nasa contractor report · nasa contractor report 1.75184 ... - ratio of molecular thermal...

- . 4

NASA Contractor Report 1.75184

(NASA-CZ- 1781 &4) SPACE-BASEC L A $ E J - D H I V E N wa7-1 i s 3 7

lac.) 5 2 p C S C L 1oc

MIJD G E N E F A T O R : E E A S I B I L I T Y SSULY F i 1 l a . l Report (Infcraraticn ard Ccntrc l S y s t e m s ,

U n c l a s G 3 / 2 0 44917

SPACE-BASED LASER-DRIVEN MHD GENERATOR: F E A S I B I L I T Y STUDY

S. H. Choi

INFORMATION & CONTROL SYSTEMS, I NC . Hampton, V i r g i n i a

P u r c h a s e Order L-28161B O c t o b e r 1986

National Aeronautics and Space Administration

Langley Research Center Hampton,Virginia 23665

https://ntrs.nasa.gov/search.jsp?R=19870002404 2018-06-02T05:29:21+00:00Z

SPACE-BASED LASER-DRIVEN MHD GENEMTOK: FEASIBILITY STUDY

S. H. Choi Informat ion & Control Systems, Inc .

SUMMARY

The f e a s i b i l i t y of a l a s e r - d r i v e n MHD g e n e r a t o r , as a c a n d i d a t e r e c e i v e r f o r a space-based laser power t r ansmiss ion system, w a s i n v e s t i g a t e d .

An e x t e n s i v e l i t e r a tu re s e a r c h of r e s e a r c h on MHD g e n e r a t o r s and laser- produced plasmas w a s c a r r i e d o u t . The MHD g e n e r a t o r s were t a b u l a t e d accord- i n g t o c h a r a c t e r i s t i c s such as t h e energy source , working f l u i d , g e n e r a t o r type , f low rate, tempera ture , e l e c t r i c a l c o n d u c t i v i t y , power d e n s i t y , gener- a t o r dimension, e f f i c i e n c y , magnetic f i e l d s t r e n g t h , seed material, type of c y c l e , and o p e r a t i n g mode. Laser-produced plasma and laser plasma i n t e r - a c t i o n s were t a b u l a t e d w i t h r e s p e c t t o plasma t empera ture , laser type and energy, plasma c o n d u c t i v i t y , a b s o r p t i o n of laser r a d i a t i o n , f l ow v e l o c i t y , carr ier gas , and seed material.

On t h e b a s i s of r easonab le parameters ob ta ined i n t h e l i t e r a t u r e s e a r c h , a nodel of tile l a s e r - d r i v e n MHD gene ra to r w a s developed w i t h t h e assumptions of c1 s t e a d y , t u r b u l e n t , two-dimensional flow. The assumpt ions used i n t h i s stLdy were b a s e d on t h e cont inuous and s t e a d y g e n e r a t i o n of p lasmas by t h e exposure of t h e cont inuous wave laser beam t h u s induc ing a s t e a d y back p r e s - s i re t h a t e n a b l e s t h e medium t o flow s t e a d i l y . The model cons ide red h e r e took t h e t u r b u l e n t n a t u r e of plasmas i n t o account i n t h e two-dimensional geometry of t h e g e n e r a t o r . For t h e s e c o n d i t i o n s w i t h t h e plasma parameters d e f i n i n g t h e thermal c o n d u c t i v i t y , v i s c o s i t y , e lec t r ica l c o n d u c t i v i t y f o r t h e plasma flow, a g e n e r a t o r e f f i c i e n c y of 5 3 . 5 p e r c e n t was c a l c u l a t e d . I f t u r b u l e n t e f f e c t s and nonequilfbriurn i o n i z a t i o n are taken i n t o accoun t , t h e e f f i c i e n c y is 4 3 . 2 percen t .

The s t u d y shows t h a t t h e l a s e r - d r i v e n MHD system h a s p o t e n t i a l as a l a s e r power receiver f o r space a p p l i c a t i o n s because of i t s h igh energy convers ion e f f i c i e n c y , h igh energy d e n s i t y and r e l a t i v e l y s imple mechanism as compared to o t h e r energy conversion c y c l e s .

LIST OF FIGURES

page FIGUKI', 1..

FIGUKE 2 .

FIGURE 3 .

FIGURE 4 .

FIGURE 5.

FIGURE 6 .

FIGURE 7 .

FIGURE 8.

FIGURE 9 .

FIGURE l o .

FIGURE 11.

FIGURE 1 2 .

LASER-DKIVEN MHD GENERATOR . . . . . . . . . . . . . . . LASER-DRIVEN MHD SYSTEM EFFICIENCY BI.OCK DIAGRAM . . . . A COMPILATION OF THE EXPEKIMENTAL RESULTS ON BKEAKDOWN THRESHOLD AS A FUNCTION OF PRESSURE FOR A NUMBER OF GASES . . . . . . . . . . . . . . . . . . . . . . . . . BREAKDOWN THRESHOLD FOR A r (PRESSURE 5 . 2 x .LO TORR) AS A FUNCTION OF CHARACTERISTIC FOCAL DIMENSION . . . . . . BREAKDOWN TIME AS A FUNCTION OF PEAK IRRADIANCE AND PEAK

I N VARIOUS GASES . . . . . . . . . . . . . . . . . . . . OPTICAL TRANSMISSIVITY OF AIR AT A PRESSURE OF 746 TORR AS A FUNCTION OF PEAK POWER I N A RUBY LASER PULSE FOCUSED BY A 2.06 - c m FOCAL LENGTH LENS . . . . . . . . . . . . BREAKDOWN THRESHOLD AS A FUNCTION OF WAVELENGTH OF INPUT RADIATION FOR A r AT FOUR SELECTED PRESSURES . . . . . . MHD CHANNEL . . . . . . . . . . . . . . . . . . . . . . CALCULATED VELOCITY PROFILE OF TURBULENT FLOW I N THE MHD CHANNEL . . . . . . . . . . . . . . . . . . . . . . . . CALCULATED TEMPERATURE PROFILES AT THREE DIFFERENT LOCATIONS FROM THE ENTRANCE OF THE MHD CHANNEL . . . . . CALCULATED ELECTRICAL CONDUCTIVITY PROFILES AT FOUR DIFFERENT LOCATIONS FROM THE ENTRANCE OF THE MHD CHANNEL . . . . . . . . . . . . . . . . . . . . . . . . CALCULATED EFFECTIVE ELECTRICAL CONDUCTIVITY PROFILES AT THREE DIFFERENT LOCATIONS FROM THE ENTRANCE OF THE MtiD CHANNEL . . . . . . . . . . . . . . . . . . . . . .

4

ELECTRIC FIELD FOR A Q-SWITCHED RUBY LASER PULSE FOCUSED

17

18

1 9

20

2 1

22

2 3

24

25

26

27

28

4

ii

page . . . . . . . . . . . . . . . . . . . . . 29 TABLE I. PLASMAMHD

TABLE I. PLASMA MHD (CONCLUDED) . . . . . . . . . . . . . . . 30

31 TABLE 11. LM MHD GENERATOR . . . . . . . . . . . . . . . . . . TABLE 11. LM MHD GENERATOR (CONCLUDED) . . . . . . . . . . . . 32

33 TABLE 111. ALKALI METAL PARAMETERS . . . . . . . . . . . . . . 34 TABLE IV. LASER-PLASMA INTERACTION . . . . . . . . . . . . . .

TABLE V . PARAMETERS NECESSARY FOR CALCULATING THE MHD 35 GENERATOR PERFORMANCE . . . . . . . . . . . . . . .

TABLE V I . LASER-PLASMA INTERACTION PAMMETERS USED FOR LASER- 36 D R I V E N M H D . . . . . . . . . . . . . . . . . . . . .

TABLE VII. COMPARISON OF EFFECTS OF TURBULENCE ANI) NON- 37 EQUILIBRIUM IONIZATION . . . . . . . . . . . . . . .

iii

a

A - A

A r - b

B

c

cf

c S

D J

e

Ec

gC

h

H

H a

H e

J

k

K - K

L

n

N

e

LIST OF SYMBOLS

- degree of i o n i z a t i o n

- g e n e r a t o r c r o s s - s e c t i o n a l area, m 2

- Van Driest c o n s t a n t

- Argon

- M e i and Squ i re c o n s t a n t

- magnetic f i e l d

- s p e c i f i c h e a t , J/kg*K

- f r i c t i o n c o e f f i c i e n t

- Cesium

- plasma d iame te r , m

- e l e c t r o n i c charge , C

- Ecker t number, U / C T

- g r a v i t y , m / s

-2 P w

2

- Planck c o n s t a n t

- h e i g h t , m

- Hartmann number, LB ($) !L - H e l i u m

- c u r r e n t , A

- non-dimensional c u r r e n t

- thermal c o n d u c t i v i t y , W/mk

- r a t i o of load t o open c i r c u i t v o l t a g e s

- voii Karn-wn c o n s t a n t

- c h a r a c t e r i s t i c l e n g t h , m

- e l e c t r o n d e n s i t y , m -3

- r a t i o of molecular thermal conduct ion t o r a d i a t i o n for a gas

iv

.

LIST OF SYMBOLS (CONTINUED)

- d e n s i t y of Argon o r helium

3 - power d e n s i t y o u t p u t , W/m 3 - power d e n s i t y i n p u t , W/m

- P r a n d t l number

- t u r b u l e n t P r a n d t l number

- r a d i a t i o n h e a t f l u x , W/m

- r a d i a t i o n hea t flux i n t h e x - d i r e c t i o n , W/m

- r a d i a t i o n h e a t f l u x in thc y - d i r e c t i o n , W/m

- heat f l u x through the boundary, W/m

- r a d i a t i o n h e a t flux r a t i o i n t h e x - d i r e c t i o n

- r a d i a t i o n h e a t flux r a t i o i n t h e y - d i r e c t i o n

NB P

'in

Pr

Prt

q;

q;

%l ,2

QX

0,

2

2

2

2 I 1

Q(T) - c o l l i s i o n a l c r o s s s e c t i o n

R e - Reynolds number

- t i r rbu lcn t Reynolds number Ret

r - h y d r a u l i c r a d i u s

t: - scit 1 c b c l t h e

n

t' - t i m e , s

T' - rcmperturc, K

U' - v e l o c i t y , m/s - U - average v e l o c i t y , m l s

- c e n t e r l i n e v e l o c i t y , m / s

- v e l o c i t y r a t i o , U'/U "C

z V

1.1 W - width, m

X ' - x ' d i r e c t i o n l e n g t h i n t h e c o o r d i n a t e , m

V

X

Y'

Y

Z - Z

Greek:

LIST OF SYMBOLS (CONTINUED)

- s c a l e d l e n g t h i n t h e x' d i r e c t i o n

- y ' d i r e c t i o n l e n g t h i n t h e c o o r d i n a t e , rn

- s c a l e d l e n g t h i n t h e y ' d i r e c t i o n

- z ' d i r e c t i o n l e n g t h i n t h e c o o r d i n a t e , m

- s c a l e d l e n g t h i n t h e z ' d i r e c t i o n

- t u r b u l e n t d i s t a n c e

2 a - thermal d i f f u s i t y , m / s

a - t u r b u l e n t thermal d i f f u s i v i t y , m / s

13 - r a t io of t h e e l e c t r o n mean-free-path t o t h e Larmor r a d i u s

F3 - p c r m i t i v i t y of f r e e space

2 T

0

P - d e n s i t y , kg/m

- Debyc r a d i u s Yi K - Boltzmann c o n s t a n t , J / K

IC - a b s o r p t i o n c o e f f i c i e n t

8 - s c a l e d tempera ture

T - o p t i c a l th ickness , m

U - e lec t r i ca l c o n d u c t i v i t y , S/m

-

0

- e f f e c t i v e e l e c t r i c a l c o n d u c t i v i t y , S/m ef f U

2 V - kinematic v i s c o s i t y , m / s

V - t u r b u l e n t k inemat ic v i s c o s i t y , m / s

Y' - s h e a r stess, Pa

Y

Q - s c a l e d d i s t a n c e , o r e f f i c i e n c y

2 T

- t h e lower ing of t h e i o n i z a t i o n p o t e n t i a l by t h e Debye c l o u d

.

v i

LIST OF SYMIlOLS (CONCLUDED)

Greek (cont inued) :

5 - plasma t u r b u l e n c e f a c t o r

IJ - e l e c t r o n m o b i l i t y

5

A

2 - a parameter de f ined by H,/(Ret-n) i n the Funct ion F1

- c h a r a c t e r i s t i c f o c a l dimension def ined by A = 11(4.8/D)Z -k ( n / L ) Z

S u b s c r i p t s :

B

c

d

M

t

W

w1

w2

X

- combination of the He and A r

- c c n t e r l i n c

- cesium

- Debye

- Magnetic f i e l d

- turbulent :

- wall - wall 1 - wall 2

- x d i r e c t i o n

- y d i r e c t i o n

v i i

ABBREVIATIONS

UT - United Technology

GE - General E lec t r ic Company

AV CO - AVCO - E v e r e t t Research Lab

BM I - Battel le Memorial I n s t i t u t e

UTSI - Univers i ty of Tennessec Spncc l n s t i t u t c

su - Stanford U n i v e r s i t y

ARGAS-I - MHD Generator name, by Elndhoven

MIT - Massachusset ts I n s t i t u t e of Technology

JPL - Jet Propuls ion Lab

ANL - Argonne Nat iona l Lab

A I - A t o m i c I n t e r n a t i o n a l

,

v i i i

INTRODUCTION

The advantages of u s ing a laser t o t r ansmi t power i n space is based on t h r e e f e a t u r e s of t h e l aser :

1. The laser beam can be t r ansmi t t ed over l ong d i s t a n c e s wi thout a p p r e c i a b l e a t t e n u a t i o n o r d ive rgence ,

2 . The laser p rov ides a h igh s o u r c e i n t e n s i t y a t t h e r e c e i v e r ,

3 . The laser does no t r e q u i r e p h y s i r a l c o n t a c t between energy source and power gene ra to r .

While t h e laser appea r s t o b e an advantageous means of t r a n s m i t t i n g en- e r g y i n space, t h e means of beam gene ra t ion and beam convers ion t o a more use- f u l form of energy ( i . e . ? e lec t r ic i ty o r p ropu l s ion ) are n o t w e l l de f ined . Converter systems, i n p a r t i c u l a r , must meet t h e requi rements of h igh con- v e r s i o n e f f i c i e n c y a t a h igh energy d e n s i t y wh i l e remaining small, l i g h t weight and s imple . One c o n v e r t e r s y s t e m which may meet t h e r equ i r emen t s is t h e l a se r -d r iven MHD g e n e r a t o r which is shown i n F igure 1. The plasma i s produced by focus ing the l a s e r beam i n t o t h e plasma product ion chamber. A t s u f f i c i e n t l y high i n t e n s i t y , breakdown w i l l occur i n t h e gas medium producing a plasma. laser r a d i a t i o n which w i l l h e a t t h e p l a s m a . Although t h e laser d r i v e n MHD g e n e r a t o r is a n e f f i c i e n t c a n d i d a t e energy convers ion system f o r space ab- p l i c a t i o n , t h e a b s o r p t i o n of t r ansmi t t ed beam energy by t h e p a r t i c i p a t i n g aedium i n t h e plasma product ion chamber becomes t h e key f a c t o r i n d e t e r - mining t h e g e n e r a t o r e f f i c i e n c y . With t h e proper plasma c o n d i t i o n s such as laser peak power, gas p r e s s u r e , gas s p e c i e s , f o c a l volume d e n s i t y , and plasma tempera ture , a b s o r p t i o n of t h e laser beam can r each 80% w i t h Nd l o n g p u l s e laser l i g h t of approxim t e l y 10l8 W/m2 and 65% w i t h C02 long p u l s e laser l i g h t of roughly 10’’ W/m2 (Ref. 1). F igure 2 shows ~ L 1 . i e s t ima ted e f f i c i e n c i e s of a l a s e r - d r i v e n MHD g e n e r a t o r subsystem.

Once t h e plasma is e s t a b l i s h e d , i t w i l l absorb t h e

T h i s p re l imina ry s tudy of t h e l a s e r d r i v e n MHD g e n e r a t o r i n c l u d e s a l i t e r a t u r e survey and a development of a s i m p l i f i e d t h e o r e t i c a l model f o r the s y s t e m . The l i t e r a t u r e survey was conducted t o e s t a b l i s h r ea l i s t i c para- ~ ~ l r t e r s , such as tempera ture and d c n s i t y , f o r laser produced plasmas and also t o de te rmine those des ign parameters of MHD channe l s which a re a f f e c t e d by t he plasma c o n d i t i o n s such as plasma t empera ture and d e n s i t y . Both plasina and 3 i q u i d metal MHD g e n e r a t o r s were inc luded i n t h e l i t e r a t u r e survey.

- ..

The primary purpose of the s tudy w a s of e x i s t i n g MHD generator systems so t h a t i n t h e development o f a p ro to type des ign System c h a r n c t e r i s t i c s S U C J I a s t h e eiic-rgy f l u i d , working f l u i d flow, t empera ture , t *

s i t y , g e n e r a t o r d i m c ~ n s i o r i , magnetic f i t . I t l mode of ope ra t ion w e r e cons ide red -

t o i d e n t i f y c e r t a i n c h a r a c t e r i s t i c s t h e s e c h a r a c t e r i s t i c s could be used or a l a se r d r i v e n MHD g e n e r a t o r . sou rce , generat o r ~ y p e , working e r t r i c a l c o n d u c t i v i t y , power den- c y c l e f e a t u r e s , seed material and

1. Plasma MHD

The c h a r a c t e r i s t i c s of plasma MHD g e n e r a t o r systems are g iven i n Table I. The systems can be d iv ided i n t o f o u r groups: 1 ) shock-driven, 2 ) a rc , 3) combustion ( inc lud ing c o a l bu rn ing ) , and 4 ) explos ive-dr iven ( i n c l u d i n g rocke t and de tona t ion ) . The primary d i f f e r e n c e between t h e s e systems and t h e l a se r -d r iven MHD g e n e r a t o r is t h e method of plasma product ion , a l though some d i f f e r e n c e s i n t h e f low of t h e plasma through t h e channel occur s . The shock o r explos ive d r i v e n MHD g e n e r a t o r s , f o r example, are c h a r a c t e r i z e d by q u a s i - a d i a b a t i c wave propagat ion through t h e channel and a r a p i d decay o f t h e plasma a f t e r t h e wave has passed. I n t h e l a se r -d r iven MHD g e n e r a t o r , on t h e o t h e r hand, t h e plasma f low w i l l be exposed t o t h e laser r a d i a t i o n (so long as t h e c r i t i c a l charge d e n s i t y which produces o p t i c a l r e f l e c t i o n is not. reached) , and hea t ing of t h e p l a s m a throughout the channel w i l l o ccu r . T h e flow i n t h e l a se r -d r iven MHD channel i s expected t o be a n uns teady , tu rbu- l e n t f low wi th a h e a t sou rce . on t h e ave rage channel v e l o c i t y , t h e magnet ic f i e l d i n t e n s i t y , and t h e elec- t r i c a l conduc t iv i ty .

The power d e n s i t y i n a MHD g e n e r a t o r depends

2. Liquid Metal MHD

The characterist ics of l i q u i d metal MHD systems a re g iven i n Table 11. The conceptua l and exper imenta l works done so f a r a re d i r e c t l y a p p l i c a b l e t o t h e l a se r -d r iven l i q u i d metal MHD system, s i n c e t h e c o n f i g u r a t i o n of t h e conven t iona l l i q u i d metal MHD systems is the same except f o r t h e laser beam receiver. The laser energy i s s u p p l i e d through t h e o p t i c a l system i n which t h e beam energy is converted i n t o the d r i v i n g power of Lhcr l i q u i d metal (two-phase f low).

L iquid metal MHD s y s t e m s u s u a l l y d e a l w i th low tempera ture energy s o u r c e s . Hence, they do not have t h e hardware r e l a t e d problems,such a s meicing, i h i may t a k e p l a c e i n t h e plasma MHD gene ra to r . of gas from l i q u i d ( i n t h e case o f two-phase f low) a r e t h e main problems t o be so lved .

The c o r r o s i o n and t h e s e p a r a t i o n

Table 111 g i v e s t h e a l k a l i m e t a l parameters such as t h e i o n i z a t i o n

2

L

-- 3. Laser Plasma I n t e r a c t i o n

The plasma is produced by a gas breakdown a f t e r t h r e s h o l d i r r a d i a n c e h a s been achieved . T h i s g a s breakdown process proceeds i n t h e fo l lowing s t e p s : (1) t h e product ion of t h e i n i t i a l i o n i z a t i o n , and (2) t h e subsequent cascade by which t h e i o n i z t i o n grows and t h e shock wave propagates , and d i s s i p a t e s .

A f t e r t h e i n i t i a l i o n i z a t i o n i s produced, i t s growth becomes t h e domi- nan t p rocess . Following a sma l l amount of i o n i z a t i o n , f r e e e l e c t r o n s abso rb photon energy by i n v e r s e bremsstrahlung. When a n e l e c t r o n h a s ga ined enough energy , i t can i o n i z e an a d d i t i o n a l atom i n a c o l l i s i o n . The e l e c t r o n is then r ep laced by two e l e c t r o n s wi th lower energy i n t h e f r e e e l e c t r o n con- tinuum. Both e l e c t r o n s then abso rb energy by i n v e r s e bremss t rah lung , and cascad ing of t h e i o n i z a t i o n occur s . This cascade p rocess , f ed by t h e ab- s o r p t i o n of laser l i g h t i n t h e inve r se bremss t rah lung p rocess , is t h e mechanism which produces t h e growth of t h e i o n i z a t i o n .

Breakdown t h r e s h o l d of t h e g a s , as a f u n c t i o n of i n t e n s i t y , depends on t h e f o c a l volume. A s t h e f o c a l volume becomes smaller, l o s s e s , e i t h e r by d i f f u s i o n of t h e e l e c t r o n s o u t of the f o c a l r e g i o n o r by r a d i a t i o n , l i m i t t h e b u i l d up and i n c r e a s e t h e th re sho ld . r a p i d l y , f o r a g iven i r r a d i a n c e , w i t h a l a r g e r f o c a l volume. To ma in ta in t h e growth of t h e cascade f o r a s table plasma w i t h i n t h e f o c a l volume, t h e fo l lowing c r i te r ia should b e m e t :

The cascade p rocess proceeds more

(1 ) l a r g e f o c a l volume

18 ( 2 ) h igh beam f l u x d e n s i t y (over 7 x 10 W/m2)

( 3 ) cont inuous wave beam f l u x (CW l a se r . )

( 4 ) h igh gas d e n s i t y

(5 ) low boundary e f f e c t s .

The power ou tpu t requi rements of t h e laser as a n energy s o u r c e f o r a l a s e r - d r i v e n MHD g e n e r a t o r can b e chosen by t h e f o c a l volume of t h e plasma chamber, g a s p r e s s u r e , g a s s p e c i e s , MHD channel geometry, etc.

Breakdown c h a r a c t e r i s t i c s are shown i n F igu res 2 , 4 , 5 and 6 . The gas breakdown t h r e s h o l d i s a f u n c t i o n of t h e g a s p r e s s u r e and f o c a l volume. The breakdown t h r e s h o l d e x h i b i t s a l i n e a r r e l a t i o n s h i p w i t h t h e peak i r r a d i a n c e , b u t t h i s r e l a t i o n s h i p a l s o depends on t h e s p e c i e s and p r e s s u r e s o f t h e gas . For a rgon g a s a t p r e s s u r e s of 1 a t m , 2 a t m , and 38.2 a t m ( l i nes C, D , and E shoiv~i iii Fig . 5 ) , t h e breakdown has a d i f f e r e n t behavior a t 1 atm than a t 3 a t m . A t c o n s t a n t p r e s s u r e of a p a r t i c i p a t i n g gas, t h e a b s o r p t i o n

3

of laser beam energy depends on t h e peak i n p u t power. F igu re 6 shows t h e as- p e c t of beam t r ansmiss ion through t h e a i r a t a p r e s s u r e of 746 t o r r when a Ruby laser pu l se i s focused through a 0.0206 m f o c a l lengt t . l e n s . Breakdown i s a l s o a func t ion of t h e i n c i d e n t r a d i a t i o n wavelength and t h e d e n s i t y of t h e medium ( s e e Fig. 7 ) . The a b s o r p t i o n of t h e laser beam o c c u r s a t h igh p r e s s u r e ( o r d e n s i t y ) , and t h e t i m e r e q u i r e d f o r breakdown t h r e s h o l d m u s t be s h o r t due t o f a s t energy accumula t ions . A t t h i s s t a t e a f t e r breakdown, t h e dominant energy t r a n s f e r mechanism (on a microscopic t h e s c a l e ) i s i n v e r s e bremsstrahlung r a t h e r than conduct ion o r d i f f u s i o n .

”

I n Table I V , t h e r e l e v a n t laser-plasma i n t e r a c t i o n parameters o b t a i n e d from t h e l i t e r a tu re survey are t a b u l a t e d i n o r d e r of t h e laser s o u r c e s , tar- g e t medium, breakdown laser power, plasma t empera tu re , plasma e l e c t r o n den- s i t y , dimension of t h e p lasma, and p ropaga t ion v e l o c i t y .

The laser cons idered i n t h e t a b u l a t i o n of Table I V are t h e 10.6 I-lm C02, Ruby p u l s e , and Nd-glass lasers. The media were a i r , a rgon , helium, n i t r o g e n , deuterium, and p l a s t i c p e l l e t a t v a r i o u s p r e s s u r e s .

4

&

I

The MHD system s e l e c t e d h e r e f o r s tudy is a plasma MHD g e n e r a t o r . model of a s e l e c t e d MIID gene ra to r i s se t -up and s i m p l i f i e d w i t h t h e assump- t i o n s t h a t t h e system i s under ope ra t ion .

The

1. MHD Channel Model

The channel schemat ic s e l e c t e d f o r s tudy is d e p i c t e d i n F i g u r e s 1 and 8 and c o n s i s t s of a hydrodynamically,thermally s t a b l e t u r b u l e n t f low of a n elec- t r i c a l l y conduct ing and r a d i a t i n g gas, between e l e c t r o d e p l a t e s w i th a uniform, c o n s t a n t magnetic f i e l d a p p l i e d i n the p o s i t i v e x - d i r e c t i o n . The channel s i d e w a l l s and t h e e l e c t r o d e walls have eiLher a c o n s t a n t h e a t f l u x o r a c o n s t a n t tempera ture . The p h y s i c a l p r o p e r t i e s of tlie gas are c o n s t a n t and t h e gas i s i n l o c a l thernodynamic equ i l ib r ium. and s c a t t e r i n g e f f e c t s are n e g l i g i b l e .

The g:is has a r e f r a c t i v e index of u n i t y ,

.Fo r t h e c a l c u l a t i o n s , t h e geometr ica l dimensions and t h e boundary con- d i t i o n s f o r t h e channel mus t be cons idered . Table V shows t h e parameters which are necessa ry f o r c a l c u l a t i n g t h e NHD g e n e r a t o r performance. The i n i - t i a l and boundary c o n d i t i o n s f o r t he governing e q u a t i o n s are determined from s o l u t i o n s t o t h e equa t ions f o r t h e laser-plasma i n t e r a c t i o n . For s i m u l a t i o n purposes, t h e i n i t i a l and boundary c o n d i t i o n s can be ob ta ined from expe r i - m e n t a l d a t a .

2 . Energy Balance

The thermal energy equa t ion i n t h i s s tudy c o n s i d e r s t h e f u l l y deve l - oped, t u r b u l e n t f low of an e l e c t r i c a l l y conduct ing and r a d i a t i n g gas i n a r e c t a n g u l a r d u c t , where v i s c o u s d i s s i p a t i o n and J o u l e h e a t i n g e f f e c t s are cons ide red ; bu t a x i a l components of conduct ion and r a d i a t i o n are neg lec t ed ( s i n c e t h e i r c o n t r i b u t i o n s t o t h e v e l o c i t y and tempera ture f i e l d s are s m a l l compared t o t h o s e of t h e o t h e r terms i n t h e e q u a t i o n ) . equa t ion may be w r i t t e n i n t h e fol lowing form:

Thus t h e energy

5

t

ORIGINAL PAGE IS OF POOR QUALflY

The f i r s t two terms on the r i g h t hand s i d e (RHS) ' represent t h e n e t t h e r - m a l energy t r a n s p o r t due t o molecular f low and t u r b u l e n t t r a n s p o r t w i t h at deno t ing t h e t u r b u l e n t d i f f u s i v i t y of h e a t . The rest of t h e terms on t h e RHS

own) : t h e molecular and t u r b u l e v i s c o u s d i s s i p a t i o n wi th bulen t v i s c o u s d i s s i p a t i o n of mo tum, Jou le h e a t i n g wi th

oeff deno t ing t h e g a s e l e c t r i c a l c o n d u c t i v i t y , and d ive rgence of t h e r a d i a t i v e f l u x . The t u r b u l e n t t r a n s p o r t q u a n t i t i e s are assumed t o v a r y a c r o s s t h e chan- n e l . p o s s i b l e c a s e s :

The boundary c o n d i t i o n s f o r t h e above e q u a t i o n s are d e s c r i b e d by two

1) Constant w a l l t cmpera ture

2 ) Constant h e a t f l u x

\ -

(2b) I t

aT ' W 4w2 aT'(x,O) = - (X' -) = - - ax ax' 2 k

where 4" and 6'' are t h e h e a t f l u x e s through t h e boundary. 1 w2 W

The i n i t i a l c o n d i t i o n s depend on t h e e n t r y plasma c h a r a c t e r i s t i c s . These can be def ined by. e x p e t h e n t a l measurement.and t r e a t e d a s i n p u t v a r i - a b l e s . I n d t i a l l y th,ese c o n d i t i w s , l i s t e d i n t h e bottom of Table 11, were s e l e c t e d from t h e l i t e r a tu re f o r t h e s tudy . The boundary c o n d i t i o n s i n t h e z - d i r e c t i o n t o t a l l y depend on t h e i n i t i a l c o u d i t i o n s and on t h e t ime dependence of tempera ture a t every nodal p o i n t .

The fo l lowing d imens ionless q u a n t i t i e s a re in t roduced

6

.

where P r and Pr t = molecular and t u r b u l e n t P r a n d t l numbers, r e s p e c t i v e l y .

H a = t h e Hartmann number based on t h e half-channel wid th - , N = t h e r a t i o of molecular thermal conduct ion t o r a d i a t i o n f o r

H 2

a g a s wi th a n a b s o r p t i o n c o e f f i c i e n t and o p t i c a l t h i c k n e s s T . 0

Before nondimensional iz ing t h e energy e q u a t i o n , i t can be s i m p l i f i e d by Ug >> U& and U; ( s i n c e t h e v e l o c i t i e s p e r p e n d i c u l a r t o t h e ax ia l d i r e c t i o n are much smaller i n low P r a n d t l number f l u i d s as compared to t h e ax ia l f low, even i n t h e boundary). Therefore , t he 2nd and 3rd terms on t h e l e f t hand s i d e can be neglec ted . energy e q u a t i o n

Applying t h e nondimensional v a r i a b l e s we have t h e ,

V V a 0 ae P r t 30 - + v - =

+ RetPr ax t RetPr 3y t a t az

V Ec + - (1

Ret

2 TOX * 2

+ H a ~e t N-Rcrzrt ay +- N.RetPr t 3x 2 Ec J2 + T O -- W Y (3)

For s t e a d y plasma f low between the two p a r a l l e l e l e c t r o L 2 p l a t e s , y-, i r e c t i o n v a r i a t o n on ly , no v i s c o u s d i s s i p a t i o n , and t h e plasma w i t h a dominant con- ductive l o s s i n t h e channel , the above e q u a t i o n can be w r i t t e n i n t h e s imple f 3rm

The above equat ion , coupled w i i h ihe f e l l o w i n g e q u a t i o n s , is n m e r i c a l l y solved by t h e f i n i t e d i f f e r e n c e method. The purpose of t h e computat ion w a s t o show t h e tempera ture and the e l e c t r i c a l c o n d u c t i v i t y p r o f i l e s between two e l e c t r o d e s a l o n g t h e MHD channel, t o g i v e t h e power o u t p u t assuming a l o a d t o be a p p l i e d , and to de te rmine t h e g e n e r a t o r e f f i c i e n c y . The power o u t p u t d e n s i t y , cons ider ing t tic cbffcctive e l ec t r i ca l c o n d u c t i v i t y is given b y :

7

where

K = (.Jl+o2- 1 ) @-2 .

The c u r r e n t i n the MHD channel , is

J = J - ,

and t h e e f f i c i e n c y i s

Veloc i ty

C - = '(') (9)' [6.154 + 2.457 I n ( R e t q) + F 1 ( q

'C

A

Kruger and Sonju (Ref. 2 ) , employing t h e Karman-Pollhausen technique , e s t i m a t e d t h e wal l s h e a r stress and boundary-layer t h i c k n e s s corresponding t o t h e semi-empirical v e l o c i t y c o r r e l a t i o n s proposed by Harris (Ref. 3 ) . The loca l v e l o c i t y normalized w i t h t h e c e n t e r l i n e v a l u e i s e v a l u a t e d from

where q is e q u i v a l e n t t o y.

Graphica l resul ts f o r t h e asymptot ic f r i c t i o n c o e f f i c i e n t presented by Kruger and Sonju (Ref. 1 ) may be approximated by

cf - = b 0 . 5 3 6 + 0.929 I n (E) + 0.0222 l n 2 (E)] x 2 (9)

2 2 . where = H a / R e is t h e i n t e r a c t i o n parameter . The t u r b u l e n t Reynolds number is d e f i n e d by

The funct ion F ( c ) is presented g r a p h i c a l l y by H a r r i s (Ref. 3) and may be approximated by &he fo l lowing e x p r e s s i o n (Ref. 2 ) :

8

for 4 5 0 . 6

F, (c ) = 2.502 + 21.9305 - (6.359 + 53.7475 + 649.535 5 ) 2 % I

and

f o r 5 > 0.6

F1(5) =-2.07 - 2.457 I n (5) . where t h e parameter 5 is e q u i v a l e n t

Near t h e w a l l , when n is small, v e l

2

t

H a to - n. R e

c i t i e s ev n e g a t i v e as a r e s u l t o f t h e loga r i thmic term.

l u a t e d from Equation (8) become There fo re , i n a manner similar

t o t h a t employed i n o r d i n a r y hydrodynamic (OHD) t u r b u l e n t f lows f o r t h e laminar s u b l a y e r , v e l o c i t i e s are c a l c u l a t e d u t i l i z i n g t h e product of R e t e n up t o t h e p o s i t i o n where t h i s product equals Equation (8). For t h e s u b l a y e r

U = L n d . P V

The sear stress on t h e w a l l is def ined by 'I

where rh i s t h e h y d r a u l i c r a d i u s . t h e channel , t h e h y d r a u l i c r a d i u s is

For t h e r e c t a n g u l a r c r o s s s e c t i o n area of

LH h 4(L+H) r =

There fo re , t h e v e l o c i t y i n t h e sublayer i s

L+H 314 .- -- 0.01757 (-1 R e t uC 1.i n .

Turbulen t V i s c o s i t y

For t h e v i s c o u s boundary and w a l l h e a t l o s s , t h e v i s c o s i t y and thermal c o n d t c t i v i t y must be cons idered . In most practical MHD a p p l i c a t i o n s , t h e flow is t u r b u l e n t so t h a t t h e t r a n s p o r t p rocesses are dominated by turbu- 1cnt flw. e r a l l y based on t h o s e f o r t u r b u l e n t v i s c o s i t y f o r t h e MHD f low w i t h modi- f i c a t i o n s t o account f o r such f a c t o r s as t h e damping of t h e t u r b u l e n t v i s c o s i t y as t h e magnetic f i e l d is increased .

Expressicnc f e r t h e t u r b u l e n t v i s c o s i t y f o r MHD f lows are gen-

9

The OHD t u r b u l e n t v i s c o s i t y model used by Van Driest (Ref. 4 ) is modified by t h e Mei and Squi re channel f a c t o r (Ref. 5 ) , and is u t i l i z e d w i t h a mul t i - p l i c a t i v e magnetic damping f u n c t i o n by Five land (Ref. 6 ) . Wi th t h e s e cor - r e c t i o n s ,

-2-2 _ - v t - u / [ 1 + 4 K Z ( 1 - e 9

1 + Grl V

- and t h e t u r b u l e n t d i s t a n c e , Z , i s d e f i n e d by

- Z = q R e .

t

The magnetic damping f u n c t i o n used by F ive land (Ref. 6) i s

2 2 -700 Ha /Ret D = e

T h e r m a l Conduct iv i ty

In a plasma, u n l i k e t h e c a s e of v i s c o s i t y , t h e i n t e r n a l s t r u c t u r e of t h e c o l l i d i n g p a r t i c l e s p lay an impor tan t r o l e i n de te rmining t h e thermal con- d u c t i b i t y . Th i s is due t o t h e f a c t t h a t energy may be s t o r e d i n i n t e r n a l de- g r e e s of freedom such as r o t a t i o n , v i b r a t i o n , and e l e c t r o n i c e x c i t a t i o n . I n a mix tu re , which i s i n thermal equ i l ib r ium, p a r t i c l e s recombine when they move a g a i n s t a temperature g r a d i e n t and then release t h e e n e r g i e s of d i s - s o c i a t i o n o r i o n i z a t i o n . However, t h e k i n e t i c t heo ry p rov ides t h e s i m p l e s t methods f o r e s t ima t ing t h e t r a n s f e r c o e f f i c i e n t s f o r a s i n g l e component, mono- atomic gas. t i c l e s by m e , and t h e e f f e c t i v e c o l l i s i o n c r o s s s e c t i o n f o r a s o l i d s p h e r e molecular model Q ( T ) , t h e c o e f f i c i e n t of thermal c o n d u c t i v i t y f o r i on ized gas i s desc r ibed by

Denoting t h e p a r t i c l e c o n c e n t r a t i o n by ne, t h e mass of t h e par -

25 16 - k = -

Q(T) me

The equat ion d e s c r i b e s t h e thermal c o n d u c t i v i t y which would be v a l i d i f t h e COmFGsitiCn of d i s s c c i a t e d gas were f rozen . That i s , t h e p rocesses a r e i d e a l l y f a s t e r than any chemical k i n e t i c p rocess .

- I n Equation 19 , t h e c o l l i s i o n c r o s s 2 s e c t i o n s , Q(T), f o r r i g i d s p h e r i -

c a l molecules of d iameter D is equa l t o 3 .,ID*. used t o estimate Q(T) f o r c o l l i s i o n s between l i k e molecules .

Th i s r e l a t i o n s h i p can be

10

E l e c t r i c a l Conduct iv i ty

The c u r r e n t d e n s i t y i n t h e MHD channel i s p r o p o r t i o n a l t o t h e e l e c t r i c a l c o n d u c t i v i t y of t h e working medium. The fo rmula t ion of c u r r e n t d e n s i t y , j , i n t h e channel i s g iven

j = aUZ B(l - K) (20)

where K is t h e g e n e r a t o r c o e f f i c i e n t and o i s t h e e l e c t r i c a l c o n d u c t i v i t y . The e l ec t r i ca l c o n d u c t i v i t y is r e l a t e d t o t h e e l e c t r o n d e n s i t y , ne, and t h e m o b i l i t y , p, of t h e gas by a gene ra l form (Ref. 7 ) :

For MHD g e n e r a t o r s u s i n g a lka l i seeded noble g a s e s as working f l u i d s , non- e q u i l i b r i u m i o n i z a t i o n o c c u r s when J o u l e h e a t i n g of t h e gas by t h e c u r r e n t c a u s e s t h e e l e c t r o n tempera ture , Te, t o b e h i g h e r t han t h e g a s tempera ture ,

Tg. e q u i l i b r i u m i o n i z a t i o n i n MHD g e n e r a t o r s , t h e e f f e c t i v e e lectr ical con- d u c t i v i t y r a t h e r t han t h e scalar c o n d u c t i v i t y h a s t o be used i n t h e b a s i c MHD equa t ions .

To compute t h e e lectr ical c o n d u c t i v i t y , t a k i n g i n t o account t h e non-

The e f f e c t i v e c o n d u c t i v i t y is g iven by Zampaglione (Ref. 8) as

where B is t h e H a l l parameter and i s a plasma t u r b u l e n c e f a c t o r r ang ing from 0.5 KO 1.0. The Hall parameter is

The e l e c t r o n m o b i l i t y , u , i s g iven by

e

where v2 is t h e c o l l i s i o n frequency of e l e c t r o n s and n e u t r a l s .

To c a l c u l a t e t h e e l e c t r o n d e n s i t y , ne, Saha ' s e q u a t i o n is modified because Te > Tg and t h e e f f e c t i v e i o n i z a t i o n p o t e n t i a l of t h e seed is lowered by t h e Debye c loud . The modi f ied Saha ' s equa t ion f o r ne (Refs. 9 , 10 and 11) is

11

where

- Fp c = (1+F) K T ' g

2 Z: (2nme~Te) K = - 3 exp [-e (Vo - y ) / r T e ] .

h ' 1 z;

I n t h e s e equa t ions , F is t h e mole f r a c t i o n of t h e seed , p i s t h e t o t a l p r e s - s u r e , 2; is t h e e l e c t r o n i c p a r t i t i o n f u n c t i o n of t h e seed i o n , Zg i s t h e p a r t i t i o n func t ion of t h e seed n e u t r a l s , h' i s P l a n k ' s c o n s t a n t , Vo is t h e i o n i z a t i o n p o t e n t i a l , and y is t h e lower ing of t h e i o n i z a t i o n p o t e n t i a l by t h e Debye cloud. The lower ing f a c t o r of t h e i o n i z a t i o n p o t e n t i a l by che Debye c loud is de f ined by

The Debye r a d i u s i s g iven by

2 e ne 'd

where z = 1 f o r atoms, 2 f o r + i o n s , and 3 f o r fl- i o n s , and t i v i t y of f r e e space.

i s t h e permi-

The degree of i o n i z a t i o n i s g iven by

where nB i s t h e d e n s i t y of H e o r A r . f u n c t i o n of a , i s then de f ined by t h e approximation ( R e f . 1 2 ) ,

The c o l l i s i o n frequency f o r H e , a s a

v2 = k.10 + (8085 a - 0 . 2 2 6 4 ) O . ~ ~ ] x

i f (8085 a - 0.2264) > 0. Equation (29) becomes

n H e '

1 2

- 1 la u = 3.10 x 10 *-. nHe, if (8085 a - 0.22643 < 0. 2

- For Ar

v 2 = 10.53 + 0.641 x (10 4 a) 0.721 x 10-14 nAr ,

(30)

(3 1) L

3 where n and n are here in units of particle/cm . He Ar

The initial electron temperature at the entrance of the MHD channel can be defined by solving a set of equations describing the laser-plasma interaction. The electron temperature in the MHD channel can be replaced by the plasma gas temperature which is implicitly computed by a set of equations for the MHD channel. In this simplified model, the entrance electron temperature was set at 2500 K.

1 3

I

RESULTS

The breakdown th re sho ld f o r plasma p roduc t ion by laser r a d i a t i o n depends on t..e medium p res su re (F ig . 3 ) , t h e f o c a l volume (F ig . 4 ) , t h e peak ir- rad iance ( F i g s . 5 and 61, and t h e a b s o r p t i o n band (F ig . 7 ) . The growth of p lasma beyond the breakdown th re sho ld , however, depends e n t i r e l y on a b s o r p t i o n which f a l l s i n t o two d i f f e r e n t c a t a g o r i e s , namely, s h o r t and long p u l s e s (Ref. 1). I n a s i n g l e s h o r t p u l s e r e g i o n , i n v e r s e bremss t rah lung comprises about 40% absorp t ion . On t h e o t h e r hand, i n a long p u l s e , a b s o r p t i o n of ove r 80% occur s up t o t h e p o i n t where t h e t r a n s i t i o n from c l a s s i c a l t o anomalous behavior beg ins . Beyond t h e t r a n s i t i o n p o i n t , t h e a b s o r p t i o n r a p i d l y drops t o about 50% due t o t h e ion-acous t ic t u rbu lence , t h e B r i l l o u i n b a c k s c a t t e r , t h e s p e c u l a r r e f l e c t i o n , and the non- l inear behavior of t h e plasma. The ab- s o r p t i o n of high laser i r r a d i a n c e i n t h e long p u l s e mode by a n expanding plasma b a l l can be improved by a wel l -designed i n t e r a c t i o n chamber. The s p e c u l a r r e f l e c t i o n and t h e s c a t t e r i n g a t t h e c r i t i c a l d e n s i t y s u r f a c e of t h e plasma comprise about 40% of t h e t o t a l i r r a d i a n c e i n t h e long pu l se mode. Such l o s s e s are s e n s i t i v e t o t h e laser power level and can be p a r t l y re- t r i e v e d by cons ide r ing the des ign of t h e o p t i c s and geomet r i ca l c o n f i g u r a t i o n , magne t i ca l ly c o n t r o l l e d plasma boundary, and by f a b r i c a t i n g t h e plasma chamber wi th h i g h l y r e f l e c t i v e s u r f a c e s . That is , wel l -designed o p t i c s and a geometry c o n f i g u r a t i o n with h igh ly r e f l e c t i v e s u r f a c e s can r e f o c u s t h e beam r e f l e c t e d from t h e plasma s u r f a c e back t o t h e plasma. chamber w a l l s can also be a l l e v i a t e d by magne t i ca l ly c o n t r o l l i n g t h e plasma boundary. peak i r r a d i a n c e of a long pulsed laser. This i s t h e opt imized v a l u e of t h e convers ion e f f i c i e n c y of t h e laser i n c i d e n t beam energy as shown i n F igu re

The damage to t h e r e f l e c t i v e

I n t h i s c a se , t h e t o t a l a b s o r p t i o n would be above 80% a t t h e

2 .

The c h a r a c t e r i s t i c s of t h i s abso rp t ion mechanism, as w e l l a s t h e c r u c i a l e f f e c t of t h e cold boundary, have t o be accounted f o r i n t h e plasma expansion, s i n c e t h e p o s s i b i l i t y e x i s t s t h a t t h e plasma would decay b e f o r e pas s ing through t h e MHD genera tor . Applying a magnetic f i e l d t o pinch t h e plasma r a d i a l l y un- t il t h e plasma passes through’ t h e gene ra to r may s o l v e t h e c o l d boundary prob- l e m , or, on t h e o t h e r hand, alleviates t h e damage t o t h e w a l l by t h e h i g h l y expanding plasma, from t h e c o l d wall . S ince t h e c o l d w a l l i s i n c o n t a c t w i t h t h e plasma, i t i n - duces i n t a b i l i t i e s which enhance thermal conduct ion l o s s e s (Ref. 13). Table V I d e s c r i b e s the laser sources , t h e medium, t h e breakdown t h r e s h o l d , t h e plasma tempera ture , the f o c a l volume, and more. t h e dynamics and c h a r a c t e r i s t i c s of t h e laser - induced p lasma w i t h r e s p e c t t o t h e i r r a d i a n t power, t h e time t o breakdown, growth, decay, t h e t o t a l a b s o r p t i o n , and t h e medium p res su re . duce a plasma i n a chamber of improved geomet r i ca l f e a t u r e s with s.;ecific r a d i a t i v e p r o p e r t i e s should a l s o be i n v e s t i g a t e d .

The magnet ic f i e l d may be used t o the rma l ly i n s u l a t e t h e plasma

More r e s e a r c h i s needed t o e s t a b l i s h

How e f f e c t i v e l y t h e laser energy can b e used t o pro-

The power d e n s i t y and t h e system e f f i c i e n c y of t h e MHD c y c l e is much h ighe r compared t o t h o s e of t h e convent iona l thermal c y c l e s . main problems i n t h e development of MHD g e n e r a t o r s are t h e h igh tempera tures r equ i r ed and t h e c o r r o s i v e gas medium which can e a s i l y damage t h e e l e c t r o d e s

However, t h e

and w a l l of t h e gene ra to r .

I

Though well-known concepts and well-developed a n a l y s i s exis t , t h e MHD g e n e r a t o r s s t i l l r e q u i r e i n t e n s i v e r e sea rch f o r u s e i n space. a n a l y s i s r e l a t e d t o t h e convent iona l MHD g e n e r a t o r may n o t b e s u f f i c i e n t f o r t h e d i r e c t a p p l i c a t i o n t o t h e l a se r -d r iven plasma MHD system because t h e energy s o u r c e is i n t h e form of a l i g h t beam. p e n e t r a t e s t h e plasma product ion chamber, bu t a l s o ex tends t h e energy inpu t through t h e g e n e r a t o r , and t h u s may d e p o s i t t h e inpu t energy unevenly throughout t h e plasma.

The e x i s t i n g

The l i g h t beam not on ly

From a s i m p l i f i e d model computation, t h e tempera ture , v e l o c i t y , and e l e c t r i c a l c o n d u c t i v i t y d i s t r i b u t i o n were ob ta ined . cu rves from t h e c e n t e r of t h e channel t o t h e e l e c t r o d e a t d i f f e r e n t - p o i n t s a long t h e a x i a l d i r e c t i o n are shown i n t h e F igu res 9 , 10, 11, and 12 . The v a r i a b l e s were non-dimensionalized so t h a t t h e numbers i n t h e f i g u r e s are desc r ibed w i t h t h e s c a l e d va lues . w a s ob ta ined wi th t h e assumption of a t u r b u l e n t channel f low. proach is reasonable , since t h e MHD f low u s u a l l y h a s a t u r b u l e n t f low p r o f i l e . Based upon t h e v e l o c i t y p r o f i l e , t h e tempera ture and electrical c o n d u c t i v i t y f o r t h e medium w e r e c a l c u l a t e d . The tempera ture p r o f i l e s i n F igu re 10 are s c a l e d by t h e uniform w a l l temperature . By c o n s i d e r i n g t h e e l e c t r o n m o b i l i t y and plasma tu rbu lences w i t h t h e above v e l o c i t y and temp- e r a t u r e p r o f i l e s , t h e e f f e c t i v e e l e c t r i c a l c o n d u c t i v i t y w a s computed and is shown i n F igure 12. The e l e c t r i c a l c o n d u c t i v i t y is s i g n i f i c a n t l y a f - f e c t e d (as much as 55 pe rcen t ) by the e l e c t r o n m o b i l i t y and t h e plasma t u r - bulence (which i s a l s o a f u n c t i o n of t empera tu re ) . From t h e above computa- t i o n a l results, t h e average v a l u e s of v e l o c i t y , t empera ture , and e f f e c t i v e e lectr ical c o n d u c t i v i t y are obta ined . These average v a l u e s can be used t o c a l c u l a t e t h e Hall parameter and the g e n e r a t o r c o e f f i c i e n t which are, i n t u r n , used t o c a l c u l a t e t h e power output d e n s i t y and t h e e f f i c i e n c y . The power ou tpu t d e n s i t y and t h e e f f i c i e n c y cons ide r ing t h e e l e c t r o n m o b i l i t y and plasma tu rbu lence was 0.2254 W/cm3 and 43 percen t . improved by op t imiz ing t h e d e s i g n of t h e channel . p u t d e n s i t y , an e f f i c i e n c y of 54 percent is c a l c u l a t e d based on t h e e l e c t r o n d e n s i t y of 1 .315 x 1019/cm3, t h e medium average tempera ture , 2500 K, and ig - no r ing t u r b u l e n t e f f e c t s and non-equilibrium i o n i z a t i o n . Table V I 1 shows c:.c Faraaeters of a MHD g e n e r a t o r used f o r t h e t w o cases.

T h e s e d i s t r i b u t i o n

The v e l o c i t y p r o f i l e i n F igu re 9 T h i s ap-

These v a l u e s can be For t h e same power out -

15

CONCLUSIONS

In conclus ion , t h e l i t e r a t u r e survey and t h e s i m p l i f i e d model c a l c u l a t i o n s show t h a t based on i t s e f f i c i e n c y and power d e n s i t y , t h e l a s e r - d r i v e n MHD sys- t e m is pract ical and may have a p p l i c a t i o n s f o r f u t u r e s p a c e c r a f t energy system in space .

From t h e s i m p l i f i e d model t h e g e n e r a t o r e f f i c i e n c y is 53.5 p e r c e n t , i f t u r - bulence and non-equilibrium i o n i z a t i o n are ignored. i n t o account , the e f f i c i e n c y is reduced t o 43 .2 p e r c e n t .

I f t h e s e e f f e c t s are t aken

F u r t h e r d e t a i l e d t h e o r e t i c a l and expe r imen ta l a n a l y s i s of t h e laser- d r i v e n MHD gene ra to r are necessa ry t o r e a l i z e a h igh p o t e n t i a l f o r space ap- p l i c a t i o n .

16

CAR MAKE

a nwn i w s r n ' I BEAM I

RECEl V 1 NG

1 I RlER GAS & FOCUSING I

,-UP SUPPLY

GAS MIXING

7--

I COMPRESSOR

SEED GAS MAKE-UP SUPPLY

GAS SEPARATOR Lf--J SYSTEM

Y I C U R E 1. LASER-DKTVEN M111) GENEIIA'J'OK

1 7 i ,

I

8 0 00

W U 3 !z a n 5 W I- I- W -1 Z

5 a 0 LL z 3

w

-

-

0

z 0 I- o W -1 LL W U

U -1 3 o W n v)

-

a

0

* I I 1

a 0 0

m m l 8 0 m

F II

W (3 v z w

H 0 H D4 cr w

2 r: z w 3 U

W > W 0 W U

- H p: a a

m w 0 mJ

8 0 00

e I I

8 0 cv

a mJ

s t W M

H cr

0

a mJ

18

i . I

0 0 0 r

0 0 r

0 l-

r 3

23 0 3

Ln

m b.4 a: 3 2

19

0 I v) W

IO'(

W U m

10

CHARACTERISTIC FOCAL DIMENSION A [cm]

f .

FIGURE 4 . BREAKDOWN THRESHOLD FOR A r (PRESSURE 5.2 x 10' TORR) AS A FUNCTION OF CHARACTERISTIC FOCAL DIMENSION A. (REF. 53)

20

- 187 cn

80-

60-

40-

20-

c 140

160 =a c

Q) v) 0

cu c I -

5 0 cI I 2 O l 100

\ E: A r - 1 . 0 atm

\ Ar - 3.0 atm

He-38.2

B: N2 - 34.2 atm

\ atm

\ C: Ar-38.2 atm

01 I I I I I I

0 2 4 6 8 10 12x10'

PEAK ELECTRIC FIELD [V/cml I I I I I I

IO9 1o'O 5xlo10 IO" 2x1O1' PEAK IRRADIANCE W/cm2 I

FIGURE 5 . BREAKDOWN TIME AS A FUNCTION OF PEAK IRRADIANCE AND PEAK ELECTRIC F I E L D FOR A Q-SWITCHED RUBY LASER PULSE FOCUSED I N VARIOUS GASES. ( R E F . 5 4 )

21

* 0

0 cv

1

NOISSIWSNWUI AW3N3 l N 3 3 U3d

22

. 1000 Torr

Torr

Torr

Torr

# I l l I I I I I I

-10,000 5,000 1,000

WAVELENGTH [AI

FIGURE 7. BREAKDOWN THRESHOLD A S A FUNCTION O F WAVELENGTH O F I N P U T RADIATION FOR A r A T FOUR SELECTED PRESSURES. (REF. 56)

23

f k H

FIGURE 8. FMD CHANNEL

J is t h e c u r r e n t d e n s i t y a long t h e y d i r e c t i o n

B i s t h e magnetic f l u x a l o n g t h e x d i r e c t i o n

U i s the v e l o c i t y a l o n g the z d i r e c t i o n

H is t h e h e i g h t of t h e g e n e r a t o r between e l e c t r o d e s

W i s t h e width of t h e g e n e r a t o r

L i s t h e l e n g t h of t h e g e n e r a t o r

.

24

01 I I I I

1=25r---

i 0=25 t DISTANCE 2y/H

FIGURE 9. CALCULATED VELOCITY PROFILE OF TURBULENT FLOW I N THE MHD CHANNEL

The v e l o c i t y is t h e r a t i o of a l o c a l v e l o c i t y based on t h e v e l o c i t y Uc a t t h e ax ia l c e n t e r of the generator

25

2.2

1.9

1.6

1.3

1 0 0.2 0.4 0.6 0.8 1

DISTANCE 2y/H

FIGURE 10. CALCULATED TEMPERATURE PROFILES AT T H E E DIFFEKENT LOCATIONS FROM THE ENTRANCE OF THE MHD CHANNEL

The c o n s t a n t w a l l t e m p e r a t u r e of 1 0 0 0 k w a s used i n t h e c a l c u l a t i o n

26

130

U

b

> 1- 104

91

78

0

I I I I

U Y I I I I

0 0.2 0.4 0.6 0.8 1

DISTANCE 2y/H

FIGURE 11. CALCULATED ELECTRICAL CONDUCTIVITY PROFILES AT FOUR DIFFERENT LOCATIONS FROM THE ENTRANCE OF THE MHD CP!\?!NEL

27

0.448

0.447

0.446

0.445

I I

z/H =1 (fiorn Enhance)'

z/H =5 \

I I I I 7 0 0.2 0.4 0.6 0.8

DISTANCE 2Y/H

1

FIGURE 12. CALCULATED EFFECTIVE ELECTRICAL CONDUCTIVITY PROFILES AT THREE DIFFERENT LOCATIONS FKOM THE ENTRANCE OF THE MHD CHANNEL

28

H H

w l-l FQ 4 ic

n

c, rl u z 0 U W

LX 0

3 W

H H

W c-l m $

32

TABLE 111. ALKALI METAL PARAMETERS

GAS RESONANCE RADIA- IONIZATION PERCENT LENGTH FOR 90% TION WAVELENGTHS POTENTIAL IONIZATION ABSORPTION

(A) (ev) T=2500 K, P=760 torr T=2500 K , P=760 torr

POTASSIUM 7665 7669 4.45 3 .3 52 c m

I 8521 8944 3.87 12. 50 c m

1 SODIUM I

5890 5896 5.12 0 . 7 50 em

33

TABLE ‘4. BADAYETEP,S ?!ECESSAP,Y FOR CALCULATING THE MHn GENERATnR PERFOWLAN C E

NECESSARY FOR Tw 17 DUCT WALL TEMPERATURE

1 NO. PARAMETERS SYMBOL CODE REMARKS I TYPE OF GAS

TYPE OF SEED MATERIAL

COMPOSITION RATIO, SEED/GAS

AMOUNT OF SEED

GAS DENSITY N

SEED GAS DENSITY

MOLE FRACTION OF SEED F

INITIAL ELECTRON DENSITY N

IONIZATION POTENTIAL v

g

Ncs

0

NECESSARY FOR

CALCULATING THE

STATE VARIABLES

AND THE ELECTRICAL

CONDUCTIVITY

10 CHARGE OF THE ATOM Z

11 TOTAL PRESSURE P

0 12 INITIAL ELECTRON TEMPERATURE T,

13 DUCT LENGTH

14 DUCT WIDTH

z or R

x or W

GEOMETRY

18 MAGNETIC FIELD INTENSITY B

19 FLOW RATE til

20 GENERATOR COEFFICIENT K

CALCULATING THE

MHD OUTPUT POWER

i 1 21 LOAD CURRENT I

22 INTERACTION COEE’FICENT 1 35

TABLE VI. LASER-PLASMA INTERACTION PARAMETERS USED FOR LASER-DRIVEN MHD

LASER

WORKING FLUID

BREAKDOWN THRESHOLD LASER POWER

LASER POWER

AVERAGE MEDIUM TEMPERATURE IN THE GENERATOR VOLUME

ELECTRON DENSITY

PROPAGATING VELOCITY

PLASMA LENGTH

PLASMA RADIUS

SEED MATERIAL

10.6~ C02 PULSED

AIR - 1 atm

6 2 1.3 x 10 W/cm

100 - 150 J, 200 ns 10 Hz (EQIUV. CW MODE 50 - 75 MW)

- > 1600 K

lo6 - 10 7 cm/s

15 cm

1 cm

CESIUM

,

36

TABLE VII. COMPARISON OF EFFECTS OF TURBULENCE AND NON-EQUILIBRIUM IONIZATION

- ~~

PARAMETERS

geometry

TURBULENCE AND NON-EQUILIBRIUM IONIZATION IGNORED

~-

rectangle cross section

1.315~10

2 500

0.3360

0.231

3.17

0.225364

**0.420961

19

53.5

TURBULENCE AND NON-EQUILIBRIUM IONIZATION TAKEN INTO ACCOUNT

rectangle cross section

19 1.315~10

2500 (3100 *)

0.3180

0.2843

2.31

0.225364

0.521918

43.2

* The temperature necessary to achieve the efficiency of 53.5% = (n KT )AU per unit volume where ‘in e e ** Based on Te, n and U, e

A is the cross section area

37

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4 .

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29. Palmer, A. J.: "Radiatively Sustained Cesium Plasmas for Solar Electric Conversion," Radiation Energy Conversion in Space, edited by K. W. Billman, Progress in Astronautics and Aeronautics, Vol. 61, AIAA, 1978.

30. Cerini, D. J. and D. G. Elliott: "Performance Characteristics of a Single-Wavelength Liqiud Metal MHD Induction Generator with Endless Compensation," 8th Symposium on Engineering Aspects of MHD, Stanford, p. 11, 1967.

31. Rowe, I., T. C. Wand and S . J. Dudzinsky: "Experimental Results with the Variable Fluid and Field Velocity MHD Generator," 8th Symposium on Engineering Aspects of MHD, Stanford, p. 31, 1967.

32. Amend, M., C. Hsu, M. Petrick and J. Roberts: "Performance of a Quasi- Ericsson Two-Phase Two-Component Liquid Metal MHD Power Cycle," 11th Symposium on Engineering Aspects of MHD, Caltec, Pasadena, p. 154, 1970.

33. Amend, W. E., J. C. Cutting and M. Petrick: "Analysis of Liqiud-Metal MHD Power Cycles for Central Station Power Generation," 12th Symposium on Engineering Aspects of MHD, Argonne, p . N-1.1, 1972.

3 4 . Cerini, D. J.: "Nak-Nitrogen Liquid Metal MHD Generator Tests at 30 KW," 13th Symposium on Engineering Aspects of MHD, Stanford, p. 111-2.2, 1973.

35. Hays, L. G., R. L. Phen and P. S . Zygielbaum: "A Cesium-Lithium MHD Topping Plant for Central Station Power Generation," 13th Symposium on Engineering Aspects of MHD, Stanford, p. 111-6.1, 1973.

36. Elliott, D. G.: "Performance Capabilities of Liqiud Metal MHD Induction Generators," International Atomic Energy Agency, -- Proceedings of a Symposium on MHD Electrical Power Generation, Section 2, pp. 1311-2092, July 1968.

37. Petrick, M., P. F. Dunn, E. S . Pierson, P. V. Dauzvardis and I. Pollack: "Liquid Metal MHD Energy Conversion," ANL/MHD-78-5, Argonne National Laboratory, May 1979.

38. Pierson, E. S . , H. Branover, G. Fabris and C. B. Reed" "Solor-Powered Liquid Metal MHD Power Systems," ASME, 79-WA/SOL.-22.

39. Batteh, J. H. and D. R. Keefer: "Two Dimensional Generalization of Raizer's Analysis for the Subsonic Propagation of Laser Sparks," IEEE Transactions on Plasma Science, Vol. PS-2, pp. 122-129, September 1974.

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40. Frazen, E. i. t " C U i i ~ i n i i ~ i i s Lzser-Sustnined ? 1 3 s x i c , " J . App1, Phys.: Vol . 44, No. 4 , pp. 1727-1723, A p r i l 1 9 7 3 .

41. George, E. V . , G. Bekef i and B. Ya'akobi: " S t r u c t u r e o f t h e Plasma F i r e - b a l l Produced by a C 0 2 Laser," The Phys ics of F l u i d s , V o l . 1 4 , No. 1 2 , pp. 2708-2713, December 1971.

42. Hoffman, A. L.: "Strong Axial Laser Heat ing of a Theta-Pinch Plasma," Appl. Phys. L e t t . , Vol. 23, p. 693, 1974.

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41

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56. "Frequency Dependence

.

4 2

1. Roport No.

NASA CR-178184

Space-Based Laser-Driven MHD Generator: F e a s i b i l i t y Study

2. Government Accasion No.

~~ ~

7. Author(s)

S. H . Choi

7. Key Words (Suggested by Author(r))

Space power transmission, l a s e r s , MHD

9. Performing Organization Name and Address

Informat ion & Control Systems, Inc. 28 Research Drive Hampton, VA 23666

18. Distribution Statement

Unclassified-Unl imi ted

Subject Category 20

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration Washington, DC 20546

Langley Technical Monitor: Nelson Jalufka 15. Supplementary Notos

Final Report

9. Security Classif. (of this report)

Unclassified

3. Recipient's Catalog No.

20. Sccurity Clauif. (of this page) 21. No, of Pages 22. Rice

Uncl ass i f i ed 51 A04

5. Roport Dato

6. Performing Organization Cod. October 1986

8. Performinq Orgonirrtion Report No.

681 104 10. Work Unit No.

11. Contract or Grant No.

L-28161 B 13. Type of Report and Poriod Covered

Contractor Rep0 r t 14. Sponsoring Agency Code

506-41-41-02

16. Abstract The f e a s i b i l i t y of a laser-driven MHD generator, as a candidate receiver

f o r a space-based l a s e r power transmission system, was investigated.

On the basis of reasonable parameters obtained i n the l i t e r a t u r e search, a model of the laser-driven MHD generator was developed w i t h the assumptions of a steady, turbulent , two-dimensional flow. based on the continuous and steady generation of plasmas by the exposure of the continuous wave l a s e r beam thus inducing a steady back pressure t h a t enables the medium t o flow s teadi ly . The model considered here took the turbulent nature of plasmas into account i n the two-dimensional geometry of the generator. conditions w i t h the plasma parameters defining the thermal conductivity, viscosi t j e l e c t r i c a l conductivity f o r the plasma flow, a generator eff ic iency of 53.3% was calculated. account, the eff ic iency i s 43.2%.

The assumptions used i n this study were

For these

If turbulent e f f e c t s and nonequilibrium ionizat ion a r e taken i n t o

An extensive l i t e r a t u r e search of research on MHD generators and laser - produced plasmas was car r ied out. The study shows t h a t the laser-driven MHD system has potential as a l a s e r power receiver f o r space appl icat ions because of i t s h i g h energy conversion eff ic iency, h i g h energy densi ty and r e l a t i v e l y simple mechanism as compared t o other energy conversion cycles.

nasa contractor report · nasa contractor report 1.75184 ... - ratio of molecular thermal...

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