ANALYSIS OF FLUID AND HEAT FLOWS IN A CLOSED CYCLE CIRCULATOR FOR HIGH ENERGY PULSED LASERS

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ANALYSIS OF FLUID AND HEAT FLOWS IN A

CLOSED CYCLE CIRCULATOR FOR HIGH

ENERGY PULSED LASERS

C. Shih, C. Cason

To cite this version:

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JOURNAL DE PHYSIQUE CoZZoque C9, suppzdment a u n O 1 l , Tome 41, novembre 1980, page C9-343

ANALYSIS OF F L U I D AND HEAT FLOWS

I N A CLOSED CYCLE CIRCULATOR

FOR H I G H ENERGY PULSED LASERS

C.C. Shih and C.

aso on*.

.University o f AZabama i n HuntsviZZe, H u n t s u i l l e , Alabama 35899, U. S. A..

Army D i r e c t e d Energy D i r e c t o r a t e ,

U.

S. Army

MissiZe

Cornand, R e d s t o n e A r s e n a l , Alabama 35809, U. S. A.

.

RQsum6.- Un systzme en reduction B circulation de gaz pour laser a 6td conqu et fabriqu6 pour d6ve-

lopper les donnges technologiques de base concernant les applications du maniement thermique d'un cycle ferm6. Le projet choisi, disposant de bons instruments de contr6le automatique et d'un large champ de fonctionnement, dtait bas6 sur le besoin de faire connartre les donndes et informations de

fabrication ndcessaires pour permettre de passer

P

de vastes systsmes de faible poids qui peuvent

&tre ngcessaires pour les lasers de grande puissance. Des modsles de graduation th6orique sont dgve- lopp6s pour le flux des gaz remis en circulation, y compris les fionctions d'dchangeur de tempdrature

pour d6velopper et maintenir l'dquilibre de chaleur B la fois pour les op6rations transitoires et

pour les opdrations fixes. Ce papier pr6sente Lgalement les rdsultats de prdc6dentes expsrimenta- tions men6es pour vgrifier l'utilitd des modsles de graduation.

Abstract.- A small scale laser gas circulating system was designed and fabricated to develop the technology data base for closed cycle thermal management applications. The chosen design, having good instrumentation and a wide performance range, was based on the need to develop the data and enginee- ring information required to permit scaling to large light weight systems that may be required for high power lasers. Theoretical scaling models are developed for the recirculating gas flow, including the functions of the heat exchangers to develop and maintain the heat balance for both transient and steady state operation. This paper also presents the results of early experiments conducted to verify the usefulness of the scaling models.

INTRODUCTION

High power gas lasers designed for long run-

ning times require a closed cycle circulator for 'a

minimum weight system. Thermal problems result

because about 80% of the input electrical energy

used to excite a C02 laser gas mixture is convert-

ed into thermal energy. This resultant heat must

be removed from the laser gas before it may be

efficiently excited again.

A

closed cycle cir-

culator equipped with heat exchangers presents

new technical problems not found in open cycle ga's

laser systems because of the transients in the heat

balance that occurs during start-up and during

turn-off of the input electrical power.

When it became apparent that long laser run

times would be of possible interest, the authors

proposed a plan[11 to develop a Closed Cycle Cir-

culator (CCC) to develop the technology data base

for future designs. The plan required a CCC to be

designed for various operating conditions to ex-

perimentally investigate the following: fluid and

thermal characteristics of recCrEulating laser gas

flow in steady and transient states under pulsed

energy loading, capability of input power loading,

efficiency of laser level pumping, capacity of

acoustic attenuating and performance of heat ex-

changer cooling. The CCC project was expected to

provide the experimental data for comparison with

predictions of the above processes by mathematical

models-for their verif

m.

The purpose of this paper is to report the in-

vestigation of fluid and thermal characteristics

of recirculating gas flow and heat exchanger per-

formance. Various operating conditions were

chosen to understand scalability to large cir-

culators. Emphasis in this paper was placed on

the analysis of the heat exchanger performance

and the recirculating, laser-gas flow.

23

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c9-344 JOURNAL DE PHYSIQUE

CIRCULATOR SYSTEMS DESCRIPTION

AND

SPECIFICATIONS

The circulator system is shown schematically

in Figure 1 and consists of the following major

components: a 150 horse power motor driven com-

pressor; a diverter valve and

4

inch (0.102 m)

by-pass to permit varying flow rates; a compressor

exit heat exchanger; a Daniel flow meter; a cavity

inlet heat exchanger; a laser cavity; acoustic

attenuators upstream and downstream of the cavity;

a compressor inlet heat exchanger; a pulsed

electron beam gun and laser gas excitation power

modulator producing 50 kV peak voltage and 1000

ampere peak current at a pulse repetition frequency

up to 125 pulse per second; an instrumentation

system including data recording and reduction; a

control system for starting and stopping the cir-

culator operation; interconnecting ducts.

The instrumentation system pertinent to this

study consists of six Kistler pressure transducers

(Model 6602A) having a frequency response to 30 kH

for the measurement of unsteady pressures around

the circulator, six hot-wire anemometers (TSI

Model 1050) for the measurement of unsteady

velocities and temperatures with a frequency

response to 15 kH twelve thermocouples

(HY-CAL

z'

Model RIS-31-A-100-B-8-3-600) and nine pressure

transducers (Sanso-Matrix Model SP91A5.0) for

measurements of steady flow temperature and

pressure in the circulator, respectively. The ex-

perimental data collected are recorded in a multi-

channel tape recorder and then digitized for later

reduction and analysis through a computer.

THEORETICAL ANALYSIS

Fluid and thermal characteristics of the re-

circulating laser gas flow may be analyzed by

solving the following set of differential

equations of mass, momentum and energy conservation

for unsteady one-dimensional flow:

Continuity equation;

Momentum equation;

(4)

Ener.gy e q u a t i o n ; ( 3 )

.-,

ap P ~ P

*

_{a t}

- C2&

_{a t}

+

V -

_ax

- C

-

_ax

- (k-l) p (q+VF) = 0 4f

vL

where P =

-

,

t h e f r i c t i o n a l r e s i s t a n c e D 2 i n f o r c e p e r u n i t mass The above e q u a t i o n s a c c o u n t f o r t h e e f f e c t s of

f r i c t i o n and h e a t t r a n s f e r i n t o and o u t from t h e

g a s a s i t f l o w s around t h e c i r c u l a t o r system.

.-

T

Figure 3 Typical Transient Differential Temperature Variations a t the Heat Exchanger Outlet and I n l e t

For b r e v i t y , n o m e n c l a t u r e of e q u a t i o n

symbols i s p r e s e n t e d a t t h e end of t h i s p a p e r .

A. Heat Exchanger A n a l y s i s

The h e a t exchanger c o u n t e r flow p r o c e s s , shown

i n F i g u r e 2 , i s modeled by t h e f o l l o w i n g s e t of d i f f e r e n t i a l e q u a t i o n s [*l f o r t h e assumption of z e r o t u b e w a l l h e a t r e s i s t a n c e and z e r o time v a r y i n g w a l l t e m p e r a t u r e g r a d i e n t : B. Steady R e c i r c u l a t i n g Flow A n a l y s i s S t e a d y s t a t e s o l u t i o n s t o Eqs. ( 1 ) t h r o u g h (3) ( 4 ) _{d e r i v e d by t h e a u t h o r s [ 3 ] p r o v i d e t h e changes of} f l o w and t h e r m a l p r o p e r t i e s from s e c t i o n t o s e c t i o n ( 5 )

through t h e components around t h e c i r c u l a t o r l o o p a s

( 6 ) shown i n F i g . 4.

Both s t e a d y and u n s t e a d y s o l u t i o n s of E q s . ( 4 )

through ( 6 ) were o b t a i n e d by t h e a u t h o r s 131, and a r e p r e s e n t e d q u a l i t a t i v e l y i n F i g s . 2 and 3 , r e s - p e c t i v e l y .

Figure 6 Diagram of Circulator System Showing Duct Sections, Principal Components and Direction of Heat and Mass Flow

Figure 2 Hear Exchanger Schematic and Temperature

px

Di:tribution4

p ~ - ~ & j

coolant

ic

t

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~ 9 - 3 4 6 JOURNAL DE PHYSIQUE S i n c e h e a t l o s s e s i n t h e by-pass d u c t and s h o r t i n t e r c o n n e c t i n g d u c t a r e known t o b e r e l a t i v e l y s m a l l compared w i t h t h e t o t a l energy l e v e l i n t h e r e c i r c u l a t i n g f l o w , t h e assumption of a d i a t i c pro- c & s s w i t h f r i c t i o n i s j u s t i f i e d f o r t h e s o l u t i o n s i n t h e d u c t s between S e c t i o n s

@

and

@,@

and

0,

@

and

a,

@

and

@

,

and

@

and

@

.

As t h e g a s flows t h r o u g h t h e t h r e e h e a t ex-

c h a n g e r s , c a v i t y and compressor, a s i g n i f i c a n t

p r e s s u r e l o s s and h e a t exchange may b e e x p e c t e d .

T h e r e f o r e , e f f e c t s of f r i c t i o n o r minor h e a t l o s s e s

a s w e l l a s h e a t t r a n s f e r a r e i n c o r p o r a t e d i n t h e

flow a n a l y s i s r e p r e s e n t e d by t h e f o l l o w i n g e q u a t i o n ,

r e s u l t i n g from t h e combination of Eqs. ( 1 ) through

Approximate s o l u t i o n s of Eq. (7) t h r o u g h t r i a l i t e r a t i o n p r o c e d u r e s [31 y i e l d d a t a of f l o w and t h e r m a l p r o p e r t i e s a t S e c t i o n s

@

and

@

a c r o s s t h e h e a t exchanger HXI, S e c t i o n s

@

and

@

a c r o s s H X I I , S e c t i o n s

@

and

@

a c r o s s t h e c a v i t y , S e c t i o n s

0

and

0

a c r o s s H X I I I and S e c t i o n s

@

and a c r o s s t h e compressor. T h i s s t e a d y flow a n l a y s i s h a s r e s u l t e d i n a t h e o r e t i c a l p r e d i c t i o n of t h e l a s e r g a s p r e s s u r e and t e m p e r a t u r e around t h e c i r c u l a t o r f o r a t y p i c a l flow c o n d i t i o n of 1 . 4 lbm p e r second a s shown i n F i g s . 5 and 6 , r e s p e c t i v e l y .

C. Unsteady Flow A n a l y s i s Around t h e C a v i t y

The e l e c t r i c a l energy i s i n p u t t o t h e g a s i n p u l s e d form under c o n t r o l of t h e e l e c t r o n beam gun.

A f t e r l a s i n g , a b o u t 8 0 p e r c e n t of t h e i n p u t e n e r g y i s

converted i n t o t h e r m a l energy which produces a

h i g h l y l o c a l i z e d h e a t e d s l u g of g a s i n t h e l a s e r

c a v i t y . T h i s change i n thermodynamic p r o p e r t i e s

t a k e s p l a c e i n t i m e much l e s s t h e n a c o u s t i c t r a n -

s i e n t time a c r o s s t h e c a v i t y . T h i s l o c a l i z e d r e g i o n

h a s a sudden i n c r e a s e i n p r e s s u r e and t e m p e r a t u r e

t h a t g e n e r a t e s shock waves and r a r e f a c t i o n waves

t h a t i n t e r a c t s w'ith t h e c o n t a c t s u r f a c e s which i s

t h e hot-cold g a s boundary. T h i s t r a n s i e n t pheno-

mena l e a d s t o o t h e r t h e r m a l d i s t u r b a n c e s i n t h e

r e c i r c u l a t i n g flow. These d i s t u r b a n c e s w i l l degrade

t h e l a s e r beam o p t i c a l q u a l i t y d u r i n g r e p e t i -

t i v e l y p u l s e d o p e r a t i o n . Normalizing Eqs. (1) and

( 2 ) and combining them w i t h t h e f i r s t and second laws of thermodynamics y i e l d a s e t of s o l u t i o n equa-

t i o n s f o r which we used t h e method of c h a r a c t e r i s t i c s

t o develop a one-dimensional d e s c r i p t i o n of t h e un-

s t e a d y flow p r o c e s s e s . 6& 2 _a(1nx)

₊

_A

_-

6?1s1

₊

_(k-l) _A

_-

D ~ S '

E

A*U =

-

AU

-

%

6.c D 6+

a

where

-

6T =

-

a T + ( U ' A ) -

4 a

Through a f i n i t e d i f f e r e n c e scheme, Eqs. ( 8 )

. ( g ) , and (10) a r e n u m e r i c a l l y s o l v e d a l o n g l e f t and r i g h t - r u n n i n g c h a r a c t e r i s t i c s . The s o l u t i o n s a r e g r a p h i c a l l y p r e s e n t e d a s temporal and s p a t i a l d i s - t u r b a n c e s of thermodynamic p r o p e r t i e s f o l l o w i n g a p u l s e of i n p u t energy. F i g u r e s 7 , 8 , and 9 p r e s e n t n u m e r i c a l r e s u l t s f o r a t y p i c a l energy i n p u t of 900 J o u l e p e r l i t r e of c a v i t y volume assuming t h e f l u i d t o be i n v i s c i d and f r i c t i o n l e s s . I n p a r t i c u l a r , F i g u r e 7 d e p i c t s t h e c o n f i g u r a t i o n s of shock waves and r a r e f a c t i o n waves p r o p a g a t i n g

upstream and downstream from t h e l a s e r c a v i t y a s

w e l l a s showing t h e c o n t a c t s u r f a c e motion t h a t

e n c l o s e s t h e h e a t e d gas volume i n t h e space-time

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tributions of temperature for three normalized time _T

(C, m s e c )

I

Contact Surface

frames for the same energy input. Figure

9

gives

the temporal or time varying distribution of

pressures at three stations upstream, downstream

and within the cavity, respectively (5 =

10,

11,

and 12).

i at Cavity Pentane H X I I

a

Run A 1.634 lbmlsec off

D

Run B 0.154 lbmlsec off

A

Run C 0.213 lbmlsec on

1 . Run D 1.383 lbmlsec on -Theoretical 1.4 lbmlsec on

(5 cm)

Figure 7 Configurations of Wave Propagationa and Contact Surfaces Temperature

R

t

at r = 0.4 (t=.0551 a sec)

l O L . . ' .

. .

. -

.

1 3 4 5 6 7 8 11 12 Section

Comp- HXI H X I I Cavity H X I I I Comp-

ressor ressor

Figure 5

-

Pressure Distributions Around the Circulator for Various Flow Conditions

9.0 10.0 11.0 12.0

Cavity ( 5 cm)

5

& at Cavity Pentane HMI_

a

Run A 1,634 lbmlsec off

B Run B 0.154 Ibmlsec off

a

Run C 0.213 lbmlsec on

Run D 1.383 lbmlsec

-

on

Theoretical 1.4 lbmlsec on

Figure 8 Spatial Distribution of Temperature for Times

(T = 0, 0.2, and 0.4) T

( t , m s e c )

at at

5 = 10 5 = 11

(2.5 cm upstream 1 (in cavity)

1

f.m cavity)

,

.

. .

A . I I

1 3 4 5 6 7 8 11 12 Section

-

Compressor HXI M 1 1 Cavity m 1 1 1 Compressor

Figure 6

-

Temperature Distributions Around the Circulator for Various Flow Conditions

Pressure (atmosphere) Figure 9 Temporal Distributions of Pressures at Sections

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JOURNAL DE PHYSIQUE

EXPERIMENTAL THERMAL PERFORMANCE DATA AND DISCUS- SION

A s e r i e s of a c c e p t a n c e t e s t s were performed by

~ o c k e t d ~ n e ' ~ ' t o c o l l e c t d a t a c o l l e c t e d f o r v a r i o u s

f l o w c o n d i t i o n s . Some of t h e d a t a was a n a l y z e d by

t h e above methods i s p r e s e n t e d ' i n T a b l e I and i s

p l o t t e d i n F i g u r e s 5 and 6. F o r t h e p r e s e n t a n a l -

y s i s of t h e d a t a , t h e f o l l o w i n g e q u a t i o n was u s e d

f o r c a l c u l a t i n g t h e h e a t t r a n s f e r performance o f

t h e h e a t exchanger f o r g i v e n end t e m p e r a t u r e s , and

h e a t t r a n s f e r c o e f f i c i e n t p r o v i d e d by t h e manufac-

t u r e r and t h e s p e c i f i e d t u b e s u r f a c e a r e a ;

ATi

-

ATo

q = C _h

(The

-

Thi) = _AT. HS ( 11)

I n

2

ATo The a n a l y z e d d a t a p r e s e n t e d i n T a b l e I shows t h a t a s t h e mass f l o w r a t e i s i n c r e a s e d , t h e h e a t f l u x i s r a i s e d a c c o r d i n g l y f o r compressor e x i t and c a v i t y i n l e t h e a t exchangers. T h i s t r e n d i s r e -

v e r s e d f o r t h e compressor i n l e t h e a t exchanger due

t o t h e e f f e c t s from t h e d i v e r t e r v a l v e . As t h e d i v e r t e r v a l v e r e d u c e s t h e g a s f l o w i n t o t h e c a v i t y , a n i n c r e a s i n g f r a c t i o n of t h e h i g h t e m p e r a t u r e g a s f l o w i s d i v e r t e d t h r o u g h t h e 4-in by-pass p i p e d i r e c t l y i n t o t h e compressor i n l e t h e a t exchanger, c a u s i n g t h e a d v e r s e e f f e c t s . E v a l u a t i o n of t h e a n a l y z e d d a t a shows t h a t o n l y minor a d j u s t m e n t S i n t h e m a n u f a c t u r e r g i v e n h e a t t r a n s f e r c o e f f i c i e n t s were r e q u i r e d t o v e r i f y t h e t h e o r e t i c a l r e s u l t s [ 3 1 . T h i s e v a l u a t i o n v e r i f i e s t h a t t h e s e e q u a t i o n s a r e a u s e f u l t o o l f o r f i r s t o r d e r t r e n d p r e d i c t i o n s and e a r l y s y s t e m d e s i g n .

F i g u r e s 5 and 6 d e p i c t s measured p r e s s u r e and t e m p e r a t u r e d i s t r i b u t i o n s around t h e c i r c u l a t o r .

The d i s t i n c t i v e e f f e c t s of t h e c a v i t y i n l e t h e a t

exchanger o p e r a t i n g w i t h p e n t a n e a s t h e c o o l a n t i s

c l e a r l y noted. When t h e c a v i t y i n l e t g a s tempera-

t u r e must b e m a i n t a i n e d a t a p p r o x i m a t e l y 3 6 0 ° ~ , t h e

c a v i t y i n l e t h e a t exchanger i s r e q u i r e d t o e x t r a c t n e a r l y 100 BTU/sec of h e a t f l u x from t h e g a s f l o w ,

w h i l e t h e compressor i n l e t h e a t exchanger (HXIII)

i s shown t o add h e a t f l u x of more t h a n 30 BTU/sec i n t o t h e l a s e r g a s flow a s l i s t e d i n T a b l e I.

When t h e d i v e r t e r v a l v e i s s h i f t i n g a major p o r t i o n of g a s flow i n t o t h e bypass l o o p , s u p p l y -

i n g o n l y a b o u t 1 0 p e r c e n t of t h e flow i n t o t h e

c a v i t y , H X I I I c a r r i e s a main l o a d of h e a t e x t r a c -

t i o n from t h e g a s flow and (HXI and H X I I f u n c t i o n

o n l y i n a minor way i n k e e p i n g t h e h e a t b a l a n c e a s

shown by t h e h e a t f l u x , q i n T a b l e I.

These s t e a d y s t a t e e x p e r i m e n t a l d a t a of tem-

p e r a t u r e and p r e s s u r e f o r f o u r flow r a t e s w i t h and

w i t h o u t H X I I i n o p e r a t i o n w i t h p e n t a n e a r e compared

w i t h t h e r e s u l t s of t h e o r e t i c a l models d e l i n e a t e d

i n [ 3 1 and a r e shown i n F i g u r e s 5 and 6 . E x c e l l e n t agreement between t h e experiment and t h e o r y was

n o t e d a f t e r p r o p e r a d j u s t m e n t s of f r i c t i o n and h e a t t r a n s f e r c o e f f i c i e n t s were made i n t h e t h e o r e t i c a l model f o r IS = 1 . 4 lbm/sec, t h e r e b y v e r i f y i n g t h e t h e o r y and p r o v i d i n g a t o o l f o r a c c u r a t e p r e d i c - t i o n s of f l u i d and t h e r m a l c h a r a c t e r i s t i c s of t h e r e c i r c u l a t i n g flow. T h i s t o o l i s t h e n d i r e c t l y u s e f u l f o r d e v e l o p i n g s c a l i n g laws i n t h e e n g i n e e r - i n g d e s i g n of l a r g e r c i r c u l a t o r s y s t e m s based on t h e p r i n c i p l e of s i m i l i t u d e t r e a t i n g t h e t h e o r e t i - c a l model t h r o u g h d i m e n s i o n l e s s p a r a m e t e r s . CONCLUSIONS T h e o r e t i c a l models d e p i c t i n g t h e s t e a d y and t r a n s i e n t s t a t e s of r e c i r c u l a t i n g f l o w s i n t h e c l o s e d c y c l e a i r c i r c u l a t o r a r e p r e s e n t e d . Based on t h e l i m i t e d e x p e r i m e n t a l d a t a c o l l e c t e d t o d a t e ,

t h e s t e a d y s t a t e t h e o r e t i c a l model was compared

w i t h e x p e r i m e n t a l r e s u l t s and was s a t i s f a c t o r i l y

v e r i f i e d . S i n c e t h e models were developed i n t e r m s

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t h e s c a l i n g laws e x t a b l i s h e d through t h i s s t u d y

w i t h t h e s m a l l s c a l e CCC system i s a p p l i c a b l e f o r

d e s i g n i n g a l a r g e r s c a l e CCC system.

REFERENCES

[ l ] Cason, C. e t a l . "A Small S c a l e Closed Cycle C i r c u l a t o r E x p e r i m e n t a l P l a n f o r R e p e t i v e l y P u l s e d 2 0 0 ' ~ High P r e s s u r e E l e c t r i c D i s c h a r g e Lasers" Tech Report RH-76-12, Aug. 1976, U.S. Army M i s s i l e Command, Redstone A r s e n a l , A l . , 35809

121 K a l i n i n , E.K. "Tubular Heat Exchangers w i t h B i l a t e r a l Heat T r a n s f e r Augmentation and Cal-

c u l a t i o n of a Heat Exchanger under Unsteady O p e r a t i n g Conditions", Chpt. 8 , Heat Exchangers: Design & Theory Sourcebook by Afgan, N. & S c h l u n d e r , E. U . , McGraw-Hill Book Co., 1974.

131 S h i h , C.C., and Cason, C "Heat T r a n s f e r C h a r a c t e r i s t i c s of a Small Closed Cycle C i r c u l a t o r f o r High Energy P u l s e d L a s e r " , ASME 80-HT-132.

141 H i c k s , B. L., e t a l . "The One- Dimensional Theory of S t e a d y F l u i d Flow i n Ducts w i t h F r i c t i o n and Heat Addition", NASA Tech. Note, No. 1336 (1974).

[51 P e r r i s , D.F., F i n a l Report "Closed Cycle G a s R e c i r c u l a t o r " , Aug. 1977, DAAH01-76-0- 0961, Rocketdyne Div. Rockwell I n t e r n a t i o n a l , C a l i f .

NOMENCLATURE

A f l o w s c r o s s - s e c t i o n a l a r e a C a c o u s t i c v e l o c i t v

Ch = (fi C P ) ~ h o t l a s e r gas flow c a p a c i t y r a t e Cc = (h CP c c o l l a n t flow c a p a c i t y r a t e CD S o e c i f i c h e a t under c o n s t a n t D r e s s u r e CO S t a g n a t i o n a c o u s t i c v e l o c i t y Cpc Cp of c o o l a n t D d u c t d i a m e t e r T a b l e I Heat Exchanger F f r i c t i o n a l r e s i s t a n c e p e r u n i t mass f f r i c t i o n a l c o e f f i c i e n t H o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t k s p e c i f i c h e a t r a t i o L d u c t l e n g t h

ha,

maximum d u c t l e n g t h f o r c o n i c shocking o c c u r r e n c e i n t h e d u c t

M mach number

M2 mach number a t S e c t i o n 2 f o r example

h mass flow r a t e !

A mass flow r a t e i n t h e main l o o F

r n ~ mass flow r a t e i n t h e bypass l o o p P s t a t i c p r e s s u r e q t h e r m a l o r mechanical energy e f f l u x p e r u n i t mass R e n g i n e e r i n g g a s c o n s t a n t S t u b e s u r f a c e a r e a Tc s t a t i c t e m p e r a t u r e of c o o l a n t flow T c i c o o l a n t t e m p e r a t u r e a t h e a t exchanger i n l e t Tco c o o l a n t t e m p e r a t u r e a t h e a t exchanger o u t l e t Th s t a t i c t e m p e r a t u r e of l a s e r g a s f l o w T h i l a s e r g a s t e m p e r a t u r e a t h e a t exchanger i n l e t

The

l a s e r g a s t e m p e r a t u r e a t h e a t T x c h a n g e r o u t l e t To s t a g n a t i o n t e m p e r a t u r e T03 s t a g n a t i o n t e m p e r a t u r e a t S e c t i o n 2 f o r example AT t e m p e r a t u r e d i f f e r e n c e between l a s e r g a s and c o o l a n t f l o w s a c r o s s t h e t u b e ATi t e m p e r a t u r e d i f f e r e n c e b e t w e e r 7 h e c o u n t e r f l o w s a t h e a t exchanger i n l e t ATo t e m p e r a t u r e d i f f e r e n c e between t h e c o u n t e r f l o w s a t h e a t exchanger e x i t AT, i n i t i a l t e m p e r a t u r e d i f f e r e n c e between t h e c o u n t e r f l o w s i n t h e h e a t exchanger t t i m e V f l o w v e l o c i t y VC c o o l a n t f l o w v e l o c i t y Vh l a s e r g a s flow v e l o c i t y W t u b e w e t t e d p e r i m e t e r X one-dimensional s p a c e c o o r d i n a t e p f l u i d d e n s i t y pc c o o l a n t d e n s i t y t i m e d u r a t i o n f o r t r a n s i e n t p r o c e s s SUPERSCRIPT

*

f l u i d and t h e r m a l p r o p e r t i e s a t t h e Mach number i s u n i t y P e r f o r m a n c e Data Heat Exchanger

_%

_r6 T . _C₁ ( l b m l s e c (lbm/gec) (OR) Thi (OR) Tco

Model HF-803-DR-1P 1.634** 4.0 707 567.8 592 530 61.62 (Young R a d i a t o r ) 0.154** 4.0 709 530.7 536 5 3 1 . 1 8 . 7 4 8.38" X 27" 0.213* 4.0 6 3 1 527.5 531 527.8 6.98 C o o l a n t - Water 1.383* 4.0 635 5 3 6 . 3 548 528.5 39.45 s e c Model HF-804-DR-1P 1.634** 3 . 1 592 524.9 580 (Young R a d i a t o r ) 0.154* 3 . 1 536 521.7 538 8.38" X 27" 0.213* 3 . 1 5 3 1 321.9 327 306 C o o l a n t - P q n t a n e 1.383* 3 . 1 548 355.2 348 287 S = 67.1 f t H = 0.0118 B T u / f t 2 OR s e c Model F-1002-DR-18 1.634** 2.0 577 527.8 559 517.8 (Young R a d i a t o r ) 0.154** 2.0 659 551.6 578 531.1 10.75" X 18" 0.213* 2.0 468.7 527.8 Coolant - W

₉

t e r 1.383* 2.0 416 468 5 2 8 . 5 S = 52.0 f t H = 0.01136 B T u / f t Z OR s e c

Note:

*

P e n t a n e Heat Exchanger i n o p e r a t i o n