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NASA Technical Memorandum 4257

Automatic Control Study of

the Icing Research Tunnel

Refrigeration System

Arthur W. Kieffer and Ronald H. Soeder

Lewis Research Center

Cleveland, Ohio

National Aeronautics and

Space Administration

Office of Management

Scientific and Technical

Information Division

1991

Contents

Summary ..............................................................................................................

Introduction ...........................................................................................................

System Description .................................................................................................. 1

Computer Model ..................................................................................................... 2

Model Description ................................................................................................ 2

Model Validation .................................................................................................. 3

Control Development ............................................................................................... 3

System Characteristics ........................................................................................... 3

Controller Description ............................................................................................ 3

Control Run Results ................................................................................................. 4

Run 1--Nominal Case ............................................................................................ 5

Run 2--Compressor Change .................................................................................... 6

Run 3--Control Valve Change ................................................................................. 6

Run 4--Change in Operating Point ............................................................................ 6

Run 5--Controller Gain Change ............................................................................... 6

Run 6--Setpoint Ramp ........................................................................................... 7

Run 7--Small Setpoint Change

(Actual Tunnel Run Comparison) .............................................................................. 7

Run 8--Heat Load Ramp ........................................................................................ 7

Run 9--Setpoint Increase ........................................................................................ 8

Runs 10 to 13--Additional Runs

With Setpoint Increases .......................................................................................... 8

Small Setpoint Disturbances ....................................................................................... 8

Controller Variation Runs ....................................................................................... 8

System Variation Runs ........................................................................................... 9

Heat Load Variation Runs ....................................................................................... 9

Compressor Variation Runs ..................................................................................... 10

Noise Injection ..................................................................................................... 10

Concluding Remarks ................................................................................................ 10

Appendix A--Computer Simulation Equations

of the IRT Refrigeration System .................................................................................. 12

Refrigeration Cycle ............................................................................................... 12

Basic Computer Model Equations ............................................................................. 12

Flash Cooler Equations (Evaporator) ......................................................................... 13

Heat Exchanger Equations ...................................................................................... 14

Pump Flow Loop Equations .................................................................................... 15

Accumulator Equations .......................................................................................... 16

Compressor Equations ........................................................................................... 16

Condenser Equations ............................................................................................. 17

Economizer Equations ............................................................................................ 18

Derivation of Evaporation Equation ........................................................................... 19

Appendix B--Symbols .............................................................................................. 2 I

References ............................................................................................................. 23

Page

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Summary

The Icing Research Tunnel (IRT) at the NASA Lewis

Research Center is a subsonic closed-return atmospheric

tunnel. The tunnel includes a heat exchanger and a refrigeration

plant to achieve the desired air temperature and a spray system

to generate the type of icing conditions that would be

encountered by aircraft. At the present time, the tunnel air

temperature is controlled by manual adjustment of freon

refrigerant flow control valves. An upgrade of this facility calls

for these control valves to be adjusted by an automatic controller. This report discusses the digital computer simulation

of the IRT refrigeration plant and the automatic controller that

was used in the simulation.

Introduction

The Icing Research Tunnel (IRT) at the NASA Lewis

Research Center is a closed-return, atmospheric tunnel

equipped for testing low-speed aerodynamic models. A standard centrifugal compressor refrigeration cycle is used to

reduce the tunnel air temperature to the desired test conditions.

At present, the temperature is controlled manually by a

refrigeration system operator who manipulates the freon

refrigerant flow control valves. As part of an upgrading and

rehabilitation of the IRT Facility, this study was performed

to design an automatic control which could be used as an

alternative to the manual control. Automatic control would

make more efficient use of the tunnel run time. Presently it

takes the system operator considerable time to change the

tunnel air temperature from one operating point to another.

This study demonstrates that an automatic controller could

accomplish this in less time. For this investigation, the IRT

refrigeration system was simulated on a digital computer. The

purpose of the simulation was two-fold: (1) to test various

temperature control schemes and design a suitable controller

and (2) to study future facility automation in areas such as

startup, shutdown, and decision-making capabilities (such as

changing the number of compressors during run time).

System Description

The major components of the Icing Research Tunnel (IRT)

Refrigeration System are compressors, pumps, condensers,

economizers, a flash cooler, and a heat exchanger. The system

removes heat from the IRT by means of a heat exchanger and

maintains the tunnel air temperature at the required operating

point. A standard centrifugal compressor refrigeration cycle

is used, with Freon- 12 as the refrigerant. The system is operated

in a flooded manner where subcooled refrigerant is continually

circulated through the tunnel heat exchanger. This feature

improves heat transfer by keeping the refrigerant a liquid until

near the end of its passage through the heat exchanger.

The refrigeration system is shown schematically in figure I.

Liquid freon is taken at low pressure and temperature from

the bottom of the flash cooler and is pumped through a series

of pipes (approximately 240 ft long) and headers leading

to tunnel heat exchanger coils. At the design flow rate of

150 lb/sec, it takes the liquid freon approximately 50 sec to

travel from the flash cooler to the heat exchanger. The heat

exchanger, located inside the tunnel, consists of 80 individual

heat exchanger panels arranged in a pleated design. Rectangular

sheet fins attached to copper coils carry heat from the tunnel

air into the copper coils, causing the freon flowing inside the

coils to partially vaporize before leaving the heat exchanger

and returning to the flash cooler.

In the flash cooler the liquid freon drops to the bottom of

the tank to be again recirculated by the pump. The freon vapor

in the flash cooler flows through damper valves into an

accumulator tank. The damper valves control the tunnel

temperature by regulating the flow in the compressor loop.

From one to six parallel-operated damper valves can be used

depending on tunnel heat load. As the freon vapor leaves the

accumulator, it enters the compressor where its pressure and

temperature are raised. A super-heated freon vapor then leaves

the compressors and enters the tube-in-shell condensers where

cooling-tower water is used to remove heat from the highpressure, high-temperature freon vapor. The heat removed

from the freon causes the refrigerant vapor to condense into

a saturated liquid.
¢-- Cooling

I

I

I

J

Economizer--

I

t

I

I

1

towerwater

Condenser

Compressor

//

Damper (flow

control) valves--,"'

7

/

/

/

/

I- Suction

I header

I

Tunnel heat

exchanger

Figure l.--Refrigeration system for Icing Research Tunnel. (Compressor-condenser-economizer unit shown inside dashed lines.)

Freon from the condenser may flow into a two-stage

economizer (compressor interstage cooler) or may bypass the

economizer and flow back to the flash cooler depending on

the operating conditions. When the economizers are used,

liquid freon enters through a set of orifices which results

in a pressure drop and causes part of the fluid to flash to the

vapor state. The flash vapor is routed back to the inlet of the

second and third stages of the centrifugal compressors. The

liquid part of the freon leaves the economizers at a low pressure

and temperature and returns to the flash cooler where part of

it flashes to vapor and again becomes available to be drawn

through the damper valves for a restart of the vapor cycle.

The liquid part of the refrigerant in the flash cooler is

available to be pumped to the tunnel heat exchanger for tunnel

heat removal.

The four-stage centrifugal compressor, a two-pass tube-inshell water-cooled condenser, and a two-stage economizer

(used to improve the efficiency of the process) are all part of

a self-contained unit. One Compressor-condenser-economizer

unit is shown schematically within the dashed lines of figure I.

A 1500-hp induction motor drives each unit. At present the

refrigeration system contains 13 such units which can be used

during a run.

Computer Model

Model Description

A computer model was made of the IRT Refrigeration

System and was used to formulate and test the IRT temperature

control design presented here. This model can be used for

further automatic control studies in areas such as startup and

shutdown.

The computer model uses algebraic and time differential

equations to describe steady-state as well as transient conditions. A lumped-parameter approximation of the system

components is made using control volumes. Transient equations of conservation of mass, conservation of energy, and

equations of state are used to solve for the temperature and

pressure for these components. Appropriate flow equations for

the vapor flow through the damper valves (control valves),

condensation flow in the condenser, and evaporative flow in

the flash cooler and economizer are used. Line pressure drops,

and transients that have no effect on the control design were

neglected. A schematic of the computer model is shown in

figure 2. A detailed description of the refrigeration system

computer model with equations is presented in appendix A.
I Heat removed I

t

[ Coo*nser >

I Economizer I

Damper

valves ---,,

Compressor

Accumulator

Flash

cooler

Heat input [

from tunnel

Heat

exchanger

Figure 2.--Simulation diagram for Icing Research Tunnel. (Compressorcondenser-economizer unit shown inside dashed lines.)

The computer simulation was programmed in the CSMP3

simulation language. This simulation language is well suited

for modeling systems that can be described by ordinary timedependent nonlinear differential equations.

variables except the compressor motor current. A much higher

motor current was needed in the actual tunnel run than was

predicted by the computer model. This indicates that the

compressor-motor unit was probably operating at a much

lower efficiency (40 percent) than was used in the simulation (70 percent). This was not surprising since the system

was operating at off-design conditions.

Control Development

System Characteristics

The IRT Refrigeration System is not well suited for

automatic control mainly because of the numerous operating

constraints of the system:

(l) Operating constraint caused by compressor surge

(2) Upper limit of compressor inlet (accumulator) pressure

of 12 psia (because of seal limitations)

(3) Upper limit of condenser pressure of 125 psia (because

of structural limitations)

(4) Upper limit of compressor motor current of 300 A

Compressor surge and compressor inlet pressure are the

most frequently encountered constraints. They can be exceeded

whenever the tunnel operating temperature is changed too

rapidly. The compressor can surge when the tunnel temperature is increased, and the compressor inlet pressure can

exceed 12 psia when the tunnel temperature is decreased. This

study focused primarily on the compressor inlet pressure

constraint because the compressor surge was not well defined

and will not be as much of a problem.

Model Validation

The refrigeration system was instrumented for pressure and

temperature at various points of interest primarily to obtain

a valid compressor characteristic curve at the 6650-rpm design

operating point. These temperature and pressure data were

also compared with the predicted steady-state results of the

computer model.

Table I compares data from a tunnel run with those from

a similar computer run. The two runs closely agree for all

TABLE I.--TUNNEL DATA COMPARED WITH COMPUTER RESULTS

Variable Tunnel run data Computer results

Temperatures, *R

Tunnel

Flash cooler

Compressor inlet

Compressor exit

Water exit

Pressures, psia

Flash cooler

Compressor inlet

Compressor exit

Compressor motor current, A

Compressor loop flow, lb/sec

460

448

453

679

529

19.3

8.3

99.0

250

a24

460.0

454.6

454.5

676.7

530.8

21.2

8.8

98.1

175.2

23.6

aCalcutated from data,

Controller Description

The controller was designed to bring the tunnel air to the

desired operating temperature as fast as possible without

exceeding any system constraints. This was best accomplished

by changing the temperature at a constant rate. Moreover, to

minimize time delays, the controller was designed to bring

the temperature to its new steady-state value with little overshoot and minimum settling time.

Standard control analysis techniques were not used in this

study because the system is nonlinear. Instead, various temperature control schemes were tried on the computer. In the scheme

that was selected, the outer control loop controlled the tunnel

temperature, an intermediate loop regulated the flash cooler

temperature, and an inner loop controlled the valve position.

The flash cooler temperature is used as the intermediate loop

because it closely approximates the tunnel temperature in

steady state and responds immediately to a change in control

valve position. The tunnel temperature responds more slowly

because the large thermal capacity of the tunnel heat exchanger

introduces considerable temperature lag between the flash

cooler and tunnel temperatures.

In addition to the thermal lag, there is a temperature transport lag caused by the fluid flowing into the heat exchanger.
Tunnel tern )erature KS

Tunnel

,_t _x_inr_; ure

Flash coolerpressure

set point

Flashcooler

temperature

set point

Flash

cooler

pressure __ _ Error, _

e Control

" -= _ algorithm

Valve

= position

I

Valve

Valve _ position

and

actuator set point

Figure 3.--Tunnel temperaturecontroller.

It takes 50 sec for the liquid freon to travel from the flash

cooler to the heat exchanger. This long dead time, if it were

a predominant effect, would be a serious hindrance in the

design of an effective automatic temperature controller.

However this is not the case here because any immediate freon

temperature change is due to a change in control valve position.

The valve position, which affects the flash cooler pressure and

hence flash cooler temperature, also affects the heat exchanger

temperature because both pressures are essentially the same.

Therefore the temperature of the freon in the heat exchanger

changes at the same time as the flash cooler temperature and

is not dependent on the fluid flowing in from the flash cooler.

The temperature of this fluid should have only a minor effect

on the temperature transients in the heat exchanger. The

computer model therefore neglects this transport delay.

The setpoint for the flash cooler temperature control is

generated by the outer control loop. At steady state, the flash

cooler temperature generally is 5* lower than the tunnel

temperature. Therefore to account for this difference, the flash

cooler temperature setpoint was made 5* lower than the tunnel

temperature setpoint. Because the difference is not quite constant

and may change somewhat for different operating conditions, a proportional temperature control was added. The

proportional controller not only corrects for the steady-state

temperature difference, but also speeds up the control response.

Because the flash cooler fluid is saturated, its vapor pressure

is strictly a function of temperature. As a result, the flash

cooler temperature control can be converted to a pressure control. This conversion should improve the controller response

because the flash cooler pressure response is faster than the temperature response. Also, pressure control may be more desirable

than temperature control, from a measurement perspective.

Valve position was added as an inner control loop so that

the system could be switched to manual control. Since the

dynamics of the inner loop are much faster than those of the

other components in the temperature controller, the inner loop

has essentially no effect on the overall response.

A block diagram of the Tunnel Temperature Controller is

presented in figure 3. The KTblock represents a gain constant

for the outer temperature control loop. The KS block represents a correction for the steady-state temperature differences

between the flash cooler temperature and the tunnel temperature. The "sat curve" block represents a lookup table which

converts freon temperature to pressure. The "LIMIT" block

limits the flash cooler pressure error signal before it enters

the Control Algorithm block. The block output M k represents

the control valve position setpoint. The KV block is a gain

constant for the valve position control loop. The equations for

the control algorithm of the pressure control loop follow.

Control Algorithm

The control algorithm is depicted in the block diagram shown

in figure 3 as follows:

gk-2 = gk-,

gk-i =gk

er__ 2 = er__ I

erk- 1 = erk

Test for setpoint step change; if step, reset

erk_ l = erk_ 2 = O and Mk_ I = Mk + FM

Then continue

FM = G(-0.799 er k_ I + 1.998 ere=_2)

Mk = 1.3Mk_l -- 0.3Mk-2 + Gerk + FM

where G is a controller gain which is variable and a function

of tunnel heat load, the control valve position, and the number

of compressors in operation; er is the control algorithm input;

M is the control algorithm output; the subscript k-n represents

the (k-n) th sampling instant. The algorithm of the pressure

control loop was not tuned for tunnel pressure response, but

rather for satisfactory tunnel temperature response.

Control Run Results

The controller was tested at various operating conditions

and for various setpoint changes. When the controller is

implemented in the field, the tunnel temperature changes will

probably be made with step changes in the temperature
TABLE II.--NOMINAL OPERATING CONDITIONS

[Step setpoint change.]

Initial temperature, °R ........................................................ 490

Tunnel heat load, Btu/sec .................................................. 1200

Compressor used .................................................................. 1

Control valves used .............................................................. 3

Evaporation constant ......................................................... 10.0

Control constants

Error limit .................................................................... 8.0

Sample rate, samples/see ..................................................... 2

Valve loop gain, KV....................................................... 10.0

Outer loop gain, KT ....................................................... 15.0

setpoint. Consequently, all but one of the computer runs that

are presented are for step setpoint changes of various sizes

and at various operating temperatures.

The evaporation rate in the flash cooler and the heat transfer

coefficient in the tunnel heat exchanger were two parameters

whose values were considered to be very uncertain. Since these

parameters were deemed important to the system response,

control runs were made where these parameters were varied.

Other important system parameters were also investigated: the

tunnel heat load, the number of compressor units in operation,

the number of control valve units being used, the effect of

controller gain (change in the limit of the pressure error signal),

and controller sampling rate. Because of the uncertainty of

the compressor characteristic curve, a control run was made

where the slope of the compressor curve was increased by 100

percent to determine its effect on the closed-loop response.

A typical tunnel operating condition and controller setting

were selected and termed as the nominal case. Nominal

operating parameters are presented in table II. The time

response for runs with different operating conditions are

compared with this nominal case whenever applicable.

Run 1--Nominal Case

The first run presented is for the nominal case with the tunnel

operating at a temperature setpoint of 490 OR. At 80 sec after

the start of the run, the tunnel temperature setpoint was stepped

from 490 to 450 °R. The controller performed according to

design expectations in that the tunnel temperature response

(fig. 4) was similar to a ramp and (very importantly) the

response showed no overshoot. It took 485 sec (from 80th to

565th sec) for the tunnel temperature to reach its new setpoint

of 450 °R. The control valve movement for the run is presented in figure 5. The valve started from an initial position

of approximately 2 ° and moved to a final position of approximately 4.7 °. The compressor inlet (accumulator) pressure is

a critical parameter in these runs because its upper limit of

14

\

2

• I I

0 100 200 300 400 500 600 700

Time, sec

Figure 5.--Control valve movement for tunnel temperature setpoint decrease

from 490 to 450 *R.

12

-8

8 lo

"_ 8

8.

_ s

4

12

10

==

= 8

I I I I I ] I

0 100 200 300 400 500 600 700

Time, sec

490 Figure 6.--Accumulator pressure for tunnel temperature setpoinl

decrease from 490 to 450 °R.

480

g 470 ,oF35

E 460

2s

45O

F , , , , 440 I I 15

0 100 200 300 400 50O 600 700 0 100 200 3O0 4O0 5OO 600 7OO

"lqme, sec Time, see

Figure 4.--Tunnel temperature response for setpoint decrease from 490 Figure 7. Flash cooler pressure change for tunnel temperature setpoint

to 450 °R. decrease from 490 to 450 °R.
12psiacanoften be exceeded during the transients. The

accumulator pressure (fig. 6) was initially 8.1 psia. At the

start of the transients it reached a peak of 10.6 psia and then

settled to a new steady-state value of 7.1 psia. The 12-psia limit

was not exceeded during this run. The flash cooler pressure

is provided in figure 7 as a matter of interest,

Run 2--Compressor Change

Run 2 was identical to run 1 except that two compressors

were used instead of one. This change increased the tunnel

temperature response time by about 45 sec (fig. 8). The

temperature reached steady state at about 520 sec with a slight

overshoot. (In run 1, there was no overshoot.) As was expected,

the system responded faster when more compressors were

added to the system.

Run 3--Control Valve Change

Run 3 was also identical to run 1 except that four control

valve units were used instead of three. The tunnel temperature

(fig. 9) reached steady state at approximately 450 sec with no

overshoot. The response is at least 100 sec faster than the

nominal case (fig. 4) of run 1.

Run 4--Change in Operating Point

Because the system is nonlinear, run 4 was made to show

controller performance at other operating points. Run 4 started

490

48o470 --

_460 _

E

45o--

440 I ,,[ I 1 I I I I

0 " 100 200 300 400 500 600 700

Time, sec

Figure 8.--Tunnel temperature response for tunnel temperature setpoint

decrease from 490 to 450 *R with two compressors.

490 -- _

m"470 --

_ 460 --

E

_ 4so -

440 I 1 I I I I

0 1IX) 200 300 400 500 600

]]me, sec

Figure 9,--Tunnel temperature response for tunnel temperature setpoint

decrease from 490 to 450 *R with four damper valves.

520

510

5O0

_ 490

E 480-

470

D

m

m

460 I I I I I

0 100 200 300 400 500

lime,see

Figure lO.-- Tunnel temperature response for tunnel temperature setpoinl

decrease from 520 to 470 °R.

18

16

'_ 14

o.

_ to

8

6 , I

0 1O0 200 300 400 500 600

Time, see

Figure 1 [.--Accumulator pressure change for tunnel temperature setpoint

decrease from 520 to 470 *R.

12

11 --

_" 10

8

7 I

0 200 400 600 800 1000

"lime, see

Figure 12.--Accumulator pressure change for tunnel temperature setpoint

decrease from 520 to 470 *R with controller gain reduced by 50 percent.

from an initial operating point of 520 *R. At 80 sec the setpoint

was stepped from 520 to 470 °R. The tunnel temperature

response (fig. 10) showed a slight overshoot. Even though the

setpoint change was 10 ° larger for this run than for run 1,

the response is more than 140 sec faster because the required

change in cooling power is smaller at the higher temperatures.

One other observation is noteworthy. The higher tunnel

operating temperature generally raised the pressure and

temperature of the entire refrigeration system, increasing the

likelihood of the accumulator pressure limit being exceeded

during transients. Figure 11 shows the accumulator pressure.

It exceeds its 12 psia limit and briefly rises above 17 psia.
520

510

g 5oo

490

E 480

I--

470

460 I I I I

0 200 400 600 800 1000

Time, sec

Figure 13.--Tunnel temperature response for tunnel temperature setpoint

decrease from 520 to 470 *R with controller gain reduced by 50 percent.

520

_c 510

_5o0

_490

_- 480

470 I I

0 100 200 300 400 500

"lqme, sec

Figure 14.--Tunnel temperature response for tunnel temperature setpoint

ramped from 520 to 470 *R in 100 see.

460

455

g 4so

F440

435

0 103 2O0 300 400 5O0

Time, sec

Figure 15.--Tunnel temperature response for tunncJ temperature setpoJnt

decrease from 460 to 440 °R.

I

600

this facility is automated. The new accumulator pressure limit

will then be approximately 20 psia.

Run 6--Setpoint Ramp

In the previous runs all temperature setpoint changes were

step changes. To test the controller for a ramp setpoint change,

run 6 was made with the tunnel temperature setpoint ramped

from 520 to 480 °R in 100 sec. The tunnel temperature response

(fig. 14) is similar to a step setpoint change.

Run 7--Small Setpoint Change (Actual Tunnel Run

Comparison)

A small setpoint change was made from 460 to 440 *R at

80 sec. It takes 380 sec or 6.3 rain for the temperature to reach

steady state at its new operating point (fig. 15). This run was

compared with data from an actual run where the operator

controlled the tunnel temperature manually. The system

operator took 20 min to manually change the tunnel temperature from 460 to 440 *R. This is more than three times longer

than by automatic control.

Run 8--Heat Load Ramp

The tunnel fan speed is often changed during tunnel operation

to accommodate wind tunnel test requirements. Because

the fan is the major tunnel heat source, changing the fan speed

also changes the tunnel heat load. The effect of this heat

load change on the temperature control was studied by ramping

the heat load from 800 Btu/sec (at 100 sec) to 1500 Btu/sec

(at 200 see). The setpoint was held at 460 *R during the ramp.

The automatic controller was able to maintain the tunnel

temperature near its setpoint with essentially no temperature

change (fig. 16). Figure 17 shows the valve position change

460.2 [-.- /-- 800 Btu/sec

460.0 ___.'_ "'_- 1500 Btu/sec

I I I I I I

i_ 459.8

0 100 200 300 400 500 600

Time, SeC

Figure 16.--Tunnel temperature variation during a tunnel heat load increase

of 700 Btu/sec.

Run 5--Controller Gain Change

A lower controller gain is needed to keep the accumulator

pressure in run 4 below its limit. Consequently, run 4 was

repeated with the controller gain (limit on the pressure error

signal) lowered by 50 percent. The reduced gain kept the

accumulator pressure transient below the 12-psia limit

(fig. 12), but it also produced a slower temperature response

(fig. 13; about 340 sec slower than in run 4). The gain will

probably not have to be lowered, for this case, because a

refurbished set of compressors should be installed by the time

° a

I I

0 100 200 300 400 500

Time, sec

Figure 17.--Control valve position during a tunnel heat load increaseof

700 Btu/sec.
made by the controller in order to maintain the temperature

at its setpoint during the heat load ramp. The valve moved

from an initial position of approximately 2.4* to a final position of 4.9 °.

Run 9--Setpoint Increase

The general operating procedure for all tunnel runs is to

start at ambient conditions and then decrease the tunnel

temperature to the desired operating point. Therefore, all of

the computer runs presented thus far were for decreases in

the temperature setpoint. Occasionally, however, the tunnel

temperature needs to be increased to a new operating point.

Figure 18 shows such a computer:run where the temperature

setpoint is increased from 450 to 490 °R at 700 sec into the

run (run 9). The quality of the response is similar to the step

decreases shown in the previous runs. For this run it takes

690 sec for the temperature to go from 450 to 490 °R. There

is no overshoot. During this excursion the accumulator pressure transient moves away from the 12-psia limit. This is

typical for all runs where the tunnel temperature is increased.

Because the accumulator pressure is not a problem for these

runs, it is not examined when the tunnel temperature is

increased. Compressor surge, however, can be a problem for

large, rapid tunnel temperature increases. The problem was

investigated; but because the compressor surge line for the

present compressors is not well defined, the run results from

this investigation are not presented here. If compressor surgc

becomes a problem for the automated system, the controller

gain will have to be reduced for certain runs involving tunnel

temperature increases.

Thc response to a setpoint increase in the tunnel temperature

is often limited by the present configuration of the refrigeration

system. For this system, the control valve usually needs to

be operated near its closed position--a practice that restricts

any valve movement in the closed direction and, consequently,

limits the response for tunnel temperature increases. The valve

movement for run 9 is shown in figure 19. Prior to the setpoint

49O

480

F

470

i

E 460

1-

450

440

D

I I I I I

600 800 1000 1200 1400 1600

Time,see

Figure lB.--Tunnel temperature response for tunnel temperature setpoint

increase from 450 to 490 °R.

5

4

o3

1

0 I I I I I

600 800 1000 1200 1400 1600

"13me,sec

Figure 19.--Control valve position for tunnel temperature setpoint increase

from 450 to 490 °R.

increase, the valve position was 4.6*. As soon as the setpoint

increased, the valve nearly closed and remained so until the

tunnel temperature had almost reached the new setpoint value.

At that time, the valve moved to a final steady-state position

of 1.4 °.

Runs 10 to 13--Additional Runs With Setpoint Increases

Other runs tested different temperature setpoint increases

similar to that in run 9. The tunnel temperature response for

each of these runs was very satisfactory with essentially no

overshoot or oscillation as is shown in figure 20. The operating

conditions for these runs were similar to the previously

presented runs.

Small Setpoint Disturbances

The next set of runs were made to further demonstrate the

robustness of the controller and to show the effect of various

parameters on closed-loop performance. For these runs the

setpoint was stepped from 460 to 440 °R. Run 7 will be

considered as the reference or nominal case, and all parametric

vartattons of the controller and the system will be compared

to figure 15 of run 7.

Controller Variation Runs

Figure 21 shows the effect of two important controller

settings on the temperature response. First, the controller

sampling rate was reduced from 2 samples per sec to 1 sample

per sec (the limit on the error signal was doubled to offset

the gain change caused by the sampling rate). The sampling

rate change showed virtually no effect on the system. Next,

the limiter output of the error signal was changed from its

nominal value of 8 to a value of 12 (see fig. 3). The temperature shows no overshoot and reaches its setpoint value

about 80 sec sooner and its steady-state value almost 150 sec

sooner than for the nominal gain setting.
455

450

445

o_

I

460

455

450

445

440

600 8OO

I 1 I (a)l

490

480 --

470

460

450

I I I (°)1

I I I (b)l 440 I (d)l

I000 1200 1400 1600 600 1400 1600

I I I

800 1000 1200

Time, see

(a) Setpoint increase from 440 to 480 *R at nominal operating conditions. (c) Setpoint increase from 440 to 460 *R with three compressors and a tunnel

(b) Setpoint increase from 440 to 460 °R with controller gain at 150 percent, heat load of 2000 Btu/sec.

(d) Setpoint increase from 450 to 490 °R with tunnel heat load at 2('100Btu/sec.

Figure 20.--Tunnel temperature response for various tunnel temperature setpoint increases.

System Variation Runs

Two system parameters which were thought to be important,

and yet whose values are very uncertain, are the evaporation

rate in the flash cooler and the heat transfer coefficient in the

tunnel heat exchanger. A large part of the heat transfer

coefficient uncertainty comes from the approximate calculation

of the fluid quality in the heat exchanger. Figure 22 shows

the temperature response for a nominal value of the

evaporation rate constant, KVE, and for a 100 percent increase

of KVE. The increase had little effect on the temperature

response. The temperature response increased slightly when

the heat transfer coefficient was changed to twice its nominal

value, but the results are not presented here.

Heat Load Variation Runs

The tunnel heat load is mostlY a function of tunnel fan speed

(rpm) and, to some extent, the outside ambient temperature.

Figure 23 shows the controller performance for different tunnel

heat loads--1200 (nominal), 2000, and 800 Btu/sec. As would

be expected, the lowest heat load shows the best response.

460

450

I--

430

Controller setting

Nominal sampling rate and gain

50-percent sampling rate 460

_ _ (1 sample/sec); nominal gain

"_ 150-percent gain; nominal 455

"__"_,_ sampling rate O: o

" ... ff 450

440

I I I I I I

0 1O0 200 300 400 500 600 435

Time, sec

Figure 2l.--Tunnel temperature response for various controller settings

(sampling rate and gain).

--"--_ Ev:POomr:ti:nrate

I I I I I I

0 100 200 300 400 500 600

"rime, seE:

Figure 22.--Tunnel temperature response to variations in evaporation rate.
Tunnel

heatload,

460 "_ Btu/sec

F 455 "_" _'._.,_ 20001200 (nominal)

450 -__'_ , 800

440

435 I I I I I I

0 1O0 200 300 400 500 600

"lqme,sec

Figure 23.--Tunnel temperatureresponse for various tunnel heat loads.

Compressor Variation Runs

Because of the uncertainty in the compressor characteristic

curve, and the likelihood that a refurbished compressor will

be installed in the system, a control run was made where the

slope of the current compressor characteristic curve was

increased by 100 percent (values for compressor head were

doubled). The temperature response with the new compressor

slope is shown in figure 24. The response shows no overshoot.

The temperature reaches its steady state approximately 30 sec

sooner than for the run with the nominal compressor characteristic curve.

Noise Injection

The controller was also tested with Gaussian noise added

to the control signals of the flash cooler and to the tunnel

temperature. The added noise was considerably higher than

can ever be expected in the actual instrumentation. Since its

effect on the controller was essentially negligible, the results

are not presented here.

460

F 455

450

440

435

Slopeof

compressor

m _ characteristic

%_,,_.. Curve

_ Nominal

.... 2 x nominal

I I I I I

0 100 200 300 400 500 600

"lime, SeC

Figure 24.--Tunnel temperature response to a change in compressor

characteristic curve.

Concluding Remarks

Although the Icing Research Tunnel (IRT) was designed to

operate at temperatures below 440 °R, most tunnel runs are

currently made above 440 *R. Consequently, operating constraints are frequently encountered. These constraints are

(1) Operating constraint caused by compressor surge

(2) Upper limit of compressor inlet (accumulator) pressure

of 12 psia

(3) Upper limit of condenser pressure of 125 psia

(4) Upper limit of compressor motor current of 300 A

The most frequently encountered operating constraint

appears to be the upper limit of the compressor inlet pressure.

To avoid this constraint, an additional compressor unit is

brought on line. This allows the control valves to operate at

a more closed position, thereby causing a larger pressure drop

and, consequently, a lower compressor inlet pressure. Since

this practice brings more compressors on line than would

otherwise be needed, it reduces the efficiency of the operation,

and frequently steam must be injected into the tunnel to

maintain the desired tunnel temperature. The compressor inlet

pressure also poses a problem for the automatic temperature

control. The controller must be designed so that this pressure

constraint is not exceeded during control transients.

The primary incentive for adding an automatic temperature

control is to make more efficient use of the tunnel run time.

Consequently, the automatic temperature control was designed

to reach the desired operating point as quickly as possible

without creating excessive transients that would exceed system

constraints. The objective was to ramp the tunnel temperature

to its desired value with a constant rate and little overshoot.

For the runs that were made in this study, the control design

met this objective. Study results showed that the automatic

temperature controller can change the tunnel temperature in

less than half the time needed by manual control. We compared

a computer run with an actual, manually controlled tunnel run.

For the computer run, the automatic control lowered the tunnel

temperature from 460 to 440 °R in only 6.3 min, whereas

for the actual run with manual control, 20 rain were needed

to make the same change. The automatic controller, however,

frequently caused a transient, excessive compressor inlet pressure when the controller gain was set too high.

System constraints could be avoided if automatic control

were used for selected runs only--when there is no danger

of exceeding system operating limits. The alternative would

be to use automatic control at all times but with a low controller

gain. This would avoid the large transients which exceed the

operating limits. However, with a low gain, the system would

respond slowly, and the tunnel run time would not be

significantly reduced compared with manual operation. The

only benefit of using an automatic control with the low gain

option, would be to free the system operator from the task

of manually controlling the tunnel temperature.

10
In theinterestof savingtunnelruntimeandmakingthe

compressor operationmoreefficient,automatictemperature

controlshouldbeaddedtothefacility,andthefacilityshould

bemodifiedto allowa highercompressor inletpressure.

Currentlythecompressors aebeingoverhauledtomakethem

moresuitableforhighertunneltemperatureruns.Theoverhauledcompressors willpermitoperationatasuctionheader

(accumulator) pessureofupto20psia.Nomajorchangein

thecontrolshouldbe requiredfor operationwith the

overhauledcompressors.

Theautomaticcontrolstudypresentedheredoesnotaddress

anautomaticcontroldesignforstartupandshutdownorany

decision-making capabilitieswherebythecomputer wouldtake

thenecessary actiontoavoidthevariousoperatingconstraints.

Thesedecisionsandtaskswill stillhavetobeperformedby

thesystemoperator.It isrecommended, however,that,after

successfullyimplementingthisinitialphaseof theautomatic

control,automationoftheseremainingtasksshouldalsobe

considered. Thepresentcomputermodelwasmadewith

sufficient detailtoallowtheseadditional controlstudiestobe

performedwithminimalchanges.

LewisResearchCenter

NationalAeronauticsandSpaceAdministration

Cleveland, Ohio,August13,1990

11
Appendix A

Computer Simulation Equations of the

Refrigeration Cycle

The refrigeration cycle for the compressor loop is depicted in

figure 25. Saturated gas in the flash cooler (evaporator) moves

through the control valves to the accumulator, or compressor

inlet. The gas is then compressed to the superheated region

at the compressor outlet. From the compressor outlet the gas

flows into the condenser region, where heat is removed and

the gas condenses to a saturated liquid. The liquid then

flows into the economizer region (fig. 25 depicts a two-stage

economizer), where it loses more heat at a reduced pressure

and temperature. From there it flows back to the flash cooler.

A diagram of the computer model is shown in figure 26.

Basic Computer Model Equations

The following basic fluid flow and energy equations are used

repeatedly throughout the simulation. The equations are based

on a control volume concept of finite difference equations,

where i and o represent flow into and out of the control

volume, respectively.

Continuity equation

dM

--= w,.- Wo (1)

dt

Energy equation

dE

-- = w,_ - w,_/,,+ a (2)

(It

where the total enthalpy E is defined as the mass M times the

enthalpy H, or

E=MH

IRT Refrigeration System

Cooling tower water

! Tw I Tunnel air

I IQco_ C°mpressor I T"

Condenser W p h p J

l D T I-- CO c°l I- rci Qa -con --con I_ 1 _ , ?

I Tc°l I To,

Wc°n / _ Heat exchanger

,wG..__ I Px I

i T- I J I .x I

Economizer i,_ c, I Tx

/¢ e,_ _ Accumulator

[ T I (suction

Damper _ header)

valves---_ _ wac

\_------_ Flash

/" P'G,e I G,e_Gooler

Wec __._( WG.e _t _= WG.x

WL,x

Freon pump _ Wp

Figure 26--Simulation diagram.

and Q represents external heat conducted into or out of the

control volume. For convective heat transfer,

Q = hS( Tn.id - Twa,) (3)

where

h heat transfer coefficient

S heat transfer area

Since dH = cp dT, and if the term dM/dt can be assumed to

be negligible, an alternate form of equation (2) is

ft..

Condenser __

region_

Economizer I J /

region _Of I Evaporator/ J

/ Accumulator

(ae)

Enthalpy

Figure 25--Refrigeration cycle.

Compressor

outlet

(co)

Gas

dT WiT' - W°T° + Q.

Cp (2a)

dt M

Perfect gas law

OHfice equation

P = pRT

_/ 2g,P, (Pi - Po) W = 0.6A _f

(4)

(5)

12
Evaporation equation l

W = KVE(P_t - Pc;)

where

KVE = KrA_

(6)

The preceding equations are applied in the mathematical

description of the system components presented next.

Flash Cooler Equations (Evaporator)

Energy equation.--From the energy equation (2), we have

the following differential equation for the flash cooler

(evaporator) liquid, where N,. accounts for the number of

compressor units in operation:

d(EL,,,)

dt

- N,.Wt.e,HL.,,,.+ WL,xHL,.,.

- W,,HL._- Wc,,,Hv._

Since Wp = WL,x + W6, x and HL,, = HL,e because the

pressure of the freon in the heat exchanger and the flash cooler

are essentially the same, we can simplify the above equation

as follows:

d(El.,,,)

dt

--NcWL,ecHL,ec- WG,eHv, e -- WG,xHL, e

Likewise, the energy equation for the flash cooler gas is

d(Ec,,.)

- WG,xH6, x - W.cHG, _ + W_,eHv.,.

dt

Ev, c

I-Iv, d --

MG,e

From the saturation curve on the pressure-enthalpy (PH)

diagram for freon (fig. 25), the freon liquid temperature is

given by

TL,e= U(HL,_)

1See Derivation of Evaporation Equation, p. 19.

Likewise, the freon gas temperature can be obtained from the

saturation curve of the PH diagram

TG.e = f(HG,e)

Also, the enthalpy of the evaporating frcon can be obtained

from the freon saturation curve:

kit.,,. = f ( TL,,,)

And again, since the pressure of the freon in the heat exchanger

and the flash cooler are essentially the same,

HG,x = Hv,,,

Continuity equation.--From the continuity equation (!), we

have for the liquid

d(mL.,)

-wt.,,,.+wL.._-w_._-wp dt

and for the gas we have

d(M_.e)

-wo,.,+w_,_-w.,.

dt

Equation ofstate.--From the definition of density we have

for the density of the gas PG,e = MG.e/V6,,,, and from the

density of the liquid, VL._ = MLx/pL_. The flash cooler

consists of both gaseous and liquid freon. Therefore the total

flash cooler volume V_,= VG,_ + VL,_. Using these three

relations, we can now solve for the density of the flash cooler

gas as follows:

mG,e

PG, e --

ML,e

Ve---

PL,e

From the perfect gas law we can solve for the freon gas

pressure

PG,_ = ZPG,eRTG,e

The density of the freon liquid varies as a function of the

temperature as follows:

PL,e = 138.84 - O. 105TL.e

Evaporation rate.--Equation (6) is used to solve for the

evaporation rate of freon in the flash cooler:

Wo,e = KVE,, (P_,,,. - Pa.,,)

13
where

/ g,.

KVE e = KrAe "_ [

2 _rR TL,e

The freon saturation pressure Psat,e can be obtained from the

saturation curve

Ps.,,e=f(TL,_)

Heat Exchanger Equations

Energy equation for freon.--The flow throughout the heat

exchanger loop is assumed to be equal to the pump flow in

the loop. The energy equation for the enthalpy at the heat

exchanger exit can then be written as follows:

d(EO

- Wp(HLe - Hx) + Q.x

dt

E_

M_

where Me is the mass of the fluid inside the heat exchanger

and Wp is the pump flow rate. The heat flow from the heat

exchanger wall into the freon liquid, Qx, is shown in the

following equation:

Ox = hxS,(Tm -- TL,x)

Since freon in the heat exchanger is assumed to be at the

saturation pressure of the flash cooler, we have

TL,x = TL,e PG,x = PG,e HG,x = Hv, e

In a two-phase system, X is called the quality of the mixture

and is defined as the weight fraction of the material in the vapor

phase, or

M_

X=--

M

From the definition of X, we can likewise define the enthalpy

of the gas and liquid mixture Hx as

H_, = (1 -X)HL, _ + XHo. x

Rearranging the above equation we can solve for the quality

of the fluid in the heat exchanger as follows:

XX

__ HL, X

where

zxn_=n_,_-nL,x

Let us now solve for the mass of the two-phase fluid inside

the heat exchanger. Assume that the mass of the gas in the

heat exchanger increases linearly as the fluid flows through

the heat exchanger. We can then express the differential mass

along the heat exchanger as follows:

d(M a) = pGA6 de

d(ML) = PL(Ax -- AG)de

where

AG gas flow area

Ax total flow area

de differential length

Since it can be assumed that the gas density is constant along

the heat exchanger, we can state that the cross-sectional flow

area of the gas for the heat exchanger of length L varies linearly

from zero at the entrance, to some value AG, o at the exit.

Then at any length f of the heat exchanger,

Now the total mass of the gas in the heat exchanger is

MG L= _ (dM 6) = PGA6 de

.0

PGAG o _ L

- ' J e dg L o

A L

Similarly the mass of the liquid in the heat exchanger is

The total mass of the fluid in the heat exchanger is

Mx = ML + MG = PLAx L + AG,o (L) _ (PG -- OL)

From the definition of quality, the quality at the heat exchanger

outlet is

Xo _

dMG,o PGAG,o

dMo,o + dML,o PGAG,o + PL(Ax -- AG,o)

14
Solving for An, o we have

AG, o

XoPLAx

Pc( 1 - Xo) + XoPL

After substituting for AG,o in the previous equation, the mass

of freon in the heat exchanger as a function of quality is

Mx _

pc(1 - xo) + XopL

where

Vx = AxL

The following heat transfer coefficient was used for the freon

side of the heat exchanger (ref. 1):

/k "_//W,D N_°'75 I_.c Xx(AHx_l°375

hx = 0.02251 '_//-=-e-_- i (J)

Heat transfer to the fluid is assumed negligible as it flows from

the flash cooler to the heat exchanger. Therefore,

nt,x _ nt,e

_XH_= aHe

from the definition of quality we can solve for the gas flow rate:

Wax = x_w_

Since the pump flow is the total heat exchanger flow, we have

for the liquid flow

Energy equation for the heat exchanger wall.--Consider

the energy balance for the heat exchanger wall. Heat Q_

flows from the tunnel air into the wall and heat Q_ flows out

of the wall into the freon heat exchanger fluid. The energy

equation (2a), has the following form for the wall:

: (6° -

dt M_%,,.

the equation for the heat flowing from the tunnel air into the

wall can be written as follows:

where

the following heat transfer coefficient (ref. 2) was used for

the air side of the heat exchanger:

ha 0.1376 ka (WoDa_ °'6_

= Do

Energy equation for the tunnel air.--The tunnel air is

divided into two control volumes. One volume V_,x consists

of the heat exchanger portion of the tunnel air. The other

volume V_j consists of the remaining tunnel air which

includes the tunnel fan where the heat is generated; Taj is the

air temperature at the heat exchanger entrance, and Ta,x is the

air temperature at the heat exchanger exit. The flow rate in

the tunnel circuit, Wa, is assumed to be the same in both

control volumes. The energy equation for the heat exchanger

control volume can be written as follows:

aa

Wa(Toj- T.,_) -

d ( Ta,_) ep,o

dt Ma, x

where

Ma, x = paVa,x

likewise the energy equation for the fan portion of the control

volume can be written as follows:

Cp,a

at M.,t

where

Moj = p.Voj

The heat rate generated by the fan Qf depends on the fan

speed.

Pump Flow Loop Equations

Initially this part of the simulation was more detailed but

was later simplified because of some occasional computational

problems and because it was found that a small variation in

pump flow had little effect on the system. The pump flow was

therefore made constant, where

Wp = 150

15
Accumulator Equations

Continuity equation and equation of state.--From the

continuity equation we have

dt V,,,,

The pressure in the accumulator can now be obtained from

the perfect gas law

Pac = P,,c ZRT.,.

Orifice equation.--The orifice equation is used to solve for

the flow through each control valve unit, or

/

Wv 0.6Av._ ] 2g,Po,_(Pa,_ - P.,.)

ZRT.,

where T.,., the temperature in the accumulator, is assumed

to be equal to the temperature of the freon gas in the flash

cooler. The effective control valve flow area Av is shown in

figure 27. The flow into the accumulator is

W,,c = NvWv

'*'here Nv is the number of damper valve units in operation.

Energy equations.--The energy equation for the accumulator is

where

_I('

N,W.

d(E,,,)

d!

-- = (W,,Ha, e - N,.WciII_,, )

flow into the accumulator

total flow leaving the accumulator

100

8o

>

2O

I I I [ I

20 40 60 80 100

Effectiveflowarea, percent

Figure 27 --Control valve area

EUC

, --

Pa,Va,.

T.,. =f(H,, c)

Compressor Equations

Compressor characteristic curve.--The compressor characteristic curve shown in figure 28 was obtained from a limited

amount of available tunnel run data. The ordinate represents

the compressor head in thousands of feet and the abscissa is

the compressor volumetric flow rate in thousands of cubic feet

per minute.

Compressor flow equations. --The equations are

HEAD=ZRT"i_¢(_7-_- I)[ \P,-i/ -1

Q = f(HEAD)

QPoc

Wci _-- --

60

The compressor outlet flow is equal to the compressor inlet

flow plus the vapor flow from the economizer, or

W,.o = W,., + Wo,_c

Line pressure drops from the accumulator to the compressor

inlet and from the compressor outlet to the condenser are

neglected, or

Pci = Pac

PCO --_- PC01

There is also no heat transfer from the accumulator up to the

compressor inlet, or

Tel = Tac

18x103

16 --

12

0 1 2 3 4 5x103

Flowrate,ft3/sec

Figure 28.--Compressor characteristic curve; speed, 6650 rpm.

16
Compressor energy equations.--The compressor is divided

into two segments. All of the economizer gas is assumed to

discharge into the compressor at the entrance of segment 2.

The equation below is the temperature rise of the fluid for

compressor segment 1:

\P. /

Since dHactual = 1/rta(dHisentropic ) and since dH = Cp dT, we

have for the enthalpy

\ _./

The vapor from the economizer with enthalpy Hv, e,. is

returned to the compressor and mixes with the compressor

fluid of segment 1. From the energy equation, we can express

the enthalpy of the mixture as follows:

Hc2 w

W,.iHcl + WGx,Hv.ec

WCO

or the temperature of the mixture

Tc2 --_

w,.iL_ + Wc,_cTL,e_

Woo

Fluid with enthalpy H,.2 and temperature T¢2enters the second

segment of the compressor and rises to a temperature 7",.o at

the compressor exit, or

L,o = L,2 (Pco -- "*

\ Pec,d /

The enthalpy at the compressor exit then is

Hen = Hc2 + (_a I(Tco--To2)

Condenser Equations

Energy equations.--The energy equation for the condenser

can be written as follows:

where the flow into the condenser is assumed to be the flow

out of the compressor W,.o. Also the enthalpy H,, out of the

compressor is assumed to be the same as the enthalpy flowing

into the condenser. The variables W¢on and HL,con are,

respectively, the flow and the enthalpy of the liquid freon

leaving the condenser.

By neglecting the heat capacity of the condenser piping, the

heat rate removed from the condenser by the water, Q_on, can

be written as follows:

0con= hcon&on(TL,_o. - Tw)

The average condenser water temperature T,, is calculated as

follows:

T,,.= 0.5(Tw_+ rw,,)

The heat transfer coefficient for the condenser is too complex

to be calculated analytically. An overall heat transfer coefficient

hcon,0 was calculated based on results of known system

operating conditions. The 0 assigned to variables represents

tunnel run d_ita which was obtained either directly or calculated from data. This data was used to calculate hcon,0.

The equations used in the calculation hcon,0 are based on

the steady-state part of the energy equation (2) and also

equation (3), or

Qcon,0= hcon,oScon(TL,con,O- T.,,o)

But in steady state the heat rejected at the condenser is equal

to the heat added by the compressor plus the heat added in

the tunnel, or

0 o°,o= o_,,o+ 0 ,o: W on,Omco,O - + Oj:o

solving for h¢on.0 we have

hcon,o

Q.f,o + (Hc,,,o - H6x,o)W¢o_,O

Soon(TL,¢o.,O- Tw,o)

A heat transfer coefficient was used which is a function of

the cube root of condenser flow, or

1,, td r_rl 0. 333

ncon.O JXh" con,O

Using the above equation to solve for Kh gives

d ( EL xon)

clt

- Wcon(Ho,con - HLxon) -- Qcon

EL,coil

nt,con --

Mz,con

hen.,0

gh = II_" 0.333

rr con,0

The value of Kh calculated above from tunnel run data is now

used to calculate hco n for al[ other operating conditions, or

17
hcon -_- vlXhrr uz 0.333 con ' Or by eliminating Kh we can write the heat

transfer coefficient in the condenser as follows:

hcon = hcono ( Wc°n ) °333

' \W_on,Oi

The freon leaving the condenser is assumed to be saturated

liquid. We can therefore obtain the corresponding temperature

of the liquid from the saturation curve for freon, or

TL,co.= f(/-/L,¢o.)

The energy equation for the water leaving the condenser is

d(T,.,)

Qcoll

w., (T,,,i- T,,o) +--

cp,w

dt V,,O.,

where W., is the water flow rate through the condenser and

Two is the outlet water temperature for the condenser. The

inlet water temperature Twi is assumed to be constant.

Continuity equation.--From the continuity equation

d(M_o.)

dt

= W,.,,- W_o.

where Moo. is the total mass of freon inside the condenser and

W_,,n is the liquid freon leaving the condenser (assumed equal

to the freon condensation rate).

The relative volume occupied by the gas and liquid inside

the condenser is assumed to remain constant (i.e., FL,con is

constant). The mass of the gas and the liquid freon inside the

condenser can then be obtained from the following two

equations:

eL,con ----- l/'L,con PL

MG,con _ Mcon - ML,con

Freon condensation rate.--Equation (6) is used to solve for

the condensation rate of freon in the condenser, or

W_on= XVE_on(Pco.- P._,._o,)

where

gc KVEcon = KrAcon 27rRTL,con

Equation ofstate.--From the definition of density we can

obtain the density of the gas as follows:

MG,col_

PG,con =

VG,con

From the perfect gas law, we can now solve for the pressure

of the freon inside the condenser, or

/°con --"PG.conZRTG,con

_.t,co. is the saturation pressure of the freon in the condenser.

It can be obtained from the freon saturation curve of the PH

diagram:

e,.,._o° = f(TL,_o.)

Economizer equations

The system uses two economizer stages where part of the fre,on

liquid is flashed to gas and returned to the inlet of compressor

stages 2 and 3. For simplicity, these will be approximated in

the simulation by one economizer only. Because the fluid

volumes in the economizers are relatively small, the transients

in the economizer are neglected.

Flow equation.--The economizer gas is returned to the

center stage of the compressor. The average pressure at the

center stage is estimated as follows, where K_,t is a constant:

P_,.,d = KeaPco + ( 1 - K_a) P._

The frictional loss of the economizer gas discharge flow is

assumed to be negligible. Consequently, the pressure P_,.

inside the economizer is assumed to be equal to the discharge

pressure at the compressor Pet,d, or

Pec _-- Pec,d

Since the fluid in the economizer is at saturation, it is assumed

that the economizer saturation pressure P_t,.. is equal to P_,,:

Psal,ec = Pec

Since economizer transients are neglected, the steady-state

continuity equation results in

Energy equation.--From the steady-state energy equation,

we can write for the economizer

W_,,.nL,.,n-- Wc,..n_,._ - WL,,.,HL,_= 0

18
Substitutingthepreviousexpressionfor WL,.,, and after

rearranging, the freon vapor returning to the compressor is

W_.o°(HL,co. - I-IL,,,,)

HG,e,. -- HL,ec

The fluid inside the economizer is assumed to be in the

saturated region. The freon temperature and the freon enthalpies of the liquid and gas can then be obtained from the

saturation curves, or

TL,,,,.= f(P_at,,,,.)

HL.,,c = f(TL.,.,.)

H_;,,,,. = f(Tl..e,.)

Derivation of Evaporation Equation (from ref. 3)

A nonrigorous derivation of the equation used in calculating

the evaporation flow is given here. Because of the complexity

of the molecular motion, this equation cannot give good

quantitative results. The equation is used mainly to account

for the transient dynamics of evaporation in the flash cooler

and the condenser. According to gas kinetic theory the number

of molecules striking a unit area per unit time is

where

nlV number of molecules per volume

C,, mean velocity of the molecules

The mass of the molecules striking a surface area A per unit

time can be expressed as follows:

where

Na Avogadro's number

m mass of molecule = mw/Na

mw molecular weight

By expressing the gas density p as follows,

M lllll

V V

we can now rewrite the mass flow rate W as

/ c,,",

":

From gas kinetic theory, the kinetic energy of a gas molecule is

where T is the temperature and k_ is the Boltzmann constant.

From the perfect gas law PV = nk_T," kinetic energy KE is

then equal to

3pV

and from the definition of kinetic energy we have

Then equating the two kinetic energy equations gives

(3/2)P(V/n) = me (2g,.), and substituting for n (reV) =

M/V = p = P/ (RT) and rearranging we have

C = _if--_3g,RT

The mean velocity 6". is related to the root mean square

velocity C as follows:

or

Now since W= Ap(C,/4)=A(PIRIT)(C,,/4) and after

substituting for C,, and rearranging we have for the mass

flow rate

W = PA'% I _"

27rRT

19
The preceding equation describes the ideal gas condensation

rate. It assumes that all of the molecules that strike the surface

of the liquid will condense. In actuality some of the molecules

will be reflected back. To account for this, the equation is

modified as follows:

/

g,. W = KrAP'_I

27rRT

where the reflection coefficient Kr is the fraction of the

molecules that hit the surface and are absorbed by the liquid.

Now suppose we have a closed vessel where the liquid resides.

Then at equilibrium the condensation rate Woon is equal to

the evaporation rate Wev. Let us suppose further that the

evaporation flow rate can be expressed similarly except that

T is the temperature of the liquid and P is the saturation

pressure of the liquid. We can now express the net flow

between the gas and the liquid as follows:

w = wev - Woo.

_/ gc KrAPc_ gc

= KrAP_a , 27rRTL 2toRT c

Since the temperature of the gas T6 can be assumed to be

equal to the temperature of the liquid TL, we then have

W= KrA_2_TL (Psat--PG)

2O
A

Av

&

C

c.

ce

D

de

e

er

FRco_

f(HEAD)

G

g

gc

H

Hv

HEAD

h

J

Ke,d

KE

Kr

KS

KT

k

kB

L

f

M

Mk

?n

mw

Uc

No

&,

Na

n

Pec,d

Appendix B

Symbols

flow area, ft 2 ePG

total valve area, ft2 Psat

freon flow area in heat exchanger P

root mean square velocity, fi/sec Q

mean velocity, fi/sec

specific heat, Btu/Ibm-*R R

diameter, ft S

differential length T

error t

error (limiter output) V

fraction of condenser volume occupied by gas V,,,f

compressor characteristic curve Va,r

controller gain V_,.

gravitational constant, ft/sec 2 Vx

conversion constant, 32.2 lbm-ft/lbf-sec 2 W

enthalpy, Btu/lbm X

enthalpy of saturated vapor, Btu/Ibm Z

ft-lbf/lbm AH

heat transfer coefficient, Btu/sec-fi2-°R "t'

conversion constant, 778 ft-lbf/Btu rta

flash cooler flow discharge constant rb

friction constant #

kinetic energy 0

fraction of molecules absorbed by liquid

controller constant

controller gain constant a

controller gain constant ac

thermal conductivity, Btu/sec-ft-°R c

Boltzmann constant ci

length, ft co

variable length of heat exchanger, ft con

mass, Ibm cl

controller output c2

mass of molecule, mw/Na d

molecular weight e

number of compressor units in operation ec

pump speed, rpm ev

damper valve units f

Avogadro number G

number of molecules i

economizer discharge pressure, psf k-n

freon gas pressure, psf

saturation pressure, psf

pressure, psf

volumetric flow rate, ft3/min

heat flow rate, Btu/sec

freon gas constant, 12.776 ft-lbf/lbm-°R

surface area, ft 2

temperature, °R

time, sec

volume, ft 3

tunnel air volume outside of heat exchanger, fix

total tunnel air volume, ft 3

tunnel air volume assigned to heat exchanger, fi3

freon volume in heat exchanger, ft 3

flow rate, lbm/sec

quality, dimensionless

gas compressibility factor, dimensionless

heat of vaporization, Btu/lbm

specific heat ratio, dimensionless

adiabatic efficiency

compressor efficiency

viscosity, lbm/ft-sec

density, lbm/ft 3

Subscripts:

air; adiabatic

accumulator

compressor

compressor inlet

compressor outlet

condenser

compressor segment 1

compressor segment 2

discharge

flash cooler (evaporator)

economizer

evaporator

fan

gas

inlet

(k-n) th sampling constant

21
L

m

o

P

sat

V

V

liquid

heat exchanger metal

outlet

pump

saturation

valve

vapor

_¢_.,

wi

WO

X

0

water

water in

water out

heat exchanger

tunnel run data or calculated from tunnel

run data

22
References

1. Airman, M.; Norris, R.H.; and Staub, F.W.: Local and Average HeatTransfer and Pressure-Drop for Refrigerants Evaporating in Horizontal

Tubes. ASME Trans.--J. Heat Transfer, vol. 82, Ser. C, no. 3, Aug.

1960, pp. 189-198.

2. McAdams, W.H.: Heat Transmission. Third ed. McGraw-Hill, 1954,

pp. 272-273.

3. Nesmeyanov, A.N.: Vapour Pressure ofthe Elements. Chapter 1, Academic

Press, 1963, pp. 3-119.

23
National Aeronautics and Report Documentation Page

Space Administration

1. Report No. 2. Government Accession No.

NASA TM-4257

4, Title and Subtitle

Automatic Control Study of the Icing Research Tunnel Refrigeration System

7. Author(s)

Arthur W. Kieffer and Ronald H. Seeder

9. Performing Organization Name and Address

National Aeronautics and Space Administration

Lewis Research Center

Cleveland, Ohio 44135-3191

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Washington, D.C. 20546-0001

3. Recipient's Catalog No.

5. Report Date

February 1991

6. Performing Organization Code

8. Performing Organization Report No,

E-5588

10, Work Unit No.

505-62-3B

11, Contract or Grant No,

13. Type of Report and Period Covered

Technical Memorandum

14. Sponsoring Agency Code

15. Supplementary Notes

16, Abstract

The Icing Research Tunnel (IRT) at the NASA Lewis Research Center is a subsonic, closed-return atmospheric

tunnel. The tunnel includes a heat exchanger and a refrigeration plant to achieve the desired air temperature and

a spray system to generate the type of icing conditions that would be encountered by aircraft. At the present

time, the tunnel air temperature is controlled by manual adjustment of freon refrigerant flow control valves. An

upgrade of this facility calls for these control valves to be adjusted by an automatic controller. This report

discusses the digital computer simulation of the IRT refrigeration plant and the automatic controller that was used

in the simulation.

17. Key Words (Suggested by Author(s))

Wind tunnel refrigeration system

Automatic control study

Two-phase fluid

Digital computer simulation

18. Distribution Statement

Unclassified - Unlimited

Subject Categories 66 and 31

19. Security Classif. (of this report) 20, Security Classif. (of this page)

Unclassified Unclassified

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