medium Change 

For this situation the energy transferred in the radial direction is: 

( ) ( ) ( ) 2, (1, )1

2 2

A B

n n

k k r z T T

r

+ ⎛ ⎞ ∆ ∆Θ∆ − ⎜ ⎟ ⎝ ⎠ ∆ . 

The energy transferred into and out of the node in the vertical direction is: 

( ) ( ) ( ) ( ) ( ) 1, 1 1, ( ) ( ) 1, (1, 1)

1 1

8 8 B A n n n n

r r k r T T k r T T

z z − +

⎛ ⎞ ∆ ∆ ∆Θ∆ − − ∆Θ∆ − ⎜ ⎟ ⎝ ⎠ ∆ ∆ , 

which is simplified to: 

(2,n)

CL

(1,n+1)

Medium A

(1,n)

Medium B

(1,n-1)

72
( )

( )2 ( ) ( ) 1, 1 (1, ) ( ) ( ) 1, 1 (1, ) 8 B n n A n n

r r z

k T T k T T

z − +

∆ ∆ ∆Θ∆ ⎡ ⎤ − + − ⎣ ⎦ ∆ . 

The energy stored in the node is again: 

( ) ( )( ( ) , , ( ) )

2 8

A B m n m n A P B P t t t

P

C C T T T r C r z

t t

ρ ρ

ρ +∆ + − ∆ ∆⎛ ⎞ ∀ = ⎜ ⎟ ∆ ∆Θ∆

∆ ∆ ⎝ ⎠ . 

Canceling similar terms and assembling these terms results in the following relationship: 

( ) ( ( ) ( ) ) ( )( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( )

, ,

2, 1,

2 1, 1 1, 1, 1 1,

2 8 4

8

A B m n m n A P B P t t t A B

n n

B A n n n n

C C T T

r k k

T T

t r

r k T T k T T

z

ρ ρ +∆

− +

+ − ⎛ ⎞ ∆ + = − ⎜ ⎟ ⎝ ⎠ ∆ ∆

∆

+ − ⎡ ⎤ + − ⎣ ⎦ ∆

which is rewritten as: 

( ) ( )

( )

( )( ) ( ) ( ) ( )

( )( ) ( ) ( ) ( ) ( ) ( ) ( )

, , 2 2, 1,

2 1, 1 1, 1, 1 1,

4

2

A B

A B

A B

m n m n n n t t t A P B P

B A n n n n

A P B P

k k t

T T T T

C C r

t k T T k T T

C C z

ρ ρ

ρ ρ

+∆

− +

+ ∆

= + − + ∆

∆

+ − ⎡ ⎤ + ⎣ ⎦ + ∆ −

z

This relationship can then be used to calculate the temperature distribution along the 

centerline at interfaces between two media. 

7.3 Nodal Spacing and Code Structure 

Now that relations have been established for each type of node in the domain, the node 

size and time step must be determined. Numerical codes involving forward marching in time 

require that each nodal solution have some dependence on its solution at the previous time step; 

therefore, the selection of an appropriate time step is critical for stability [59]. For simplicity, the

node size is selected such that the radial increments are equal to the vertical increments, i.e. 

. Then the dependence of a future time step’s solution on the previous time step is found 

by gathering temperature terms for the

∆ = r ∆

(m n, ) node. 

( ) ( )

( )

( )

( )

( )

( )

( ) , , 2 2 2

2 2

1 _ m n m n t t t

t t t

T T other terms

m r r z

α α α

+∆

⎛ ⎞ ∆ ∆ ∆ = − ⎜ ⎟ − + +

⋅ ∆ ∆ ∆ ⎝ ⎠

And checking the stability criterion at the limiting nodes along m=1, the relation of the previous 

time step to the future time step is: 

( ) ( )

( )

( ) , , 2

5

1 m n m n t t t

t

T T

r

α

+∆

⎛ ⎞ ∆ = − ⎜ ⎟ ⎜ ⎟ ∆ ⎝ ⎠

In order to have stable iterations throughout the code, the time step must be selected such that 

( )

( )

( )

2

2

5

1 0

5

t

r

r t

α

α

⎛ ⎞ ∆ ⎜ ⎟ − > ⎜ ⎟ ∆ ⎝ ⎠

∆

∴∆ <

73
To begin this analysis, a nodal distance must be selected. Since the smallest feature on 

this device is the thickness of the membrane, at 150 μm, this is the largest possible node size. 

According to the relationship derived above, considering nodal spacing of 150 μm and the 

thermal properties of brass (the highest thermal diffusivity of all materials used here), the 

maximum allowable time step is 133 μs. Thus a time step of 100 μs will be used. Using the 

maximum spacing of 150 μm by 150 μm nodes, the grid for this device is represented by an 

array 52 nodes wide and 216 nodes tall, for an overall total of 11 232 nodes. 

A C++ code was created to simulate the transient thermal response of the capsule [65]. 

The flowchart for this code consists is rather simplistic, it is seen below in Figure 7.8. The raw 

code can be found in Appendix A. 

Set constants 

Set IC’s and BC’s for 

T (current) and T (previous) 

While: convergence=0

Update time 

Calculate Temps at next time step 

Check RMS change in Temp

Figure 7.8 Flowchart for Code Execution 

At the onset of the program, all of the initial of the constants are set. Next, the 

temperatures at the boundaries are set and the initial temperature distribution is read from a file. 

Then the code enters a loop in which all temperatures within the domain are calculated at the 

next time step. As the code iterates through the time steps, the root mean square (rms) temporal 

change and the total running time are calculated. Either of these parameters may be used to 

determine the stopping condition. For the first set of runs, the rms temperature change was used 

for the convergence test. According to the physics of the simulated situation, the temperature 

distribution will always change as it asymptotically approaches a solution. Once the rms change 

becomes less than a specified level (1.5X10-8 for this code which corresponds to a rate of change 

of less than 0.0001 °C/s) the convergence parameter is set to a value that will kick it out of the 

loop. 

Once the code has converged on a temperature distribution, it calculates the average oil 

temperature. Since this system is in cylindrical coordinates, the average oil temperature is 

calculated by weighting the temperature at each node by its distance from the z-axis. 

For these simulations, constant temperature boundaries were fixed: 5 °C at the top of the 

nickel membrane (due to the flashing refrigerant) and 25 °C at the outer edges of the brass 

Convergence 

criteria met? 

yes

convergence=1

no 

74
portion (ambient condition). For the first test of this code, an initial temperature distribution was 

imposed, with 20 °C throughout the device. The output from the code was the steady state 

temperature distribution, the time required to bring the system to steady state from the imposed 

isothermal initial condition, and the average oil temperature. 

The output of this run showed convergence at time = 490.27040 s with an average oil 

temperature of 21.302 °C. The steady state temperature distribution is shown below in 

Figure 7.9. 

0

50

100

150

200

250

0 20 40 60

Radial Coordinate

Axial Coordinate

T=5

T=6

T=7

T=8

T=9

T=10

T=11

T=12

T=13

T=14

T=15

T=16

T=17

T=18

T=19

T=20

T=21

T=22

T=23

T=24

T=25

Figure 7.9 Steady State Temperature Distribution

The solid dark line on this figure denotes the transition between the brass capsule and the 

oil contained in the reservoir. The nickel membrane at the top is difficult to delineate due to the 

very steep temperature gradients in its vicinity. 

After the results were inspected, the next step was to verify that the nodal spacing was 

appropriate. To perform this task, the grid spacing was divided in half. The code was modified 

for 75 μm by 75 μm grid spacing. For this nodal spacing, the maximum allowable time step is 

33.15 μs; therefore, a time step of 30 μs was used. 

Because the steady state criteria in the original code was based on the root mean square 

of the temperature change of all the nodes, a change in the grid spacing, time step and number of 

nodes would change the steady state criteria. Therefore, a better comparison between the two 

codes is made by marching forward for an equivalent time period. This modified code was 

marched out in time for the same amount of time that was determined to bring the system to 

steady state for the grid with 150 μm by 150 μm nodes. The average oil temperature was found 

to be 21.255 oC, which is 0.047 °C colder than the previous solution, and the temperature 

distribution plot looks identical to that shown in Figure 7.9. This demonstrates that the solutions 

are close enough to continue with the 150 μm by 150 μm grid spacing. 

75
7.4 Transient Response Experiments 

Once this code was developed, it was used to analyze the device’s response to thermal 

input from the heater in the capsule. For this task, a series of simulations were performed with 

the heater load set to four levels of heat dissipation: 0.25 W, 0.50 W, 0.75 W, and 1.00 W. At 

the onset of each of these simulations, the initial power-off temperature distribution found in the 

previous section was fed into the code as the starting point. The temperature distribution was 

calculated in response to steady heat input and was output from the code at discrete time

intervals. Figure 7.10 shows some of the results from the simulation of the device’s response to 

a 1 W input from the heater. 

76
0

50

100

150

200

0 20 40

Radial Cordinate

Axial Coordinate

0

50

100

150

200

0 20 40

Radial Coordinate

0

50

100

150

200

0 20 40

Radial Coordinate

t = 1 s t = 60 s t = 180 s 

+

0

50

100

150

200

0 20 40

Radial Coordinate

Axial Coordinate

0

50

100

150

200

0 20 40

Radial Coordinate

 t = 300 s t = 720 s 

Figure 7.10 Time Elapsed Temperature Distribution at 1 W of Heat Generation 

The overall average oil temperature (the variable of interest in this section) was 

calculated from each temperature distribution returned from the code. Figure 7.11 below shows 

how the average oil temperature relates to time and the heater output. 

77
20

25

30

35

40

45

50

55

60

65

70

0 100 200 300 400 500 600 700

Time (s)

Average Oil Temp (deg C)

0.25 W

0.50 W

0.75 W

1.00 W

Figure 7.11 Transient Thermal Response of Device to Heat Input 

The generalized functional form of this response somewhat resembles that of a simple 

exponential decay, which was expected. There exists an effect, however, which causes slight

deviations from this functional form. It is caused by differences in the material properties. Since 

the heater is centered in the oil, which has a much lower thermal diffusivity than the brass and 

nickel sections, there exists a time lag between the heater switch and the point where the 

remainder of the system reacts to the addition of this energy. This can be seen in Figure 7.12, 

which shows the first 120 s of transient response. Notice that the thermal response tends to be 

concave upwards during the first 10 s to 15 s, until the temperature gradients within the oil 

capsule are established.

78
20

22

24

26

28

30

32

34

36

0 20 40 60 80 100

Time (s)

Average Oil Temp (deg C)

120

0.25 W

0.50 W

0.75 W

1.00 W

Figure 7.12 Immediate Response of Device to Heat Input 

The temperatures that would be acquired at steady state and the time constant of the 

system were determined by curve fitting. For these fits, the initial two data points (at time = 1 s 

and 10 s) were left out, so that the time lag brought about by the large differences in material 

property would be left out. The device’s time response must be of the following functional form: 

( )exp( ( ε ) /τ ) T = Θ − Θ − Θ0 − t −

In which case Θ0 is the steady state temperature with no power input, Θ is the steady state 

temperature at a given power input, ε is the time lag necessary to establish the thermal gradients, 

and τ is the device’s thermal time constant. The time constant was found first by plotting the 

natural log of (Θ - Θ0) against the time, and adjusting the steady state temperature until the locus 

of points could be fit with a straight line having the resulting R2

 greater than 0.9999999. The 

slope of this best fit straight line is equal to the device’s thermal time constant, τ. 

Using the thermal time constant, the steady state power on temperature, and the steady 

state power off temperature, the time lag term is determined from a least squares fit of the 

functional form. Table 7.1 shows the results of these curve fits. 

79
Table 7.1 Curve Fit Parameters for Device’s Time Response 

Heat Input 

(W) 

Steady State Temp

(oC) 

Time Constant 

(s) 

Time Lag 

(s) 

0.00 21.30229 N/A N/A

0.25 31.176 114.21817 17.482

0.50 41.033 114.21049 14.768

0.75 50.890 114.20765 13.849

1.00 60.747 114.2063 13.385

The thermal time constant for system response to steady input, τ, is approximately 

114.21 s, as was determined for each set of data. The time lag is more significantly pronounced 

at the lowest heater input, due to the lower driving potential. The steady state oil temperature is 

proportional to the heater output, which was also expected, and can be approximated by: 

Θ = 21.30229 + 39.450 *Q

Where Q (W) is the heat generated by the heater. This parameter is directly tied to the 

displacement of the piston on top of the nickel membrane, as outlined in Chapter 6. Therefore, 

we can combine the relationship between the oil temperature and the piston displacement with 

those derived in this section. 

7.5 Summary 

This section outlined a method for predicting the transient response of the heater-oil 

reservoir system. Since this device is comprised of a complex geometry and three different 

materials, an analytic solution is not possible. Therefore, a numerical code was developed to 

simulate the time dependent response of the system to steady thermal input from the heater. 

Derivations of each type of nodal equation were presented in this section, as well as a code 

structure and demonstration of the code developed for the device as designed. In the future, a 

design engineer can use this approach to determine the transient response with different design 

parameters. 

80
CHAPTER 8 

Numerical Simulations

Computationally describing the expansion of a refrigerant as it passes through a short 

tube, or in this case a short tube with an obstruction, is not possible with current methods. The 

problem involves multiphase fluid mechanics, with the liquid phase experiencing metastable 

conditions and vapor phase flowing at or near its sonic velocity. The full physics of this situation 

are not well understood today. Most of the information used to predict refrigerant expansion is 

based on black-box or grey-box modeling of experimental data. 

In order to predict the functionality of this device, however, a physically based 

description of the device’s performance must be computed. For this reason, a Computational 

Fluid Dynamics (CFD) based analysis was performed with the device’s geometry, for a single 

phase gaseous fluid passing through the flow channel. A commercially available CFD package 

was used to perform the simulations at various levels of actuation. These calculations were used 

to generate a tool for the prediction of the device’s performance over a range of conditions. The 

results of these simulations were then compared to the laboratory results for gaseous flow 

through the prototype. 

The software package consists of three modules. The pre-processing software is a 

general purpose geometry and grid generation software package. The solver solves the 

appropriate differential equations specified by the user over the domains generated with the preprocessing package. The post processing software is an interactive graphics program that allows 

the user to view the results of the CFD simulations. 

8.1 Initial Simulations

Initial simulations were performed with the CFD package to verify the methodology. 

The task was to find the mass flow rate of compressed air through the device as it entered at a 

pressure of 316 kPa and 300 K, and exited at a lower pressure of 202 kPa, while the device was 

in the fully open or unactuated position. These are representative of conditions that could be 

easily observed under laboratory conditions. 

The first task was to generate the domain over which to solve the equations of mass, 

momentum, and energy conservation. The unactuated flow channel can be described as a 

rectangular channel, 500 μm tall by 1 000 μm wide, with a length of 19 600 μm. Each end of the 

flow channel is abruptly connected to a 6.35 mm diameter section of tubing. By selecting the 

geometry of an unactuated device, it was possible to take advantage of two planes of symmetry, 

which drastically reduced the computational time. The computational domain for this simulation 

can be seen below in Figure 8.1. 

81
Figure 8.1 Portion of Device used for Initial CFD Simulations 

After utilizing symmetry to reduce the computational domain, the remaining flow field 

was divided into 7 volumes, three forming the flow inlet (termed i1, i2, and i3), three forming the 

outlet (termed e1, e2, and e3), and one representing the channel. The domain that represented 

the flow channel was of rectangular shape, with a length of 19 600 μm, width of 500 μm and a 

height of 250 μm. The inlet and exit plane volumes (i1 and e1) were of the same cross sectional 

area, but had a length of 10 000 μm. These volumes were a projection of the flow channel into 

the pipe connections. Finally, the remaining 4 volumes can each be described as a 45 degree 

sweep of the connected pipe, minus the volume occupied by volumes i1 and e1. 

A mesh was generated which divided each entity by 25 points, so that 24 evenly spaced 

sections were bounded on each entity. Altogether, this created a mesh of 96 768 cells over 

which to solve for the flow field. 

Once the geometry was constructed and the mesh was generated, the data file was 

imported into the CFD solver environment. The problem types of “flow” and “heat transfer” 

were selected so that the continuity of mass, momentum, and energy equations were computed. 

The heat transfer calculations were combined into the analysis so that the temperature 

distribution (and therefore the density) would be more accurate. 

Gravitational and transient effects were turned off. The fluid was set to “air” which 

obtains information from the package’s database. The density was calculated using the ideal gas 

law, and the dynamic viscosity of air was computed using Sutherland’s law. 

Next, the boundary conditions were set. For this problem, the inlet surfaces of volumes 

i1, i2, and i3 were held at a constant pressure of 316 kPa and a temperature of 300 K. At the 

opposite end of the flow field, the exit planes of the volumes e1, e2, and e3 were held at a 

constant pressure of 202 kPa. All wall surfaces were modeled as adiabatic and given the 

boundary condition of zero velocity. All symmetry planes were given the boundary conditions 

of zero gradients for all properties and velocities. The interface planes between all of the 

volumes were left unbounded and were to be determined by the solver. The initial conditions 

used are shown in Table 8.1. 

82
Table 8.1 Initial Conditions used for Preliminary Simulations 

Ux 

(m/s) 

Uy 

(m/s) 

Uz 

(m/s) 

P 

(kPa) 

T 

(K) 

i1 10 0 0 316 300

i2 10 0 0 316 300

i3 10 0 0 316 300

Flow channel 150 0 0 251 280 

e1 100 0 0 202 260

e2 10 0 0 202 260

e3 10 0 0 202 260

The solver was set to calculate the velocity and density with an upwind spatial 

differencing. The convergence criteria were set to a maximum residual of 0.0001 for the each 

component of velocity, pressure and enthalpy. The inertial relaxation parameters for the 

velocity, pressure correction, and enthalpy were continuously manipulated throughout each 

simulation; therefore, it would not be accurate to state the number of iterations required for 

convergence. The process time is a much more informative bit of information. The process time 

for this situation was approximately 30 s per iteration on a personal computer with a 3.0 GHz 

processor. 

The critical piece of information obtained from this exercise is the mass flow rate through 

the device. The output data file from the simulation showed the mass flow rate into the device as

6.8687E-5 kg/s. Multiplying by 4, the total mass flow rate through an entire device was found to 

be 2.74748E-4 kg/s. 

The convergence of these calculations were rather time consuming; therefore, another 

simulation was run with the same configuration, except this time the heat transfer model was 

turned off. The heat transfer model was initially used so that the temperature field would be 

solved and this information would be used to calculate the density of air at each node using the 

ideal gas law. Upon examining the results of the CFD simulation, it was investigated whether 

including the temperature effects on density was necessary, considering the large pressure effect 

on the air density. 

The next simulations were performed in the same manner, using an isothermal flowfield 

with all nodes held at 300 K. The end result was a mass flow rate through the device of as 

6.86263E-5 kg/s. Multiplying by 4, the total mass flow rate through an entire device was found 

to be 2.745052E-4 kg/s, which is less than a 0.1 % difference from the calculations that included 

the heat transfer analysis. The computational time, however, was vastly improved. Each 

iteration took approximately 8 s, roughly one quarter of the time of the previous simulation. 

More importantly, with the elimination of the heat transfer analysis, the number of iterations was 

drastically decreased. 

One more test was required before this simulation tool could be properly used. This test 

was needed to determine whether the mesh was fine enough for this flow situation. In order to 

test this, another mesh was generated with the same geometry. This time, however, the grid was 

doubled so that each entity was divided by 50 points into 49 sections. This increased the number 

of cells by a factor of 8 to 774 144. The data file for this configuration was very large, 108 MB. 

This mesh was brought into the solver and ran with the same initial conditions, boundary 

conditions, and convergence criteria as the previous problem. The convergence of this problem

83
was extremely slow; the iterations each took approximately 2 minutes of computational time. 

The largest obstacle to overcome with this problem was memory allocation; this problem

required a minimum of 1.1 GB of random access memory to avoid the use of hard disk space for 

file usage. 

The end result of this simulation showed that the mass flow through the device was 

6.92669E-5 kg/s, which is less than one percent above the previous calculation. Therefore, it 

was determined that 25 nodes per entity would be adequate for these simulations, and this mesh 

structure would be used for the remainder of this analysis. 

8.2 Verification of Initial Simulation 

Now that the initial simulations have been performed, it is necessary to verify the CFD 

results with a physical model. Intuitively, this problem does not have an exact analytical 

solution, which is why the CFD analysis was performed; however, with a few assumptions, the 

results of portions of the CFD work can be checked against an analytical model. 

The CFD results show that the flow through the channel is subsonic throughout the entire 

domain. This can be easily verified by examining some of the pressures input to the CFD solver. 

The flow situation occurring within the flow channel is adiabatic frictional flow without area 

change, Fanno flow. Therefore, since the flow begins from stagnant air, the maximum flow rate

would result in a Mach number of unity at the flow channel exit; below this flow rate, the flow 

will be subsonic throughout the entire channel [66]. 

If the flow rate of air through the channel were at this maximum flow rate, then the 

pressure at the flow channel outlet would have to be greater than or equal to 202 kPa, the 

pressure at the exit plane of the downstream tube fitting. With the known bound on the static 

pressure and a Mach number of one, the stagnation pressure can be calculated: 

1

2

0 2

1 1 −

⎥

⎦

⎤ ⎢

⎣

⎡ − = +

γ

γ

γ P P M

( ) 1 382.37kPa

2

1.4 1 202kPa 1

1.4 1

1.4

2

0 ≥ ⎥

⎦

⎤ ⎢

⎣

⎡ − ≥ + −

P

In order for sonic conditions to exist at the exit of the flow channel, the exit stagnation pressure 

must be greater than 382.37 kPa. This is not possible because the stagnation pressure at the inlet 

of the upstream tube fitting is 316 kPa, and stagnation pressure can only decrease with friction. 

Therefore, the flow is in fact subsonic throughout the entire domain. 

At this point, it is not possible to analytically determine the mass flow rate through the 

device; therefore, the approach is to approximate the flow properties based on the one 

dimensional analytic equations, the mass flow rate of 2.74748E-4 kg/s returned from the CFD 

solver, and the other known properties. It is known that, since the flow is entirely subsonic, the 

channel exit pressure is 202 kPa. And, since there is no heat addition, the stagnation temperature 

is known to be 300 K. Based on these properties and the mass flow rate, a one dimensional 

analysis can be used to calculate the exit Mach number as shown below. 

The mass flow rate is related to the static temperature, static pressure and Mach number 

84
( ) cs

cs cs

RT MA

RT

P

m UA CMA

γ

ρ ρ

⎟

⎠

⎞ ⎜

⎝

⎛ =

& = =

The static temperature is related to the stagnation temperature through the one dimensional 

isentropic relationship: 

⎟

⎠

⎞ ⎜

⎝

⎛ − +

= 2

0

2

1 1 M

T

T

γ

Therefore, the mass flow rate is related to the static pressure, Mach number and stagnation 

temperature through the following relationship: 

0

2

R

2

1 1

T

M

m PMAcs

⎟

⎠

⎞ ⎜

⎝

⎛ − +

=

γ γ

&

Substituting the known values results in a flow channel exit Mach number of 0.647951. With 

this Mach number, the flow channel exit static temperature is found from the one dimensional 

relationship: 

( )

276.76K

0.647951

2

1.4 1 1

300K

2

1 1 2 2

0 =

⎟

⎠

⎞ ⎜

⎝

⎛ − +

=

⎟

⎠

⎞ ⎜

⎝

⎛ − +

=

M

T T

γ

And the stagnation pressure at the flow channel exit is found from the one dimensional 

relationship: 

( )

( ) 267.8608kPa

0.647951

2

1 1

202kPa

2

1 1

1.4 1

1.4

2 1

2

0 =

⎟

⎠

⎞ ⎜

⎝

⎛ − +

=

⎟

⎠

⎞ ⎜

⎝

⎛ − +

= − − ⎟

⎠

⎞ ⎜

⎝

⎛ − −

γ γ γ

γ

M

P P

The speed of sound at the flow channel exit is: 

( ) ( )

s

m 276.76K 333.47

kgK

J R 1.4 287 = ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ C = γ T =

And the one dimensional approximation of the velocity at the flow channel exit is: 

85
s

m 216.0721

s

m U = MC = 0.647951*333.47 = . 

The static pressure that would result if the flow length were increased until choking conditions 

occur, P*, is calculated from the relationship: 

( )

( )( ) ( )

( ) 124.397kPa

2

1.4 1

0.647951

2

1.4 1 1

202kPa 0.647951

2

1

2

1 1

2

1

2

2

1

2

*

=

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

+

− +

=

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎣

⎡

+

− +

= γ

γ M

P PM

At this point, all of the parameters for a one dimensional approximation are known at the 

flow channel exit. However, it is not possible to use this information for a closed form analytical 

solution because the integrals involved do not have exact solutions; therefore, the flowfield must 

be numerically integrated backwards from the exit plane to the flow channel entrance. 

The sequence used to solve the parameters in this flowfield is as follows. First, the static 

density is calculated from the static temperature and static pressure using the ideal gas law. 

Second, the velocity is calculated from the mass flow rate, cross sectional area, and the density. 

The third step is to calculate the dynamic viscosity using Sutherland’s Law with the static 

temperature. The fourth step is to calculate the kinematic viscosity using the dynamic viscosity 

and the density. The fifth step is to calculate the Reynolds number from the kinematic viscosity, 

the velocity, and the hydraulic diameter. The sixth step is to calculate the smooth tube friction 

factor using the Reynolds number and the relationship: 

4

1

Re

0.3164 f =

Next, the downstream pressure gradient due to friction is calculated from: 

d 2

d 2 U

D

f

x

P

h

ρ =

Finally, the static pressure at a location one incremental element upstream is then calculated by: 

x

x

P Pupstream = Pdownstream + ∆

d

d

With this upstream pressure and the Fanno frictional choking pressure, P*=124.397 kPa, 

the upstream Mach number is calculated. Once the Mach number is known, the static 

86
temperature and the stagnation pressure are calculated from the one dimensional isentropic 

relationships. This entire process is marched backwards from the flow channel exit to the flow 

channel inlet to produce an estimate of each of the flow properties within the flow channel. 

Figures 8.2 through 8.5 show the one dimensional analytical solution compared to the three 

dimensional CFD solution at various locations relative to the channel centerline. 

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Mach Number

1D Mach

centerline Mach

y=62.5 Mach

y=125 Mach

y=187.5 Mach

Length Along Channel (μm)

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Mach Number

1D Mach

centerline Mach

y=62.5 Mach

y=125 Mach

y=187.5 Mach

Length Along Channel (μm)

Figure 8.2 Comparison of Mach Number 

100

120

140

160

180

200

220

240

260

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Velocity (m/s)

1D velocity

centerline velocity

y=62.5 velocity

y=125 velocity

y=187.5 velocity

Length Along Channel (μm)

100

120

140

160

180

200

220

240

260

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Velocity (m/s)

1D velocity

centerline velocity

y=62.5 velocity

y=125 velocity

y=187.5 velocity

Length Along Channel (μm)

Figure 8.3 Comparison of Velocity 

87
y p

190000

200000

210000

220000

230000

240000

250000

260000

270000

280000

290000

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Pressure (Pa)

1DPressure

centerline pressure

y=62.5 pressure

y=125 pressure

y=187.5 pressure

Length Along Channel (μm)

y p

190000

200000

210000

220000

230000

240000

250000

260000

270000

280000

290000

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Pressure (Pa)

1DPressure

centerline pressure

y=62.5 pressure

y=125 pressure

y=187.5 pressure

Length Along Channel (μm)

Figure 8.4 Comparison of Pressure 

265

270

275

280

285

290

295

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Te

mperature (K)

1D Temp

centerline temp

y=62.5 temp

y=125 temp

y=187.5 temp

Length Along Channel (μm)

265

270

275

280

285

290

295

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

Length along channel (microns)

Te

mperature (K)

1D Temp

centerline temp

y=62.5 temp

y=125 temp

y=187.5 temp

Length Along Channel (μm)

Figure 8.5 Comparison of Temperature 

It is seen from these figures that the analytically based solution is generally bounded and in 

proximity of the CFD solution. The differences are due to the wall effects and the entrance 

effects which are taken into account in the CFD solution, but not in the 1D solution. This does, 

however, verify that solutions of this flow situation developed with the CFD solver can be used 

to predict the flow rate of air through this device. 

88
8.3 Flow Control Prediction Curve

Using the CFD analysis, it was possible to formulate a curve which predicts the flow 

control ability of the device. The geometry of the device including the flow obstruction was 

created using pre-processing software package. This time, however, the inclusion of the flow 

obstruction limited the available symmetrical planes to one. 

The flow obstruction was modeled as a cylinder. The width of the flow obstruction 

spanned the entire width of the channel. In order to fit a continuous grid throughout the flow 

channel, it was divided into 5 sections; one semi-cylindrical volume at the center of the channel, 

two volumes upstream of the cylinder, and two volumes downstream of the cylinder. Figure 8.6 

below illustrates the geometrical configuration used for these simulations. Figure 8.7 shows a 

close up of the flow obstruction within the device. Note that the plane of symmetry in this device 

is towards the rear of the snapshot and that only the upper and lower walls are shaded. 

Figure 8.6 Geometry used for CFD Analysis 

Figure 8.7 Close-Up of Flow Obstruction Geometry 

Using a single symmetry plane resulted in a mesh that consists of 17 independent 

volumes: 5 for the channel as stated above and 6 sections each upstream and downstream 

representing the device’s connection to a 6.35 mm tube at each end. Each entity was again 

89
evenly divided by 25 nodes resulting in 24 sections per entity. Therefore, each volume contained 

a total of 13,824 cells and each entire configuration consists of 235 008 cells. 

Geometries were constructed to determine the mass flow rate of air through the device 

when the flow obstruction is elevated to various positions. For these simulations, the inlet and 

exit pressures were held constant at 316 kPa and 202 kPa, respectively. The only variable that 

was changed was the position of the flow obstruction. The piston positions used to generate a 

predictive curve are shown below in Table 5.2. 

Table 8.2 Test Matrix for Simulations 

Obstruction Position 

(μm)

% Closure of 

Channel 

Comments 

0 0 Used information from initial simulation 

125 25

180 36

250 50

320 64

375 75

500 100 No simulation, mass flow is zero 

Unfortunately, due to the nature of the CFD preprocessing package, a new geometry had 

to be constructed for each position of the flow obstruction position. There was one exception 

which expedited the generation of the geometries. The flow obstruction is modeled as a cylinder 

that has a range of motion from zero actuation (forming a continuous boundary with the wall) to 

fully closed (extending to the top of the flow channel). For any position within this range, there 

exists a complimentary position. In other words, since the flow channel is 500 μm tall, the 

geometry created to simulate the situation when the obstruction was 125 μm into the flow can be 

used to simulate the situation when the obstruction is 375 μm into the flow with very little 

adjustment. The only changes needed were the addition of a complimentary volume of the 

piston, and the removal of the original piston. 

The speed at which these numerical simulations converged was highly dependent on the 

initial conditions that were given to the solver. For this reason, the simulations were ran in order 

of lowest to highest position of the obstruction and the solutions from each run were used to 

determine the initial conditions for the present run. This provided a good starting point for the 

solver. The data obtained through the simulations is shown below in Figure 8.8. 

90
0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0 50 100 150 200 250 300 350 400 450 500

Obstruction Position (microns)

Air Mass Flow Rate (kg/s)

Obstruction Position (μm)

Air Mass Flow Rate (kg/s) 0.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0 50 100 150 200 250 300 350 400 450 500

Obstruction Position (microns)

Air Mass Flow Rate (kg/s)

Obstruction Position (μm)

Air Mass Flow Rate (kg/s)

Figure 8.8 Results from CFD Simulations 

It is interesting to note that two flow regimes exist over the range simulated with the CFD 

package. The results from the first two data points, which correspond to zero actuation and a 

piston height of 125 μm, show a flow regime that is subsonic throughout the entire domain. A 

transition between flow regimes occurs somewhere between the 125 μm data point and the 

180 μm data point. Here, the passage becomes small enough to choke the flow between the 

piston top and the upper channel wall. For any level of actuation beyond this transition point, the 

flow rate is directly related to the cross sectional flow area or 500 μm less the obstruction 

position. 

91
CHAPTER 9 

Gas Flow Measurements 

9.1 Flow Control Measurement

Once the prototype was assembled, its ability to control flow was demonstrated in the 

compressed air test apparatus. To do this, a pair of 6.35 mm copper tubes were glued to the ends 

of the flow channel and it was connected to the test apparatus. 

The objective of these tests was to measure the flow rate of air through the prototype for 

a varying position of the piston, while holding the inlet and exit pressure constant. 

Measurements were performed on four separate occasions. Each set of measurements was taken

by increasing the oil temperature from 22.9 oC to 44.8 °C in small increments. At each

increment, a measure of the air flow rate was taken, 19 points in all. 

The supply and back pressures were held as close to 316 kPa and 202 kPa as could be 

attained with manual control. In all cases, the supply pressure was less than 317.6 kPa and 

greater than 312.5 kPa; the back pressure was between 204 kPa and 200 kPa. These conditions 

correspond to those in the CFD simulations. The data collected during these tests and the 

corresponding measurement uncertainty is shown below in Figure 9.1. The data for these tests is 

in Appendix B. 

0.00015

0.00017

0.00019

0.00021

0.00023

0.00025

20 25 30 35 40 45

Oil Temperature (deg C)

Mass Flow Rate (kg/s)

Oil Temperature (oC)

0.00015

0.00017

0.00019

0.00021

0.00023

0.00025

20 25 30 35 40 45

Oil Temperature (deg C)

Mass Flow Rate (kg/s)

Oil Temperature (oC)

Figure 9.1 Results of Air Flow Measurements 

These measurements show that the air flow rate was reduced by 22 % as the piston was 

pushed into the flow channel. Using the curve generated for the relationship between the oil 

temperature and the piston position, the range of operating temperatures corresponds to piston 

positions ranging from 0 μm to 300 μm above the floor of the channel. All things considered, 

92
the flow rate of air through the device proved to be quite reasonable. This demonstrates that the 

prototype can induce the marginal flow resistance on demand. 

9.2 Comparison to CFD Simulations 

The results of these air flow measurements are shown below in Figure 9.3 compared to 

the results of the CFD analysis. 

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0 50 100 150 200 250 300 350 400 450 500

Piston Position (microns)

Mass Flo

w Rate (kg/s)

Predicted mass flow rate

Measured mass flow rate

Piston Position (μm)

Mass Flow Rate (kg/s)

0

0.00005

0.0001

0.00015

0.0002

0.00025

0.0003

0 50 100 150 200 250 300 350 400 450 500

Piston Position (microns)

Mass Flo

w Rate (kg/s)

Predicted mass flow rate

Measured mass flow rate

Piston Position (μm)

Mass Flow Rate (kg/s) Figure 9.2 Comparison Between Gas Flow Measurements and CFD Analysis 

Comparison of these measurements to the CFD simulations gives a lot of information 

about the device. First of all, it is seen that the measured air flow rate at low actuation is 17 % 

less than the simulated value. This is because the simulated device dimensions were different 

than those of the actual device. The simulated geometry was a rectangular cross section with a 

width of 1 000 μm and a height of 500 μm, which results in a cross sectional area of 

500 000 μm2

. The fabricated device is has a slightly different configuration with a cross 

sectional area that is 14 % less than that of the simulated device. The difference in the flow rate 

of the fully open device is attributed to this. 

Another difference between the simulated and measured data is seen by the trends is the 

data. The slope of the simulated data changes in the vicinity of 150 μm piston displacement, 

whereas the slope of the measured data does not change significantly over the range of data. 

This difference is because of the fact that the piston, as fabricated, does not entirely block off the 

flow channel, as it was modeled in the CFD work. In other words, the discontinuity in the 

boundary introduced by the piston is affecting the flow, but it does not restrict the flow in the 

same manner. The CFD analysis showed that, at a certain level of actuation, the flow became 

choked. Once the flow is choked, the mass flow rate should be directly proportional to the cross 

sectional flow area, which is inversely related to the piston displacement. This is why, at a 

93
certain level, the CFD results show a change in the relationship between the mass flow rate and 

the displacement. The measured results do not show this shift in flow regime because the piston 

is not seal off enough of the flow path to choke the flow; but it does affect the mass flow rate 

through protrusion and area reduction. 

94
Chapter 10 

R134a Vapor Compression Test Results and Discussion 

This chapter presents the results of the device’s ability to control flashing of R134a 

within a vapor compression system. We performed to measure the mass flow rate of the 

refrigerant passing through the device under conditions similar to those that would occur in a 

household refrigerating appliance using the vapor compression test apparatus described in 

Chapter 3. We took two sets of test data, the first data set demonstrates steady state performance 

with a fixed set of operating conditions, the second data set shows the HVAC system’s response 

to the device’s actuation.

It needs to be noted that the pressure that the device is subject to in the vapor 

compression system is considerably higher than the pressures used in the air flow test bench; 

therefore precautions were taken to ensure proper operation prior to inserting the device into the 

vapor compression system. To do this, the connections to the 6.35 mm copper tubes were 

reinforced with multiple layers of epoxy. Also, to help prevent the pipe connections from

leaking, the upstream pressure used during testing was slightly lower than most HVAC&R 

applications. Typical household refrigerating appliances have a design liquid line pressure of 

approximately 963 kPa, which corresponds to a condensing temperature of 38 oC. For these 

measurements, the liquid line pressure was kept at 750 kPa for the steady state tests, which 

corresponds to a condensing temperature of 29 oC, and slightly lower for the transient response 

tests. All raw test data is in Appendix C. 

10.1 Steady State Operation 

The condenser exit pressure was held constant at 750 kPa, while the level of liquid line 

subcooling was varied by changing the condenser HTF temperature and adding or removing 

refrigerant from the system. The evaporator HTF inlet was held constant at 4 oC. 

Two levels of actuation were used to characterize the operation of the device, 

corresponding to high and low levels of interaction between the piston and the flashing 

refrigerant. For the low actuation level, the measured oil temperature in the device was held 

constant at 25 oC, which corresponds to no actuation; while the measured oil temperature was 

held at 40 oC, corresponding to a piston height of 202 μm for the high actuation level tests. 

A total of 781 data points were taken to characterize the steady state operation of the 

device under constant inlet pressure, two different levels of actuation, and a range of subcooling. 

Figure 10.1 shows the results of these measurements. 

95
0.009

0.0095

0.01

0.0105

0.011

0.0115

0.012

0 1234 5 6

Subcooling (degrees C)

Refrigerant Mass Flow Rate (kg/s)

Refrigerant mass flow rate: No actuation

Refrigerant mass flow rate: 200 micron actuation

Subcooling (oC)

Refrigerant Mass Flow Rate: No actuation

Refrigerant Mass Flow Rate: 200 μm actuation

Refrigerant Mass Flow Rate (kg/s)

0.009

0.0095

0.01

0.0105

0.011

0.0115

0.012

0 1234 5 6

Subcooling (degrees C)

Refrigerant Mass Flow Rate (kg/s)

Refrigerant mass flow rate: No actuation

Refrigerant mass flow rate: 200 micron actuation

Subcooling (oC)

Refrigerant Mass Flow Rate: No actuation

Refrigerant Mass Flow Rate: 200 μm actuation

Refrigerant Mass Flow Rate (kg/s)

Figure 10.1 Steady State Refrigerant Mass Flow Rate for Two Levels of Actuation 

(750 kPa inlet pressure) 

It is interesting that the effect on the mass flow rate from actuating the device seems to be 

strongly related to the level of subcooling. At low levels of subcooling the effect is very small, 

showing on average 3.5 % difference at 0.6 oC subcooling. As the level of subcooling is 

increased, so is the impact of the device’s actuation; at 5 oC subcooling, there is a 10.7 % 

difference in the refrigerant mass flow rate. 

10.2 Quasi-Transient Operation 

The second set of data seems to give a bit more information, as it depicts the system’s 

response to the device. For these tests, the power to the device’s electrical resistance heater was 

abruptly switched up and down, and the system’s response was recorded. For these tests, three 

power-up periods were input to the device, with progressively higher power each time until the 

maximum output of 2.75 W from the heater was reached. The three power-on periods brought 

the measured oil temperature from 25 oC up to 46 oC, 49 oC, and 52 oC, respectively, which 

correspond to actuation levels of zero up to 324 μm, 384 μm, and 445 μm. For the initial 

operation, the condenser exit conditions were approximately 725 kPa with 4 oC of subcooling. 

Figures 10.2 through 10.4 depict the system response to the changing valve oil 

temperature. Figure 10.2 shows the change in condensing pressure and subcooling, Figure 10.3 

shows the change in refrigerant mass flow rate and system capacity, and Figure 10.4 shows the 

response of the evaporator exit superheat. The measured quantities in Figures 10.2 and 10.3 are 

normalized to each parameter’s maximum value to better illustrate the change in each of the 

quantities. 

96
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100

Time (min) 

Piston Position

P condensing

T subcooling

Figure 10.2 System Response – Normalized Piston Position, Condensing Pressure, and 

Subcooling 

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100

Time (min)

Piston Position

Mass Flow Rate

Capacity

Figure 10.3 System Response – Normalized Piston Position, Refrigerant Mass Flow Rate, and 

System Capacity 

97
0

0.2

0.4

0.6

0.8

1

1.2

Time 

Normalized Piston Position

0

1

2

3

4

5

6

7

Superheat (deg C)

Piston Position

T superheat

S

u

p

erh

e

at (o

C)

0 10 20 30 40 50 60 70 80 90 100 

Time (min)

0

0.2

0.4

0.6

0.8

1

1.2

Time 

Normalized Piston Position

0

1

2

3

4

5

6

7

Superheat (deg C)

Piston Position

T superheat

S

u

p

erh

e

at (o

C)

0 10 20 30 40 50 60 70 80 90 100 

Time (min)

Figure 10.4 System Response – Evaporator Exit Superheat and Normalized Piston Position 

The qualitative system response to the change in oil temperature is as would be expected. 

Heat is added to the oil reservoir in the device, which causes the piston to move into the 

refrigerant flow path, thereby creating a more restrictive metering device. This, in turn, reduces 

the refrigerant mass flow rate and therefore system capacity. This reduction in mass flow rate 

causes more refrigerant to accumulate in the condensing portion of the system which, in turn, 

causes the condensing pressure and subcooling to increase. Since less refrigerant remains in the 

evaporator, each unit of refrigerant that passes through evaporator must absorb a little more 

energy and therefore its exit temperature is higher. 

Quantitatively, however, the system response is somewhat diminished by the changing

operational parameters. The quantitative system capacity is shown below in Figure 10.5. 

. 

98
1700

1720

1740

1760

1780

1800

1820

1840

0 10 20 30 40 50 60 70 80 90 10

Time (min) 

Capacity (W)

0

Figure 10.5 System Capacity in Response to Device Operation 

10.3 Discussion 

It is shown in the figure above that the change in system capacity is approximately 5 %, 

when comparing the low and high actuation levels. Since this work represents a very preliminary 

look into the way flashing refrigerant responds to this new geometrical configuration, it is not 

surprising that the magnitude of the shift is in this range. There are a few factors that can help 

explain why the magnitude is in this range. 

The first reason has to do with the way that the oil temperature is measured. The capsule 

consists of a brass tubular section, approximately 33.0 mm in length with a diameter varying 

between 7.0 mm and 11.0 mm. Within the capsule are an electrical resistance heater and the tip 

of a thermocouple probe, with the probe aligned to the centerline of the tubular section. The oil 

in the capsule has a relatively low thermal diffusivity, as was discussed in Chapter 8, and the 

brass walls of the capsule have a large thermal conductivity. The inherent obstacle to obtain a 

good measurement of the overall average oil temperature is the thermal gradient within the 

capsule. 

The oil in the reservoir rejects heat through the brass wall of the reservoir, which causes 

the oil near the walls to be colder than that along the centerline, where the thermocouple probe is 

placed. Furthermore, since the top of the capsule is kept cold by contact with the flashing 

refrigerant and the capsule itself is a very good thermal conductor, all of the walls of the capsule 

will be near the refrigerant flashing temperature. For this reason, a temperature measured at the 

centerline of the oil reservoir during operation in the vapor compression system will be warmer 

that the true average oil temperature. It is apparent from the data shown in Figures 10.2 through 

10.4 that this may be a factor because the illustrated properties all begin to change when the 

piston position, based on the measured oil temperature, is around 200 μm. Since any interaction 

99
between the piston and the refrigerant should impart some change in these properties, it is logical 

that the measured oil temperature must be a little warmer than the average oil temperature. 

The exact relationship between the measured and true average oil temperature, however, 

is not known. When performing the measurements to obtain the relationship between measured 

oil temperature and piston displacement, an attempt was made to hold the top of the device at a 

5 oC (similar temperature to the test data flashing temperature) by packing the tube connections 

is dry ice. This, however proved to be a very difficult task and good data could not be obtained, 

therefore the relationship shown in Figure 6.22 was used. 

The second reason for this level of response is that width of the piston, as fabricated, is 

smaller than the width of the flow channel, and therefore does not completely block off this area. 

As fabricated, the piston blocks off 81 % to 83 % of the width of the flow channel, depending on 

orientation. Therefore, at the highest piston elevation experienced in these tests (again based on 

the measured temperature – position relationship), the maximum blockage is approximately 

73 % of the flow channel. 

The third reason for the small change in capacity is the compounded effect of the 

increased inlet pressure and increased subcooling. The behavior of this device is, in general, 

similar to that of a short tube restrictor; and the flow rate through a short tube restrictor is 

strongly influenced by the inlet pressure and the level of subcooling. 

When the device is actuated, the condensing pressure increases and the evaporating 

pressure decreases. This is due to the migration of refrigerant from the low pressure side of the 

system to the high pressure side. With any type of flow metering device, the pressure differential 

across the device is the driving potential for the flow, and therefore raising the condensing 

pressure and lowering the evaporating pressure will increase the potential (although with short 

tubes the evaporating pressure is not very influential). This is a common obstacle for all flow 

controlling devices. 

The subcooling, however, is not an obstacle for most other types of flow controlling 

devices. Needle valves and traditional boss-and-valve-seat type devices, which are the general 

basis for most other types of flow restricting devices, are not affected by the level of subcooling 

in the upstream liquid line, provided that the flow is not two phase at the entrance of the device. 

This is because the refrigerant is flashed at the exit plane of these devices due to the abrupt 

changes in flow area and geometry. The flow through the device is single phase throughout, and 

the thermodynamic properties relative to saturation are not a factor in the flow. 

With short tube restrictors, however, subcooling is one of the most important parameters 

governing the flow [67]. In typical applications, subcooled refrigerant enters a short tube, and a 

large pressure reduction is realized due to the abrupt area change. As the refrigerant flows 

through the short tube, the pressure is further reduced through friction until the exit plane. 

Within this portion, some of the refrigerant changes phase to vapor. When phase change occurs, 

the flow begins to exhibit some properties similar to choked flow. It is not choked, per se, but it 

exhibits some behavior similar to that of choked flow; the flow is relatively insensitive to, but 

not completely independent of the downstream pressure. In typical HVAC&R short tube 

applications the liquid density of a fluid inside a short tube is approximately 100 times that of the 

vapor density. Furthermore, the speed of sound is about 4 times faster in liquid than the vapor 

phase. Therefore, the generally accepted theory is that as some of the liquid refrigerant begins to 

change phase to vapor, the Mach number of the phase changing particles increases by a factor of 

approximately 400. This is a relatively crude approximation because liquid-vapor interactions 

exists, however the order of magnitude is important here. This vast increase in Mach number 

100
generally brings the vapor phase of the flow to sonic conditions. The two phases flow together 

and the vapor phase is choked but some downstream information is able to propagate upstream

within the liquid portion; this phenomenon is termed “approximately choked” flow. 

If the liquid refrigerant entering the short tube has a large degree of subcooling, it must 

undergo a substantial reduction in pressure before liquid particles begin to vaporize. Once 

vaporization begins, the mass flow rate through the device is somewhat limited. Therefore, the 

level of subcooling determines when and where the transition to vapor begins, and therefore has 

a profound impact on the mass flow rate. 

Due to the fact that the upstream pressure and subcooling both increase when the device 

is actuated, two driving potentials for the flow are increased and the overall impact of the 

increase restriction is lessened. 

For the measurements in Chapter 9, it was demonstrated that this device could change the 

mass flow of air by approximately 22 % with 300 μm piston elevation. However, the underlying 

physics of flow with liquid to vapor phase change is vastly different from single phase gaseous 

flow. With this type of flow, the piston interaction will cause a significant pressure drop within 

the device, which will certainly impact if not be the cause of the onset of the liquid to vapor 

transition. The data shown in Figure 10.1 shows that the flow through the device with some

piston actuation is less sensitive to subcooling than the flow through the unactuated device. A 

possible explanation is that the location of the flow’s liquid-to-vapor transition point is fixed by 

the piston, which would limit the subcooling’s effect on the mass flow rate. 

However, given all of these effects the fact does remain that in the case of the 

measurements shown in Figure 10.5, a device input of 2.75 W of power was able to change the 

system capacity by approximately 100 W, and this may be a sufficient level of modulation for 

some applications. Different operating conditions will, of course, produce different results. 

10.3.1 Subcooling Influence

It is known from the steady state data that, although greater subcooling results in greater 

mass flow, the loci of points from the actuated device vs. those of the unactuated device diverge. 

In other words, the influence that subcooling has on the mass flow rate is greatly reduced when 

the device is powered on. Therefore, during transient operation, when the device is powered up, 

the piston will engage the flow in the short tube which will increase the restriction. This will, in 

turn, increase the subcooling which increases the driving potential for the flow. However, since 

the slope of the actuated device’s mass flow rate vs. subcooling (Figure 10.1) diverges from that 

of the unactuated device, the impact that the device has on the mass flow rate will be greater if

the initial degree of subcooling is high. Therefore, operation with a larger degree of inlet 

subcooling at a given inlet pressure would allow the device more control over the system. 

10.3.2 Inlet Pressure Influence

By selecting data points from the quasi-transient data that correspond to the same level of 

subcooling while in the hot and cold position, and comparing this to the steady state data, we can 

see that the inlet pressure will also affect the level of influence that the device will have on the 

flow. Figure 10.6 shows four data points that were measured with a constant subcooling of 

4.6 oC. 

101
0.0095

0.01

0.0105

0.011

0.0115

0.012

725 730 735 740 745 750

Inlet Pressure (kPa)

Mass Flow Rate (kg/s)

mass flow rate (T_oil=25)

mass flow rate (T_oil=40)

*T_oil=45.9C

Figure 10.6 Mass Flow Rate vs. Inlet Pressure for 4.6 oC Subcooling 

These four points are shown with the mass flow rate plotted against the inlet pressure. We can 

see from this figure that as the pressure increases, the two curves diverge. Note that the low 

pressure, high actuation data point was measured with an oil temperature of 45.9 oC, not 40.0 oC, 

and therefore the difference between the slopes of the curves is actually larger than what is 

depicted, since an oil temperature of 40.0 oC would result in greater mass flow than the data 

point shown above. Since these curves diverge as the inlet pressure is raised, the device’s 

influence on the flow of refrigerant will be better at higher pressures than at lower pressures. 

10.3.3 Temporal Response

The quasi-transient data also gives some insight into the transient response of the device. 

The data acquisition system requires a total of 40 s to multiplex through each channel and there 

is a 3 s delay between successive scans, therefore the total time lapse between successive scans 

of each channel is 43 s. The device’s thermal time constant is determined from this data in the 

same manner as was done in Chapter 7 of this report. First, a section of the data was selected to 

encompass the power-up response of the device. For this analysis, only the third power-up 

sequence from the data in Figure 10.2 was used because the power was adjusted slightly during 

the other two sequences. 

The data points which correspond to the first two scans after the obvious point of the 

heater switch were discarded. This is because exact time that the heater was switched on relative 

to the successive multiplexer scans is unknown. Next, the natural logarithm of the difference 

between the final steady state temperature and each scanned temperature was plotted against the 

elapsed time. This locus was fit with a straight line using a least squares regression, and the final 

temperature was adjusted until the highest R2

 value was obtained. This resulted in a final high 

102
power temperature of 51.1 oC and a thermal time constant of 126.5 s, the R2

 for this linear fit was 

0.998. This measured time constant is within 11 % of the value from the simulations of 114.2 s. 

This is remarkably good considering all of the differences between the actual device and the 

simplified estimations used in the simulations. 

The geometry used in the simulations was a simple tubular section of oil surrounded by a 

brass cavity, with a heavy brass weight near the bottom. The actual device’s oil capsule consists 

of at least four different diameters within the capsule. 

The heat source used in the simulations consisted of a very thin heater located along the 

centerline of the device. In fact, the heater that was actually used in the capsule was fitted into 

the capsule and consequently took on the circular shape of the capsule; therefore the heat in the 

actual device was added into the oil near the outer edge of the reservoir rather than along its 

centerline. 

Finally, isothermal boundary conditions at the outer edges of the capsule were used for 

the simulations. The isothermal boundary condition of the top of the nickel membrane is 

probably fairly accurate, since the flashing refrigerant has an extremely large convection 

coefficient, but the boundary condition around the outside of the brass capsule is probably not 

very accurate. Since brass and nickel are very good thermal conductors, thermal energy in the 

brass would tend to leave the system readily via conduction to the nickel membrane. Instead, a 

simplified isothermal boundary condition was used for the outer edge of the brass. The true exit 

path of thermal energy in the brass must be two-fold, through the outer edge of the brass capsule 

into the ambient and through conduction to the nickel membrane; therefore, a more accurate 

simulation solution would lie somewhere between the case simulated in chapter 7 and a case 

where the outer edge of the brass were treated as perfectly insulated, forcing all of the heat loss 

through the nickel membrane. 

It is obvious from the simulation results’ temperature distribution that this should not 

have much of an effect on the time constant, since the overwhelming majority of the heat transfer 

resistance between the heat source and sink occurs within the oil. This is confirmed by the time

constant measured in the test results. The parameter that is greatly affected is the relationship 

between heat input and the device’s final temperature. The simulation results estimate that the 

oil temperature should increase by 39.5 oC for every one watt of power input; whereas the actual 

measured temperature was considerably colder in the laboratory measurements. The warmest oil 

temperature was experienced during the quasi-transient tests; the oil temperature reached 

51.86 oC at the maximum heater output of 2.75 W. According to the estimate from the 

simulation work, power input of approximately 0.77 W should bring the oil temperature to this 

level. This is the result of the actual heat sink being greater than that modeled in the simulations. 

10.4 Summary 

The results of this section show the device’s ability to modulate the expansion of 

refrigerant passing through it. Steady state data was taken to map the flow rate for a given inlet 

pressure. These results showed that the device has greater influence over the flow when the 

refrigerant inlet subcooling is high. Next, quasi-transient measurements were taken to depict the 

HVAC system’s response to the device’s actuation. The results of the steady state and quasitransient were used to further understand the inlet conditions that impact the device’s ability to 

control the mass flow rate. 

Next, information from the quasi-transient measurements was compared to computer 

simulations. The data showed that the computer code predicted the device’s time constant fairly 

103
well, but the assumed thermal boundary conditions used in the simulations resulted in an 

estimate which underpredicted the amount of heat loss. Therefore, the actual level of increased 

temperature was not as high as that found in the simulations. 

104
CHAPTER 11 

Summary and Future Work 

11.1 Summary

The design, fabrication and testing of a microfabricated thermopneumatic refrigerant 

expansion device is presented in this work. An initial prototype of this device was fabricated out 

of silicon using deep reactive ion etching. A vapor compression system test apparatus was 

constructed and outfitted with measurement equipment, and testing of the silicon prototype was 

attempted. Based on the findings of this experiment, changes were made to the device’s design 

and material to improve the reliability and ease of assembly. 

The material of the device was changed to nickel, which is a more ductile material than

silicon, thereby reducing the chance of fracture. A process for forming micromolded nickel 

pieces with characteristic heights of 150 μm to 1.2 mm was developed as part of this project. 

Traditionally, the drive for new fabrication techniques has focused on moving towards smaller, 

better tolerance features in order to produce lighter, faster responding products. Through this 

motivation, however, the difficulties associated with meso-scale fabrication techniques are often 

neglected. Fabrication processes were developed to make thick layer nickel electroplating within 

SU8 micromolds a feasible option with inexpensive processes. Until recently, very little work 

had been done with SU8-nickel micromolding in the meso-scale. Many obstacles were 

overcome to develop these processes. 

A second test apparatus was constructed to characterize the performance of the device 

using compressed air. There are two reasons for this second test method. First, it is not possible 

to analytically or numerically calculate parameters associated with refrigerant expansion through 

this device. Using compressed air flow instead of refrigerant expansion as a test bench allows 

for a basis of comparison to computational fluid dynamics (CFD) simulations. Secondly, using 

compressed air instead of a refrigerant is less stressful on the device, which is desired during the 

developmental stage. 

Optimal fabrication process parameters for this device were determined and a working 

prototype was fabricated. The prototype components were characterized to document the 

capabilities of these new fabrication techniques. 

Three dimensional CFD simulations were performed on the flowfield within the device at 

various levels of actuation to predict the device’s ability to control mass flow rate of compressed 

air. The assembled prototype was demonstrated on the air flow test bench and the results were 

compared to the CFD results. 

A numerical code was developed to determine the device’s temporal response. 

Simulations were performed with this code at various levels of power input to the device and the 

results were used to determine the device’s time constant and relationship between actuation 

level and power input. 

Next, the device was tested in an R134a vapor compression system. Both steady state 

and transient tests were performed. Testing in the vapor compression system showed greater 

heat input to the device was necessary to overcome the heat loss to the refrigerant to improve 

mass flow rate control. The steady state tests showed that the level of flow control is strongly 

dependent on the refrigerant subcooling. The transient tests were performed to demonstrate the 

HVAC system’s response to actuation of the device, and to benchmark the device’s time 

constant. The measured time constant matched well with the calculated time constant from the 

105
temporal response simulation code; but the relationship between the actuation level and power 

input was offset by the device’s refrigerant heat sink. 

11.2 Significant Contributions

A number of significant contributions were made through this effort. The development 

of this flow metering device is a novel contribution. This device was designed to be used as the 

main throttling device in a small HVAC&R system, where traditional active expansion devices 

are too large or too costly. However, it was also demonstrated with compressed air and due to 

the structural and material integrity of this device, it may be used to vary the flow rate of many 

fluids in many different flow scenarios. 

This device works on the principle of introduction or removal of a boundary discontinuity 

which can be applied to numerous situations. As demonstrated in this work, this principle can be

used to vary the flow rate of a passing fluid. However, this principle can also be used in external 

flow situations by assembling the device without the top piece, i.e. so that the lower flow channel 

wall is the uppermost piece. This concept could be used for vortex generation or to encourage 

laminar to turbulent boundary layer transition. 

Theoretical and numerical descriptions of the device were derived to predict the motion 

of, the stresses within, the flow rate through, and the temporal response of the device. These 

efforts provide tools for future engineers to continue this work with a map of how different 

materials and alternate dimensions affect the response. 

Lastly, fabrication steps were developed to enable the deposition of very tall SU8 layers. 

This method was used to prepare molds with depths as deep as 1.2 mm, which were then filled 

with metal through electrodeposition. Through this work an inexpensive UV lithography method 

to create meso-scale structures has been contributed. 

11.3 Future Work 

In order to bring this device to a usable standard within industry, a considerable amount 

of work must be done. First, the prototype tested during this effort demonstrated a lot of the 

difficulties inherent to initial designs. A number of the auxiliary components should be 

redesigned to improve the performance of this device. 

One major shortcoming was due to the uncertainty of the actual piston position within the 

flow path during actuation in the vapor compression system. The piston position was measured 

in relation to the oil reservoir temperature under ambient conditions, but the relationship between 

the oil temperature and position in the system could not be determined very well. A method of 

benchmarking this relationship should be devised and used to help describe the fluid mechanics 

occurring within the flow channel. 

The oil used for this prototype was selected because it already exists within the HVAC 

test apparatus, and if it were to leak into the system there would be no catastrophic consequence. 

This oil has a low thermal diffusivity and a high heat flux exists from the heater to the 

membrane; therefore, large temperature gradients can exist within the oil reservoir. This adds 

considerably to the uncertainty of the actual piston position. Selecting a different liquid to be 

used in the chamber will reduce the uncertainty. The search for an appropriate candidate fluid 

should find one with a large coefficient of thermal expansion, a higher thermal diffusivity, and 

have the ability to exist in the vicinity of an electrical resistance heater without causing damage 

to the heater. 

106
Thirdly, the heater used in this prototype was unable to raise the oil temperature to a level 

capable to bringing the piston to the top of the flow path when operating in the HVAC system. 

An electric resistance heater with a greater capacity should be used a future design. 

These steps are all intermediate design steps, as commercially available parts would 

likely be too expensive to use in a real world device. After all of the relevant information is 

obtained, new chamber materials geometry would have to be developed for mass production. 

On the fabrication front, there are certain feature limitations that are inherent to the 

processes. Specifically, since SU8 is a negative type photoresist, any alignment, dosage, or 

scattering imperfections will ultimately result in nickel pieces whose vertical structures are 

thinner than the mask dark fields, and whose trench structures are wider than the mask light 

fields. Although these affects have been minimized through process development, they are still 

not perfect. The piston described in the prototype had a diameter at its tip between 900 μm and 

913 μm; the target diameter for this feature was 950 μm. This ultimately resulted in the piston 

blocking off a smaller portion of the channel than desired. In order to improve the device 

performance, the simplest method is to factor in these process limitations during the design at the 

mask level; i.e. generate new masks with 1000 μm diameter dark fields if 950 μm are desired. 

Another task that needs to be done to bring this device from laboratory exploratory work 

to a commercially viable product is the determination of appropriate assembling and packaging. 

Specifically, techniques should be developed to assemble these devices at the wafer level. 

Individual assembly of these devices would likely lead to a product that was too costly for 

market acceptance. 

Finally, the results of the HVAC system tests bring about questions related to refrigerant 

expansion within the geometry prescribed by this device. The steady state data shows that the 

device’s ability to affect the mass flow rate of refrigerant is heavily dependent on the level of

subcooling. Specifically, when plotting the mass flow rate against the subcooling, the actuated 

device and unactuated device data points diverge. It has been observed through short tube flow 

visualization experiments, that as subcooling is increased the transition point from liquid to twophase moves further downstream within the short tube. Extending these observations to the 

work in this report, it seems likely that these trends can be explained by the transition point from

liquid to two-phase being fixed at the point of interaction with the piston. This is purely

speculative and not completely understood at the present; laboratory experimentation would be 

necessary to verify or reject any plausible explanations. 

107
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High Resolution Ultra-Thick Photoresist, J. Vac. Scien. Technol. B 13 (1995), pp. 3012-3016. 

[37] J. M. Shaw, J. D. Gelorme, N. C. LaBianca, W. E. Conley, and S. J. Holmes, Negative 

Photoresists for Optical Lithography, IBM Journal of Research and Development, 41(1997), pp. 

81-94. 

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Low-Cost Negative Resist for MEMS, MicroMechanics Europ MME 96, Spain, (1996), pp. 32-

35. 

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111
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Dissertation, Texas A&M University, College Station TX, 1993. 

112
Appendix A 

Raw Code for Transient Analysis 

113
#include<stdio.h> 

#include<math.h> 

void main() 

{ 

 int m, n, conv, weight_factor; 

 double t, totalheatgen, heatgen, timestep, change; 

 double heatgenpercell, mschange, rms_change, weighted_temp, average_temp; 

 double T_old[53][217], T_new[53][217]; 

conv=0; 

totalheatgen=0.0; 

timestep=0.0001; 

t=0.0-timestep; 

heatgen=totalheatgen/146.0; 

heatgenpercell=4*heatgen/(0.000000000003375*3.1415927); 

/**********************/ 

/* Set initial values */

/**********************/ 

for(m=1; m<52; m++){ 

 for(n=1; n<=216; n++){ 

 T_old[m][n]=20; 

 } 

 } 

/*****************************/ 

/*Set the boundary conditions*/

/*****************************/ 

for(n=1; n<=216; n++){ 

 T_old[52][n]=25.0; 

 T_new[52][n]=25.0;} 

for(m=1; m<=52;m++){ 

 T_old[m][1]=25.0; 

 T_new[m][1]=25.0; 

 T_old[m][216]=5.0; 

 T_new[m][216]=5.0;} 

/*******************************/ 

/* Temperature calculation loop*/ 

/*******************************/ 

while(conv==0){ 

114
 t=t+timestep; 

 mschange=0.0; 

/************************/ 

/*Calculate temperatures*/ 

/************************/ 

 for(m=1; m<=51; m++){ 

 for(n=2; n<=215; n++){ 

 if(m==1){ 

 if(n==68){ 

 /*USE EQUATION #7 FOR OIL-BRASS*/ 

 T_new[m][n]=T_old[m][n]+ 

 0.36149573*(T_old[m+1][n]-T_old[m][n])+ 

 0.00163896*(110*(T_old[m][n-1]-T_old[m][n])+ 

 0.282*(T_old[m][n+1]-T_old[m][n])); 

 } 

 else{ 

 if(n==215){ 

 /*USE EQUATION #7 FOR NI-OIL*/ 

 T_new[m][n]=T_old[m][n]+ 

 0.26370056*(T_old[m+1][n]-T_old[m][n])+ 

 0.00144919*(0.282*(T_old[m][n-1]-T_old[m][n])+ 

 90.7*(T_old[m][n+1]-T_old[m][n])); 

 } 

 else{ 

 if(n>68){ 

 /*USE EQUATION #6 FOR OIL*/ 

 T_new[m][n]=T_old[m][n]+ 

 0.002297422*(T_old[m+1][n]-T_old[m][n])+ 

 0.000574356*(T_old[m][n-1]+T_old[m][n+1]-2*T_old[m][n])+ 

 +0.000000000045826*heatgenpercell; 

 } 

 else{

 /*USE EQUATION #6 FOR BRASS*/ 

 T_new[m][n]=T_old[m][n]+ 

 0.603306667*(T_old[m+1][n]-T_old[m][n])+ 

 0.150826667*(T_old[m][n-1]+T_old[m][n+1]-2*T_old[m][n]); 

 } 

 } 

 } 

 } 

 else{ 

 if(n==68){ 

 if(m==42){ 

 /*USE EQUATION #5 FOR OIL-BRASS*/ 

 T_new[m][n]=T_old[m][n]+ 

 (0.001493141536/m)*(55.141*((m-0.5)*(T_old[m-1][n]-T_old[m][n]))- 

115
 110*((m+0.5)*(T_old[m][n]-T_old[m+1][n])))+ 

 0.001493141536*(110*(T_old[m][n-1]-T_old[m][n])-55.141*(T_old[m][n]- 

 T_old[m][n+1])); 

 } 

 else{ 

 if(m>42){ 

 /*USE EQUATION #1 FOR BRASS*/ 

 T_new[m][n]=T_old[m][n]+ 

 (0.15082646/(m*m))*(T_old[m+1][n]-T_old[m][n]+m*m*(T_old[m+1][n]+T_old[m-1][n]- 

 2*T_old[m][n]))+0.15082646*(T_old[m][n+1]+T_old[m][n-1]-2*T_old[m][n]); 

 } 

 else{ 

 /*USE EQUATION #2 FOR OIL-BRASS*/ 

 T_new[m][n]=T_old[m][n]+(0.090373933/m)*((m-0.5)*(T_old[m-1][n]-T_old[m][n])- 

 (m+0.5)*(T_old[m-1][n]-T_old[m][n]))+0.0016389607*(110*(T_old[m][n-1]- 

 T_old[m][n])-0.282*(T_old[m][n]-T_old[m][n+1])); 

 } 

 } 

 } 

 else{ 

 if(n==215){ 

 if(m==42){ 

 /*USE EQUATION #4 FOR NI-OIL*/ 

 T_new[m][n]=T_old[m][n]+(0.0012665039/m)*(45.491*(m-0.5)*(T_old[m-1][n]- 

 T_old[m][n])-90.7*(m+0.5)*(T_old[m][n]-T_old[m+1][n]))+ 

 0.0012665039*(45.491*(T_old[m][n-1]-T_old[m][n])-90.7*(T_old[m][n]- 

 T_old[m][n+1])); 

 } 

 else{ 

 if(m>42){ 

 /*USE EQUATION #2 FOR NI-BRASS*/ 

 T_new[m][n]=T_old[m][n]+(0.1240094536/m)*((m-0.5)*(T_old[m-1][n]-T_old[m][n])- 

 (m+0.5)*(T_old[m-1][n]-T_old[m][n]))+0.00123576934*(110*(T_old[m][n-1]- 

 T_old[m][n])-90.7*(T_old[m][n]-T_old[m][n+1])); 

 } 

 else{ 

 /*USE EQUATION #2 FOR NI-OIL*/ 

 T_new[m][n]=T_old[m][n]+(0.06592514/m)*((m-0.5)*(T_old[m-1][n]-T_old[m][n])- 

 (m+0.5)*(T_old[m-1][n]-T_old[m][n]))+0.00144919083*(0.282*(T_old[m][n-1]- 

 T_old[m][n])-90.7*(T_old[m][n]-T_old[m][n+1])); 

 } 

 } 

 } 

 else{ 

 if(m==42){ 

 if(n>68){ 

116
 /*USE EQUATION #1 FOR BRASS*/ 

 T_new[m][n]=T_old[m][n]+(0.15082646/(m*m))*(T_old[m+1][n]- 

 T_old[m][n]+m*m*(T_old[m+1][n]+T_old[m-1][n]-2*T_old[m][n]))+ 

 0.15082646*(T_old[m][n+1]+T_old[m][n-1]-2*T_old[m][n]); 

 } 

 else{ 

 /*USE EQUATION #3 FOR OIL-BRASS*/ 

 T_new[m][n]=T_old[m][n]+(0.00163896072/m)*(0.282*((m-0.5)*(T_old[m-1][n]- 

 T_old[m][n]))-110*((m+0.5)*(T_old[m][n]-T_old[m+1][n])))+ 

 (0.090373933)*(T_old[m][n-1]+T_old[m][n+1]-2*T_old[m][n]); 

 } 

 } 

 else{ 

 if(n>68 && m<42){ 

 /*USE EQUATION #1 FOR OIL*/ 

 T_new[m][n]=T_old[m][n]+(0.00057435556/(m*m))*(T_old[m+1][n]- 

 T_old[m][n]+m*m*(T_old[m+1][n]+T_old[m-1][n]-2*T_old[m][n]))+ 

 0.00057435556*(T_old[m][n+1]+T_old[m][n-1]-2*T_old[m][n]); 

 } 

 else{ 

 /*USE EQUATION #1 FOR BRASS*/ 

 T_new[m][n]=T_old[m][n]+(0.15082646/(m*m))*(T_old[m+1][n]- 

 T_old[m][n]+m*m*(T_old[m+1][n]+T_old[m-1][n]-2*T_old[m][n]))+ 

 0.15082646*(T_old[m][n+1]+T_old[m][n-1]-2*T_old[m][n]); 

 } 

 } 

 } 

 } 

 } 

 change=(T_old[m][n]-T_new[m][n])/T_old[m][n]; 

 mschange=mschange+change*change; 

 T_old[m][n]=T_new[m][n]; 

 }/*next n*/ 

 }/*next m*/ 

rms_change=sqrt(mschange/(10650.0)); 

 if(rms_change<0.000001){ 

 conv=1; 

 } 

 

 /*if(floor(t)==t){ 

 printf("The temperature distribution at time %d is\n", t); 

 printf(" m n Temperature\n"); 

 for(m=0;m<51;m++){ 

 for(n=0;n<215;n++){ 

 printf(" %d %d %f\n", m, n, T_old[m][n]); 

117
 } 

 } 

 }*/ 

 

 } /*closes while*/ 

/***********************************/ 

/*Calculate average oil temperature*/ 

/***********************************/ 

weighted_temp=0.0; 

weight_factor=0; 

for(m=1; m<42; m++){ 

 for(n=68; n<215; n++){ 

 weighted_temp=weighted_temp+m*T_old[m][n]; 

 weight_factor=weight_factor+m; 

 } /*next n*/ 

 } /*next m*/ 

average_temp=weighted_temp/weight_factor; 

/****************/ 

/*Output Results*/

/****************/ 

printf("The solution achieved steady state at time %f\n", t); 

printf("The average oil temperature is %f\n", average_temp); 

printf(" m n Temperature\n"); 

for(m=1;m<=52;m++){ 

 for(n=1;n<=216;n++){ 

 printf(" %d %d %f\n", m, n, T_old[m][n]); 

 } 

 } 

}/*closes main*/ 

118
Appendix B 

Air Flow Measurement Data and Uncertainty

B.1 Raw Data 

Table B.1 Data Set #1 – Data Taken November 4, 2005, 9 am 

Point Oil

Temperature 

(°C) 

Upstream

Pressure 

(kPa) 

Time

(s) 

Volume 

of Air 

Collected 

(l) 

Air 

Temperature 

(°C) 

Calculated 

Air 

Density

(kg/m3

) 

Calculated 

Mass Flow 

Rate (kg/s) 

1 22.89 312.5 40 7.8 29.44 1.1635736 0.000226897

2 27.39 315.8 40 7.5 27.44 1.1655004 0.000218531

3 29.78 315.0 40 7.3 28.56 1.1670035 0.000212978

4 35.83 313.5 45 7.8 29.67 1.1627193 0.000201538

5 41.83 316.3 45 7.3 29.28 1.1642152 0.000188862

Table B.2 Data Set #2 – Data Taken November 4, 2005, 1 pm 

Point Oil

Temperature 

(°C) 

Upstream

Pressure 

(kPa) 

Time

(s) 

Volume 

of Air 

Collected 

(l) 

Air 

Temperature 

(°C) 

Calculated 

Air 

Density

(kg/m3

) 

Calculated 

Mass Flow 

Rate (kg/s) 

6 23.00 315.0 40 7.6 28.00 1.1691574 0.00022214

7 28.22 316.6 40 7.6 29.61 1.1629328 0.000220957

8 30.06 315.6 40 7.3 29.28 1.1642152 0.000212469

9 37.00 314.1 45 7.7 28.44 1.1674336 0.000199761

10 44.44 315.0 50 8.0 29.39 1.1637874 0.000186206

Table B.3 Data Set #3 – Data Taken November 4, 2005, 5 pm 

Point Oil

Temperature 

(°C) 

Upstream

Pressure 

(kPa) 

Time

(s) 

Volume 

of Air 

Collected 

(l) 

Air 

Temperature 

(°C) 

Calculated 

Air 

Density

(kg/m3

) 

Calculated 

Mass Flow 

Rate (kg/s) 

11 23.06 316.2 40 7.8 29.0 1.1652860 0.000227231

12 28.89 317.6 40 7.5 29.56 1.1631463 0.000218090

13 33.28 315.2 45 8.0 28.72 1.1663588 0.000207353

14 37.67 316.5 45 7.7 27.94 1.1693732 0.000200093

15 44.83 315.6 45 7.2 29.17 1.1646433 0.000186343

119
Table B.4 Data Set #4 – Data Taken November 4, 2005, 7 pm 

Point Oil

Temperature 

(°C) 

Upstream

Pressure 

(kPa) 

Time

(s) 

Volume 

of Air 

Collected 

(l) 

Air 

Temperature 

(°C) 

Calculated 

Air 

Density

(kg/m3

) 

Calculated 

Mass Flow 

Rate (kg/s) 

16 23.06 315.9 40 7.7 29.61 1.1629328 0.000223865

17 29.22 317.0 40 7.5 29.78 1.1622926 0.00021793

18 35.33 312.7 45 7.8 29.61 1.1629328 0.000201575

19 41.39 317.6 45 7.2 29.00 1.1652860 0.000186446

B.2 Uncertainty Analysis for Gas Flow Measurements 

The air flow rate is calculated from the measured atmospheric air pressure, the volume and 

temperature of the air collected in the cylinder, and the time elapsed during the collection. The 

mass flow rate is related through these parameters as follows: 

( ) Patm Tair t t

m ρ , ρ ∀ = ∀ & = 

Although Refprop [27] was used to calculate the density of the air in the cylinder, it is 

convenient to use the ideal gas law for the purposes of the uncertainty analysis. 

air

atm

T

P

t

m

R

∀ & =

Therefore the influence of each measured parameter is: 

air

atm

t T

m P

R = ∂∀

∂ &

atm Tair P t

m

R

∀ = ∂∂ &

air

atm

t T

P

t

m

R

2

∀ = − ∂

∂ &

( )2 R air

atm

ait t T

P

T

m ∀ = − ∂∂ &

And the uncertainty of the mass flow rate is found from the uncertainty of each measurement. 

2 2 2 2

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ ⎟ + ⎠

⎞ ⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ ⎟ + ⎠

⎞ ⎜

⎝

⎛

∂∀

∂ = ∀ atm Tair

air

P t

atm

m U

T

m U

t

m U

P

m Um U & & & & &

120
Table B.5 Calculated Uncertainty for all data 

Point dm_dot/dV dm_dot/dP_atm dm_dot/dt dm_dot/dT_air Uncertainty U (%)

1 0.029214725 2.24729E-09 5.69687E-06 7.53444E-07 4.08096E-06 1.799%

2 0.029263103 2.16443E-09 5.48683E-06 7.26866E-07 4.01185E-06 1.836%

3 0.029300841 2.10943E-09 5.3474E-06 7.09309E-07 3.96725E-06 1.863%

4 0.025949578 1.99612E-09 4.49793E-06 6.68745E-07 3.43455E-06 1.704%

5 0.025982963 1.87057E-09 4.21501E-06 6.27488E-07 3.34614E-06 1.772%

6 0.029354921 2.20017E-09 5.57744E-06 7.41187E-07 4.04964E-06 1.823%

7 0.029198635 2.18846E-09 5.54774E-06 7.33316E-07 4.02807E-06 1.823%

8 0.029230833 2.10439E-09 5.33463E-06 7.05924E-07 3.95777E-06 1.863%

9 0.026054792 1.97852E-09 4.45826E-06 6.65535E-07 3.42957E-06 1.717%

10 0.023376074 1.84427E-09 3.74017E-06 6.18437E-07 2.99424E-06 1.608%

11 0.02925772 2.25059E-09 5.70526E-06 7.55663E-07 4.08697E-06 1.799%

12 0.029203996 2.16006E-09 5.47575E-06 7.23933E-07 4.00374E-06 1.836%

13 0.026030805 2.05371E-09 4.6277E-06 6.90193E-07 3.48349E-06 1.680%

14 0.02609808 1.98181E-09 4.46567E-06 6.67749E-07 3.43527E-06 1.717%

15 0.025992517 1.84562E-09 4.1588E-06 6.19347E-07 3.32924E-06 1.787%

16 0.029198635 2.21725E-09 5.62074E-06 7.42965E-07 4.05331E-06 1.811%

17 0.029182562 2.15847E-09 5.47173E-06 7.22871E-07 4.0008E-06 1.836%

18 0.025954342 1.99649E-09 4.49875E-06 6.6899E-07 3.43518E-06 1.704%

19 0.026006862 1.84664E-09 4.1611E-06 6.20031E-07 3.33108E-06 1.787%

121
Appendix C 

Test Data and Uncertainty for Refrigerant Flow Control Measurements 

In the interest of saving space, the measurement uncertainty methodology is presented in 

the beginning of this section and the Uncertainty is included in the raw data portion of this 

appendix. 

C.1 Uncertainty Analysis 

The capacity of heat transferred in the evaporator is measured on the refrigerant side and 

on the HTF side. 

HTF side uncertainty

The HTF side capacity is determined by measuring the HTF temperature at the inlet and 

exit of the evaporator, and the HTF mass flow rate. The average of the inlet and exit temperature 

is used to determine the HTF specific heat, Cp. 

Cp = 1.805(THTF,in + THTF,out)+ 3304.357

Therefore, the uncertainty of the specific heat measurement is: 

( ) 2 2

, , 1.805 Cp THTF in THTF out U = U +U

Since each temperature is measured with 5 thermocouples, each having a measurement 

uncertainty of 0.15 oC, the uncertainty of each of these values is 0.0067 oC, and the uncertainty 

of the specific heat is a constant 0.00127, which is insignificant for specific heats in the range of 

3300 and will be left off of the remainder of the calculations. 

The capacity is calculated from the product of the mass flow rate with the difference 

between the inlet temperature and the exit temperature. 

( ) Q = mCP THTF ,in −THTF ,out &

Therefore the uncertainty due to the mass flow measurement uncertainty is: 

( ) HTF in HTF out

P

T T

C

m

Q

, − ,

= ∂

∂

&

And the uncertainties due to the measured temperatures are: 

P

HTF in

mC

T

Q = & ∂∂

,

122
P

HTF in

mC

T

Q = & ∂∂

,

Therefore, the measurement uncertainty of the HTF side capacity is 

2

,

2

,

2

, ,

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎥

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛

∂

∂ = HTF in THTF in

HTF in

T

HTF in

Q m U

T

Q U

T

Q U

m

Q U & &

The refrigerant side capacity is calculated by measuring the valve inlet temperature, the 

evaporator exit temperature, pressure, and volumetric flow rate. The valve inlet temperature is 

used to determine the liquid enthalpy, the evaporator exit temperature and pressure are used to 

determine the vapor enthalpy and the vapor density. The capacity is then calculated from:

( ) ref vap ref liq Q h h = ∀ , − , ρ&

The uncertainty of the liquid enthalpy is: 

rev liq Tref liq

ref liq

liq

h U

T

h

U , ,

, ∂

∂ =

And the uncertainty of the vapor enthalpy is: 

2

,

2

,

, , , ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ = rev vap ref vap Pref vap

ref vap

vap

T

ref vap

vap

h U

P

h

U

T

h

U

The uncertainty of the density term is 

2

,

2

,

, , ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ = ref vap Pref vap

ref vap

T

ref vap

U

P

U

T

U ρ ρ

ρ

Therefore, the uncertainty of the capacity measurement is: 

( ) ( ) ( ) 2 2 2 2

, , ⎟

⎠

⎞ ⎜

⎝

⎛ = ∀ + ∀ + ∀∆ + ∆ •

∀

U U U hU h U

ref ref vap ref liq Q ρ& h ρ& h & ρ ρ

123