od

5

A 11 ID 3 7 1 E 1 1 4

NISTIR 3951

TRANSIENT HYDROGEN HEAT TRANSFER

Final Report for April 1986-April 1989

Louie

.G. Steward

. U56

//3951

1991

United States Department of Commerce

National Institute of Standards and Technology

NISTIR 3951 iQe

TRANSIENT HYDROGEN HEAT TRANSFER

Final Report for April 1986-April 1989

Chemical Engineering Division

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

*FluidTherm Engineering

Boulder, Colorado 80302

October 1991

B. Louie

W.G. Steward*

U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director

CONTENTS

Abstract

1. INTRODUCTION

2. EXPERIMENTAL APPARATUS AND PROCEDURE

2.1 Overview of the Experimental Apparatus

2.2 Power Generation Devices

2.3 Transient Response Thermometry

2.4 Data Acquisition

2.5 Experimental Procedure

3. ANALYSIS OF TRANSIENT CONDUCTION HEAT TRANSFER

3.1 Thin Films on Solid Substrates

3.2 Ribbon Heater/Thermometer Without a Substrate .

4. RESULTS AND DISCUSSION

4.1 Transient Heat Transfer to Liquid Hydrogen Using Carbon Films

4.2 Premature Film Boiling Using Pt Foil Heater/Thermometers . . .

4.3 Estimation of Heater Temperature Rise During Film Boiling . . .

4.4 Transient Conduction Heat Transfer From Pt Ribbons

5. SUMMARY AND CONCLUSIONS

6. ACKNOWLEDGMENTS

7. NOMENCLATURE .

8. REFERENCES

Appendix A

Appendix B

Page

1

1

2

2

2

4

8

oo

10

10

10

11

11

11

16

16

21

22

22

23

24

31

in
LIST OF FIGURES

Page

1. Schematic of experimental apparatus . 3

2. Schematic of electrical circuit for transient hydrogen heat transfer experiment ... 5

3. Schematic of vapor-deposited Pt film on a quartz substrate for use as a heater and

thermometer ..................................................... 5

4. Schematic of Pt foil deposited on quartz substrate for use as a heater/thermometer 7

5. Schematic of unsupported Pt foil heater/thermometer ...................... 7

6. Schematic of carbon thin film on a quartz substrate used as a heater/thermometer 9

7. Results of transient heat transfer experiments using carbon thin film to LH2 for heat

fluxes ranging from 1.15 to 10.8 W/cm2 12

8. Results of transient heat transfer experiments from a carbon thin film to LH2 for heat

fluxes ranging from 13 to 42 W/cm2 ................................... 12

9. Experimental data from transient heat transfer experiments using a carbon film in

LH2 which show the time of transition to film boiling for various applied heat fluxes.

The data are compared to Equations (6) and (7) which predict the time for the onset

of film boiling 13

10. Experimental data for unsupported Pt films exposed to LH2 on both sides compared

to prediction for onset of film boiling presented in Equation (6) 15

11. Results of transient heat transfer to supported Pt foil in LH2 17

12. Comparison of data to calculation, based on Equation (1), of temperature rise during

transition to film boiling of a substrate-mounted carbon film in LH2 .......... 18

13. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for

power input of 3 W/cm2 19

14. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for

power input of 6 W/cm2 19

15. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for

power input of 7 W/cm2 20

16. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for

power input of 9 W/cm2 20

iv
Transient Hydrogen Heat Transfer

Final Report for April 1986 - April 1989

B. Louie

Chemical Engineering Division

National Institute of Standards and Technology

Boulder, Colorado 80303-3328

W.G. Steward

FluidTherm Engineering

Boulder, Colorado 80302

We have investigated transient heat transfer to liquid hydrogen. This carbon films and

Pt foils submerged in liquid hydrogen received stepped inputs of power ranging from 1 to

42 W/cm2

, and the onset of nucleate or film boiling was obtained for each power level. The

critical heat flux was found to be approximately 8 W/cm2

, with the transition to film boiling

occurring in times less than 10' 3s. Premature film boiling can be related to the positive

temperature coefficient of resistance and the narrowness of the heaters. Thermometric

devices and power generation equipment selection are discussed.

Key words: boiling; conduction; hydrogen; premature film boiling; thermometry; transient heat

transfer.

1. INTRODUCTION

The goal of this study is to fill the void in data for transient heat transfer in liquid hydrogen.

The experimental technique has been previously used in liquid helium [1,2,3] and liquid nitrogen

[1,4,5] and uses stepped inputs of power to submerged heaters. The duration of the input ranges from

10

-5

to 10 s, with the onset of nucleate boiling occurring in times on the order of 10' 3

s. The surface

temperature is monitored through out the period of application of power.

In section 2 the report described the selection and assembly of the experimental apparatus,

including the safety considerations for using liquid hydrogen at NIST, and the various

heater/thermometers used. An analysis of transient heat transfer behavior is presented in section 3,

followed by a presentation of experimental results in section 4. Finally, the conclusions are given in

section 5.

1
2. EXPERIMENTAL APPARATUS AND PROCEDURE

Procedures used in these experiments were subject to the NIST guidelines for the laboratory use of liquid hydrogen [6]. The prevention of backflow of air into the apparatus, dewar breakage, and

the normal venting from the experiment were specifically identified as safety concerns. Because this

study focused on transient behavior, many potential hazards were minimized by the size of the

experiment. Less than 2 liters of liquid hydrogen were used in any one experiment, and the duration

of an experiment was less than half a day. Also, experiment in liquid nitrogen enabled us to identify

potentially hazardous techniques, which were then modified for use with liquid hydrogen.

The experimental technique used for this study was the application of a step in power to a thin

film resistance device. The change in resistance of this device was used to determine the temperature

change and heat transfer characteristics at its surface. The selection of the appropriate electronic

equipment and test devices is summarized in this section.

2.1 Overview of the Experimental Apparatus

A small, vacuum-jacketed dewar with optical viewports was used as the cryostat. Liquid nitrogen

shielded the dewar. The test section was mounted vertically at the end of a long rod in the neck of

the dewar. The temperature of the bath was measured with a germanium resistance thermometer.

The assembly is shown in figure 1. The dewar was surrounded with a plexiglass shield and metal

curb, which served as protection from glass fragments from dewar breakage. O-ring seals were used

on the flange fitting for the main dewar compartment and for the electrical leads.

During an experiment the vent gas left the dewar and was warmed to ambient temperature within

a large copper coil, passed through two check valves, and exited above the rooftop. The check valves

prevented backflow of air into the apparatus. An electrochemical hydrogen detector was located

above the dewar. The instrument rack was purged with fresh air during experiments.

2.2 Power Generation Devices

An ideal step or pulse input of power has a very short rise time with a minimal overshoot, a period of steady power, and a fast shutoff with a minimal backswing. Most power supplies are designed for a specific resistive load in order to produce the ideal waveform. Changing the size of

the resistive load can significantly distort the shape of the power input. Consider, too, that limitations

in the range of a power supply can dictate what the resistance of the load must be. Finding

acceptable solutions to this trial-and-error problem is most important in obtaining useful data.

Several power generators were used in this study to attempt to match impedances with the various test sections. Following is a summary of the various power supplies used.

Square wave pulse generator. This pulse generator was built by the Materials Reliability Division

of NIST. It had a pulse width of either 10“6 or 10~ 5

s, a maximum current of 20 A and voltage output

of 50 V, and was designed to handle a resistive load of 2.5 to 2.6 ohms. This unit was limited to the

production of repetitive pulses which were unfortunately characterized by large negative backswings;

hence, it was used only to obtain preliminary data.

2
Figure 1. Schematic of experimental apparatus.

3
High-power pulse generator. This commercially available generator could produce either single or repetitive pulses (up to 30 Khz) and variable pulse widths (approximately 10'6

to 10~ 3

s), by using

different plug-in modules to set the output. The voltage ranged from 48 to 1000 V and the current,

from 5 to 100 A, depending on the module. The pulses produced by the apparatus exhibited an

overshoot of up to 15 percent and negative backswing, but both characteristics were modulated by

proper choice of load impedance and by the addition of several electrical components on the output.

The electrical circuit is shown in figure 2. The largest drawback of this unit was the duration of the

pulse. It was found that constant power could not be maintained for longer than 10‘ 3

s, which is the

minimum time required to reach steady-state boiling in either liquid nitrogen or liquid hydrogen.

Also, some of the output units exhibited a ramping output power atypical of specifications. This unit

was limited for use only in producing short, high-power pulses.

Sauare-wave pulse generator with built-in delay. We also used on a limited basis a third pulse

generator fabricated in our Division for other transient heat-transfer experiments. This unit has a

single 1 to 100 A square pulse of 10“ 3

s to 1 s duration. This generator is incapable of producing

pulses shorter than 10“ 3s or less than 1 A in amplitude. Since it was an integral component of another

experiment, its availability was restricted.

Bipolar power amplifier with function generator. A bipolar amplifier with a function generator

was used to provide step inputs of low to medium power. Its maximum voltage is 72 V. Power inputs

of 0.01 to 55 W/cm2 were used. This unit has a maximum current output of 5 A, which was found

to be insufficient for some tests. Since it can operate in a fast mode, with ramp times of less than 2.5 x 10~ 5

s, it was able to produce clean, square, stepped input of power.

2.3 Transient Response Thermometry

The selection of thin film resistance devices for transient response thermometry was guided by

several factors. It is desirable to select a material which has a fast response as a heater and whose

resistance is a known function of temperature. A single device used as both the heater and

thermometer wold eliminate the temperature difference and time lags in heat transfer between the

heater and thermometer. Platinum was identified as a potential material because of its suitable

resistance response in the 20 K range and its ease of fabrication into usable devices. Carbon films

demonstrated characteristics which proved beneficial to obtaining fast temperature responses. For

all devices used, significant study was required to match the impedance of the heater/thermometer

with that of the power generator, while optimizing the heat-transfer geometry. This section will

discuss our experience with each type of heater/thermometer, briefly indicating the suitability of each

device.

Vapor-deposited films . Several vapor-deposited, platinum thin film resistance devices on quartz

substrates were fabricated to our design by the Cryoelectronics Division at NIST in Boulder to serve

as heaters and as thermometers. A schematic of a film is shown in figure 3. The thickness of the

devices ranged from 1 to 4 x 10' 5 cm. The resistance was adjusted by increasing path length of the

platinum with a serpentine pattern. These test sections exhibited poor sensitivity at low temperatures,

with an average resistivity ratio Rrt /RR273 at 77 K of 0.6. Although annealing the thin films at

550 °C appeared to relieve fabrication stress points, the resistivity ratio at 77 K improved only to 0.45.

The resistivity ratios at 20 K and 4 K were both 0.25, indicating no sensitivity at these lower

temperatures. This behavior is similar to that of an impure metal and suggests that the mean free path

of the electrons is larger than the thickness of the film. Attempts to increase the thickness of the

films failed. Consequently, these heater/thermometers could not be used in these experiments.

4
Figure 2. Schematic of electrical circuit for transient hydrogen

heat transfer experiments.

Platinum Film

Voltage Tap

Quartz

Substrate

Voltage Tap

Current Taps

Figure 3. Schematic of vapor-deposited Pt film on a quartz substrate

for use as a heater and thermometer.

5
Platinum foil on quartz and fiberglass-epoxv substrates . Pieces of platinum foil 4 x 10'4 cm thick

were mounted on quartz or fiberglass epoxy substrates and cut into serpentine patterns to reach a specific resistance. A schematic drawing of this heater/thermometer is shown in figure 4. The

resistivity ratios at 77 K and 4 K for unsupported samples of foil were RRrt /RR273 = 0.185 and

0.0138, respectively. Preliminary data for heat fluxes less than 20 W/cm2 in saturated liquid hydrogen

showed fast response and high sensitivity.

There were problems with this design. These thermometers had to be "trained” before they would

hold a steady resistance at low temperatures. After cycling 20 to 30 times between LN2 and room

temperature, the resistance would stabilize at 77 K and below. We postulate that the difference in

the thermal expansion between the substrate and the platinum foil induced stress points in the

serpentine structure. Frequently the devices exhibited an open circuit at low temperatures. Another

problem was that data for heat fluxes higher than 20 W/cm2 were unobtainable, due to current

limitations in the power supplies.

Another concern was an unusual temperature response prior to true nucleate boiling, which was

not supported by known conduction behavior. We speculated that the response might be attributed

to substrate effects, poor convection at the heater surface, or an inelastic interaction between the

heater surface and substrate. Additional data now indicates that the pattern of the Pt foil encourages

the early transient behavior. A detailed discussion of these results is given later in this report.

Thick film platinum resistance devices on alumina. It was assumed that current limitations would

not be encountered when using these small, thick film devices. These commercially manufactured

temperature detectors have a meandering pattern of Pt, which appears to be sputtered on the alumina

support. The pattern could be partially shunted to change the overall resistance of the device and

thereby match the desired impedances. We obtained a resistance of 10 to 12 ft at 77 K, and the

resistivity ratio Rrt /RR273 was 0.02. During calibration in LN2 significant self-heating was found.

Also, unusually small changes in resistance in response to large power inputs were observed.

Calculations confirmed the experimental results and showed that 90 percent of the heat input was

absorbed by the alumina. Several devices were burned out during preliminary testing.

Unsupported platinum foil . Calculations show that a quartz or fiberglass epoxy substrate could

absorb up to 30 percent of the heat input in liquid nitrogen and 10 percent in liquid hydrogen. These

calculations, combined with the data indicating the previously described, unusual transient behavior

prompted the development of an unsupported platinum foil heater/thermometer. Our experience

with the multichannel, supported heater/thermometer indicated that a single ribbon of platinum could

be used as the test section. A schematic of this configuration is shown in figure 5. We used various

devices of this type to study premature film boiling as a function of size and heat input. A detailed

discussion of the results is provided in section 4.

Carbon films . Carbon has a negative temperature coefficient of resistance, the opposite of

platinum, and a relatively high resistance. These attributes made it difficult to choose a carbon test section for use with the existing electronics. For example, the resistance of an unsupported Pt film

at 20 K often was 1 Q or less, while the carbon film had resistance of nearly 800 f1. Several benefits

were found from using the carbon devices. First, a large voltage could be obtained which could

overcome system noise. This meant a voltage response which was up to 800 times larger than that of

the unsupported Pt foil was recorded. A second result was the reduction in the current required. The

current required was typically 0.1 A or less, a value well below the 5 A limit of the power supply.

The limiting factor, therefore, was not the magnitude of the heat input, but whether the carbon

device could physically withstand high power.

6
Figure 4. Schematic of Pt foil deposited on quartz substrate for use

as a heater/thermometer.

Pt Ribbon

Figure 5. Schematic of unsupported Pt foil heater/thermometer.

7
Several carbon films were tested. The first "film" was a strand of fine carbon fibers stretched

across a quartz substrate. Its indefinite heat transfer area made this device of questionable value. The

second film was made of pressed graphite powder on quartz. This device showed good sensitivity

when calibrated in the temperature range within ±5 K of 77 K. However, the voltage response

prematurely leveled out during applications of pulses between 5 and 20 W/cm2

. Based on previous

transient LN2 studies [1] a transition to nucleate boiling occurs at 10' 2 to 10‘ 3

s; by contrast, our

results show a steady state voltage occurring as early as 8 x 10"4

s. We surmise that the results are related to the quality of the carbon film. Since the film was made by rubbing graphite onto quartz,

the particles are only loosely held together in a film of varying thickness. Perhaps this combination

of roughness and agglomeration enables the formation of "channels" which divert the flow of electrons

through a path of least resistance, which decreases as more heat it applied.

The third device, shown in figure 6, is a thin carbon film deposited on quartz by an electron

beam. The device has been used in previous heat transfer experiments [7]. Its dimensions are approximately 4.1 1 mm x 6.35 mm. Preliminary results with this heater/thermometer submerged in

LN2 confirmed earlier results reported by Steward [1], which warranted its use in LH2

.

2.4 Data Acquisition

A two-channel digital oscilloscope was used to record the voltage response of the

heater/thermometer and the standard resistance wire from which current was determined. The

oscilloscope has ranges of 200 mV to 80 V full scale. A total of 7964 points can be obtained for each

channel with 12-bit resolution at 100 ns/point. The voltage responses were displayed on the display screen and recorded on diskette. An 80286-based desktop computer was used for data analysis

following each run. Data were transmitted by RS-232 cable using a commercially available software

package.

2.5 Experimental Procedure

The experimental dewar was filled according to the NIST guidelines [6]. The dewar was purged

with gaseous nitrogen followed by gaseous hydrogen, prior to filling with liquid hydrogen. Safety

procedures included posting warning signs, donning conducting ankle straps, and arming the hydrogen

leak detection alarms.

Electrical connections were made through an air-tight feedthrough at the top of the dewar. A

schematic circuit diagram is shown in figure 2. The test procedure began by applying a low voltage

to the test section until the desired heat flux was verified by a spot computation. The step inputs

were initially of 10' 4

s duration, and incrementally increased up to 10 s. The power was likewise

modified in small increments, and each response was recorded.

8
Figure 6. Schematic of carbon thin film deposited on a quartz substrate

used as a heater/thermometer.

/

"T

2 cm

9
3. ANALYSIS OF TRANSIENT CONDUCTION HEAT TRANSFER

Immediately following a step heat input, until the beginning of natural convection and boiling,

the heat transfer from solid to liquid obeys the law of conduction. Comparison of the measured

temperatures with conduction calculations is a reliable way of verifying the accuracy of transient

temperature measurements, and the point of digression marks the beginning of convection and

boiling. The tow configurations, (1) thin films of Pt or carbon deposited on a solid substrate, and (2)

suspended Pt ribbons with out a substrate, require two different solutions of the transient conduction

equation.

3.1 Thin Films on Solid Substrates

Vapor-deposited films have so little mass compared to the substrate that the sensible heat of the

film, its thickness, and any temperature difference across it may be neglected. The following

expression, for which the variables are defined in the Nomenclature section at the end of the paper.

Q V t

k s

, k>-»

\/~Os \Tof

(

1 )

for the heater surface temperature of a thin film was derived previously [1] and is presented in

Appendix A of this report.

3.2 Ribbon Heater/Thermometer Without a Substrate

Free-standing ribbons are thicker than vapor deposited films, and the heat capacity of the solid

as well as possible temperature gradients must be accounted for. The two required differential

equations are for the deposited film and the liquid, rather than its substrate and the liquid. The

following closed-form solution for the temperature may be obtained through use of Laplace

transforms:

A full derivation is presented in Appendix B.

(2)

10
4. RESULTS AND DISCUSSION

From measurements of voltage across the test section of a heat/thermometer and voltage across

a standard resistor in series, the power per unit surface area. A, is

Q = (Vt)(Vs )/(RsA), (3)

and the test section resistance is

Rt= (Vt)(Rs)/Vs . (4)

The test section temperature T is found from

T = T(Rt ) , (5)

where T(Rt ) is the calibration function for the particular heater/thermometer.

4.1 Transient Heat Transfer to Liquid Hydrogen Using Carbon Films

Calculations of conduction heat transfer compared to the experimental data carbon films are shown in figures 7 and 8 for powers from 1.15 to 42 W/cm2

, with heater temperature rise as a function of time. The data agree with calculations within experimental error except for a slight

deviation toward the end of the period, possibly due to early nucleation at preferred sites. The

deviation in slope of the data from the conduction calculations indicate that steady nucleate boiling

has been reached. At 7.8 W/cm2

, after a period of steady temperature the data exhibit a small

overshoot at 0.05 s. Since the slope of the temperature data returns to the previous level, this change

in slope may indicate localized film boiling. The heat flux of 7.8 W/cm2 corresponds well to the

steady-state Kutateladze prediction [8] of 9 W/cm2 for the nucleate boiling maximum or critical heat

flux in liquid hydrogen. For heat fluxes of 10.8 W/cm2 and higher, sharp transitions into film boiling

can be discerned after a period of metastable nucleate boiling, shown by a gradual increase in

temperature.

4.2 Premature Film Boiling Using Pt Foil Heater/Thermometers

Heater/thermometers of supported and unsupported Pt foil were used to study premature film

boiling in LH2

. Premature film boiling, distinguished by a sudden, unexpected transition to film

boiling, has been noted for LN2 and LH2 in transient stepped power tests with thin Pt films [4,5]. We

never observed this behavior with the carbon film.

An estimate for the time, tf

, when a transition to film boiling takes place at a solid-liquid

interface can provide a basis for evaluating premature film boiling. Schmidt [2] developed a correlation for LHe for tf

, which is given by

tf = 7

2 P c

L

(6)

Equation (6) is plotted on figure 9 and has a slope proportional to Q'2

; 7 is computed from carbon

film experimental data and fluid properties for LH2

. We modified eq (6) to reflect that fact that t

f

11
100

LU

GO

DC

LU

DC

ID

I—

<

DC

LU

0_

LU

10

1

TIME, s

Figure 7. Results of transient heat transfer experiments from a carbon thin film to LH2 for heat fluxes ranging from 1.15 to 10.8 W/cm2

.

LU

CO

DC

LU

DC3

H

<

DC

LU

CL

I

LU

h”

TIME, s

Figure 8. Results of transient heat transfer experiments from a carbon thin film to LH2 for heat fluxes ranging from 13 to 43 W/cm2

.

12
Figure 9. Experimental data from transient heat transfer experiments using a carbon film in LH2 which show the time of transition to film boiling for various applied heat fluxes. The data are compared to equations (6) and (7) which predict the time for the onset of film boiling.

13
approached infinity at the critical heat flux, and to compute tf from the time of the end of the

conduction period rather than from the time of the beginning of the application of power:

tf = t c + 7

2 r k 1

—

\

t1 *

P c

* t

«CD| 0

(7)

The carbon film data points show reasonable agreement with eq (6). The slight curvature in the slop

of the data points at the higher heat fluxes is similar to the curved line of eq (7) in figure 9. The

agreement may be enhanced by optimizing 7.

Observations in liquid nitrogen. Sinha et al. [4] report that following stepped power inputs,

transitions to stable film boiling in LN2 on horizontal 0.102 mm Pt wires were observed for heat

fluxes as low as 40 percent of the maximum steady-state heat flux for film boiling. Tsukamoto, et

aL [6] photographed premature film boiling resulting from stepped power inputs to a horizontal 0.05

mm Pt wire at 50 percent of the steady-state burnout heat flux. We recorded experiments in LN2 on

high -speed video which used a 0.38 mm wide, unsupported Pt ribbon. We observed the development

of periodic bubbles, which coalesced and enveloped the ribbon, as well as the corresponding

transitions to film boiling [1]. We assume similar behavior for liquid hydrogen, due to the similarity

in results.

Liquid hydrogen results . We found that early and unpredictable transitions to film boiling in LH2 occurred using unsupported Pt ribbons with widths of 0.178 mm to 1.524 mm. The data, shown in

figure 10, do not follow the Q"2 dependence predicted by eq (6) and exhibit widely varying transition

times for the same heat flux. The heater width is on the order of the width of the average nucleate

boiling bubble. An average bubble size, between 0.246 to 0.52 mm, and time of departure from the

heater surface, between 5 to 36 ms, has been reported by Thome and Davey [9], for mixtures of LN2 and LAr, and be Bewilogua et al. [10], for bubble formation in boiling hydrogen. In the experiments

of Sinha et al. [4] and of Tsukamoto et al. [5] the Pt wire diameters, respectively 0.102 mm and 0.05

mm, were smaller than the average bubble size.

Premature film boiling might be a manifestation of nonuniform heating promoted by a positive

temperature coefficient of resistance combined with the small width of the heater. In particular, if

the width of a heater is nearly as small as a nucleate boiling bubble, a small number of bubbles might

effectively insulate a segment of heater and cause the temperature of that segment to rise above the

average. The local Joule heating and temperature would then increase further. The absence of a nearby heat sink or substrate would encourage this process to continue.

Hydrodynamic instability . We apply the Taylor-Helmholtz analysis to our data. A harmonic,

surface-tension wave on the vapor-liquid interface with a small amplitude perturbation may be

described by [1 1]

z = zoebt cos (mx) .

* (8)

The stability of the system is determined by b. There is a dominant wavelength which corresponds

to the maximum value of b. A maximum value of b describes when the minimum thickness of vapor

required for stable film boiling has been reached [11]. The maximum value of b, 44.5 s'

1

, corresponds

to a dominant wavelength of 20 mm. Comparing the corresponding time of 22.5 ms to figure 10

shows that many transitions occurred at even earlier times, a reasonable indication that stable film

14
ONSET

OF

FILM

BOILING,

10 I III "T I iii

C/)

0.1

O Supported Pt, 0.127 mm

A Unsupported Pt, 0.178 mm

Unsupported Pt, 1 .524 mm

V Unsupported Pt, 1 .1 43 mm

A

0.01 . O'

Aa

0.001 .

0.0001

10

fc I I li 10

HEAT FLUX, W/cm

10

Figure 10. Experimental data for unsupported Pt films exposed to LH2 on both sides compared to

prediction for onset of film boiling presented in Equation (6).

15
boiling has been reached in those cases. Other factors which may account for premature film boiling

include: (1) reduced surface tension with a vertical test section, and (2) the width of the Pt ribbon,

many times smaller than the dominant wavelength, which encourages the coalescence of the nucleate

boiling bubbles.

Temperature excursions in substrate-mounted Pt devices. The data of figure 11, for substratemounted Pt devices in LH2 , differ from those of the carbon film and from the unsupported Pt foil

in LH2 in two respects: (1) a large temperature overshoot at the onset of nucleate boiling, and (2) a brief temperature excursion preceding the overshoot. These phenomena are associated with the use of narrowest (0.127 mm wide) serpentine pattern Pt heater mounted on a quartz substrate. This heater

also had a number of imperfections, such as pinholes and ragged cut edges, which could promote the

formation of a hot spot as discussed earlier. The temperature excursion can be explained by the

development of such a film boiling spot, and the substrate acted as a poor heat sink imperfectly

connected to the foil through the epoxy adhesive. The relatively large temperature overshoot could

also be related to this poor thermal coupling.

4.3 Estimation of Heater Temperature Rise During Film Boiling

For heat fluxes greater than the nucleate boiling maximum, a period of extraordinarily low heat

transfer resistance, metastable nucleate boiling ends with a rise in temperature toward the film boiling

level. For practical applications it can be assumed that the heat transfer coefficient falls immediately

to a value of 30 to 50 mW/(cm2»K), corresponding to film boiling [8], and the thermal properties of

solid materials control temperature rise. Heaters with very small mass, such as the Pt ribbons, jump

quite abruptly to steady-state film boiling temperature.

4.4 Transient Conduction Heat Transfer From Pt Ribbons

Figures 13-16 show temperature rise versus time for heat transfer to saturated LH2 from a Pt

ribbon 1.778 x 10

-2

cm wide, 3.48 cm long, and 4 /im thick, exposed to the liquid on both sides.

Stepped power inputs were 3, 6, 7, and 9 W/cm2 (fig. 13), and the transition time recedes as the power

increases (figs. 14-16). At 9 W/cm2 the transition to boiling begins at about 0.4 ms. In order to

describe the conduction period realistically, the computations used temperature dependent liquid and

solid properties, and the time dependent power as determined experimentally. The resulting

computations, shown as the solid lines in figures 13 - 16, agree well with measurements made during

periods when the power is not constant; the variations in power are reflected i the different slopes

at early times.

16
TEMPERATURE

RISE,

AT,

K

Figure 11. Results of transient heat transfer to supported Pt foil in LH2

.

17
TEMPERATURE

RISE,

K

TIME, s

Figure 12. Comparison of data to calculation, based on Equation 1, of temperature rise during

transition to film boiling of a substrate-mounted carbon film in LH2

.

18
Figure 13. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for power input of

3 W/cm2

.

Figure 14. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for power input of

6 W/cm2

.

19
TIME, s

Figure 15. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for power input of

7 W/cm2 /

Figure 16. Comparison of experimental data for unsupported Pt ribbon to computation with

temperature dependent solid and liquid properties and the time dependent power for power input of

9 W/cm2

.

20
5. SUMMARY AND CONCLUSIONS

We studies transient heat transfer to carbon film and Pt foil devices submerged in LH2, with

emphasis placed on the onset of conduction and of film boiling. The experimental results are summarized in Table 1 for each heater/thermometer used. A solution of eq (1) for the transient

conduction differential equation for a massless heater bounded by a solid substrate on one side and

liquid on the other was used to analyze the carbon film data. Representation of the unsupported

ribbon data required a new solution, which is presented in this paper as eq (2). Except in cases of

premature film boiling, the empirical expression of Schmidt [2], eq (6), and the modification in eq

(7) predict tf at the higher heat fluxes. Premature film boiling can be related to the narrowness 1.524

mm or less of the heaters relative to the size of nucleate boiling bubbles, irregularities in the heater

material, and a positive coefficient of electrical resistance.

Table 1. Summary of Transient Heat Transfer to Liquid Hydrogen

Type

of

Heater

Transient

Conduction

Period

Equation

for Trans

.

Conduction

Time to

Onset of

Film

Boiling

Equation

for Onset

of Film

Boiling

Comments

or

Exceptions

Carbon

Thin

Film

10 /zs to

20 ms

Eq(l) 10 ms for

10.8 V/cm2 Eqs (6)

and (7)

Critical

Heat Flux

7.8 V/cm2

Pt Foil

Ribbons

Boiling

10 /zs to

1 ms

Eq (2) 3 ms

for

7 V/cm2

Eqs (6)

and (7)

Premature

Film

related to

narrow

heaters

Pt Foil

on

Quartz

1 /zs to

5 ms

Eq (1) 20 ms

for

12 V/cm2

(not

studied)

Temp

.

excursions

due to

hot spots,

substrate

effects

21
6. ACKNOWLEDGMENTS

The authors wish to recognize the contributions of N. V. Frederick who designed, constructed,

and tested important electronic components for this study. His assistance has been invaluable and is greatly appreciated.

Work performed under WPAFB MIPR contract number FY1455-89-N0604.

7. NOMENCLATURE

A surface area, cm T heater surface temperature, K

b growth parameter T

1 dimensionless temperature = Tas/(q<$

2

) c specific heat, J/(g K) vt voltage across the test section, V

k thermal conductivity, W/(cm K) V8 voltage across the standard resistor, V

L heat of vaporization, J/g X length of fluid-vapor interface, cm

m wave number = 2ir/\ z amplitude of perturbation, cm

Q applied heat flux, W/(cm2

s) zo

perturbation constant

Qcr critical heat flux, W/(cm2 s) a thermal diffusivity = k/(p«c), cm2 /s

q heat flux per unit volume, W/cm3

P dimensionless parameter = (k

a/kf)(a

s/af

) RS resistance of standard resistor, Cl 8 ribbon thickness, cm

Rt resistance of test resistor. Cl 1 fit factor

t time s P density, g/cm3

t' dimensionless time = totJS

2, A wavelength, cm

tc time of conduction period, s a surface tension, dyn/cm

time of onset of film boiling, s 9 integration variable for time

v , denote vapor, liquid

s f denote solid, fluid

e’rfc complementary error function

22
6. REFERENCES

[1] W. G. Steward, Transient Helium Heat Transfer Phase I - Static Coolant, Int. J. Heat Mass

Transfer, 21:863 (1978).

[2] C. Schmidt, Transient Heat Transfer into a Closed Small Volume of Liquid or Supercritical

Helium, Cryogenics, 28:585 (1988).

[3] O. Tsukamoto, T. Uyemura, and Y. Ishida, Observation of Bubble Formation Mechanism of

Liquid Helium Subjected to Transient Heating, Proc. Eighth Int. Cryog. Eng. Conf.,

Butterworth, Guildford, UK (1980), p. 251.

[4] D. N. Sinha et al., Premature Transition to Stable Film Boiling Initiated by Power Transients in

Liquid Nitrogen, Cryogenics, 19:225 (1979).

[5] O. Tsukamoto, T. Uyemura, and T. Uyemura, Observation of Bubble Formation Mechanism of

Liquid Nitrogen Subjected to Transient Heating, Advances in Cryogenic Engineering, vol. 25,

(1980), p. 476.

[6] K. B. Martin and V. J. Johnson, Safety Instruction and Safety Guide for Handling Gaseous and

Liquid Hydrogen at the Boulder Laboratories, Nat. Bur. Stand. (U.S.) Monogr. CM-4; (1960).

[7] P. J. Giarratano and W. G. Steward, Transient Forced Convection Heat Transfer to Helium

During a Step in Heat Flux, J. Heat Transfer, 105:350 (1983).

[8] E. G. Brentari, P. J. Giarratano, and R. V. Smith, Boiling Heat Transfer or Oxygen, Nitrogen,

Hydrogen, and Helium, Nat. Bur. Stand. (U.S.) Tech Note 317 (1965).

[9] J. R. Thome and G. Davey, Bubble Growth Rates in Liquid Nitrogen, Argon and Their

Mixtures, Int. J. Heat Mass Transfer, 24:89 (1981).

[10] L. Bewilogua, R. Knoner, and H. Vinzelberg, Studies on Bubble Formation in Low Boiling

Liquids, Cryogenics, 10:69 (1970).

[11] S. Van Stralen and R. Cole, Boiling Phenomena, Hemisphere, Washington (1979), p. 615.

23
Appendix A

TRANSIENT CONDUCTION HEAT TRANSFER - FLAT PLATE HEATER ON A SOLID SUBSTRATE WITH LIQUID COOLANT

Assume:

L Infinite flat plate heater in the x - y plane at z - 0. Note: If the substrate were finite in the —z direction one would have to make an assumption about heat transfer at a bottom boundary.

The results are the same until a temperature wave penetrates the finite substrate.

2. Heater has zero thickness.

3. Stagnant liquid hydrogen lies above the plate (z > 0); no forced convection is present.

4. A solid substrate lies below the plate (z < 0).

5. Times of concern are short enough that thermal convection currents are not established and

no bubbles have formed. This would mean non-equilibrium of phases (superheating) in cases where Tf > Tssturation .

6. Heating is at constant volume, i.e. no work of compression.

7. Radiation heat transfer is much less than conduction heat transfer.

8. Fluid and solid properties are constant.

The Fourier heat conduction equation in 1 dimension is presented for the following cases:

A. Solid Substrate (subscript s

)

<3T S 1 <5T S dz 2 ” as dO

where T8 = temperature of substrate at z and time 0 = temperature before disturbance

6 = time

K s a8 = thermal diffusivity = —p

P sbps

Ks = thermal conductivity

pB = density

Cpa = specific heat

Boundary Conditions for the Substrate

(

1 )

TS (M) =0

(2)

24
the part of the heater

power being dissipated

in the substrate

<92 Tf 1 <9Tf = al M

z - 0

where Tf = temperature of fluid at z,

6 = temperature before disturbance.

Boundary Conditions for the Fluid

Tf (z,0) =0

part of the heater power

being dissipated in the

fluid.

C.

D.

Condition at the Substrate/Heater/Liquid Interface

p = pf + ps

TS (O,0) =Tf (0,tf)

Solution for the Substrate

Laplace transform with respect to 9

total heater power

known parameter

lira Tf(z, 6) = 0

Z-Kd

<9T1

Pf=-Kf dz 0J

lim Ts (z , 0) - 0

Z->

CD

r cfi l Ps - dz

0,6

B. Conduction Equation for the Fluid

(3)

(4)

(5)

(6)

(7)

( 8 )

(9)

( 10 )

d

2 t 1 (ll)

dz 7 ( Z)S ) =

c*7 t st ( z > s ) ' T ( z >°)] • From B.C. #2 T(z,0) — 0,

where t(z,s) = L[T(z,0)]

s = the Laplace transform parameter.

The solution of (11) is

t = Ci ezv

^^ + C 2 .

25
From B.C. #3 C2 = 0. Therefore,

t = C 16 zyjs /as

( 12 )

Transform B.C. #4:

Then from eq (12),

p s r Ks

dt

dz

0,s

^ = KSC, Js/ZTs e

2'^

z=0

or

Therefore,

Ps 1

Cl = s~K7 ^s / 0s '

t =

s

Jcx. s / s e zVs/as (13)

*It is assumed in the following development of equations that P8 is constant. Further

explanation is provided in the addendum following this appendix.

Use the following transform relations:

1 e z

2/4 as 0

y/irO

1 e-aVs/as

Is

(14)

and

“ rO

Jo

F(r) dr = I

f (s) (15)

Then combining eqs (13) and (14) yields the following expression:

t = ii r JaJJWV) e^2/

26
From eq (15)

rd

t = L

(where r = dummy variable).

Therefore,

0

K s /on/(irr) e-2 '/ dr

^ _____

Ts = sjOt-s/ 7T I

0

,-z 2/(4as r)

dr .

A change of variables is now introduced:

Let ^ ~

Therefore J_ = «, aad r = Jt z 4A 2 as

Hence,

Also,

dr =

2 z

2 dA

4 A tts

1 z 2 dA

2 A

2 as

r = 0 => A = QD

r - 9 =» A = 2Jg^9

The following expression can be derived:

Ts - £ v^s

2^as 9 —

A

:

-N /• 2\/5sz A

_1 z 2 2 A as dA

QD

(16)

or ' QD

2Jas 9

( 17 )

27
Now we perform an integration by parts: udv = uv — vdu.

Let

, dA , _ 1

dv — 3nd v — —

Then,

u = e ^ and du = —2Ae ^ dA .

m _ Ps Z

ig _ —

Ks /

K

r -a 2 T®

rQD -2

z

-A 2 e A

dA

2ja^6 2 JclsQ

or

Ts =

K.

-z r®

2Jas 8 @

spK

2z -A 2 e A dA

2^Jas 0

'

z° erfc

2^cas 0

Therefore,

T _ Ps

Ks

2JclsO/tt e~z2/^ as ^ — z- erf

c

2^ (18)

at z < 0

Substrate Surface Temperature (z = 0)

TS (O,0) • K s

(19)

Ee Solution for the Fluid

By starting with eq (5) and boundary conditions (6), (7), and (8) we get the same solution as (18) except the properties are fluid properties and the power if Pf

„

Tf = K f 2^UJ1 e~z2 / 4af^ — z • erfc

2^a{0

( 20 )

28
at z > 0 ,

or

Tf = — PfV5

r -x*2 e — yj'K r x*erf c x , X* -

t/i . KJ f to 2Joif9

and at the liquid surface the temperature is:

2Pf y/Of

( 21 )

F. Solution in Terms of P and 9

At the interface P8 + Pf = P, and Tg(O,0) = T^O,#) = T(O,0). Therefore, from eqs (19) and (21):

p

_ T (0;Q1 JttJD +

Kfl

y/al Vaf. ( 21 a)

ADDENDUM - PROOF THAT Pg AND Pf ARE CONSTANT

From eq (12) we know that t = Ci 0

ZVs / as for the substrate (z < 0).

For the fluid t =

, (z > 0) .

At z = 0 the temperature of the substrate = temperature of liquid, therefore C1 = C3 = C.

Ps = s C KfVs/ af , and

Pf — S C Ks^/s j

Cl§ '

Therefore,

Ps Kf 0's P7

= Klja?=

( const )‘ »

P = Pf + Ps = (const) 2 (given) ,

P = Pf(l + const i) = (const) 2

.

(A)

(B)

29
(const)

2

~ 1 + (const) i (const) 3

.

Similarity Ps = (const4)

.

It is not necessary to know that P8 is constant. Using condition (A) above and eq (22) give the

same result.

30
Appendix B

TRANSIENT CONDUCTION HEAT TRANSFER FROM A RIBBON HEATER

WITH INTERNAL HEAT GENERATION

The unsteady state conduction equation is

1 ofl

a dt 9

where q = generated heat f lux/volume

k = thermal conductivity

a = thermal diffusivity

T = temperature — initial temperature

t = time

A. Development of equations for the solid

Equation (1) for the solid is:

d2 T q 1 5T

0^2

+ Kl

= a75t • (2 )

Boundary Conditions:

T(y,0) = 0 (initial condition) . (3)

dl

(0,t) = 0 (symmetry)

.

Change to dimens ionaless variables:

y

Let y' = -g (dimensionless space variable)

.

To write Equation (2) in dimensionless terms, the following must exist:

<92T q T

dy 2 ~ K s " y

2

T

Let T' = j

.

T'A q q<$ 2 Then

(y' 6) 2 t =

] kT °

r A = '

31
t

Let t

/ =

g

. Then,

1 5T 1 AT' q

al dt H aW H rs

‘

T' q£2

Since p- [=] 1 and 7 = ^— ,

1 q62 1 q

aK7“B 3K7 ’

where B = —— . OL

Recap: The dimensionless space coordinate, temperature, and time are:

y

y' = 1

or y

= Sy' (4)

TK S q62 v or T = T' 5— (4)

t CX s t' <52 t' = p- or

0!s

(4)

When these variables are substituted into Equation (2) we have the dimensionless

equation for the solid:

d2 T' dl'

W* + 1 = dt 7

B. Development of equations for the liquid

The conduction equation for the liquid lacks the heat generation term

d2 T 1 dT

dy 2 oti dt

The dimensionless equation for the liquid is

d2 V as 5T'

dy ' 2 ~ a\ dt

Boundary condition for the liquid

T(od , t) =0 .

(6)

(7)

( 8 )

32
C. Coupling the equations

To couple Equations (2) and (6)

:

at y

= <5/2 Ts <5/2, t = Ti <5/2,

t

’dl' ' 5T’

and Ks

ii to

1

1

Ki

y=6/2

Or, in terms of the dimensionless variables:

1' =1/2 Ts '(l/2,t / ) =Ti / (l/2,t / )

and Ks dl'

w

= Ki

<5T'

y

^ y'=i /2 =1/2

D. Transformed Solution

Laplace Transform

d2 r 1

Solid: ^72 +

g = sr-r(y',0)

Initial condition. r(y' ,0) = 0)

d2 r' 1

3y7'2~ sr = ~I

where r is the Laplace—transformed temperature

s is the Laplace transform variable

Particular Solution TP "

S

2

*

Homogeneous Solution rc - Cge^^ + C 4 e

Total solution

The symmetry B.C. -»

From Equation (11)

,

which gives

w + + - t = C3ev J + C4e 2

•

dr

fy

7

y' = 0

' dl

'

[ dy

/ \ y'=0

C 3#e'/iy ' -CWse

-^'

y'=0 ’

(9)

(10)

( 9 ')

( 10 ')

( 11 )

33
c 3 = c 4

.

Therefore,

r = C 3 e^y' + e-^r +

2

* (12)

For the liquid

d

2 r 0's

dy77

oq

ST - r(r$.

= C|evW«I 'JW + Cje-Vas/aiv/sF”

and

r(a,t) =0 or t(od,s) =0 —» Ci=0

Therefore,

r=C2e-^y '^m.

(13)

C 3 and C 2 can be evaluated from Equations (12) and (13) and the coupling

condition from Equation (9') at y' = 1/2:

_ e

i/s/2 + e—i/s/2 + i_ = c^-Vs/2^/<H

_ (14)

To use Equation (10')

,

differentiate Equations (12) and (13) and evaluate at

r =1/2:

K.

C 3 |e'

/i/2

+ e~^/2

J = -C2v/s e-^/2^/®1

,

K,

C 3 r [e^72

+ e-^72

J = C

.

(15)

By combining Equations (14) and (15) we obtain the following expression:

1 Kc

eVs/2

+ -VS/2 Vs/2 4. 0-Vs/2

or

C 3 = P

+ p

= - V«s/ai C 3 [ev ' + e

1

e^/2 + e-^72

+ 0

,Vs/2 _ e-^/2

(16)

K. where 0 = Ki <*s TWWh

34
By combining Equations (12) and (16) the following expression is obtained:

r = e^y' + e-^'

1 -

e

i/s/2 + e

-i/s/2 ,\/s/2 _ —v/s/2

or

r =

e^y' + e-^y'

1 -

Ae^/2 - Be '/®/ 2

where A = /? + 1

B = /? — 1

.

By long division

r = 1 - 1 e\/s(y'—1/2) , B

pi/s(y'-3/2) ^ B2 p1/s(y'-5/2)

LA

+ e A2

+ e A3

+

+

1 e~'v/s(y

/ +l/2)

+

B

e~v's(y

/ +3/2) + B

2 e~v/s(y / +5/2) + A2 A3

or

_ 1 _n re

-Vi'( 1 / 2-y

/

) + Be^3/ 2^')

s

2 A s L s A s

+

B

2 -^(5/2-y') -^(1/2+y')

+ e . . +

B e (3/2+y'

)

a -Vi(5/2-y')

+ • •

/

35
E. Time Domain Solution

The inverse transform for the solid is:

T' = t' - 1

rt'

erfc

• 1/2 -

y'- + B erfc 3 / 2 -

y'l

A

J 0 to A 2J9

+ ¥ 2 erfc rs - y

+ . . . + erfc

'1/2 + y

7

'

A 2 ye J

or

+ ® erfc

A

'3/2 +

y'" + ¥ 2erfc

"5/2 +

y'"

¥ © * o

t

to i AL J f

bO i

dd

i T

7 = t7 -

00s FI” \t

/ r erfc '2n + 1 - y

7

’

A o 0II 5 o L 1273 J

+ erfc 2n + 1 + y'

~w

A8 , —l/2<y'<l/2 (17)

36
4. TITLE AND SUBTITLE

Transient Hydrogen Heat Transfer

Final Report for April 1986 - April 1989

5. AUTHOR(S)

B. Louie, W.G. Steward

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS) 7. CONTRACT/GRANT NUMBER

U.S. DEPARTMENT OF COMMERCE WPAFB MIPR FY 145 5 -89-NO 604

NATIUNAL INoTITUTB UP alANUAnUa APlU 1 BwUNULUUT

BOULDER, COLORADO 80303-3328 8. TYPE OF REPORT AND PERIOD COVERED

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

10. SUPPLEMENTARY NOTES

BL-114A

(5-90)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER

NISTIR 3951

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBLICATION DATE

October 1991

11. ABSTRACT (A 200-WORD OR LESS FACTUAL SUMMARY OF MOST SIGNIFICANT INFORMATION. IF DOCUMENT INCLUDES A SIGNIFICANT BIBLIOGRAPHY OR

UTERATURE SURVEY, MENTION IT HERE.)

We have investigated transient heat transfer to liquid hydrogen. Thin carbon

films and Pt foils submerged in liquid hydrogen received stepped * inputs of power

ranging from 1 to 42 W/cm2

, and the onset of nucleate or film boiling was obtained

for each power level. The critical heat flux was found to be approximately 8 W/cm2

, with the transition to film boiling occurring in times less than 10' 3 s. Premature

film boiling can be related to the positive temperature coefficient of resistance

and the narrowness of the heaters. Thermometric devices and power generation equipment

selection are discussed.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

boiling; conduction; hydrogen; premature film boiling; thermometry; transient heat

transfer

X

13. AVAILABILITY UNLIMITED

FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS).

ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE,

WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD. VA 22161.

14. NUMBER OF PRINTED PAGES

44

15. PRICE

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