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UBC Theses and Dissertations

An investigation of a vortex stabilized arc Neilson, John Bruce 1981

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AN INVESTIGATION OF A VORTEX S T A B I L I Z E D ARC by JOHN BRUCE NEILSON B.Sc,  The U n i v e r s i t y M.Sc,  Of B r i t i s h  Columbia,  McMaster U n i v e r s i t y ,  1975  1978  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES (DEPARTMENT OF PHYSICS)  We a c c e p t t h i s  t h e s i s as conforming  to the required  standard.  THE UNIVERSITY OF B R I T I S H COLUMBIA S e p t e m b e r 1981 ©  J . Bruce N e i l s o n ,  1981  In p r e s e n t i n g  this  thesis i n partial  f u l f i l m e n t of the  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y of B r i t i s h Columbia, I agree that it  freely  a v a i l a b l e f o r r e f e r e n c e and study.  agree that p e r m i s s i o n f o rextensive for  the Library shall  financial  copying or p u b l i c a t i o n of this  gain  shall  J . Bruce Neilson  Department o f  Physics  The U n i v e r s i t y o f B r i t i s h 2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V6T 1W5  It i s thesis  n o t be a l l o w e d w i t h o u t my  permission.  ( 9 /~7Q\  thesis  s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e h e a d o f my  understood that  Date  I further  copying of t h i s  department o r by h i s o r h e r r e p r e s e n t a t i v e s . for  make  Columbia  September 11, 1981  written  i i  ABSTRACT  The power b a l a n c e e q u a t i o n s DC  vortex  numerically profile,  stabilized  arc  to give predicted  radiative  power  f o r t h e column of in  argon  values  and  have  for  been  calorimetry,  solved  temperature  heat t r a n s p o r t  to the w a l l .  and compared w i t h  so a s t o r e f i n e o u r  500 A  the  T h e s e q u a n t i t i e s h a v e a l s o been m e a s u r e d u s i n g and  a  understanding  spectroscopy  the t h e o r e t i c a l r e s u l t s of  the  heat  transport  processes i n the a r c . Further accurately,  study  i s required to predict convective  e s p e c i a l l y a t low power  effects  l e v e l s , but the r e s u l t s  show t h a t t h e b e h a v i o u r o f t h e c o l u m n i s p r e d i c t a b l e a t h i g h power  levels.  important  Forced convection  h a s been shown  r o l e i n the a r c column.  to  play  an  iii  TABLE OF  CONTENTS  Abstract  i i  T a b l e Of C o n t e n t s  i i i  List  Of T a b l e s  v  List  Of F i g u r e s  vi  Acknowledgements  ix  Nomenclature  x  I.  1  Introduction  II. A.  T h e o r y Of The A r c Column  8  Introduction  B. The  8  Elenbaas-Heller  Equation  9  C. The Computer C a l c u l a t i o n s  11  D.  20  Assumptions  E. C o n v e c t i v e III. A.  Transport  Experimental  24  Apparatus  37  Introduction  B. The Gas  37  System  39  C. The V o r t e x D.  41  The C o o l i n g  System  44  E. The E l e c t r i c a l  System  F. The A r c V e s s e l  And E l e c t r o d e s  IV. D i a g n o s t i c A.  Methods  AI L i n e  E. A b s o l u t e  47  52  B. The O p t i c a l S y s t e m  D.  45  52  Introduction  C. The D a t a H a n d l i n g  <  53 System  I n t e n s i t y Measurements Intensity Calibration  56 57 61  iv  F. AI L i n e W i d t h M e a s u r e m e n t s  65  G. C o n t i n u u m I n t e n s i t y M e a s u r e m e n t s  66  V. R e s u l t s And A n a l y s i s  69  A. I n t r o d u c t i o n  69  B. C a l o r i m e t r y  70  C. T e m p e r a t u r e P r o f i l e s  81  D.  85  L i n e W i d t h And C o n t i n u u m M e a s u r e m e n t s  E. S y s t e m a t i c E r r o r s  86  F. Time V a r i a t i o n  89  G. C y l i n d r i c a l  92  Symmetry  H. A x i a l V a r i a t i o n VI. Conclusions  92 96  A. I n t r o d u c t i o n  96  B. C o n c l u s i o n s  97  C. O r i g i n a l C o n t r i b u t i o n s  99  D.  100  S u g g e s t e d F u t u r e Work  Bibliography  103  A p p e n d i x A. S t e a d y S t a t e C a l c u l a t i o n P r o g r a m s  105  A p p e n d i x B. T r a n s i e n t H e a t i n g C a l c u l a t i o n P r o g r a m s  ....107  A p p e n d i x C. D a t a H a n d l i n g P r o g r a m s  110  A p p e n d i x D. Gas F l o w I n The S y s t e m  122  A p p e n d i x E. The V i s c o u s Decay Of A V o r t e x  127  V  L I S T OF TABLES  T a b l e I I - 1 . A s s u m p t i o n s F o r The S t e a d y S t a t e M o d e l  ....20  T a b l e I I - 2 . M o d e l s Of A r g o n M a t e r i a l F u n c t i o n s  25  T a b l e D-1. Gas F l o w R a t e s And P r e s s u r e s  126  L I S T OF  FIGURES  Figure  1 - 1 . The V o r t e x  Figure  11 -1 . R e g i o n s Of The A r c  Figure  II-2. Variation  S t a b i l i z e d Arc  Of  4 8  Profile  With  Starting  Temperature  12  Figure  I I - 3 . T v s R. P=1 Atm  14  Figure  I I - 4 . T v s R. P=3 Atm  15  Figure  I I - 5 . T v s R. P=5 Atm  16  Figure  I I - 6 . T v s R. P=7 Atm  17  Figure  I I - 7 . Core Temperature vs Current  19  Figure  I I - 8 . Core Radius vs Current  19  Figure  I I - 9 . K v s T (T>7000K)  26  Figure  11-10.  26  Figure  1 1 - 1 1 . e v s T, P=1 Atm  27  Figure  11-12.  27  Figure  11-13. R a d i a l Isotherms vs P o s i t i o n  29  Figure  11-14.  31  Figure  1 1 - 1 5 . T v s R, T = 1 0 0 0 0 K  Figure  11-16.  T v s R, T = 1 1 0 0 0 K  33  Figure  11-17.  1000K R a d i u s v s T i m e  34  Figure  11-18.  H e a t F l u x v s Time  34  Figure  11-19.  K v s T (T<7000K)  Q r a d v s T, P= 1 Atm  />C  p  vs T  ...32  0  0  Position  Of  The  Gas  Disc  Mass v s Time  C e n t e r Of 35  Figure  1 1 1 - 1 . B l o c k D i a g r a m Of The S y s t e m  38  Figure  I I I - 2 . The Gas S y s t e m  40  Figure  I I I - 3 . The C o o l i n g S y s t e m  46  Figure  I I I - 4 . The E l e c t r i c a l  46  Figure  I I I - 5 . Typical Current  Figure  I I I - 6 . D r a w i n g Of The A r c V e s s e l  51  Figure  I V - 1 . The D i a g n o s t i c  55  Figure  I V - 2 . The AI 430 nm L i n e  59  Figure  I V - 3 . The C a l i b r a t i o n  63  Figure  IV-4. Radiance vs Brightness  Figure  IV-5. N vs Radiance  System And V o l t a g e  Waveforms  System  Setup Temperature  ...48  64 64  F i g u r e IV-6. Temperature vs E l e c t r o n D e n s i t y  67  F i g u r e V - 1 . Power L o s s e s v s C u r r e n t ,  P=1.5 Atm  71  F i g u r e V - 2 . Power L o s s e s v s C u r r e n t ,  P=2.1  Atm  72  F i g u r e V - 3 . Power L o s s e s v s C u r r e n t ,  P=2.8 Atm  73  F i g u r e V-4. T o t a l Column L o s s e s v s C u r r e n t  75  F i g u r e V-5. R a d i a n t  76  Losses vs Current  F i g u r e V-6. W a l l L o s s e s v s C u r r e n t  77  F i g u r e V-7. The M o d i f i e d W a l l L o a d i n g P r e d i c t i o n  80  F i g u r e V-8. T y p i c a l T e m p e r a t u r e P r o f i l e s  82  F i g u r e V-9. C o r e T e m p e r a t u r e v s C u r r e n t  83  F i g u r e V-10. Core R a d i u s vs C u r r e n t  84  F i g u r e V - 1 1 . C o r e T e m p e r a t u r e s From T h r e e M e t h o d s  87  F i g u r e V-12. C u r r e n t , F i g u r e V-13. T y p i c a l  T e m p e r a t u r e And R a d i u s v s Time ..91 Intensity Profiles  93  F i g u r e V-14. Temperature v s A x i a l  Position  94  F i g u r e V-15. Core R a d i u s v s A x i a l  Position  94  F i g u r e V I - 1 . The C o n v e c t i o n F i g u r e E - 1 . The F u n c t i o n  Free Vortex  J , ( x ) / x vs x  S t a b i l i z e d A r c 121 128  viii  F i g u r e E-2.  Solid  Body V o r t e x  F i g u r e E-3.  Annular  Jet Vortex  129 129  ix  ACKNOWLEDGEMENTS  I  w o u l d l i k e t o t h a n k my s u p e r v i s o r D r . C u r z o n f o r h i s  support  throughout  suggestions of my  he  committee,  f o r their help  addition  I  discussions  work  and  have  and  a  great  a l l the  technical staff  I am i n d e b t e d  electronic  many  useful  Nodwell  i n the p r e p a r a t i o n of t h i s  gained  with  Drs. Ahlborn,  deal  members  p a r t i c u l a r l y L o m e G e t t e l and John The  f o r the  h a s made. I am a l s o g r a t e f u l t o t h e members  supervisory  White,  this  of  and  t h e s i s . In  from  many  useful  the  plasma  group,  Pearson.  h a v e a l w a y s been e x t r e m e l y  helpful,  e s p e c i a l l y t o A l C h e u c k , who f i x e d a l l  equipment  as  my  f a s t a s I c o u l d damage i t w i t h RF  p u l s e s , a n d t o E r n i e W i l l i a m s who p r e p a r e d  dozens of  quartz  tubes. I  gratefully  National Science  acknowledge  and E n g i n e e r i n g  financial Research  support Council  from t h e and  the  U n i v e r s i t y o f B.C. This  thesis  i s dedicated  t o R. A. Nordman, who  i n t r o d u c e d me t o t h e j o y s o f P h y s i c s .  first  NOMENCLATURE  arc  vessel  radius  transition probability speed o f l i g h t constant pressure s p e c i f i c vertical  spacing  electric  field  excited  state  statistical Planck  between  heat spectra  energy  weight  constant  current volume e m i s s i v i t y thermal  conductivity  Boltzmann  constant  a n g u l a r momentum a r g o n a t o m i c mass mass f l o w  rate  number o f OMA c o u n t s neutral electron excited  gas d e n s i t y density state  population  pressure power r a d i a t i v e emission of argon power r e q u i r e d  f o r gas h e a t i n g  xi  r a d i a t i v e column •  Q T  Q  •  w  r r  i  r  -  1 0  total  input  power  power l o a d on v e s s e l radial  position  radius  o f 1000K  radius  o f 10000K  R  viscous  Ro,  r a d i a n c e p e r OMA  R«  3  0  flow  integrated  T  temperature 0  wall  isotherm isotherm  resistance count  r a d i a n c e a t 430 nm  S  T  losses  center  thermal  conductivity  temperature  V  velocity  V  voltage  w  OMA  y  vertical  2  axial  V  specific  X  wavelength  f  viscosity  fi  density  a  electrical  conductivity  T  decay time  constant  channel  width  position  position heat  ratio  continuum emission U  angular v e l o c i t y  factor  1  CHAPTER I  INTRODUCTION F o r many y e a r s experimental high  a r c h a s been a m a i n s t a y  p l a s m a p h y s i c s , a s w e l l a s an e x t r e m e l y  intensity  for  the e l e c t r i c  light  source, both  spectroscopic  f o r general  investigations.  Since  useful  lighting the  first  and arc  d i s c h a r g e was p r o d u c e d by Davy a n d R i t t e r  in  c h a r c o a l e l e c t r o d e s i n a i r , many d i f f e r e n t  t y p e s o f a r c have  been  studied  by  many  historical  development  interested  reader  (1956) o r Hoyaux Before question  by  1968,  (10"  6  Kesaev  are  s),  should  discharge  arcs,  authors  comparable  we  ( i . e . an  arcs  the  consider  sparks  (Finkelnburg  1964) they easily  and and  glow  distinguished  to  the  equilibration  but  the  distinction  the  discharge  d i s c h a r g e s , and  criteria  give  current (>1A) a n d  of  Maecker  have d i f f e r e n t generally  electric  types  the  speaking,  of l a r g e c u r r e n t  1956,  being  time  of  Hoyaux  f o r separating  same  as  groupings. of  the  duration discharge  between g l o w d i s c h a r g e s a n d  some a r c s i s n o t s o c l e a r - c u t . The most is  of  first  (<100V). G e n e r a l l y t h r e e  them, a l t h o u g h Sparks  physics  of t h e  t o F i n k e l n b u r g and Maecker  a gaseous conductor)  encountered;  different  For a review  what c o n s t i t u t e s an a r c . P r a c t i c a l l y  small voltage are  basic  referred  further  an a r c i s an e l e c t r i c carried  and  between  (1968).  going  of  is  investigators.  1808  of  obvious  difference  t h e m a g n i t u d e o f t h e c u r r e n t d e n s i t y , w h i c h i s much  lower  2  i n a glow d i s c h a r g e . which  I t a p p e a r s , however, t h a t t h e mechanism  sets this density  i s a f e a t u r e of the cathode  I n an a r c , t h e v o l t a g e d r o p adjacent  plasma  between  i s of the order  of t h e g a s , a n d a c a t h o d e s p o t large  electron  combination  of thermionic  different  from  electrons  are  density,  current  the  voltage  is  potential. enhanced  cathode  occurs  from  density and f i e l d  with  and  of t h e i o n i z a t i o n  i s emitted emission.  a  very  This  much  the  potential  which  c a s e i n a glow d i s c h a r g e ,  emitted  often  the  region.  a  very  by  some  is  quite  i n which the  lower  current  from a l a r g e r s u r f a c e a r e a , and t h e cathode  on  the  The  order  presence  electron  of of  ten  a  emission  times  the  ionization  cathode spot, w i t h g r e a t l y  at  low  voltage,  therefore  d i s t i n g u i s h e s an a r c . One  of  maintaining devices,  problems  demonstrates  to  be  dealt  stability;  left  cold  drives  gas  hot  plasma  (the familiar  this behaviour).  'Jacob's  ladder'  on what  is  required.  short  so t h a t t h e attachment stabilization.  Another,  own  i n the  p u r p o s e s an a r c c a n be s t a b i l i z e d by s i m p l y  used  spectroscopy,  to i t s  S e v e r a l methods c a n be u s e d t o  t h i s tendency, depending  frequently  in  upward  many  for  with  a r c i s o f t e n s e v e r e l y d i s r u p t e d by t h e n a t u r a l  f o r c e which  surrounding  control  major  an a r c i s p o s i t i o n a l  an  convective  the  This for  and has t h e  t o the electrodes  type arc  of  advantage  keeping i t  i s sufficient  'free-burning'  lighting of  and  For  arc i s  sometimes  great  for  simplicity.  s l i g h t l y more d e m a n d i n g method o f s t a b i l i z a t i o n i s  3  to surround  the arc w i t h a w e l l - c o o l e d w a l l .  be a b l e t o a b s o r b a l a r g e h e a t f l u x w i t h o u t and  is  therefore  copper r i n g s , obvious  are  uniform, for  of  this  f o r t h i s reason used  steady  study  mainly and  wall  for  1960,  from  one  scheme  destroyed,  The  i s t h a t the w a l l i s  research,  or  where  high  Preston  cooled  another.  stabilized  reproducible  (Maecker  being  must  made o f a s t a c k o f w a t e r  isolated electrically  disadvantage  o p a q u e , and arcs  usually  This wall  'cascade'  they  provide  temperature  1977,  Baessler  plasmas  1980,  Chen  the  arc  1980) . A t h i r d method o f s t a b i l i z a t i o n s t a t i o n a r y w i t h a gas vortex has  flow.  and  intensity  and  gas  i s a l s o of  arc  stabilized; center  hold  form of a j e t or a  has  interest  with  a  great p o t e n t i a l behaviour  for c i r c u i t  Benenson  1980,  Pfender  for high  o f an a r c  breaker  in  design,  for  that  1980).  w i t h which t h i s t h e s i s i s concerned i s vortex  i n t h i s system the a r c column i s o f t h e q u a r t z v e s s e l by a gas  (see F i g u r e 1-1).  u s e d by S c h o e n h e r r (Tuchman  but  transparent  stabilized  1967,  vortex  (1909) i s b e i n g  Tarn  p o s s i b l e very high  The  1972,  intensity  in  vortex created  i n j e c t i n g a r g o n t a n g e n t i a l l y a t h i g h s p e e d i n one vessel  system,  been done on a r c s i n f l o w i n g gas  ( C h i e n and  The  thus  l i g h t i n g a p p l i c a t i o n s . The  flow  to  r e q u i r e s a more c o m p l i c a t e d  a l o n g a r c , and  much work has  reason  the  i n the  the advantage t h a t i t i s c o m p a t i b l e  wall  a  This  flow, either  is  stabilized s t u d i e d by  end  of  arc,  by the  first  s e v e r a l groups  Camm  1974,  Gettel  1980)  light  source  f o r use  in  as  a  large  4  Gas Vortex  F i g u r e 1-1.  The  vortex s t a b i l i z e d  arc  5  area  lighting,  other  a p p l i c a t i o n s . Vortek  commercial  search  model  of  and  rescue,  s o l a r s i m u l a t i o n , and  I n d u s t r i e s i s now  this  type  of  light  with  a  nearly  a  a r c . A single vortex  s t a b i l i z e d a r c lamp may be a b l e t o u s e produce  developing  lOOkW  of  power  to  s o l a r s p e c t r u m a t a b o v e 50%  efficiency. Gettel  (1980) h a s r e c e n t l y i n v e s t i g a t e d  stabilized t h e DC  arc  include supply  arc  cost  efficiency the  found t h a t  for lighting  improved  conditions  of  and  f o r an in  AC  detail  lifetimes  a r c . He  and  These  and  studied  p a r t of t h e  that  d i d parametric  a r e not c l e a r l y  motivation  vortex  f o r the  advantages  reduced the  power  electrode  s t u d i e s of t h e  o f DC a n d AC a r c s , w h i c h r e v e a l e d  arc  AC  i t h a s some a d v a n t a g e s o v e r  applications.  electrode  an  some  features  u n d e r s t o o d , and p r o v i d e d work  described  in  this  thesis. In  order  t o improve our u n d e r s t a n d i n g  of t h e a r c , w i t h a v i e w t o  increasing  of the  behaviour  i t s efficiency  and  l o n g e v i t y , t h e t e m p e r a t u r e p r o f i l e s w i t h i n t h e a r c h a v e been measured s p e c t r o s c o p i c a l l y and c a l c u l a t e d t h e o r e t i c a l l y the  power  balance  equations  over a range of c u r r e n t s and  pressures.  The h e a t l o a d i n g on e a c h component o f t h e  has  been  also  from  c a l c u l a t e d t h e o r e t i c a l l y and measured  c a l o r i m e t r y . The m e a s u r e d a n d c a l c u l a t e d r e s u l t s  have  system using been  c o m p a r e d , a n d some c o n c l u s i o n s drawn a b o u t t h e m e c h a n i s m s i n the  a r c , and  the  effect  which  p o s i t i v e c o l u m n . The p u r p o s e o f t h e  the  g a s f l o w h a s on t h e  modelling  process  has  6  n o t been s i m p l y t o p r e d i c t is  primarily  to  the behaviour of the a r c ; the aim  t e s t and improve  basic processes occurring  our u n d e r s t a n d i n g of t h e  i n t h e a r c column.  C h a p t e r I I c o n t a i n s t h e t h e o r y o f t h e column used  f o r the  calculations,  which  was  t h e a s s u m p t i o n s made, a n d t h e  r e s u l t s of those c a l c u l a t i o n s .  I t also contains the solution  of t h e c o n v e c t i v e heat l o s s problem which  arises  from  the  f a c t t h a t t h e gas f l o w c a r r i e s heat o u t of t h e a r c a x i a l l y . In  Chapter I I I t h e e x p e r i m e n t a l apparatus used f o r the  e x p e r i m e n t a l work i s d e s c r i b e d , a n d t h e are  examined  in detail.  Chapter I I a r e j u s t i f i e d  Some  of  the  flow  dynamics  o f t h e a s s u m p t i o n s made i n  i n greater depth here.  Chapter IV contains a d e s c r i p t i o n basis  gas  diagnostic  of  techniques  the  used  theoretical  and  a n a l y s i s required t o e x t r a c t the temperature  the  profiles  data from  t h e raw d a t a . In Chapter V t h e e x p e r i m e n t a l r e s u l t s a r e p r e s e n t e d and critically  examined.  Some  experimental  justification  is  p r e s e n t e d f o r a number o f a s s u m p t i o n s g i v e n i n C h a p t e r I I . The  results  are  here  compared  with  p r e d i c t i o n s , and t h e agreement i s examined Chapter VI c o n t a i n s t h e c o n c l u s i o n s evaluation  of  future  the  theoretical  and d i s c u s s e d . of  the  work,  an  p r o s p e c t s and s u g g e s t i o n s f o r f u t u r e  work. I n t h i s c h a p t e r t h e a u t h o r ' s o r i g i n a l c o n t r i b u t i o n s t o this  field  of study are a l s o presented.  A p p e n d i c e s A, B a n d C l i s t in  this thesis  t h e computer  programs  used  f o r the temperature c a l c u l a t i o n s , convective  7  transport Appendix system  calculations D  contains  the  and  Appendix  E  differential the  and  equation  b e h a v i o u r of t h e gas  data details  contains derived vortex.  analysis, of the  respectively.  t h e gas  flow i n the  solution  i n Chapter I I I which  of  the  governs  8  CHAPTER I I  THEORY OF THE ARC COLUMN  A. INTRODUCTION An a r c c a n be d i v i d e d cathode Figure by  region,  the  into three  distinct  regions;  the  anode r e g i o n , and t h e a r c column (see  11 — 1 ) . The e l e c t r o d e  regions  are strongly  influenced  t h e p r e s e n c e of t h e e l e c t r o d e s . Heat i s c o n d u c t e d t o t h e  electrodes, axial  field  radial  electric  fields  are  produced,  i s enhanced near t h e e l e c t r o d e s ,  greatly complicates  t h e b e h a v i o u r of these  Cathode Region  Column  Cathode  Figure  The c e n t r a l  and  the  a l l of which  regions.  Anode Region  7L  Anode  I I - 1 . Regions of t h e a r c  region,  or  arc  column,  i s more  easily  9  a n a l y s e d , s i n c e the e l e c t r i c  field  column  p a r t o f t h e a r c , and  makes  up  a  large  i s u n i f o r m and a x i a l .  i s t h u s of  prime concern f o r l i g h t i n g a p p l i c a t i o n s  and  point  describes  of  this  thesis.  temperature p r o f i l e  in  This the  chapter  arc  column  v a r i o u s c u r r e n t s and p r e s s u r e s . The analysis  are  also  c a l c u l a t i o n s . The  given,  the  temperature  H e l l e r e q u a t i o n , which i s d e s c r i b e d numerically literature  by  (conductivity, about  the  justified section  computer.  are  arc  used etc.)  and  at  and  to Chapter  V.  the Elenbaas-  i n s e c t i o n B,  the  comparison  is  values  properties  solved  from of  the argon  a number o f a s s u m p t i o n s a r e made The  assumptions  are  given  and  D. the  computer  model  c o n v e c t i v e heat t r a n s p o r t , required.  Another  neglects  corrections  computer  m o d e l was  the  to  the  effects  of  model  are  used t o p r e d i c t  c o r r e c t i o n s , and t h a t model i s d e s c r i b e d  in section  these  E.  ELENBAAS-HELLER EQUATION  The radially  numerical symmetric  solutions  for  temperature  the  axially  profiles  invariant,  a r e f o u n d by  method o f c o n s e r v a t i o n o f e n e r g y . I n t h i s p a r t i c u l a r the  the  i n s e c t i o n C and t h e c a l c u l a t i o n s a r e d e s c r i b e d i n  Since  B. THE  how  calculated  profile  Experimental  for  column.  focal  a l o n g w i t h the r e s u l t s of t h e s e  e v a l u a t i o n of the r e s u l t s  calculate  the  a s s u m p t i o n s made f o r t h e  w i t h the e x p e r i m e n t a l measurements i s l e f t To  is  is  The  c o n s e r v a t i o n of  energy  is  most  easily  the  system,  expressed  as  10  'power b a l a n c e ' , a  small  i . e . power i n e q u a l s  volume  power o u t . We c o n s i d e r  of plasma, and c o n s t r u c t t h e equation  that  e q u a t e s power i n t o power o u t . The a s s u m p t i o n s made s u g g e s t coordinates  t h e use  cylindrical  t o d e s c r i b e t h e p l a s m a . The d i f f e r e n t i a l  e l e m e n t i s rdrdzd© a n d we i n t e g r a t e cylindrical  shell  of  unit  2irr»KdT/dr,  and  dz  length,  2 i r r d r . The h e a t c o n d u c t e d t h r o u g h  thus  of  and  area  de  volume  to  get  2 n r , and volume  a surface at radius  t h e net heat conduction  a  r is  into the shell i s  2irdr«d/dr ( r K d T / d r ) , where K i s t h e t h e r m a l c o n d u c t i v i t y  of t h e argon i n t h e s h e l l . There i s a l s o  an  term  E  which,  for  c,  conductivity radiative °-rad  '  w  h  i  loss c  h  *  s  an  applied  i s 2irrdr«tfE ,  and  2  term  given  2irrdr«Q_  rad  field  ohmic and  finally  by t h e r a d i a t i v e  . The  power  balance  heating  electrical  there  is a  loss function equation  is  thus 27Tdr  ^r(rKg)  +  2 rrdr-aE = 2Trrdr-Q 2  1  r a d  or I d r dr  ( r K  Equation  11— 1  Elenbaas-Heller power b a l a n c e were  it  =  Q x  a E  2  (H-D  rad  , known i n t h e l i t e r a t u r e  equation,  i s the equation  i t would  equation,  i scomplicated  be  as the modified  t h a t f o l l o w s from  or conservation of energy. I f  constant,  differential  dT dr  the  a rather simple  parameters  second  order  a n d c o u l d be s o l v e d a n a l y t i c a l l y , b u t  by t h e f a c t t h a t K, Q ^ ra  and a a r e  strong  11  functions  of  temperature  p r o b l e m t r a c t a b l e o n l y by 11 — 1 c a n e a s i l y  be  and  pressure,  numerical  which  makes t h e  integration.  i n t e g r a t e d t o the  Equation  form (II-2)  and  i s then amenable t o n u m e r i c a l i n t e g r a t i o n  models used  C. THE  r a (  j and  calculation  strength.  b e g i n s by  A  radius  a.  are  0  in section  integrated  Once t h e m a t e r i a l  given,  setting  a  pressure  s t a r t i n g core temperature T  and E q u a t i o n I I - 2 i s  T  « are described  this  from  center  A.  The  is  calculation  i s t o e n f o r c e the boundary c o n d i t i o n  difficult  fraction  c o r e temperature w i t h each  did  not converge w e l l ,  iteration,  because the w a l l  temperature  electric  depends  For  field,  example, changing  very with the  the  (see  to  subtract  Figure  from  procedure such  on  the  wall  pressure  and  t e m p e r a t u r e by  c o u l d change t h e c a l c u l a t e d w a l l t e m p e r a t u r e 10000K  the  (or c o n v e r s e l y the  given  starting  as  (T=600K) a t  but t h i s  weakly a  to  of  temperature i s  a s t r o n g f u n c t i o n of the c o r e temperature  temperature).  out  of the temperature e r r o r at the w a l l  the  a  temperature  part  r = a . A f i r s t a t t e m p t a t ' n e g a t i v e f e e d b a c k ' was small  and  straightforward,  in  core  D.  i s chosen,  0  f u n c t i o n s and c o r e  integration  Appendix  the  described  a  The  COMPUTER CALCULATIONS  The field  f o r K, Q  f r o m r=0.  from  300K  I I - 2 ) . T h i s r e m a r k a b l e s w i n g i s due  s t r o n g t e m p e r a t u r e dependence of t h e r a d i a t i v e  1K to to  losses; a  12  small  change  conditions  in  core  enough  that  r e q u i r e s heat  input  be  i n , and  conducted  temperature radius.  temperature  can  maintaining  so t h e s o l u t i o n temperatures  This i l l u s t r a t e s  the f a c t  r  II-2. Variation  difficult  to  temperature  which  increase  that the w a l l  was  repeatedly u n t i l the  preset  T  temperature  1=10001 K "  \\  V  10000K  r -~»  of p r o f i l e  the  with starting but  boundary  d i v i d e d by  subtracted  it  temperature  makes  condition.  10 and  from  the  core  the c a l c u l a t e d w a l l temperature  value  (600K), the  with  T  to the c a l c u l a t i o n , enforce  must  f o r the p e r t u r b e d core  whereupon  process  the  continued,  it This  e v e n t u a l l y done by a d e c r e a s i n g s t e p m e t h o d , where correction  core  from o u t s i d e the column. T h i s heat  requires  i s not c r i t i c a l  the  that core  <- r Figure  alter  a  was fixed  temperature fell  correction until  more  the  below was core  13  temperature illustrate the  converged  on  the correct  t h i s , a sample a p p r o a c h  v a l u e f r o m a b o v e . To  t o , say,  8.46  would  be  sequence (10,9,8.9,8.8,8.7,8.6,8.5,8.49,8.48,8.47,8.46). The  results,  calculation,  well  as  convergence  process  can  the s t a b i l i t y be  arc;  seen  extinguished,  problems  they an  arc  i ti s 'locally'  t h i s range  illustrated series  of  will  and  and  in  by  this  i n the c a l c u l a t i o n s i n an a c t u a l  fact  that,  spontaneously  i . e . stable  once  restart,  over a moderate  return  to  equilibrium.  This  the  conditions  would  was  cross  begin converging t o zero current. solution  is a  perfectly  a  In f a c t ,  valid,  stable  t o t h e g i v e n e q u a t i o n s , and t o a v o i d c o n v e r g i n g t o  1= 2 i r r t f E d r ,  c a n be c a l c u l a t e d . calculated  entire  actual  or c u r r e n t d e n s i t i e s , and i f kept  Once a s e l f - c o n s i s t e n t  are  energy,  the  not  stable,  t h e method o f a p p r o a c h i n g  current  the  i n e a r l y a t t e m p t s a t c a l c u l a t i o n , when d u r i n g a  the zero c u r r e n t  it  from  will  calculations  'watershed'  solution  reflects  encountered  result  range of c o r e temperatures within  into the actual arc  t o be t h e same a s t h e c o n d i t i o n s  primarily  although  numerical  o f an o v e r h e a t e d a r c c o l u m n back t o e q u i l i b r i u m  r a d i a t i n g a n d c o n d u c t i n g away e x c e s s light  producing  g i v e s some i n t e r e s t i n g i n s i g h t s  m e c h a n i s m s . The collapse  as  solution  i s reached,  adopted. the  total  i s s e t by t h e v a l u e s o f E a n d P,  Then t h e r a d i a t i v e a n d c o n d u c t i v e  and  calculation  which  f r o m a b o v e h a d t o be  the r e s u l t s are printed. for different  pressures  losses  Repeating the and  field  Figure  I I - 3 . T v s r . P=1 Atm  Temperature 120  (K)  1(A)  0 0  6  000  A  000  .561 ,427 .300 .160 ,121  2000  e F i g u r e I I - 4 . T v s r . P=3 Atm  — i —  i  12 16 Radius(mm)  F i g u r e I I - 5 . T v s r . P=5 Atm  Temperature (K)  Figure  II-6.  T v s r . P=7  Atm  18  strengths  generates  (Figures  II-3  experimental  through  family 6)  of  which  temperature  can  be  profiles  compared  with  profiles.  Figures  II-7  and c o r e r a d i u s r increases,  a  1  and 0  8 show p l o t s o f c o r e t e m p e r a t u r e  v s p r e s s u r e a n d c u r r e n t . As t h e  t h e c o r e t e m p e r a t u r e and  radius  we  might  c u r r e n t s and as  the  intuitively  the  In  temperatures, the p r o f i l e s  radiative  losses  s h a p e o f t h e c u r v e s i s due loss.  expect.  ( w h i c h we  define  become much The  squarer change i n  t o t h e c h a n g i n g mechanism of  heat  losses are small  and  t e m p e r a t u r e p r o f i l e must h a v e a l a r g e e n o u g h g r a d i e n t t o  drive  the  radiant  c o n d u c t i v e heat l o s s .  losses  At h i g h e r temperatures  i n c r e a s e d r a m a t i c a l l y and  be r a d i a t e d w i t h o u t a l a r g e t e m p e r a t u r e way,  as  flatter  the core temperature i n t h e c e n t e r and  The to  with  a d d i t i o n , at high  begin to dominate.  A t low t e m p e r a t u r e t h e r a d i a t i v e  0  current  a s t h e r a d i u s a t w h i c h T=10000K) i n c r e a s e . T h i s a g r e e s what  T  conductivity profile  S=/KdT  analytically.  function and  gradient.  In  can this  become  squarer i n shape. are q u i t e s i m i l a r  t h o s e c a l c u l a t e d by M a e c k e r ( 1 9 5 9 ) , linear  heat  i n c r e a s e s the p r o f i l e s  low t e m p e r a t u r e p r o f i l e s  piecewise  sufficient  the  then  of  who  the  solved  modelled integrated the  i n shape *  as  a  thermal  non-radiative  3 Atm  20  D. ASSUMPTIONS I n t h e p r e c e d i n g a n a l y s i s , a number o f a s s u m p t i o n s been  made a b o u t  t h e a r c column,  justified.  The a s s u m p t i o n s  symmetry,  uniform  temperature,  and  include axial  pressure, an  optical  assumed  (i.e. conductivities  which w i l l  and  a  now be g i v e n a n d  invariance,  radial  thinness, fixed  s e t of  material  total  have  wall  functions  radiative  emission  c o e f f i c i e n t as f u n c t i o n s of temperature and p r e s s u r e ) .  T a b l e 11 — 1 . A s s u m p t i o n s  Axial  f o r the steady s t a t e  model  Invariance  Radial  Symmetry  Uniform Pressure Optical  Thinness  W a l l Temperature=600K Material Functions  The  a r c column  of t h e a r c affected  plasma  by  the  or ' p o s i t i v e ' which  i s axially  are  refers to that invariant,  e l e c t r o d e s , and i t i s o n l y t h i s  which the present a n a l y s i s measurements  column  made  i sapplicable.  in a  disc  of  The about  part  i . e . not region t o  experimental 1 mm  axial  t h i c k n e s s n e a r t h e c e n t e r o f a 100 mm l o n g a r c . I n C h a p t e r V r e s u l t s a r e g i v e n f o r m e a s u r e m e n t s a t 10 mm the  column  intervals  w h i c h show t h a t t h e t e m p e r a t u r e p r o f i l e  along changes  21  very  little  since can  over at l e a s t the center  30 mm  of the  arc,  t h e t o t a l c u r r e n t and d i a m e t e r a r e a l s o i n v a r i a n t , we  s a f e l y conclude that the a x i a l l y  makes  up  a  invariant  arc  column  l a r g e part of the a r c , i n c l u d i n g the region i n  w h i c h t h e t e m p e r a t u r e m e a s u r e m e n t s a r e made. When t h e temperature little  gradients  effect  coordinate The  on  are  the  small  profile,  the  axial  since  we  of  experimentally  gas f l o w can  radial  symmetry  profile  prior  to  processing  acceleration  gravitational  during  the  and smoothing the  is  much  data, be  justified  pressure  greater  assumption  of  uniform  described i n since  the  more  difficult the  the  is  experimental  radial  pressure  of the a r c  t o c a l c u l a t e the r a d i a l centripetal  c a l c u l a t i o n s a r e c a r r i e d out i n d e t a i l that  pressure  I t i s easy t o c a l c u l a t e the a x i a l  g r a d i e n t due t o t h e v i s c o u s d r a g  required to maintain  shown  resulting  than the asymmetric  f o r the flow c o n d i t i o n s i n the  are n e g l i g i b l e .  and  as  expected,  a p p a r a t u s we must show t h a t b o t h a x i a l a n d gradients  the  t h e two  buoyant f o r c e s .  To show t h a t t h e  is  been  departures  These a r e d e a l t w i t h by a v e r a g i n g  C h a p t e r I V . R a d i a l symmetry s h o u l d  wall,  our  also  ( s e e C h a p t e r V ) . The o n l y  of t h e p r o f i l e together  vortex  has  t i m e w h i c h show up a s f l u c t u a t i o n s i n t h e m e a s u r e d  intensity profile. halves  move  has  f r o m symmetry a r e s m a l l f l u c t u a t i o n s i n t h e a r c scanning  axial  system w i t h the gas. assumption  verified  quite  and  a x i a l pressure  vessel gradient  acceleration.  These  i n C h a p t e r I I I and i t  variation  i s completely  22  negligible radial  (on t h e o r d e r o f 1 p a r t  variation  i s about  2%  material small  functions  i s r e d u c e d , and  A  are  i s indeed  plasma  can  the purposes required,  negligible  such  and  of  o n l y average  reabsorbed  the  can  t e m p e r a t u r e s under satisfied. radiation  and  pressure  a b s o r p t i o n , and t h e i r (<5%) in at  be  Tankin  pressures  results  (Hoyaux  below  t h i c k . We  I V where we must emitted  light  10%, so  will  be  a  work  variations  condition measured  of d i a m e t e r  show a  is the  about  negligible  E v a n s 1967, O l s e n  strongest  total at  for selfdifference accepted  1963)  and t e m p e r a t u r e s atomic  well  10 mm  12000K. I t i s g e n e r a l l y  10 A t m o s p h e r e s  lines  that below  can  be  r e t u r n to t h i s q u e s t i o n i n Chapter  establish  used  should  power. I n t h i s  this  (1967)  1968,  12000K, o n l y a few o f t h e optically  i t emits.  w i t h and w i t h o u t c o r r e c t i n g  a t t e m p e r a t u r e s below  the l i t e r a t u r e  i f i t does  n e g l e c t e d . A t t h e p r e s s u r e s and  f r o m an a r g o n p l a s m a  atmospheric  thin  optical thinness  power  radiated  consideration  Evans  isobaric  f r a c t i o n of the r a d i a t i o n  of t h e model,  5%  the  valid.  i . e . the t o t a l  than  scales  s t r o n g l y w i t h p r e s s u r e , so  power m e a s u r e m e n t s a r e a c c u r a t e t o a b o u t less  the  the  be c o n s i d e r e d o p t i c a l l y  fraction  the  None o f  negligible  not absorb a s i g n i f i c a n t  of  that  so when  be on t h e o r d e r o f 0.2%.  varies  variations  approximation  is  and  5  core i s hot the r a d i a l p r e s s u r e v a r i a t i o n , which  w i t h gas d e n s i t y , w i l l  For  10 )  i n g a s a t room t e m p e r a t u r e . A t  higher temperatures the d e n s i t y arc  in  the  optical  thinness  f o r d i a g n o s t i c s , b u t h e r e a l l we  of  the  need i s  23  to  show t h a t t h e r a d i a t i o n d o e s n o t a f f e c t h e a t c o n d u c t i o n . The  one  boundary  i s required  temperature. is  c o n d i t i o n used because  The  of  i n these c a l c u l a t i o n s  the  actual wall  symmetry)  temperature  (only  i s the  wall  i n the experiment  the temperature of t h e i n s i d e surface of the quartz w a l l .  The  outside surface i s fixed  cooling  water  (290±10K)  d e t e r m i n e d by t h e  and  thermal  i s about  as  the  i s A=10"  temperature  inside The m,  2  2  of the  temperature surface  area  and t h e t o t a l  is of heat  Q=3 kW o r Q/A=300 kWm" . T a k i n g t h e t h e r m a l 2  c o n d u c t i v i t y o f q u a r t z t o be thickness  the  loading.  120 mm o f 27 mm b o r e t u b i n g flux  at  K=1.4 Wm~ K~ , 1  and  1  the  wall  Ax=1.5 mm, t h e t e m p e r a t u r e d i f f e r e n c e w i l l be  AT=QAx/KA=300K. This calculation  i s o b v i o u s l y o n l y an e s t i m a t e , b u t i t  g i v e s t h e r e a s o n a b l e v a l u e o f 600K f o r t h e w a l l w i t h an u n c e r t a i n t y o f a b o u t calculations  not  entirely  temperature The of  °^  necessary  chosen K  argon.  the  assumption  for  the  thermal  a n d e, a n d t h e t o t a l These  properties  simplifying  that  and  radiative  do  temperature and p r e s s u r e dependences, analytically  so  assumption, or s e t of assumptions,  conductivities °-rad  be shown l a t e r ,  the  wall  i s f i x e d a t 600K h a s been made.  final  models  100K ( 3 0 % i n A T ) . The n u m e r i c a l  a r e i n any case v e r y i n s e n s i t i v e t o c o n d i t i o n s  near t h e w a l l , as w i l l but  temperature,  not  i sthe set electrical emissivity  have  simple  b u t have b e e n m o d e l l e d  u s i n g p u b l i s h e d e x p e r i m e n t a l d a t a . The m o d e l s ,  shown i n F i g u r e s  I I - 9 through  12,  were  c o n s t r u c t e d by  24  plotting the  data  from t h e l i t e r a t u r e  appropriate  functional  figures)  and  form f o r each curve  choosing  pressure.  Pressures  of  be  of r e a d i n g  possible  at  the f i t i s  good  enough  source  or the  t h e graph from which t h e data from  this  was  taken.  process  are  i n Table I I - 2 .  The differ  fitting  1,3,5 a n d 7 A t m o s p h e r e s were  a n a l y t i c models which r e s u l t e d  listed  appropriate  w i t h i n the u n c e r t a i n t y of the o r i g i n a l  accuracy The  an  as c l o s e l y as  used i n t h e c a l c u l a t i o n s . G e n e r a l l y to  a r e i n d i c a t e d on  vs temperature, then  the p a r a m e t e r s t o match t h e d a t a each  (sources  only  p a r t of these  significantly  thermal  m a t e r i a l f u n c t i o n s which might  from t h e a n a l y t i c a p p r o x i m a t i o n s  c o n d u c t i v i t y K, w h i c h c a n be g r e a t l y such  as  turbulent  influenced  convective  transport  convection.  One o f t h e o b j e c t s o f t h i s t h e s i s ,  mixing  determine the importance of t u r b u l e n t mixing  The  i n f l u e n c e of forced convection  be  dealt  consider  separately,  later  fact,  is  i n the a r c .  i s significant  and  i n t h i s chapter,  a computer model o f t h e t r a n s i e n t  by  or forced  in  to  with  i s the  heating  will  when we of  the  argon gas i n t h e v o r t e x .  E.  CONVECTIVE TRANSPORT In  the  discrepancy values (1980)  course  of  a p p e a r e d between  this the  research, calculated  a  significant and  o f t h e w a l l l o a d i n g . T h i s was a l s o r e p o r t e d who  used  same d i s c r e p a n c y ,  a  measured by G e t t e l  l e s s s o p h i s t i c a t e d model but found t h e  and s u g g e s t e d  i t m i g h t be due t o t u r b u l e n t  Table I I - 2 . Models of argon m a t e r i a l  functions  <r=« /exp(Ts/T)  2  0  Q_  flf1  =Qo/exp( ( T - T m ) / T q )  K=K «exp(T/Tk)  (T>7000K)  K=K +A»T  (T<7000K  0  1  Pressure(Atm): *o(Ohm nr ) - 1  1  1  Ts(K)  1 .5E4 1.27E4  Q (Wm- ) 3  5.24E9  0  Tm(K)  1.65E4  Tq(K)  3500  K (Wm- K- ) 1  1  0  Tk(K)  1.08E-2 2400  K,(Wm"'K- )  1.1E-2  A(Wm- K" )  2.7E-5  1  1  2  2  3  5  7  1.81E4  2.07E4  2.29E4  1.41E4  1 .5E4  1.81E4  5.55E10  1 .02E1 2  6.69E13  2.0E4  2.5E4  2.7E4  4400  5700  5800  26  Region of  Figure  oJ  1 1 - 9 . K vs  1 20OO  Figure  T  1 4000  11- 10. K vs  T  interest <  (T>7000K)  T(K)  I 6000  (T<7000K)  27  6000-+- E m m o n s (1967)  0" (A m ) 1  1  Region of interest <  Mode I  4000  2000-  5000  Figure  10000  11-11.  10 -l  c vs  T, P=1  R e g i o n of  10  T(K)  Atm  interest <  "rad  (Wm" ) 3  Emmons  ( 1967)  Model  10  10  6  5000  10000  T(K)  F i g u r e 1 1 - 1 2 . Q r a d v s T, P=1 Atm  28  heat  transport.  stabilized  A  arc,  significant  however, i s the  column. In t h i s experiment, the and  if  t h a t gas  t h e c o l u m n , and power  loss  feature  of  l a r g e gas  flow  was  i s h e a t e d f r o m 300  cooled again about  loading,  and  could  occurs  mentioned discrepancy.  w e l l be  In the  t h e power l o s s f r o m t h e c o r e temperature  gradients,  losses without time  this  the core strongly course and  the  a f f e c t the  outside outer  order  of  the  have  a  cold  11-13  the  source  in  the  gas  variation  we  calculated  non-equilibrium  region  to  the  the  seen  the  been  At  the  does  same  effect  not  although  on  depend  i t will  temperature  made  diameter  i s a sketch  of  at  indicating  of  profile,  we  can  the  transient  diameter 10000K  tube,  in  the v a r i a t i o n  its in  showing s e v e r a l  d e a l w i t h the  r e l a t e the  convective  the  By m o v i n g w i t h t h e gas  c y l i n d e r . To use  larger  non-radiative  i m p o r t a n c e of t h i s  13 mm  p r o b l e m i s made s i m p l e r , and  axial  is a  above-  f l o w down a 27 mm  column.  of heat i n a u n i f o r m  This  of t h e  temperature p r o f i l e with a x i a l p o s i t i o n ,  isotherms  ,  radius.  t o examine the  w i t h a h e a t r e s e r v o i r of center. Figure  the  conditions,  t r a n s p o r t , a c a l c u l a t i o n has behaviour  to  increasing  p a r t s of  _ 1  convective  t r a n s p o r t w o u l d have l i t t l e  might a f f e c t the core In  3  3 Atm).  i s e n h a n c e d due  t e m p e r a t u r e , w h i c h we  the  lO- kgs  a  i n v o k i n g t u r b u l e n t mechanisms.  convective  on  about  (at  initial  thus  vortex  flow through  leaves,  s i g n i f i c a n t amount o f power, c o m p a r a b l e wall  the  t o 5000K when i t e n t e r s  when i t  3 kW  of  flow  the  diffusion  temporal to  mass f l o w r a t e o f a r g o n m  the to  29  E l e c t r o de  27mm  13 mm  r  5000K  300K  Figure  11-13. R a d i a l  calculate  the v e l o c i t y  which can  be  function The  of  integrated  10000K  isotherms vs  to give  the  position  position  z=/vdt  as  a  time.  c a l c u l a t i o n was  conductivity  K,  numerically  integrating  performed  p and  density  heat  the heat  by m o d e l l i n g t h e capacity  C  p  thermal  of argon  flow e q u a t i o n which can  and be  written 9T _1 3_ 3t ~ pC r 3r  (II-4)  =  P  where T ( t , r ) radius.  The  temperature and  the  i s the temperature same profile  quantity  conductivity calculation pC , p  the heat  as a f u n c t i o n model  was  (see F i g u r e s capacity  per  of used II-9 unit  time as  and  f o r the and  10)  volume a t  30  constant  pressure,  was m o d e l l e d a s shown  i n Figure  11-14.  T h e s e c a l c u l a t i o n s were p e r f o r m e d a t 1.44 Atm, s t a r t i n g w i t h a p r o f i l e made up o f T=T r>6.6 mm.  The b o u n d a r y c o n d i t i o n s  t i m e e v o l u t i o n were T=T (the  radius  of  the  conditions  are  c o l d argon  flowing  entering  a t r=6.6 mm  0  confining  quite  applied  of T , 0  Figures  T=300K  for  i n the subsequent  a n d T=300K a t r=13.5  mm  These  boundary  s i m i l a r to the conditions  i m p o s e d on  over  a  tube).  6.4 mm  10000K a n d  radius  electrode  and  11-15  and  11000R. 16  the c a l c u l a t e d  p r o f i l e s a r e shown a t i n t e r v a l s o f 5 evolve,  and  t h e a r c c o l u m n . The c a l c u l a t i o n s were p e r f o r m e d f o r  two v a l u e s In  f o r r<6.6 mm  0  a n d i t c a n be s e e n t h a t  from t h e i n i t i a l  temperature  milliseconds  as  they  t h e p r o f i l e s change smoothly  conditions, reaching  steady s t a t e i n a time  of a b o u t 20 m i l l i s e c o n d s . Figures  11-17  these p r o f i l e s , Q  and  the radius  R, a t w h i c h T=1000K a n d t h e power  conducted t o the w a l l , as f u n c t i o n s  changes  smoothly  from  undergoes a t r a n s i t i o n the  temperature step  in  the  power  loading  balance;  in  distance  w a l l should  quite wall.  6.6 t o 13.4 mm  The  radius  but the w a l l  loading  b e t w e e n t = 15 a n d 20 m i l l i s e c o n d s  is  an  significant  arc  in  which  sudden  increase  when we c o n s i d e r the  gas  when  moves  the an  i n 20 m i l l i s e c o n d s t h e t h e r m a l l o a d on  be a s t r o n g  s t e e p l y at the point The  of time.  reaches the w a l l . This  wall  appreciable the  18 show some i m p o r t a n t f e a t u r e s o f  f u n c t i o n of p o s i t i o n , i n c r e a s i n g where t h e h e a t wave  reaches  the  a x i a l p o s i t i o n h a s been c a l c u l a t e d a s a f u n c t i o n  Figure  11-14.  pCp v s T  Figure  11-15.  T vs  r,  T =10000K 0  Temperature 120 0 0  Figure  -I  11-16. T vs  r,  (K)  T = 1 1 000K 0  15 H  Vessel  radius  Rj (m m)  10 H  —r 10  t  1—  (ms)  —i— 20  F i g u r e 1 1 - 1 7 . 1000K r a d i u s v s t i m e  Q  (kWm ) 1  40  H  20  i  F i g u r e 11-18. Heat f l u x v s t i m e  35  Figure  1 1 - 1 9 . P o s i t i o n o f t h e gas time  of t i m e u s i n g E q u a t i o n I t can wave on  be  the  conductive away  which  100  included  by  i n the  the  electrical  c a n n o t be power  power i n p u t  r e l i e d upon a t  required  power. At  on  long.  gas  final  T h e s e c a l c u l a t i o n s do the  mm  be  The  19  conductive  the In  last  loading 50 mm  a d d i t i o n to  of this  carried  l e a v i n g t h e c o l u m n , and  take  to the  t o heat the  heat  this  model.  not  low  11-19.  t h a t the  l o a d i n g a s i g n i f i c a n t amount of power i s  convectively  must be  I I - 1 8 and  therefore only is  o f mass v s  i s plotted in Figure  t h e w a l l n e a r z=50 mm.  w a l l should  column,  and  seen from F i g u r e s  reaches  the  11-3  disc center  the  fact  column i s l i m i t e d ,  power gas  a c c o u n t of  levels,  that  so  they  i . e . when  the  i s more t h a n h a l f t h e  h i g h power l e v e l s t h e m o d e l i s v a l i d and  input  indicates  36  that  the  convection 50 mm was  non-radiative  losses  a s w e l l as t h e r a d i a l  of column  l e n g t h . The  should  include  axial  conduction which occurs i n  computer  program  u s e d t o make t h e c a l c u l a t i o n s i s l i s t e d  "TRANSIT" w h i c h i n Appendix  B.  37  /CHAPTER I I I  EXPERIMENTAL APPARATUS  A. INTRODUCTION The of  apparatus used f o r the e x p e r i m e n t a l  two p a r t s ;  firstly  the  equipment The  equipment  detail  A  to  r e q u i r e d t o o p e r a t e t h e a r c , and  diagnostics  and  data  processing  were u s e d t o make m e a s u r e m e n t s on t h e a r c .  used t o  maintain  the  arc  is  described  i n t h i s c h a p t e r , and t h e o p t i c a l d i a g n o s t i c  discussed  vessel  optical  which  consists  t h e a r c v e s s e l , w i r i n g , gas and water  systems and o t h e r equipment secondly  work  system i s  i n the next c h a p t e r .  v o r t e x s t a b i l i z e d a r c c a n be d e s c r i b e d  i n terms of a  i n which the a r c burns and t h r e e s e p a r a t e  provide  electrical  power,  cooling  s u p p l y . B e f o r e d e s c r i b i n g each subsystem briefly  outline the o v e r a l l  water, in  subsystems and  detail  a gas l e t us  o p e r a t i o n . F i g u r e I I I - 1 shows a  b l o c k d i a g r a m of t h e a p p a r a t u s w i t h t h e major components each  of  subsystem. The  function  arc vessel i s to  i s t h e h e a r t o f t h e s y s t e m , a n d i t s main  support the a r c stably without  with the diagnostics. glass  in  walls  maintain  the  pressure  of  and  I t c o n s i s t s o f a chamber  cooling  argon  water  vortex,  between  end  plates  interfering with  double  them, g a s j e t s t o to  contain  the  up t o 10 Atm, a n d w a t e r c o o l e d t u n g s t e n t i p p e d  e l e c t r o d e s between  which the a r c  burns.  The  power  supply  WATER -<  P U M P  (TANK  COOLING FLOW  T E M P E  METERS  VESSEL •O  FLOW  R A T U R E  METERS  a-  GAS  METER  <E>  PRESSURE METER  K>  E X CHHEAANT G E R  G A S BOTTLE & (REGULATOR  POWER STARTING  POWER  CIRCUI T  SUPPLY  F i g u r e 1 1 1 — 1 . Block diagram of the system  39  must and  provide  adjustable  a means o f s t a r t i n g  radio  frequency  equipment t o cooling  voltage  monitor  t o 500A a t a b o u t  the a r c , i n t h i s case  high  system  c u r r e n t s up  the  arc  circulates  (30kV).  It  current  and  cooling  to  measure  monitoring consists  the  flow of  B.  THE  GAS  The  rates  an  f l o w m e t e r s and  of  with  contains  voltage.  each  is  3  for  The  gas  pressure  s u b s y s t e m s i s t h e gas  the  vortex.  (absolute) are  1  and  psig built  meters  and  r e q u i r e d . The  regulator i n t o the  with  Pressures flow  supply  gas  up  to  rates  of  a  standard  is  a pressure  r e g u l a t o r . The  system, which  f o r gas  Accurate  used  is  laboratory  c a l i b r a t e d f o r a i r a t S.T.P.  k n o w l e d g e o f t h e chamber p r e s s u r e  flow  and  rate  is  t r a n s p o r t c a l c u l a t i o n s , so t h e  the  them a r e g i v e n  is  spectroscopic  critical  f o r the  f l o w r a t e and  be c a l c u l a t e d . T h e s e c a l c u l a t i o n s and  which c o n f i r m  11670 and  density.  for both the arc m o d e l l i n g mass  gas  meter c a l i b r a t e d i n  flowmeter  type  about about  rotometer  must  and  gas.  flow r a t e i s measured w i t h a Matheson  the  by  system  g r a d e a r g o n . The  and  used  component  a heat exchanger to c o o l the exhaust  argon  corrected  The  through a l l the  s h i e l d , and  temperatures.  supply  s i m p l e s t of t h e  m s~  bottle  and  argon  8 Atmospheres 4  loading  of  SYSTEM  supplies  2•10~  thermal  source  also  water  components, i n c l u d i n g a l i g h t a b s o r b i n g  a  100V  in detail  important analysis, convective  pressure the  drops  measurements  i n Appendix  D.  40  PRESSURE  REGULATOR  METER  MAIN GAS B O T T L E  J  ( A R G O N )  12 R= 2 . 0 * 1 0  1.18 m m  -3-1 s  0  R=9.4«10  P_A(PJ_ m  Nm  Nm s  7  j  3  s  t r i e  R = 1 . 6 -1O  1  r e s  j tance S  1 3  due t o  F i g u r e I I I - 2 . The g a s s y s t e m  N m  3  s  1  viscosity  41  C. THE VORTEX L e t u s now c o n s i d e r t h e a c t u a l g a s v o r t e x . The enclosed  in  a  smooth  cylinder  of r a d i u s a, and i t e n t e r s  through a t a n g e n t i a l nozzle a t the w a l l a t v e l o c i t y end,  drifts  tangentially  relatively from  s l o w l y down t h e c y l i n d e r ,  the  other  unit  thickness  while  i t d r i f t s down t h e t u b e . If  slice  and  ».  Consider  i t leaves the v i c i n i t y  a  retarding  total  exits  angular  momentum  t o r q u e on t h e s l i c e  L=J 2v  i s provided  disc  of  of the i n l e t ,  t h e gas a t r a d i u s r has a n g u l a r v e l o c i t y has  u a t one  e n d . We assume t h e g a s t o be  i d e a l w i t h d e n s i t y p and v i s c o s i t y after  gas i s  o  by  o(r),  pur dr  .  3  the  the The  viscous  d r a g on t h e w a l l a n d h a s m a g n i t u d e r =  [2*r y|^] 3  L  There  3r r=a J  i s a l s o t o r q u e due t o a x i a l v a r i a t i o n  i n u, but i t i s  p r o p o r t i o n a l t o -|jiL a n d i s much l e s s t h a n t h e t o r q u e due t o radial gradients, at least which can  are  f o r the  slowly  decaying  most i m p o r t a n t . C o n s e r v a t i o n o f a n g u l a r  momentum  t h e n be a p p l i e d t o g e t  N o t h i n g has so f a r r e s t r i c t e d t h e r a d i u s a solid wall, get  modes  to  be  s o i f we l e t a be a r b i t r a r y a n d d i f f e r e n t i a t e  the we  42  3  (VT  3co-N  3_9w  p ar-  at  3  3r  1  l  or 3w  y  cr 3  3  3r -T3r"^ The  =  solution  w(r,t) =1 — n Bessel  time  and i f the a x i a l decay  is  x ) e  such  J,  is  so  |^rl = 0  t  i n Appendix  n  solution  e  0  has  zeroes  at  ( x ^ ) and  few z e r o e s o c c u r a t 3.83, 7.02 drift  that  velocity after  the net e f f e c t  i s about  50 mm  c o m p o n e n t s a r e r e d u c e d by f a c t o r s o f respectively,  « \  n  n  function  2  10.17,  T T  function expansion  JjC-  T = a p / v = B . 8 0 s . The f i r s t  T  (III-D  c o n d i t i o n s u(a)=0,  c a n be w r i t t e n a s a B e s s e l  the  /  37^  to this equation i s outlined  E. F o r t h e b o u n d a r y  where  3un  the  0.81,  i s that  0.4 ms~ first  0.50  and the  1  three  and  the f i r s t  0.23  harmonic  t h e most i m p o r t a n t i n t h e r e g i o n o f t h e a r c . Near  t h e gas i n l e t  harmonics  0)C  gas  velocity  contains  a  mixture  of  ( s e e A p p e n d i x E) b u t t h e h i g h e r h a r m o n i c s o f t h i s  motion r a p i d l y  As t h e  the vortex  decay, l e a v i n g a f t e r  r , t )  =  oFT i i  w  J  leaves  near  the  the  1 ms" ,  the  the  velocity  in  1  r / a )  e  " i X  chamber,  outlet  0.005o a, or about 0  ( x  a few c e n t i m e t e r s  (within  t / T  the  average  2 mm  of  which i s n e g l i g i b l e  outlet  tubing. This  tangential the wall) i s compared  to  i s a s s u m e d t o be  43  true  i n Appendix  D, a n d i s i n d e e d t h e c a s e .  W i t h i n t h e column, t h e r a d i a l sufficient  pressure gradient i s just  to provide the c e n t r i p e t a l acceleration  2  2  8P  f o r u we g e t  but s u b s t i t u t i n g  AP = / pw rdr = 0 . 0 4 p u a e ~ o o 2  2  2  J  Now u a i s t h e i n j e c t i o n v e l o c i t y  2 x  l  t / x  U=180 ms"  0  The  u r , thus  and  1  p=Pm/kT.  p r e s s u r e d i f f e r e n c e a t 293K i s t h u s f  which  o  = 0.02 e -  2 x  f  t / T  i s l e s s than 2 % , and a t 3000K i t i s l e s s than 0 . 2 % and  n e e d n o t be c o n s i d e r e d . Having  solved  the  equations of motion  f l o w , we c a n a d d r e s s t h e p r o b l e m stabilized  arc. Stability  the a r c c e n t e r e d mechanism  is  consider  in  that  the of  i s a system  wall  velocity  and  the  acceleration centrifuge determines In  2  and  system  i s sufficient  o r  and  i n which a water  a i r near is a  together  i n the  vortex  r e q u i r e s some m e c h a n i s m t o k e e p  centrifuge.  i n s i d e a tube, and f o r t h a t angular  of s t a b i l i t y  vessel,  a  f o r the vortex  in  this  case  the  A u s e f u l analogy t o  and a i r m i x t u r e  spins  i t i s clear  t h a t when t h e  t h e water w i l l  s t a y near the  the  centre.  measure  of  with  the  The  the  centripetal  strength  density  of the  difference  t h e amount o f s e p a r a t i o n o b s e r v e d .  the  a r c t h e system c o n s i s t s of hot and c o l d  argon,  44  with  a  substantial  centripetal o r=1.3«l0 2  density  acceleration ms ,  5  difference  at  half  which provides  - 2  a large  k e e p t h e h o t t e r , more c o n d u c t i v e stabilizes large  the  enough  to  gravitational the  column  make  buoyant  tube  Cooling  connected  effect  force  of  the  asymmetric  pumping  keep  water  i s not r e c y c l e d is  power  so no h e a t  supplied  water  These i n c l u d e t h e  w a l l , r a d i a t i o n a b s o r b e r a n d some The  cold  by  a  supply  exchanger  turbine  pump  t o t h e m a i n s t h r o u g h a r e s e r v o i r t a n k , a n d dumped  (40 l i t r e s p e r m i n u t e ) a t a b o u t  10 Atm p r e s s u r e .  about  the c o o l i n g system s c h e m a t i c a l l y ,  shows how t h e v e s s e l water  flow  flowmeters  measure t h e f l o w temperature temperatures  i s metered  calibrated rates  (T ) 0  The  6«l0" m s" <t  3  1  Figure I I I -  and F i g u r e  III-6  i s cooled.  at  (T,-T(,)  with in  the  three  the  i n each p a r t  4.5 GPM  lab  in  rotometer  cm s~ 3  which  1  o f t h e s y s t e m . The  flowmeters  and  the  inlet outlet  of t h e b r a n c h l i n e s a r e measured  s t a t e temperature transducers  LM335).  and t h u s  SYSTEM  provides  solid  to  n e g l i g i b l e and t h e r e f o r e  t o t h e d r a i n . The w a t e r s u p p l y  type  force  centripetal acceleration i s also  the  i s r e q u i r e d and t h e water  The  is  gas a t t h e c e n t e r ,  i n t h e a r c i s a c h i e v e d by  components.  shows  radius  buoyant  a l l t h e c o m p o n e n t s t o be c o o l e d .  electrodes,  3  The  symmetric.  D. THE COOLING  through  a r c . The  the  (30:1).  temperatures  are  (National subtracted  with  Semiconductor and  digitized  45  e l e c t r o n i c a l l y and t h e d i f f e r e n c e s a r e output d i g i t a l l y m o n i t o r p a n e l . The mass f l o w change  AT  is  then  known  rate  m  and  the  temperature  f o r each branch of t h e c o o l i n g  s y s t e m , so t h e h e a t l o a d i n g Q=CmAT c a n be c a l c u l a t e d , C=4200 J k g ^ K "  E.  1  on a  where  i s the heat c a p a c i t y of water.  THE ELECTRICAL SYSTEM The  running  electrical  system p r o v i d e s  t h e a r c and i n c l u d e s d e v i c e s  power f o r s t a r t i n g a n d to monitor the current,  v o l t a g e , a n d power i n t o t h e a r c . F i g u r e  I I I - 4 i s a schematic  diagram of t h e system. The  starting circuit  i n j e c t s a high voltage pulse  RMS a t 4 MHz) t h r o u g h a t r a n s f o r m e r current (C1)  supply,  which  is  t o g r o u n d . The RF p u l s e  through  a  spark  i n s e r i e s with the  p r o t e c t e d by a c a p a c i t o r is  generated  Inc. of B e v e r l y H i l l s ,  a b o u t 10 mm (R1)  starting.  The  electrode  the l i m i t i n g  in  parallel  discharge  bought  s t a r t e d t h e e l e c t r o d e s a r e moved t o limiting  damage  RF  b r e a k s down t h e gap a n d t h e  pulse  provides  about  separation shorted  i t . The  200 A  to  the  resistor  to limit  resistor  with  The  California.  is  The  supply  and  return  from L.P. A s s o c i a t e s  s e p a r a t i o n a n d a 1 Ohm c u r r e n t  high current arc.  arc  i s i n the c i r c u i t  while  a  i n c l u d i n g r e t u r n c a p a c i t o r C 1 , was  a s a p a c k a g e ('750 A a r c l a m p i g n i t e r ' )  the  by  high  gap w h i c h f o r m s p a r t o f an LC c i r c u i t .  starting circuit,  When  (30kV  to  electrodes  maintain  i s then increased  t o 100 mm  o u t by a h i g h c u r r e n t  SCR i s a w a t e r c o o l e d  the  SCR  assembly  TURBINE PUMP  TANK  13 fcW VESSEL  r  r~  HEAT  WALL  EXCHANGER  SWITCH  RADIATION  SC R 25 W CURRENT SHUNT  1  ABSORBER  4  \  kW  ANODE 3kW CATHODE  F i g u r e 1 1 1 - 3 . The c o o l i n g  system  RUN  VOLTAGE MONITOR  CURRENT MONITOR  F i g u r e I I I - 4 . The e l e c t r i c a l  system  47  rated  at  400 PRV  and  550 A  average  (Westinghouse  PTW7T7200455). The h i g h c u r r e n t isolation 1mH  supply  transformer  inductance  inductance  i s quite simple.  c o n n e c t e d t o 208 V RMS  about  The  0.5  t o 1 mH)  the  output  voltage  of  rectifier  this  The c u r r e n t  The  a  tubing  circuit  a  has  an  monitored  outside  mm,  for  operating  by  measuring  diameter  of  a  calibration.  The  analog  multiplying/averaging  VESSEL AND  The a u x i l i a r y arc  wall  voltage  burns  in  i s cooled  a  wall  which  can  voltage  is  and  current  also  amplifier arc.  fed which  Typical  III-5.  ELECTRODES  systems converge  t u b e between t u n g s t e n The  ripple  r e s i s t i v e v o l t a g e d i v i d e r . The  c u r r e n t and v o l t a g e w a v e f o r m s a r e shown i n F i g u r e  the  the  typical  mm,  140 mm  m e a s u r e s t h e a v e r a g e c u r r e n t a n d power i n t h e  ARC  on  the  9.5  and v o l t a g e a r e d i s p l a y e d on an o s c i l l o s c o p e  F. THE  filter  depends  and a l e n g t h o f a b o u t  accurate  m e a s u r e d u s i n g a 10:1  an  1mH  full  w a t e r c o o l e d c o p p e r t u b e o f 10"" Ohms r e s i s t a n c e .  adjusted  into  a  Hz.  is  t h i c k n e s s o f 0.89 be  and  and c u r r e n t h a v e a b o u t 20% and 50%  r e s p e c t i v e l y , a t 120  across  60Hz m a i n s ,  to c o n t r o l the c u r r e n t , a  c h a r a c t e r i s t i c s o f t h e l o a d , a n d when arc  an  f o r b a l l a s t and a s a t u r a b l e r e a c t o r ( v a r i a b l e  wave w a t e r c o o l e d d i o d e b r i d g e choke.  I t contains  a gas v o r t e x  i n t h e a r c v e s s e l , where  i n s i d e a 27 mm  bore  t i p p e d e l e c t r o d e s , a l l water by c i r c u l a t i n g w a t e r b e t w e e n t h e  quartz cooled. quartz  48  49  t u b e and a 43 mm serves  as  a  ultraviolet  bore pyrex tube o u t s i d e  UV  light  filter  block  i n t h e 220 nm  the v e s s e l , machined with  to  holes  r e g i o n . The  One  drilled  to i n t e r s e c t the inside  mm  bore  coming  copper  tubing  surface  to  (a 1.18  mm  hole  tangentially)  and  i s vented to the  i n the c o o l i n g  distinguish  i t i s not  possible  achieve  loading  along  something topic  the  which  for further The  with  is  some  direct  column  as  a  suggested  b u t i n any c a s e t h e the  measurement function  region  gas of  impossible of the w a l l  of  position,  i n C h a p t e r VI a s a  electrodes are  12 mm  diameter  brass  possible  tubes  1% t h o r i u m . The  a r e bonded t o copper d i s c s which a r e machined  and  this  study.  tungsten tips containing  silver  water  with  a n d s u c h a s e p a r a t i o n w o u l d be a l m o s t without  of  the c o n v e c t i v e heat l o s s e s from the  w o u l d be c o o l e d s u b s t a n t i a l l y w h i l e l e a v i n g  to  2m  wall.  c o n d u c t i v e l o s s e s i n the a r c column,  the column,  of  electrodes  c o n s i s t i n g of about  immersed  s h o u l d be n o t e d t h a t  vessel  plates  the  inlet  c o n t a i n s the o u t l e t , which  from the double  It  hazardous  end  which  end p l a t e c o n t a i n s t h e gas  o u t s i d e through a heat exchanger 2.4  also  f o r water c o n n e c t i o n s .  through  enter.  end  pyrex  o u t o f b r a s s , have o - r i n g s e a l s t o mate  They a l s o h a v e 13 mm  other  The  potentially  t h e t u b e s and t h r e a d e d f i t t i n g s  the  it.  tungsten to  shape  s o l d e r e d t o b r a s s t u b e s . To o b t a i n good a r c  (1980)  in this  tips and  stability  l o n g e l e c t r o d e l i f e t i m e s t h e t i p g e o m e t r i e s were  b a s e d on p r e v i o u s work by G e t t e l  capped  chosen  laboratory.  50  The and are to  c a t h o d e h a s a c o n i c a l t i p w i t h a 90 d e g r e e v e r t e x t h e anode h a s a f l a t cooled force the  connection vessel  t i p w i t h c h a m f e r e d e d g e s . The  w i t h a water f l o w , u s i n g a s m a l l e r c o a x i a l flow is  made  against  the  through  i s drawn i n F i g u r e  t i p , and  the outer  III-6.  the  brass  angle tips tube  electrical  tube.  The a r c  51  t I . W a t e r Cooling  i  111  Water Cooling Figure  1 1 1 - 6 . D r a w i n g of t h e a r c  vessel  52  CHAPTER I V  DIAGNOSTIC METHODS  A. INTRODUCTION One p u r p o s e o f t h i s  research i s to  e v a l u a t e a model f o r t h e b e h a v i o u r  develop,  test  and  of t h e column of a v o r t e x  s t a b i l i z e d a r c , and s o , i n a d d i t i o n t o t h e c a l o r i m e t r i c gathered  by m o n i t o r i n g t h e c o o l i n g s y s t e m , t h e a r c h a s been  studied  optically  profile  in  to  the  the temperatures;  intensity  measurements  determine  radial  temperature  t h e c o l u m n . T h r e e i n d e p e n d e n t m e t h o d s have been  used t o determine the t o t a l  data  of  a b s o l u t e measurements of  i n t h e AI 430 nm a t o m i c  the  continuum  line,  absolute  i n t e n s i t y a t 431.4 nm, a n d  m e a s u r e m e n t s o f t h e AI 430 nm l i n e  width.  These s p e c t r o s c o p i c measurements, w h i l e  simple  enough  in p r i n c i p l e , are complicated  by t h e f a c t t h a t t h e c o l u m n i s  cylindrical.  by  Data  obtained  viewing  i n v e r t e d t o get the a c t u a l r a d i a l p r o f i l e s . known and  as  Abel  inversion,  r e q u i r e s an o p t i c a l l y  side-on This  i s b a s e d on c y l i n d r i c a l  must  be  procedure, symmetry  t h i n p l a s m a . I f we t a k e a q u a n t i t y  ( u s u a l l y a volume e m i s s i v i t y ) F ( r ) and i n t e g r a t e i t a l o n g l i n e o f s i g h t we g e t R u Y(y) = 2 / r F ( r ) ( r - y ) ^ d r 2  2  r  which This  will  be  a r a d i a n c e , o r power e m i t t e d p e r u n i t  i n t e g r a l c a n be i n v e r t e d t o g i v e  area.  a  53  w h i c h i s known a s t h e A b e l i n t e g r a l  (Fleurier  1974). In  work t h e i n v e r s i o n has b e e n c a r r i e d o u t  by  subroutine  i n Appendix  "ABEL"  ,  which  is  listed  p r o c e d u r e r e q u i r e s l a r g e q u a n t i t i e s of  computer  data,  so  are  collected  with  (OMA), s t o r e d d i g i t a l l y A  typical  list  100 v o l u m e s  integer  r e q u i r e s about  intensity  This  chapter  computer. 40  values.  for this  the s i z e of t h i s t h e s i s ,  o f t h e d a t a h a n d l i n g i s an  data  automated.  on t a p e , and p r o c e s s e d by  a l l the s p e c t r a l data c o l l e c t e d  fill  C. T h i s  an o p t i c a l m u l t i c h a n n e l a n a l y z e r  single radial profile  e a c h c o n s i s t i n g o f 500  using  the  c o l l e c t i o n and p r o c e s s i n g s y s t e m has been l a r g e l y Data  this  spectra, Just  r e s e a r c h would  so t h e a u t o m a t i o n  i m p o r t a n t f e a t u r e of t h e  discusses the d i a g n o s t i c  s y s t e m and  system. describes  the a b s o l u t e i n t e n s i t y c a l i b r a t i o n procedures used, as as  the  to  t h e o r e t i c a l b a s i s on w h i c h t h e t e m p e r a t u r e  well  profiles  a r e e x t r a c t e d f r o m t h e raw d a t a .  B. THE  OPTICAL SYSTEM  The spot  purpose of the o p t i c a l  in  the  arc  column  onto  system the  i s t o image entrance  slit  spectrometer, which then d i s p e r s e s t h a t l i g h t onto head The  where  the d i s p e r s e d spectrum  spot from which the l i g h t  a r c column  i s sensed and  a  small of  the  a OMA  digitized.  o r i g i n a t e s i s swept a c r o s s t h e  a t a steady speed w h i l e the data are r e c o r d e d  at  54  fixed  i n t e r v a l s by t h e OMA The  image  t o produce a r a d i a l  of the a r c i s f i r s t  profile.  r o t a t e d 90 d e g r e e s by a  p a i r o f m i r r o r s mounted a t 60 d e g r e e s t o one a n o t h e r so  that  the  column  onto  the  plane  appears v e r t i c a l . of  The c o l u m n  the spectrometer entrance s l i t  f / 1 6 l e n s mounted on a s c r e w d r i v e geared  down  i s t h e n imaged  synchronous  motor  which to  w i t h a 400  is  sweep  turned  of  the column  The  w h i c h i s 0.01  sampling  o v e r 0.51 the  i s 5 so t h e 0.05  mm  rate  is  mm  mm  by 2 mm  radially  a  t h e image p o i n t  a c r o s s t h e a r c a t a c o n s t a n t s p e e d o f a b o u t 0.16 magnification  by  mm  slit  by  0.4  nuns"' .  The  s e e s an a r e a mm  axially.  such t h a t each spectrum i s averaged  r a d i a l l y , which i s  sufficient  resolution  for  data a n a l y s i s requirements. The  monochromator  is  a Spex  1702  3/4  m Czerny-Turner  s c a n n i n g s p e c t r o m e t e r w i t h an a p e r t u r e o f f / 6 . 8 a n d lines  per  430 nm  in first  attached total  mm  to  grating  order i s about  the  between  and  12.4  the  The d i s p e r s i o n a t  and  with  E a c h OMA is  c h a n n e l has limited  2 c h a n n e l s o r 0.05  (synchronized  and with  a  strobe the  disc  supply  t o a v o i d s a t u r a t i n g the  of  the  OMA  OMA.  The  a  width  crosstalk  (fwhm) w h i c h  filter  3.77%  voltage)  by  nm  f o r t h i s work. A n e u t r a l d e n s i t y  transmission  intensity  nm.  resolution  c h a n n e l s to about  i s adequate  11 nm/cm  1200  e x i t p o r t t h e 500 c h a n n e l o u t p u t c o v e r s a  range of about  w=0.0247 nm  b l a z e d a t 500 nm.  a  of  1.34%  transmission  reduce the  light  strobe,  which  c o n s i s t s o f a d i s c w i t h a n a r r o w s l o t c u t i n i t mounted on a synchronous  motor,  is  used t o sample  the l i g h t a t a  fixed  55  Arc Mirror Pair 400 mm f/16  Lens  <—>  Mot or Dri ve  Variable Phase 120 Hz _ St r o b e "  OM A Head  Spex 1702 Spectrometer  OMA Console  F i g u r e I V - 1 . The d i a g n o s t i c  Digital Tape Recorder  system  56  point  i n t h e AC c y c l e s o t h e r i p p l e  not a f f e c t is  i n t h e power s u p p l y  t h e r e s u l t s . The s y n c h r o n o u s m o t o r on t h e  mounted  on  a  frame  does  strobe  w h i c h c a n be r o t a t e d t o a l t e r t h e  phase of t h e o b s e r v a t i o n s .  C. THE DATA HANDLING SYSTEM As t h e c o l u m n image i s s c a n n e d a c r o s s t h e slit,  light  separation  pulses are  spectrometer are  50  passed  about by  0.3 ms  the  duration  strobe  disc  8 ms  through  the  as  intensities  f o r about 3 seconds and t h e t o t a l  on m a g n e t i c t a p e . T h i s p r o c e s s  times  and  a n d o n t o t h e OMA h e a d . The s p e c t r a l  integrated  digitally  of  spectrometer  the  image  i s stored  i s repeated  sweeps a c r o s s t h e s l i t ,  about  g i v i n g 50  s p e c t r a spaced u n i f o r m l y a c r o s s the a r c column. A f i l e is  then  another  written  the  tape  to  t e r m i n a t e t h e run, and  r u n c a n t h e n be made w i t h d i f f e r e n t  (current,  then  (3 f i l e  tape  containing  the  data  c o m p u t i n g c e n t e r a n d mounted on a t a p e Amdahl  computer.  Program  which a r e coded i n a form n o t  halfword  (16 b i t ) i n t e g e r s . The p r o g r a m  by  2  converts  to  each  ensure  overflow the halfword  drive  spectrum  an  also  t h a t t h e OMA l i n e a r  i n t e g e r s and  calls  to  t h e raw d a t a ,  with  to  t o t h e UBC  connected  reads  compatible  and  which  drive.  i s taken  "CONV"  coding,  value  parameters  m a r k s ) i s w r i t t e n on t h e t a p e ,  rewound a n d removed f r o m t h e t a p e  The  the  arc  p r e s s u r e , e t c . ) . A t t h e e n d o f t h e s e s s i o n an e n d  of tape marker is  on  mark  the  Amdahl  a r r a y o f 500 divides  each  range w i l l not  subroutine  "CAL"  57  which  compensates  f o r the  variations  d i f f e r e n t c h a n n e l s by s c a l i n g e a c h amount.  Each  written and  spectrum  (array  i n 16 b i t b i n a r y  a header  line  manipulation  profiles  titles and  appropriate  integers) a  i s then  disc  file,  program  of  these  the  number  of  spectra  "SCAN" a l l o w s e x a m i n a t i o n a n d data  files.  d i s p l a y p l o t s of i n d i v i d u a l  This  program  i n t h e header  The  user  can  spectra or r a d i a l  i s a l s o used t o i n s e r t  lines,  t o o b t a i n h a r d copy  i t  t o scan through q u i c k l y .  of any g i v e n c h a n n e l , smoothed o r A b e l i n v e r t e d  desired.  of  i s generated a t t h e b e g i n n i n g of each run  purpose  interactively  500  response  an  f o r m on one l i n e o f  c o n t a i n s t o a l l o w t h e computer  some  channel  of  which l a b e l s t h e r u n and g i v e s  General  in  t o g e n e r a t e an  as  appropriate  index  of  data,  ( p r i n t e d o r p l o t t e d ) output such as  the  p l o t t e d output included  are  l i s t e d i n Appendix  in this  thesis.  These  programs  C.  D. AI L I N E INTENSITY MEASUREMENTS Several  methods  can  t e m p e r a t u r e o f an a r g o n p l a s m a method q u i t e ratio lines  of  the  the  total  yield  intensities  the  levels, the  the  e m i s s i o n s . One  i s to  measure  the  spectral  and assuming  local  temperature  which  A n o t h e r a c c u r a t e method d e p e n d s on  f o r any l i n e ,  total  calculate  i n two ( o r more)  (LTE) c a l c u l a t e  that r a t i o .  to  from i t s l i g h t  w i t h w i d e l y s e p a r a t e d upper  existence,  which  used  f r e e from s y s t e m a t i c e r r o r s  thermal e q u i l i b r i u m would  be  intensity  of  a  i n that  unique line  temperature  at  i s a maximum ( s i n c e  58  at  higher temperatures t h e  stage  population  of  that  ionization  i s d e p l e t e d ) . B o t h o f t h e s e methods h a v e b e e n u s e d t o  g i v e a c c u r a t e temperatures f o r argon plasmas  (Preston  Larenz  l a r g e degree of  1951)  but  both  ionization  to  make  continuum  background,  t e m p e r a t u r e s above subject of  require  the  a  fairly  A l l spectrum  so  they  about  visible  can  12000K.  only  The  be  arc  1977,  above  the  applied  which  at  i s the  o f t h i s t h e s i s h a s maximum t e m p e r a t u r e s i n t h e a r e a  11000K, w h i c h i s t o o l o w  f o r the  A l l spectrum  to  be  usable. The methods w h i c h c a n be u s e d when o n l y t h e A I s p e c t r u m is  available  intensities  are  quite  limited.  i s proportional to  e i" 2^ E  are  t h e two u p p e r  from  13 t o 15 eV f o r u s a b l e l i n e s  is  thus  the  intensity  The  E  T  ratio  of  where  line  and  E  2  l e v e l e n e r g i e s , which have v a l u e s r a n g i n g  limited  t o about  r a t i o would  i n t h e AI s p e c t r u m .  E,-E  2  2 eV maximum, a n d a 10% e r r o r i n  t h u s i n t r o d u c e an e r r o r  which corresponds t o a temperature error of a t l e a s t  500K a t  T=10000K a n d i s u n a c c e p t a b l y l a r g e . The same p r o b l e m  occurs  for  the  ratio  intensities  are  of  AI  line  strongly  the  ratios;  dependent,  of  the  AI  temperature.  absolute line  both  but the  p r i m a r y method u s e d t o d e t e r m i n e t e m p e r a t u r e s  a r g o n s p e c t r a was  intensity  continuum  temperature  r a t i o only v a r i e s weakly w i t h The  to  at  measurement  of  430 nm. A b s o l u t e  the  from total  intensity  59  1  1  1  425  1  1  1  1  430  1  1  .  1  1  A (nm)  F i g u r e I V - 2 . The AI 4 3 0 nm  line  m e a s u r e m e n t s a r e g e n e r a l l y more d i f f i c u l t relative  measurements  procedure  was j u d g e d  The  4 3 0 nm l i n e  handled  spectroscopic literature, might  t o be t h e b e s t  perform  'than  available  alternative.  i ti svisible  and e a s i l y  many r e s e a r c h e r s have s t u d i e d i t a n d i t s  parameters  are  and i t i s w e l l  overlap  to  ( i . e . measurement o f r a t i o s ) but t h i s  was c h o s e n b e c a u s e  optically,  i  1  435  and  therefore  available  s e p a r a t e d from  cause  problems  (see F i g u r e I V - 2 ) .  This  (T<12000K,  P<10  Atm) o c c u r r i n g i n t h e a r c . T h i s c o n c l u s i o n i s s u p p o r t e d  1980),  s i n c e t h e y were  1963, Preston  (Olsen  many  of  looking  conditions  that  i s also optically  Baessler  f o r the  lines  line  by n u m e r o u s a u t h o r s  thin  other  i n the  whom  axially  1977, R i c h t e r 1965,  worked w i t h l o n g e r plasmas through  wall  stabilized  arcs. The atomic  r a d i a t e d power p e r s t e r a d i a n p e r u n i t  line  of wavelength  Xi s  v o l u m e i n an  60  J =  where A ^ upper  nm  N  n  i s the t r a n s i t i o n p r o b a b i l i t y  s t a t e n to the lower s t a t e m  density state  5^A 4TTA  of  is E  n  atoms  is  the  n. I f t h e e n e r g y o f t h e u p p e r  XT  n  = N  ~  g  o n 5  e  "  A  E  n  is N ,  we  0  have  at  i s the s t a t i s t i c a l i s low enough  T  w e i g h t o f s t a t e n. B e l o w  the  ionization  the  i d e a l g a s l a w N = P / k T a n d we g e t  ( O l s e n 1963) t h a t  we  12000K  can  use  0  J  ]i^g p_ -V n"nm kT  =  4TTX  B  Spectroscopic probability authors  A  e  k T  ( I V _ 1 )  measurements  of  the  transition  f o r t h e AI 430nm l i n e h a v e been made by many  (Olsen  recently  1963,  Baessler  Preston  and Kock  1977,  Richter  1965)  (1980) summarized t h e s e  and e x p l a i n e d most o f t h e d i s c r e p a n c i e s b e t w e e n u s i n g the r e s u l t s of t h e i r mean  number  n  N n  N  (kT«E )  XT  g  state  and  a n d t h e n e u t r a l atom d e n s i t y  low t e m p e r a t u r e  where  in  f o r an a t o m f r o m t h e  corrected  value  and  results  experiments  i n t e r f e r o m e t r i c m e a s u r e m e n t s . The  from t h e i r work, A  =3.12-10  s  s ±7% _ 1  nm h a s been u s e d The  here.  upper  level  for  E =14.51 eV a n d s t a t i s t i c a l n  P =1 .01 • l 0 N m " , 5  2  0  emissivity  which  the  transition  has  energy  weight g =5 (Olsen 1963). T a k i n g n  T = 1 0 0 0 0 K a n d J = 0.70 W i r r ' s r " 0  corresponds  1  o  to  1  count  in  ( t h e volume the  final  61  profile  - s e e s e c t i o n E) E q u a t i o n IV-1  1.68'10 K 24.81+ln(P/P )-ln(T/T )-ln(J/J )  _  T  profiles produce  from  IV-2  was  the  Abel  o  used  o  to calculate  inverted  which  u s i n g program  intensity  "FT"  , to temperature  integrates  the  i n t e n s i t y p r o f i l e , and  total  and  volume  emissivities  is listed  are converted,  profiles.  intensity  finally  p r o f i l e s are then l i s t e d "FT"  temperature  profiles  h a v e been c o l l e c t e d and f i l e d  The  unfolds  the  line line  uses E q u a t i o n IV-2 t o c o n v e r t  i n t o t e m p e r a t u r e s . The and p l o t t e d  i n Appendix  program  i n t h e A I 4 3 0 nm  f o r e a c h s p e c t r u m , t h e n s m o o t h s and A b e l  the  the  t h e r e s u l t s w h i c h a r e g i v e n i n t h e n e x t c h a p t e r . The  spectra  first  (IV-2)  5  o  Equation  becomes  temperature  for inspection.  Program  C.  E. ABSOLUTE INTENSITY CALIBRATION In o r d e r t o use t h e method of a b s o l u t e the  optical  system  must  be  calibrated  i n t e n s i t y , which i s c o m p l i c a t e d i n t h i s that and  the the  light water  calibration  line  work  source  between  used  is  them.  The  the  by  calibration  of  t u n g s t e n f i l a m e n t s o u r c e . The center of the v e s s e l  absolute the  fact  glass  walls  most  common  the carbon cathode of a  b u r n i n g a r c , but i n o r d e r t o compensate f o r the wall,  for  p a s s e s t h r o u g h two c y l i n d r i c a l jacket  intensity  the  system  f i l a m e n t was  was  arc done  mounted  (see F i g u r e I V - 3 ) , heated  freevessel  using a in  the  electrically,  62  and  p r o t e c t e d f r o m o x i d a t i o n by f l o w i n g a r g o n s l o w l y  the  vessel.  optical  The  f i l a m e n t temperature  was m e a s u r e d w i t h an  p y r o m e t e r a n d t h e r a d i a n c e a t 430 nm was c a l c u l a t e d ,  correcting  f o r the emissivity  temperature tungsten  and  temperature  I V - 4 . The  at  (T )  430 nm  as  fc  OMA  function  This calculation,  p y r o m e t e r a t 650 nm w a v e l e n g t h . Figure  as a  i n t h e CRC Handbook  f o r the radiance  brightness  of tungsten  wavelength.  e m i s s i v i t y data  in a curve  (1973), 3 0  )  different channel each  temperatures.  channel  = w  as  then  average  used  IV-5  (without the at  several  number o f c o u n t s p e r width  R  s h o u l d be  0  shows, a l o g - l o g p l o t i s linear,  constant,  of N v s R,  3 0  at  and g i v e s a v a l u e  R =wR„ /N=2.69-10-°Wm- sr- . 2  0  1  30  This constant radiance  relates  the  number  of  counts  i n v e r s i o n , and  strobe  d a t a . The s t r o b e r e d u c e s t h e number o f c o u n t s 0.0377,  to  the  f r o m t h e c o l u m n ; we must a l s o c o n s i d e r t h e e f f e c t s  of t h e data p r o c e s s i n g , A b e l  and t h e Abel  inversion gives a result  d i v i d e d by 2 0 d = l 0 . 2 mm The  in  i s w=0.0247 nm, t h e r a d i a n c e p e r c o u n t i s  I f t h e system i s l i n e a r ,  Figure  the  function i s plotted  was  v a r i o u s brightness temperatures of  versus  N was m e a s u r e d , a n d k n o w i n g t h a t t h e s p e c t r a l  Ro R»3o/N. and  The  results  measured w i t h t h e o p t i c a l  This  system  (R,  of  b a s e d on t h e  s t r o b e ) t o measure t h e r a d i a n c e of t h e f i l a m e n t  of  through  (d i s the spacing  a c t u a l volume e m i s s i v i t y p e r count  on  by a f a c t o r o f w h i c h must be  between  samples).  i s thus  R  j  _ ° _ = 0.70 Wm" sr 3  =  _1  the  (IV-3)  T ungsten Ribbon Filament  Figure  IV-3.  The c a l i b r a t i o n  setup  Figure  IV-4. Radiance vs b r i g h t n e s s  Figure  IV-5. N vs  radiance  temperature  65  and  the absolute c a l i b r a t i o n  i s complete.  F. A I L I N E WIDTH MEASUREMENTS One  of  temperature  t h e methods used t o c o n f i r m t h e l i n e  m e a s u r e m e n t s was t o m e a s u r e  A I 4 3 0 nm l i n e , w h i c h in 10  the 2 1  region  a n d 2• 1 0  23  nr  the width  3  of  i s the and  J  3.5•10"  m K-  1 6  To  a  C l / 6  line  ±1u%  by  i s predicted  theory as (IV-4)  1 / 6  (fwhm),  N. i s t h e e l e c t r o n  constant  (Richter  with  the  1965).  by c h a n n e l , t h e n  the  line  that  the  to  be  line  2.5  channels  Equation  density  width  is  ( 0 . 0 6 2 nm±l0%).  w i d t h s add l i n e a r l y  ( i . e . L o r e n t z i a n shapes) t h e instrument width and  value  i n t e r p o l a t i o n . The i n s t r u m e n t w i d t h was m e a s u r e d ,  u s i n g a He-Ne l a s e r , Assuming  a  between  the e l e c t r o n d e n s i t y , the data are f i r s t  Abel unfolded channel found  line  e  width  is  w  calculate  the  Stark broadening  w  density  of t h e  of i n t e r e s t . For e l e c t r o n d e n s i t i e s  AA = C -N - T AX.  the width  i sproportional to the electron density  a c c u r a t e l y by l i n e a r  where  intensity  N , e  IV-4 and  i n wavelength i s subtracted  i s then used t o c a l c u l a t e t h e e l e c t r o n  the  temperature  corresponding  to  that  d e n s i t y c a n be c a l c u l a t e d u n d e r t h e a s s u m p t i o n  of LTE. Olsen  (1963)  T  has  calculated  a  table  p r e s s u r e , and h i s c a l c u l a t i o n s N  e  of  N  a  f i t a curve  = N A e" o  E / k T  vs  a t 1.1 Atm  66  w i t h A=669 a n d E=8.96 eV. s e t t i n g P = 1 .01 • 1 0 N i r r 5  Again  substituting  N =P/kT  a n d T = 1 0000K we g e t  2  0  0  (IV-5)  _ 1.04-10 K " 61.45+ln(P/P )-ln(T/T )-ln(Nj 5  T 1  O  where  N  O  i s i n n r . F i g u r e IV-6 3  g  G  shows t h e c u r v e T v s N  P=1.1 Atm a n d t h e p o i n t s c a l c u l a t e d by O l s e n . E q u a t i o n is  used  to  calculate  electron density  and  0  the  profile,  temperature  which  profile  provides  an  e  at IV-5  from t h e independent  check o f t h e core t e m p e r a t u r e . G. CONTINUUM INTENSITY MEASUREMENTS The  t h i r d method of o b t a i n i n g t e m p e r a t u r e s i s from t h e  continuum  i n t e n s i t y a t 431.4 nm, w h i c h  is  proportional  to  t h e s q u a r e o f t h e e l e c t r o n d e n s i t y . The v o l u m e e m i s s i v i t y i n a wavelength  i n t e r v a l AX. i s g i v e n by J =  C N  2  (IV-6)  £(X,T)AX  X T^ 2  where  C =1.62•10"•  factor  *(x,T), which  3  c  free-free (Preston  K  1 / 2  Wm srf t  1  includes  channel from N  contributions  of  both  1.67±10%  1977).  done by u n f o l d i n g t h e d a t a 5  the  and f r e e - b o u n d r a d i a t i o n , has a v a l u e of  The t e m p e r a t u r e c a l c u l a t i o n  over  and t h e continuum e m i s s i o n  from continuum  channel  by  intensity i s  channel,  averaging  c h a n n e l s a n d u s i n g t h e a v e r a g e number o f c o u n t s p e r (AX.=0.0247 nm) t o 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  E q u a t i o n I V - 6 . The t e m p e r a t u r e  i s then c a l c u l a t e d  a s d e s c r i b e d i n s e c t i o n F. P r o g r a m "ASPEC"  ,  which  N  g  from was  67  0  5 000  Figure  IV-6.  T(K)  10000  Temperature vs e l e c t r o n  density  68  used  to  perform  calculations,  the  is listed  line  width  i n Appendix  and c o n t i n u u m C.  intensity  69  CHAPTER V  RESULTS AND ANALYSIS  A. INTRODUCTION In t h i s  research  calorimetric  and  two t y p e s  using  v o l t a g e and  average  electrical  the  rate  The  and  input  power  consist processed  i s an i m p o r t a n t  stabilized arc.  of  scanned  The  sequences  result  core,  current,  using  the  computer  prediction  the  of  model,  of  the  of a u s e f u l model of  spectroscopic  by c o m p u t e r t o g i v e r a d i a l  of  with  change  the d e t a i l s of the o v e r a l l  measurements  s p e c t r a w h i c h h a v e been temperature p r o f i l e s of  the a r c column. These p r o f i l e s p r o v i d e accuracy  made,  i n the a r c f o r comparison with the p r e d i c t i o n s  balance  the v o r t e x  temperature  measurements  o f t h e c o m p u t e r m o d e l , s i n c e an a c c u r a t e power  were  calorimetric  c o o l i n g system along  system. These p r o v i d e  power b a l a n c e  measurement  spectroscopic.  measurements c o n s i s t of f l o w measurements  of  another t e s t  particularly  s i n c e t h e t e m p e r a t u r e measurements a r e  of  the  i n the hot  only  reliable  a t t e m p e r a t u r e s a b o v e a b o u t 9000K. In presented  t h i s chapter  t h e d a t a w h i c h h a v e been c o l l e c t e d a r e  and compared w i t h t h e p r e d i c t i o n s of t h e  computer  m o d e l . The e r r o r a n a l y s i s i s a l s o d e s c r i b e d , a n d some o f t h e assumptions  used  f o r the  c o m p u t e r model a r e j u s t i f i e d evidence.  spectroscopic  a n a l y s i s and t h e  on t h e  of  basis  experimental  70  B. CALORIMETRY Throughout the o p e r a t i n g of  range of t h e a r c , measurements  t h e power d i s s i p a t e d i n e a c h component o f t h e s y s t e m h a v e  been  made.  The f o u r c o m p o n e n t s a r e t h e c a t h o d e , t h e a n o d e ,  the w a l l and t h e r a d i a t i o n a b s o r b e r . includes  convective  losses  to  The w a l l  loading  the flowing gas. Since the  computer model o n l y d e a l s w i t h t h e a r c column electrode  effects  r a d i a t i v e and electrode  wall  when  the input  temperature  power b a l a n c e d which  difficulty  the  either causing  good  power  the  of  the  measurement  input  was  measured  which be  is  read.  the  accuracy  T h e r e was some  i n t h e temperature measurements, frequently affected  the  or complete f a i l u r e . results  and  damage  h a d t o be z e r o e d  were  electronics  and  were p r o p e r l y z e r o e d t h e  10%, can  transducers and  with  t o e n s u r e t h a t t h e sum o f t h e  transducers  drifting  isolation,  neglects  power.  flowmeters  with d r i f t  and  concerned  although  t o b e t t e r than  t h e RF s t a r t i n g p u l s e  the  primarily  losses,  average e l e c t r i c a l  the  with  are  l o s s e s i s important  losses equals The  we  also  remained  transducers,  After  obtained,  since  improving  although the  susceptible  to  f r e q u e n t l y and r e p l a c e d  RF  fairly  often. F i g u r e s V-1 t o 3 show t h e f o u r power l o s s c o m p o n e n t s v s current at various pressures, downstream. Gettel  These  results  (1980) a l t h o u g h  confuses  the  w i t h the cathode upstream are  consistent  with  those of  he u s e d d i f f e r e n t a r c l e n g t h s ,  comparison.  The  behaviour  and  which  of the electrode  71  Figure  V - 1 . Power  l o s s e s vs c u r r e n t ,  P=1.5 Atm  72  Figure  V - 2 . Power  l o s s e s vs  current,  P=2.1  Atm  73  F i g u r e V - 3 . Power  l o s s e s vs  current,  P=2.8 Atm  74  losses but  i s i n t e r e s t i n g , and  in  this  properties  work  of the  Figures  V-1  i.e. with  the  losses are  about  are  concerned  to a  3  indicate  small  cathode 10%  that  change  in  downstream  greater  change  i n the  the  flow a f f e c t s the  changing the  the  with  the  the  flow  increased  shape  losses,  cathode  wall  upstream.  t o t a l power b u t  r a d i a t i v e e f f i c i e n c y , and column  column  r a d i a t i v e and  than w i t h the  would i n d i c a t e a s l i g h t l y  gas  primarily  study,  column.  d i r e c t i o n causes  This  we  c e r t a i n l y warrants further  no  seems t o i m p l y and  that  characteristics  somewhat. The  direction  c a l o r i m e t r y and a n o d e , so t h e model  are  of  a l l of the  flow  the  for  most  of  the  from cathode  to  used f o r comparison w i t h  the  c o l u m n l o s s e s QR  and  Qw  when t h e  p l o t t e d i n f i g u r e s V-4  cathode i s  t o V-6  along  with  computer model p r e d i c t i o n s . T h e s e g r a p h s show c l e a r l y  model  accurately  equivalently is  used  s p e c t r o s c o p y was  r e s u l t s which are  upstream. These a r e the  gas  too  fact,  the  s m a l l and the  predicts electric the  wall  the  field,  predicted  loading  is  mechanism w h i c h d e t e r m i n e s the power  balance;  substantially anything  small  alters  else  b a l a n c e . The  a  the  total the  the  steady  column  state  losses,  predicted wall l o s s i s too  the  prediction, since  key  radiant  radiant and  in  loss the  loss thus  or  loading  radiant  change  significantly  e f f e c t o f an  that while  large.  In the  is  essentially  core  temperature  without  changing  establishes  enhanced w a l l l o s s would  power  thus  be  F i g u r e V-4.  T o t a l column l o s s e s vs  current  F i g u r e V-5.  R a d i a n t l o s s e s vs  current  77  30 \  Q  Experiment  •+ 1.5 A t m OZ2 A t m x 2.9 A t m  (kW) 20  Modified M odel  Computer Model  3 Atm  1 Atm  10H  3 Atm 1 Atm Steady S t a t e Model 0 100  300  500  KA)  Figure V-6. Wall losses vs current  700  78  to  reduce  the  i n c r e a s i n g the  radiant total  loss  column l o s s e s , s i n c e  will  change t o accomodate the  the  total  power  correspondingly,  much.  new  This  r a d i a t i v e e f f i c i e n c y and  the  rather radiant  wall loss without  has  a  than  large  loss  changing  e f f e c t on  the for  i s therefore  of g r e a t  interest  explanation  for  enhanced w a l l  lighting applications. The  most  loading  in  this  associated in  the  obvious  with  system the  is  f l o w i n g gas  s t e a d y s t a t e m o d e l . The  heating  calculation  electrical  t h i s r e s u l t , a new  of  the  column w i t h  the column. At by  the  low  of  the  gas  heat  but  should  loading  the  be  greater  since  the  core.  i n the  it  is  under t h e s e  Using  can  last  as  is  be  50  mm  leaves  limited  conditions content  i n p u t power) i t i s t o be  expected  the  than the  gas  be  is difficult  negligible. to  estimate,  c a l c u l a t e d steady state  thermal gradients  wall  reach  there  loading  gas  gas  the c a l c u l a t e d heat  want o f a b e t t e r e s t i m a t e ,  modified  if  heating  l o s s e s to the w a l l w i l l  s t e a d y s t a t e l o a d i n g has The  gas  the  neglected  should  i n the  wall  arc core;  fact that  c a r r i e d away by  l a r g e r . For  column  available  loss  transient  gas  steady state loading  to the  exceeds  t h a t the conductive The  the  power l e v e l s t h e  the  the  the  the heat c o n t e n t of  power i n p u t  ( d i s t i n g u i s h e d by  that  p r e d i c t i o n of the  made by c o m b i n i n g t h e  convective  - a l o s s which i s  down  power  large  r e s u l t s of  indicate  steady s t a t e about halfway sufficient  the  the  will  wall  be s u b s t a n t i a l l y  a value  of t w i c e  the  been assumed. loading  can  now  be  calculated,  79  separating power  the arc c o n d i t i o n s i n t o  zero  conductive  the p r e d i c t e d steady the  convective  assumed equal the  to  be  l o s s and a c o n v e c t i v e  can  be  calculated  state profile  zero  t o the steady  regimes.  for  high  half  linearly  with current  In the t r a n s i t i o n  T  power  and Q  G  and  Q  < T  Q  P=3  region,  assumed  to  are  delimited input  i s t h e c a l c u l a t e d power l o s s by c o n v e c t i o n i f  G  the gas has r e a c h e d t h e s t e a d y illustrates  after  r e s p e c t i v e l y . H e r e 0^, i s t h e t o t a l  G  is  f r o m t h e l o w power t o t h e h i g h  power v a l u e s . The h i g h a n d l o w power r e g i o n s by Q > 2 Q  loss  half,  where t h e power i s i n t e r m e d i a t e , t h e l o s s e s a r e change  power  of t h e column and  f o r the second  hot gas has reached t h e w a l l .  low  a s s u m i n g t h e gas  and t h e c o n d u c t i v e  the f i r s t  state value  At  l o s s of t w i c e  s t a t e l o s s a r e assumed. At  loss  reaches the steady  three  how  the modified  state  profile.  Figure  V-7  w a l l l o a d i n g was c a l c u l a t e d f o r  Atm. This  modified  wall  with the experimental such  a  accurate  model of a c o n v e c t i o n techniques  the  at  possible The steady  d a t a , and  i s p l o t t e d i n Figure  shows  good  agreement  V-6 for  c r u d e m o d e l . I t w o u l d be u s e f u l t o c o n s t r u c t a more  modelling arc  loading  low  which c o u l d p r e d i c t  power  future research calorimetric state  dominated a r c using  model  levels,  and t h i s  the  numerical  behaviour  of  i s suggested as a  topic. measurements predicts  a c c u r a t e l y but g i v e s poor r e s u l t s l o s s e s . T h i s c a n be u n d e r s t o o d  the  have  shown  total  f o r the w a l l  that  column and  the  losses radiant  i n view of the important  role  80  Modified Total Convective  Conductive  Maximum Convective Loss St eady State C onductive Loss  Figure  V-7.  The m o d i f i e d  wall  loading  prediction  81  played  by  a r c , and  convection  a crude  calculation  c o u l d be a c c o u n t e d is  i n t h e power b a l a n c e shows  that  f o r by c o n v e c t i o n due  of t h i s type the  discrepancy  t o t h e gas  p o s s i b l e , b u t by no means c e r t a i n t h a t t h i s  of the enhanced w a l l in order  l o a d i n g , and  to construct  a  model  flow. I t  i s the  more work w i l l which  of  be  predicts  cause  required  the  power  balance a c c u r a t e l y .  C.  TEMPERATURE PROFILES The  temperature  p r o f i l e s were m e a s u r e d p r i m a r i l y  the absolute i n t e n s i t y Chapter  I V . The  measurements  o f t h e A I 4 3 0 nm  results  of  the  were  line  l i n e , as d e s c r i b e d i n  confirmed  width  using  and  independently  continuum  by  intensity,  w h i c h a r e d e s c r i b e d i n s e c t i o n D. Each e x p e r i m e n t a l evenly across  t h e a r c , and  analysed a temperature V-8  is  obtained.  F i g u r e V-8  v a l u e s of T  plotting  0  and  R  1 0  and  0  the  are p l o t t e d  a l o n g w i t h the p r e d i c t e d v a l u e s It  can  be  between the s t e a d y good  f a m i l i e s of c u r v e s  seen  understanding  10000K r a d i u s R i « 0  in  Figures  V-9  from the steady  s t a t e m o d e l and fair  the  measured  the the  V-10  s t a t e model. agreement values  a t low c u r r e n t s . A t  i s somewhat h o t t e r and  like  Measured and  from these graphs t h a t the  a t h i g h c u r r e n t s and  b e l o w 500A t h e a r c  in  p r o f i l e s h a v e been c h a r a c t e r i z e d by  T  and  l i k e t h e o n e s shown i n F i g u r e  w o u l d be o f l i m i t e d v a l u e  temperature  spaced  when t h e s p e c t r a a r e u n f o l d e d  profile  Since  a r c , the temperature core  r u n p r o d u c e s a b o u t 40 s p e c t r a  is  currents  narrower than  the  Temperature (K)  2000 H  -I  16  1  12  1  ©  1  4  Figure V-8. Typical  '  0  1  4  temperature  1  6  1  I  12 16 Radius(mm)  profiles  12  000  A  T ( K )  Figure  V-9. C o r e t e m p e r a t u r e v s  current  84  100  i  300  Figure V-10.  i  500  I (A)  Core r a d i u s vs  current  i  700  85  model  predicts,  which  c o u l d be a n o t h e r c o n s e q u e n c e  s t r o n g l y c o n v e c t i v e n a t u r e of t h e a r c a t low In  this  r e g i o n t h e r e i s s i m p l y i n s u f f i c i e n t power  i n t h e c o r e t o h e a t t h e g a s up a l l the  power  a r c channel  of the levels.  available  t h e way t o t h e  wall,  remains narrow, and i n order t o c a r r y t h e  r e q u i r e d amount o f c u r r e n t t h e a r c c o r e must be h o t t e r would  be  so  expected  than  i f i t were o f l a r g e r d i a m e t e r . T h i s i s  c o n s i s t e n t with the r e s u l t s of the c a l o r i m e t r y and a g a i n p o i n t s o u t t h a t  i n s e c t i o n B,  i t w o u l d be u s e f u l t o have a model  for t h e behaviour of a c o n v e c t i o n dominated a r c .  D. L I N E WIDTH AND CONTINUUM MEASUREMENTS In o r d e r t o c o n f i r m t h e any  one  spectral  quantity  m e a s u r e m e n t s o f some o t h e r There  a r e many  temperatures  processes  affect  l o c a l thermal equilibrium,  potential,  probabilities errors. from  plague  such  to  436 nm,  for  particularly  and  secondary  described  well. the as  lowering of the transition  t h e s p e c t r o s c o p i s t and produce  so  argon  spectra  t h e use of f e a t u r e s of that  temperature  s u i t a b l e . The c o n t i n u u m  measurements  is  i n t e n s i t y and t h e w i d t h  o f t h e A I 4 3 0 nm l i n e have been c h o s e n a s s e c o n d a r y as  have  phenomena  inaccurate  I n t h i s work t h e raw d a t a c o n s i s t o f  424  spectrum  often  and  and  which  deviations ionization  plasma,  as  from  from  to  quantity  emission of l i g h t from  a  i t i s desirable  independent  complicated  calculated  features,  i n C h a p t e r I V , a n d F i g u r e V-11 i l l u s t r a t e s t h e  e x c e l l e n t a g r e e m e n t among t h e t e m p e r a t u r e s c a l c u l a t e d by t h e  86  t h r e e m e t h o d s . The the  e r r o r bars  reproducibility  shown i n F i g u r e V-11  of the measurements from run  represent to  run  (1  standard  d e v i a t i o n ) as m e a s u r e d i n a s e r i e s o f r u n s a t 430  and  Atm.  1.5  considered  The  a g r e e m e n t among t h e  i n t e r m s of t h e  measurements, d e r i v e d  E.  systematic  A  t h r e e methods i s b e s t uncertainties in  these  shown on F i g u r e  V-11.  i n s e c t i o n E and  SYSTEMATIC ERRORS The  e r r o r a n a l y s i s of the c a l o r i m e t r i c system i s  simple,  and  of  complicated.  Let  The  the us  first  measured  t e m p e r a t u r e s . The accuracy  due  spectroscopic consider  values  water o n l y be  v a r i a t i o n s i n the  m e t e r s a r e c a l i b r a t e d t o w i t h i n 5%. measurements  are  accurate  to  of  uncertainty uncertainty  the  arc  The  to the  column  associated  read  rates  and  t o about  10% the  temperature  which corresponds i s not  important.  addition  there  is the  a r c . These r e g i o n s a r e g e n e r a l l y h o t t e r than the column,  but  i s c o m p e n s a t e d by  the  electrodes.  It  t h e h e a t and has  been  c a n c e l out  and  of  This assumption could  5%  100 in  mm. the  complicated  electrode regions  2%  of  this  the  In  to The  which c o n t r i b u t e s about  losses.  with  flow  digital  ±0.1K  i s 100±2 mm  more  flow r a t e , although  a b o u t 50 W a t n o r m a l f l o w r a t e s , and length  somewhat  the c a l o r i m e t r y .  are  f l o w meters can  to  system  fairly  radiation  assumed  t h a t t h e a r c c o l u m n has  c a l o r i m e t r y , but (see  f o r example  an  absorbed  that these e f f e c t s effective  i n t r o d u c e an  length  e r r o r o f up  the e l e c t r o d e r e g i o n s are Pfender  by  1980)  and  an  to  very exact  87  F i g u r e V - 1 1 . Core temperatures from t h r e e methods  88  analysis  i s beyond the  The  radiative  m e c h a n i s m s ; up the  arc,  t o 5%  and  scope of  this thesis.  losses  are  of the  between  light  5  w a l l s , w a t e r j a c k e t and  and  end  diminished  is lost  10%  by  several  from the  i s a b s o r b e d by  p l a t e s of the  vessel  ends the and  of  glass added  t o the measured w a l l l o a d i n g . These components i n c r e a s e s measured  wall  losses,  but  loading not  substantially. b e t w e e n 0 and estimate  of  The  enough  The 5%  light  to about  important  three  systematic line  power  of the  10%  is  by  flow  o f ±30%, an  temperature  measurements, 5 t o 10%  Figures  IV-4  accurate  to  of  the  lie  confirms  the  with  an  them. F o r  5.  The  estimated  as  ±10%.  used  calculate  The  different  the  continuum  of about AI  the ±20%  transition  w h i c h i m p l i e s an o v e r a l l for  the  line  intensity  a theoretical uncertainty  1977)  and  might  evidence  to  better  be  continuum i n t e n s i t y t h e r e f o r e  the  the  walls.  have  a l t h o u g h t h a t appears from e x p e r i m e n t a l (Preston  only  f r a c t i o n of  uncertainty  7%,  c o n t i n u u m f a c t o r ^ has  the  s o u r c e of e r r o r s i s  and  ±200K  but  vessel  measurements  associated  overestimate  to  generally  power, which  e r r o r i s the  temperature uncertainty m e t h o d . The  balance  c a l o r i m e t r i c measurements i s thus  c a l i b r a t i o n w h i c h has  probability  power  losses  w h i c h i s a b s o r b e d by  errors  indicated in  be  input  i n t e n s i t y m e a s u r e m e n t s one  absolute as  measured  the  leakage.  radiation emitted  and  alter  systematic  The  decrease the measured r a d i a t i v e  to  below the  accuracy  limited  and  the  electron density  with a  can  be  systematic  89  u n c e r t a i n t y o f ±25% w h i c h The due  u n c e r t a i n t y i n t h e l i n e w i d t h measurement i s p a r t l y  t o the large instrument  compared Abel  to  the  of  about  coefficient (Richter  width  system  (0.1 nm). A f t e r  ±0.01 nm  introduces  an  or  10%.  additional  The  (0.063  w i t h an  line  an  nm)  smoothing and  uncertainty  1964) s o t h e l i n e w i d t h method h a s  width o f 10%  uncertainty  ±20% i n t h e e l e c t r o n d e n s i t y . Assuming  that  the temperature as  line  width of the  i n v e r s i o n t h e l i n e w i d t h c a n o n l y be d e t e r m i n e d  accuracy  of  probably overestimates the e r r o r .  outlined  temperature ±300K  local  thermal e q u i l i b r i u m  c a n be c a l c u l a t e d in  from  Chapter  IV,  the e l e c t r o n  and t h e u n c e r t a i n t i e s  the continuum and l i n e  width  density i nthe  methods  are  a n d ±250K r e s p e c t i v e l y . T h e s e u n c e r t a i n t i e s a r e shown  i n F i g u r e V-11 a n d t h e v a l u e s f r o m agree  from  (LTE) e x i s t s ,  to well within  supports  the  experimental  the  assumption  t h e t h r e e methods  systematic of  LTE  clearly  uncertainties,  and  i s evidence  which o f good  technique.  F. TIME VARIATION The large  spectroscopy  ripple  stroboscope arc  in  but  by  the  t h e c u r r e n t , so a synchronous  disc  was  synchronized  i t i s necessary  t h e column i n o r d e r t o  behaviour.  arc  complicated  was u s e d t o e l i m i n a t e t h e t i m e d e p e n d e n c e o f t h e  c o l u m n . The s t r o b e was  maximum, of  (50%)  of the  with  the  current  t o examine t h e time e v o l u t i o n  ensure  that  we  understand  i t s  90  Figure (8.3  ms  since  current, The  V-12  the  the  the  ripple  variation  frequency  to  causing  and  time,  which  prevents  with  of  maximum  reduces  time  the Rio*  current,  current  synchronization  dependent  I t c a n be s e e n t h a t  f o l l o w the  with  120 H z )  minimum c u r r e n t , a n d t h e a r c i s n e a r l y  that  difficulty.  radius  cycle,  after  at  requirements  is  the cycle  0  3 ms  stationary  through  core temperature T , and t h e core r a d i u s  s p e c t r o s c o p y i s done c o i n c i d e n t  2.5  and  shows  quite  effects  the core closely  from  temperature through  the  a l a g o f l e s s t h a n one m i l l i s e c o n d . T h e r e i s a  c e r t a i n amount o f t i m e d e p e n d e n c e i n t h e c o l u m n , h o w e v e r , a s e v i d e n c e d by t h e f a c t t h a t  t h e c o r e c o n d i t i o n s m e a s u r e d 2 ms  a f t e r maximum c u r r e n t  not  observed short  at  time  remains  that  time,  before.  slightly  stationary point  do  As  correspond  strobed,  the  the  current  core  would p r e d i c t .  but t h i s presents  be  f r e e a r c so t h a t  decreases,  h o t t e r and l a r g e r than measurements a t t h e  for calorimetric  would  current  flowing a  dominated a r c could  ripple  a major d i f f i c u l t y  properties  be d e t e r m i n e d  entirely,  w h i c h c a n n o t be at these  high  t o p i c t o be p u r s u e d i n t h e  the c o n s t r u c t i o n the  the  measurements  power l e v e l s . A p o s s i b l e r e s e a r c h future  the  but t o the l a r g e r current  I t w o u l d be h e l p f u l t o e l i m i n a t e especially  to  of a lower power, r i p p l e of  a  steady  accurately.  convection  10001(A)  v, •  1  0  2  F i g u r e V-12. C u r r e n t ,  1 4 temperature  1 6  1 t (ms)  and r a d i u s v s  8 time  92  G. CYLINDRICAL One  of  SYMMETRY the  assumptions  made  in  both  the computer  c a l c u l a t i o n s and t h e s p e c t r o s c o p i c a n a l y s i s was  cylindrical  symmetry  i n the Abel  in  the  a r c c o l u m n . T h i s was e n f o r c e d  i n v e r s i o n by a v e r a g i n g remove  t h e two  halves  of  p r o f i l e s before profiles  show  the  data  shows some t y p i c a l  processing  the v a r i a t i o n  takes  of i n t e n s i t y  t h e A I 4 3 0 nm l i n e ) w i t h v e r t i c a l p o s i t i o n t h e y h a v e been s u p e r i m p o s e d on t h e i r symmetry.  The  the  relative the  of c y l i n d r i c a l  in  the  arc,  and  this  buoyancy  provides  clear  symmetry.  VARIATION steady  column  state  has  model  been  to the o p t i c a l  f i g u r e s V-14 Direct  the  These  ( a t the c e n t e r of  S i n c e any a s y m m e t r y due t o g r a v i t a t i o n a l  temperature  strongly  intensity  place.  is  a p p l i c a b l e t o an  i n v a r i a n t s e c t i o n of t h e a r c column, so t h e a x i a l in  to  r e f l e c t i o n s t o show t h e  would appear i n the v e r t i c a l p r o f i l e ,  H. A X I A L  profile  any a s y m m e t r y , b u t t h e raw d a t a show t h e symmetry o f  t h e c o l u m n c l e a r l y . F i g u r e V-13  evidence  the  investigated  by  axially  variation  moving t h e a r c  system. T h i s r e v e a l s the changes  profile  along  the  a r c a x i s , a s shown i n  and 15. observation  suggests  that  the  electrodes  i n f l u e n c e t h e a r c f o r a d i s t a n c e o f 10 t o 20 mm  central  in  50 mm  but  o f t h e c o l u m n a p p e a r s u n i f o r m . F i g u r e s V-  14 a n d 15 show t h a t t h e u n i f o r m r e g i o n i s  30  mm  long  and  F i g u r e V-13.  Typical  intensity  profiles  11000 T(K)  10800<  Flow  —1—  — i  -20  -10  0  z  CATHODE  10 (mm)  Direction »  —i— 20  1  30 ANODE  F i g u r e V-14. Temperature v s a x i a l  io  ->  position  i  R (mm)  Flow  -20  •-CATHODE  -10  0  -i 10  Direction >  1  z(mm)  20  F i g u r e V-15. Core r a d i u s v s a x i a l  —r~ *0  ANODE  H  position  95  that and  outside the  that region the temperature begins to decrease  radius  electrode  and  spectroscopy variation invariance.  is  gas was  to  increase,  due  to  a  combination  of  flow e f f e c t s . Near the plane i n which the done  (z=0  on  the  small enough to allow  graphs)  the  axial  the assumption of a x i a l  96  CHAPTER V I  CONCLUSIONS  A. INTRODUCTION In t h i s which  thesis the r e s u l t s are presented  was u n d e r t a k e n  performance  from  with the u l t i m a t e goal of improving the  o f t h e v o r t e x s t a b i l i z e d a r c lamp, p r i m a r i l y i n  the areas of l o n g e v i t y and r a d i a t i v e e f f i c i e n c y . has v been  approached  indirectly,  of  the  research  has  o f how  been  i t behaves.  to  The  determine  A  understand  about t h e a r c , and thus t o suggest  what  f u t u r e r e s e a r c h m i g h t most p r o f i t a b l y chapter  immediate  second  has  this  the  we  important  do a n d do n o t the  direction  take.  experimental  and  theoretical  r e s u l t s a r e s u m m a r i z e d , t h e c o n c l u s i o n s drawn f r o m presented,  and  the  work a r e d e t a i l e d . which  could  help  that the  i n o r d e r t o expand  objective  In  author's  them  answer  are  o r i g i n a l c o n t r i b u t i o n s t o the  I n a d d i t i o n , a number o f r e s e a r c h to  goal  t h e r e f o r e been t o s t u d y t h e a r c  e x p e r i m e n t a l l y and model i t t h e o r e t i c a l l y our u n d e r s t a n d i n g  This  on t h e p r i n c i p l e  s u r e s t r o a d t o improvement i s u n d e r s t a n d i n g . aim  research  many  remaining about the a r c a r e suggested.  of the q u e s t i o n s  topics still  97  B. CONCLUSIONS A  steady  conditions  state  in  model  has  been  used  at  high  suggest  currents  experimental  and  results  features  of  general nature  The  core  profiles  intuitive  flow.  currents,  and  model  this  predicts  w h i c h shows t h a t t h e understood,  although  unclear. solutions  of  profiles  the  whose  steady  state  shapes  agree  e x p e c t a t i o n s and e x p e r i m e n t a l  temperatures  and  radii  extracted  c u r r e n t s a b o v e 500 A, b u t a t somewhat  lower  hotter  currents and  results.  from  i n good a g r e e m e n t w i t h e x p e r i m e n t a l  are  These  t h i s conclusion. Despite  of t h e column i s w e l l  are  profiles  low  the arc adequately,  produce temperature  both  at  s t a t e c o n d i t i o n s the  self-consistent  equations with  dominant support  some d e t a i l s a r e s t i l l The  gas  that convective e f f e c t s are important  p e r t u r b a t i o n of steady many  predict  t h e a r c c o l u m n , a u g m e n t e d by c a l c u l a t i o n s o f  the c o n v e c t i v e l o s s e s a s s o c i a t e d w i t h the calculations  to  values at  the  narrower  these  measured than  the  c a l c u l a t i o n s p r e d i c t . This i s c o n s i s t e n t w i t h the r e s u l t s of the c o n v e c t i v e t r a n s p o r t c a l c u l a t i o n s , which under  these  conditions  column i s i n s u f f i c i e n t state  t o heat  electrical the  gas  that  power i n p u t t o t h e up  to  the  steady  t h e o r e t i c a l p r e d i c t i o n s o f t h e power b a l a n c e  i nthe  profile. The  column  are  corrected power  the  indicate  also  accurate  at  h i g h c u r r e n t s when t h e y a r e  f o r c o n v e c t i v e e f f e c t s . Due t o l i m i t a t i o n s  supply, c a l o r i m e t r i c  i n the  r e s u l t s a r e o n l y a v a i l a b l e up t o  98  a b o u t 500 A, experiment  so  most  is  in  of  the lower  convective e f f e c t s occur, l e v e l s the  predictions  convection  dominated  as  the  p r e d i c t e d . None o f t h e s e by  pressure  are  accurate.  steady  At  although results  power  the  losses,  a  result  i t has n o t been r i g o r o u s l y is  affected  substantially  has  also  shown  results.  that  the  most  important  o f an a c c u r a t e m o d e l o f t h e a r c i s t h e m o d e l l i n g o f  t h e n o n - r a d i a t i v e l o s s e s . The b e h a v i o u r the  radiative  the other to  low  i n the range of 1 t o 3 Atmospheres, n e i t h e r i n  T h i s work  that  and  l o s s e s about t w i c e  state  the c a l c u l a t i o n s nor the e x p e r i m e n t a l  feature  theory  power r e g i m e where s u b s t a n t i a l  a r c has c o n v e c t i v e  seems r e a s o n a b l e ,  of  b u t a t t h e h i g h e s t a v a i l a b l e power  l a r g e as the p r e d i c t e d  which  comparison  of the a r c  the  such  l o s s e s change t o accomodate changes i n  c o m p o n e n t s o f t h e power b a l a n c e ,  predict  is  radiative  a n d so  l o s s e s one must f i r s t  in  order  accurately  p r e d i c t t h e o t h e r power l o s s e s i n t h e c o l u m n . I n summary, t h e c o n d i t i o n s i n t h e c o l u m n stabilized  arc  can  and  have  been  accurate dominant  corrections  for  r e s u l t s but a t lower and t h e s t e a d y  applicable.  a  vortex  p r e d i c t e d by c o m p u t e r  m o d e l l i n g . A t h i g h power l e v e l s a s t e a d y substantial  of  convective  state  model,  effects,  power c o n v e c t i v e  with  produces  effects  s t a t e m o d e l o f t h e a r c i s no  are  longer  99  C. ORIGINAL CONTRIBUTIONS The  research  described  traditional  scientific  the  experimentally,  model  in  this  thesis  method o f m o d e l l i n g  follows  a system,  the  testing  and then u s i n g t h e e x p e r i m e n t a l  r e s u l t s t o r e f i n e the model. The  modelling  h a s two a s p e c t s ;  the v o r t e x c a l c u l a t i o n . programs steady  I conceived  and wrote  used f o r the t r a n s i e n t h e a t i n g  s t a t e model, which p r e s e n t e d  problems  and  required  characteristics  of  of t h e gas v o r t e x  a  the  c a l c u l a t i o n and t h e  Experimentally,  stability  understanding  of  t h e a r c column. In s t u d y i n g  I analytically  computer  some d i f f i c u l t  good  v i s c o u s decay of a gas v o r t e x  the  t h e column m o d e l l i n g and  the  the problem  solved the problem  of  the  in a cylindrical vessel.  i n addition to designing  and  assembling  a r c s y s t e m a n d t h e d i a g n o s t i c s y s t e m I made a number o f  innovations changed  i n the  the  arc  design  vessel  and  support  structure.  o f t h e v e s s e l end caps t o a l l o w e a s i e r  assembly and d i s m a n t l i n g of t h e v e s s e l and improve flow.  The  improved  I  gas  flow  the  gas  h a s t h e a d v a n t a g e o f a much  s m o o t h e r f l o w p a t t e r n due t o t h e t a n g e n t i a l  injection j e t .  T h i s makes t h e f l o w e a s i e r t o m o d e l , r e d u c e s t h e p o s s i b i l i t y of  reversed  axial  r e d u c e t h e amount o f incorporated  an  downstream end  f l o w and s t a g n a t i o n turbulence  integral cap.  I  vessel  and  designed  electrode  the  inlet.  I  also  exhaust gas heat exchanger i n the  assembly f o r the i n s i t u a b s o l u t e the  near  r e g i o n s , and should  and  built  the  c a l i b r a t i o n and  support  structure  filament redesigned  to  improve  100  accessibility  and  implemented  the  rigidity.  automated  Finally data  necessary  p a r t of t h e d i a g n o s t i c  such  this.  as  This  included  computer programs f o r d a t a digital  equipment necessary  I  conceived  handling  system which i s a  system  in  writing  handling  a  and  f o r the data  and  an  experiment  l a r g e number o f setting  up  the  collection.  D. SUGGESTED FUTURE WORK The  research  effects; posed  described  in  this  thesis  i t h a s a n s w e r e d a number o f q u e s t i o n s  as  many  more.  The g e n e r a l  behaviour  been shown t o be p r e d i c t a b l e , b u t some o f still  and  behaviour  of the convection  i n which t h e gas  temperature that  a  supply  never  profile,  computer  behaviour  of  of t h e a r c has  the  details  are  be b u i l t  reaches  d o m i n a t e d a r c , i . e . an an  axially  i s poorly understood.  model  such  an  be  constructed  invariant  I t i s suggested predict  the  a r c , and t h a t a w e l l f i l t e r e d  power  f o r use a t low c u r r e n t s  t h e power b a l a n c e  i n a convection  to  (<200 A)  to  mechanism  which  perturbs  c o n d i t i o n s . The p o s s i b i l i t y the  deviation  could  very  complex  process  understood question  (Chien  study  dominated a r c .  T h i s r e s e a r c h h a s shown t h a t f o r c e d c o n v e c t i o n the  i t has  not c l e a r . The  arc  h a s h a d two  the  steady  c o u l d be  state  r e m a i n s , however, t h a t  much  arc of  be due t o t u r b u l e n t h e a t t r a n s p o r t , a  and  i ti s essential  which  is  Benenson  still 1980).  not To  t h a t a n e x p e r i m e n t be  thoroughly  resolve designed  this to  101  measure  the  position.  w a l l l o a d i n g i n t h e a r c as a f u n c t i o n of  This  conclusions  will  which  provide  research,  I  i n keeping would  system designed and  thus  to  applied  test  the  of  the  the nature  and  arc. nature  of  this  propose the c o n s t r u c t i o n of  t o reduce the c o n v e c t i v e  improve  end  l o s s e s i n the  w i t h the  like  could create a vortex both  excellent  h a v e been drawn r e g a r d i n g  importance of the c o n v e c t i v e Finally,  an  axial  losses in  radiative efficiency.  f l o w by  i n j e c t i n g gas  caps s i m u l t a n e o u s l y  and  the  Such a  arc  system  tangentially  a l l o w i n g t h e gas  (see F i g u r e V I - 1 ) .  caps  should  reduce  axial  p o t e n t i a l of p r o d u c i n g potential valuable  is realized information  stabilized  arc.  Careful balancing  velocity  to  improved or n o t , about  a  of  minimum  efficiency.  the and  behaviour  of  the  and  flows has  Whether  the experiment should  the  at  to escape  from b o t h ends t h r o u g h gaps between the e l e c t r o d e s h a f t s end  a  the that  provide vortex  102  / Argon  out  Argon in  c  Gas Vortex  3  Argon in  \  F i g u r e V I - 1 . The c o n v e c t i o n  Argon  out  free vortex  stabilized arc  103  BIBLIOGRAPHY  B a e s s l e r , P . a n d Kock,M., J o u r n a l o f P h y s i c s BJ_3,1351 Camm,D.M. a n d  Nodwell,R.,  US  Patent  (1980)  Application  #478872  (1974) Chen,D.M.,Hsu,K.C.,Liu,C.H. a n d P f e n d e r , E . , P l a s m a S c i e n c e . PS8.425 Chien,Y.K. and PS8.411  IEEE  Trans  on  (1980)  Benenson,D.M., I E E E T r a n s on P l a s m a  Science,  (1980)  , CRC Handbook o f C h e m i s t r y a n d P h y s i c s , C h e m i c a l Company, C l e v e l a n d  Rubber  (1973)  Emmons,H.W., P h y s i c s o f F l u i d s J_0_, 1 1 25 ( 1 967) Evans,D.L.  a n d T a n k i n , R . S . , P h y s i c s o f F l u i d s J_0,1137  F l e u r i e r , C . And C h a p e l l e , J . , Computer J_0,200  Physics  Communications  (1974)  Finkelnburg,W. and  Maecker,H.,  Springer-Verlag, Berlin Gettel,L.E.,  A  stabilized  comparitive  Handbuch  der  Physik  Kesaev,I.G.,  XXII,  (1956) study  of  DC  and  AC  vortex  a r c s , Ph.D. T h e s i s , UBC ( 1 9 8 0 )  Hoyaux.M.F., A r c P h y s i c s , S p r i n g e r - V e r l a g , New Y o r k Cathode  Processes  C o n s u l t a n t s B u r e a u , New Y o r k Larenz,W.,  (1967)  Z. P h y s i k  129,327  in  (1968)  the Mercury A r c ,  (1964)  (1951)  Maecker,H.,  Z. P h y s i k  157,1 ( 1 9 5 9 )  Maecker,H.,  Z. P h v s i k  158.392  (1960)  0 1 s e n , H . N . , J . Q u a n t . S p e c , a n d Rad. T r a n s . _3_, 305 P f e n d e r , E . , P u r e a n d A p p l i e d C h e m i s t r y .52,1773  ( 1963)  (1980)  104  Preston ,R.C. , J . Richter,J.,  Z.  Schoenherr,0.,  Quant.  Spec,  Astrophysik  and R a d .  61.57  Electrotechn.  Tam,S.Y.K.  and G i b b s , B . W . ,  Tuchman,A.  and E n o s , G . , Avco  T r a n s . J_8,337  (1965)  Zeitschrift  RCA R e p o r t  (1909)  #96208-2  Corporation  (1972)  Technical j  AVSSD-0043-67-RR  (1967)  (1977)  Report  105  APPENDIX A STEADY STATE CALCULATION PROGRAMS  PROGRAM TEMPROFILE; (* 22/V/80 *) VAR  E,E2,STEP,EMAX,DR,DR2,T0,T1,T:REAL; CORR,ERR,COND,CURR,P,QWALL:REAL; Q,QRT,M,R9,SIGO,TS,KAP0,TK,QR0,TM,TQ:REAL; I,L:INTEGER;ERROR:BOOLEAN; TP:ARRAY(1..100) OF INTEGER-  PROCEDURE T I T L E ; SLINKAGE ' T I T L E ' ; PROCEDURE PLOT; SLINKAGE 'RP100'; FUNCTION K A P P A ( T : R E A L ) : R E A L ; BEGIN I F T>7000 THEN KAPPA:=KAP0*EXP(T/TK) E L S E KAPPA:=1.1E-4+2.7E-7*T; END; FUNCTION SIGMA(T:REAL):REAL; BEGIN I F T<2000 THEN SIGMA:=0 E L S E SIGMA:=SIG0/EXP(SQR(TS/T)); END; FUNCTION QRAD(T:REAL):REAL; VAR T1:REAL; BEGIN T1:=(TM-T)/TQ; I F T1>10 THEN QRAD:= 0 E L S E QRAD:=QR0/EXP(T1*T1); END; PROCEDURE INTEGRATE; VAR R,INTEGRAL:REAL; L:INTEGER; BEGIN R:=0;T:=T0;INTEGRAL:=0; FOR L:=1 TO 100 DO BEGIN I F T<100 THEN T:=0 ELSE BEGIN INTEGRAL:=INTEGRAL+(QRAD(T)-E2 * S I G M A ( T ) ) * L * D R 2 ; T:=T+INTEGRAL/(L*KAPPA(T)); END; TP(L):=INTEGER(T); END; END;  106  BEGIN  (*TEMPROFILE*) READ(INPUT,P,E,STEP,EMAX); T1:=600;DR:=135E-4;DR2:=DR*DR;ERR:=1E-3; KAP0:=108E-6;TK:=2400; I F P=1 THEN BEGIN SIG0:=150;TS:=12700;QRO : = 5240;TM: =16500;TQ:=35 ELSE I F P=3 THEN BEGIN SIG0:=181;TS:=14100;QRO:=55500;TM:=20E3;TQ:=44 ELSE I F P=5 THEN BEGIN SIG0:=207;TS:=15000;QR0:=102E4;TM:=25E3;TQ:=57 ELSE I F P=7 THEN BEGIN SIG0:=229;TS:=15600;QR0:=5.4E6;TM:=27E3;TQ:=58 ELSE ERROR:=TRUE; TITLE(6, ***TEMPROFILE***',16); I F ERROR THEN W R I T E L N C INVALID DATA: P=',P:3:0) ELSE WHILE E<=EMAX DO BEGIN E2:=E*E;CORR:=1000;T0:=15E3; WHILE CORR>ERR DO BEGIN INTEGRATE; I F T>T1 THEN T0:=T0"CORR ELSE BEGIN T0:=T0+CORR; C0RR:=C0RR/10; END; END; COND:=0; FOR L:=1 TO 100 DO COND:=COND+SIGMA(TP(L))*L; COND:=COND*DR*DR* 6.283;CURR:=E*COND; QWALL:=3.11*KAPPA(TP(99))*(TP(98)-T); Q:=E*CURR/100;QRT:=Q-QWALL; M:=QRT/QWALL; L:=1; WHILE T P ( L ) > 9 0 0 0 DO L:=L+1; R9:=L*0.125; WRITELN('4 E=',E:5:2,'V/CM I=',CURR:4:0,'A, P:2:0,' ATM, Q=',Q:4:1,'KW',EOL,' QRAD=',Q 'KW, QWALL=',QWALL:5:2,'KW, M=',M:4:2,',R(9000)=' FOR I:=1 TO 100 DO I F I MOD 10=1 THEN W R I T E ( E O L , T P ( I ) : 1 3 ) ELSE W R I T E ( T P ( I ) : 7 ) ; WRITELN; PLOT(TP,CURR,P); E:=E+STEP; END; WRITELN(';'); 1  END.  107  APPENDIX B TRANSIENT HEATING CALCULATION PROGRAMS  PROGRAM TRANSIT; (* 7/IV/81 VAR  *)  K0,TK,K1,A,T,DELTA,DR,CON1:REAL; P,TMSEC,TIME,DT,TMAX,QOUT,QIN:REAL; T0,T1,REPS,NC,L,N,M:INTEGER; TP:ARRAY(1..100) OF REAL; QCORE,QWALL,R1:REAL;  INITIAL T0=11000;DR=1.35E-4; (* I N I T I A L TEMP TO. RADIAL INCREMENT DR(M) *) K0=1.08E-2;TK=2400;K1=1.1E-2;A=2.7E-5; (* VALUES FOR FUNCTION KAPPA *) TIME=0;NC=51;P=1.44; (* NC I S THE CORE RADIUS. P I S PRESSURE(ATM) *) TP=( 11000:55,300:45 );QCORE=0;QWALL=0; (* I N I T I A L I Z E TEMPERATURE PROFILE *) PROCEDURE T I T L E ; SLINKAGE ' T I T L E ' ; FUNCTION K A P P A ( T : R E A L ) : R E A L ; (* THERMAL CONDUCTIVITY *) BEGIN I F T>7000 THEN KAPPA:=K0*EXP(T/TK) ELSE KAPPA:=K1+A*T; END; FUNCTION KDT(T1,T2:REAL):REAL; VAR KDT1:REAL; BEGIN KDT1:=KAPPA((T1+T2)/2)*(T1-T2)/DR; I F KDT1>P*1E6 THEN KDT:=P*1E6 (* DIFFUSION L I M I T *) ELSE KDT:=KDT1; END ; FUNCTION C P R ( T : R E A L ) : R E A L ; (* S P E C I F I C HEAT PER UNIT VOLUME * VAR VAL:ARRAY ( 4 . . 1 2 ) OF REAL; INDEX:INTEGER; FR:REAL; I N I T I A L VAL=(63.3,50.5,42.5,38.3,39.5,49.5,71.5,104.4, 1 38. BEGIN INDEX:=INT(T/1000) ; FR:=T/1000-INDEX; I F INDEX<4 THEN CPR:=P*2.78E5/T ELSE I F INDEX>11 THEN CPR:=P*VAL(12) ELSE C P R : = P * ( V A L ( I N D E X ) * ( 1 - F R ) + V A L ( I N D E X + 1 ) * F R ) ; END; BEGIN (*TRANSIT*)  108  END.  READ(INPUT,DT,REPS,TMAX);CON1:=DT/REPS/DR; (* PRINT INTERVAL DT HAS REPS ITERATIONS. T<TMAX *) TITLE(6,'***TRANSIT***',13); WRITELNC DT=',DT:6:4,' REPS=',REPS:3,EOL); R1:=NC*DR; WHILE TIME<=TMAX DO BEGIN WRITECO T=' ,TIME:7:4, ' SEC R1 = ' , R1 : 4 : 1 , ' MM'); W R I T E L N C QC=',QCORE:5:2,' QW=',QWALL:5:2); FOR L:=NC TO 100 DO I F L MOD 10=0 THEN W R I T E L N ( T P ( L ) : 8 : 1 ) ELSE W R I T E ( T P ( L ) : 8 : 1 ) ; TIME:=TIME+DT; I F TIME<=TMAX THEN FOR L:=1 TO REPS DO BEGIN T:=TP(NC); QIN:=RDT(T0,T)*(NC-0.5); QC0RE:=QIN/1.18E6; FOR N:=NC TO 99 DO BEGIN T:=TP(N); QOUT:=KDT(T,TP(N+1))*(N+0.5); TP(N):=T+CON1/N/CPR(T)*(QIN-QOUT); QIN:=QOUT; I F T<300.1 THEN BEGIN M:=N; QIN:=0; N:=99; END; END ; WHILE TP(M)<1000 DO M:=M-1; T:=TP(M); R1:=(T-TP(M+1)); R1:=(T-1000)/R1; R1:=(M+R1)*DR*1000; QWALL:=QIN/1.18E6; END; END; WRITELNC;');  c  C  PROGRAM TRPL  c  DIMENSION T E M P ( 5 0 ) , I Y ( 1 0 0 )  109  DATA I Y / 5 0 * 1 1 0 0 0 / 11 12 13 14  100  150  990  FORMAT(14X,F 6.4) FORMAT(7X,10F8.1 ) FORMAT(' ',6X,F4.1,1016) FORMATC ',6X,'T(MSEC)  TEMP')  CALL T I T L E ( 6 , ' * * * T R P L * * * ' , 1 0 ) WRITE(6,14) READ(0,11,END= 990) TIME TMSEC=TIME*1000. READ(0,12) TEMP DO 150 1=1,50 IY(50+I)=INT(TEMP(I)) WRITE(6,13) T M S E C , ( I Y ( 1 0 * 1 ) , I = 1 , 1 0 ) CALL RP100(IY,TMSEC,1.0) GOTO 100 STOP END  Note: subroutine "RP100" temperature p r o f i l e .  draws  a  plot  of  the  radial  110  APPENDIX C DATA HANDLING PROGRAMS  C C  PROGRAM SCAN  (10/IX/80)  c  IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR LOGICAL*1 COPY(24)/'$C -TSCAN TO -COPY(*L+1)'/,CMND(10) CALL FTNCMD('DEFAULT 7=-TSCAN',16) CALL FTNCMD('DEFAULT 1=*PRINT*',17) CALL FTNCMD('DEFAULT 0=DATA',14) CALL FTNCMD('DEFAULT 2 = I N D E X ( * L ) ' , 1 9 ) 1 2 3 4 5 C 100  110  150 c  200  F0RMAT(I4,6X,I3) FORMAT(' SCAN BEGINS. DATA CONTAINS RUNS ',14,' TO ',14 FORMAT('VALID SCAN COMMANDS ARE:', -/,'GET,LIST,STOP,$CMND,COPY,TITLE,FIX,NEWFILE,DISPLAY') FORMAT('SCAN O F F . ' / l 4 , ' PLOTS I N -PLOT#') FORMAT('RUN',15,' I S LOADED *) CALL S E T P F X ( ' ] ' , 1 ) LNRUN=1000 INDEX=0 NPLOTS=0 LAST=0 NREC=0 READ(0'LNRUN,1,END=150) NRUN,LINC I F (LINC.EQ.0) GOTO 150 LAST=LAST+1 NDIR(LAST,1)=NRUN NDIR(LAST,2)=LNRUN NDIR(LAST,3)=LINC LNRUN=LNRUN+1000*(LINC+1) GOTO 110 I F (LAST.EQ.0) GOTO 600 PRINT 2 , N D I R ( 1 , 1 ) , N D I R ( L A S T , 1 )  GET COMMAND CALL ASK(CMND,LEN) JMP=ITBLC(CMND(1),'GLS$CTFND#') GOTO ( 2 5 0 , 3 0 0 , 3 5 0 , 4 0 0 , 4 5 0 , 5 0 0 , 5 5 0 , 6 0 0 , 6 5 0 ) , J M P I F (NUMGET(CMND).NE.0) CALL IGET(NUMGET(CMND),&200) I F (LEN.GT.0) PRINT 3 I F (INDEX.GT.0) PRINT 5,NDIR(INDEX,1) GOTO 200  C C 250  INITIALIZE  COMMANDS GET CALL GET(NUMGET(CMND),&200)  111  c  300 C 350 C 400 C 450 C 500  L  CALL  LIST(NUMGET(CMND),&200)  PRINT 4,NPLOTS STOP CALL CMD(CMND,10) GOTO 200 CALL CMD(COPY,24) GOTO 200  C 600  C C  T  STOP $CMND COPY TITLES F  CALL F I X ( 7 ) GOTO 200 CALL N E W F U l 0 0 , £ 2 0 0 )  c  650  S  CALL T I T L E S U 2 0 0 )  c  550  I  CALL STOP END  DlSPLY(NUMGET(CMND),&200)  I  X  NEWFILE DISPLAY  SUBROUTINE D I S P L Y ( N , * ) IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,HBUF(500 LOGICAL*1 CMND(10)  1 2 3 4  FORMAT('RUN ',14,' RECORD ',14,' I S LOADED.') FORMAT('VALID DISPLAY COMMANDS ARE:'/ + 'DRAW,/MOD,STOP,PLOT,LI ST,RESCALE,ERASE,VIEW,GET,XHAIRS FORMAT(* 1' , 1 2 X , ' L I S T I N G OF RUN ',14,' RECORD ',14//) FORMAT(* ',6X,1016)  C  INITIALIZE CALL S E T P F X ( ' ) ' , 1 ) I F (INDEX.EQ.0) CALL G E T ( N D I R ( 1 , 1 ) ) I F (N.NE.0) CALL DRAW(N)  C 100  GET COMMAND CALL ASK(CMND,LEN) NG=NUMGET(CMND) JMP=ITBLC(CMND(1),'D/SPLREVGX') GOTO ( 2 0 0 , 2 5 0 , 3 0 0 , 3 5 0 , 4 0 0 , 4 5 0 , 5 0 0 , 5 5 0 , 6 0 0 , 6 5 0 ) , J M P I F (NG.NE.O) CALL DRAW(NREC+NG,& 100) I F (LEN.GT.0) PRINT 2 PRINT 1,NDIR(INDEX,1),NREC GOTO 100  150  COMMANDS  c  C 200  DRAW CALL DRAW(NG,&100)  1 12  C 250  /MOD CALL MOD(CMND,&100)  c  300 C 350  S  CALL S E T P F X ( ' ] ' , 1 ) RETURN1 I F (NG.NE.O) CALL ERASE(NG) CALL IGDRON('CALC') NPLOTS=NPLOTS+1 GOTO 100  c  400  c  450 C 500  c  650  C C  1 2 50 C C C  CALL RSCL(CMND,&100) CALL ERASE(NG,& 100)  _  I F (NG.NE.O) CALL GET(NG) CALL V I E W U 1 0 0 ) I F (NG.NE.O) CALL GET(NG,& 100) CALL I G E T ( 1 , &100) CALL XHAIRS GOTO 100 END  I  S  T  RESCALE ERASE V  I  E  W  GET XHAIRS  SUBROUTINE GET(N,*) IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,CBUF(100 FORMAT('THERE I S NO RUN ',15) FORMAT('GOT RUN ',14,' CONTAINING 1=1 I F ( N D I R ( I , 1 ) . E Q . N ) GOTO 100 1=1+ 1 I F ( I . L E . L A S T ) GOTO 50 '• • PRINT 1,N RETURN1  ',14,' RECORDS')  NO MATCH  ENTRY I G E T ( N , * ) I=INDEX+N I F ( ( I . L T . 1 ) . O R . ( I . G T . L A S T ) ) 1=1 N=NDIR(I,1)  c  100  P  PLOT  L  c  600  0  I F (NG.NE.O) CALL DRAW(NG) I F (NREC.EQ.0) GOTO 150 WRITE(1,3) NDIR(INDEX,1),NREC WRITE(1,4) ( H B U F ( I ) , I = 1 , L A S T R ) GOTO 100  c  550  T  INDEX=I  MATCH  11 3  150  990 C C  1 2 3  20 50 990 C C  1  50 990  CALL EMPTYF(7,&990) NL00PS=NDIR(I,3)+1 CALL READ(CBUF,HL,2,NDIR{I,2),0,&990) DO 150 J=1,NLOOPS CALL WRITE(CBUF,HL,0,LNUM,7,&990) CALL READ(CBUF,HL,0,LNUM,0,& 150) CONTINUE PRINT 2,N,NDIR(I,3) RETURN1 CALL ERROR('GET RETURN 1 END  ')  SUBROUTINE L I S T ( N D E V , * ) IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,CBUF(32) FORMAT(' 1 ' ,16X,'DATA L I ST:'//8X'RUN' ,5X,'#RECS' ,6X,'TIT FORMAT(' ',6X,30A1) FORMAT(';') I F (NDEV.EQ.0) NDEV=6 I F (NDEV.EQ.2) GOTO 20 CALL TITLE(NDEV,'***SCAN***',10) WRITE(NDEV,1) DO 50 1=1,LAST CALL R E A D ( C B U F , H L , 2 , N D I R ( I , 2 ) , 0 , & 9 9 0 ) WRITE(NDEV,2)(CBUF(J),J=1,30) WRITE(NDEV,3) RETURN1 CALL E R R O R C L I S T ') RETURN 1 END SUBROUTINE T I T L E S ( * )  IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON" I NDEX, LAST, NDI R ( 2 0 , 3 ) , NPLOTS , NREC , LASTR, CBUF ( 3 2 LOGICAL*1 C T I T L E ( 1 0 ) EQUIVALENCE ( C T I T L E ( 1 ) , C B U F ( 2 0 ) ) FORMAT('&',30A1,'  ->')  DO 50 1=1,LAST CALL R E A D ( C B U F , H L , 2 , N D I R ( I , 2 ) , 0 , & 9 9 0 ) PRINT 1 , ( C B U F ( J ) , J = 1 , 3 0 ) CALL A S K ( C T I T L E , L E N ) I F (LEN.NE.0) CALL W R I T E ( C B U F , H L , 2 , N D I R ( I , 2 ) , 0 , & 9 9 0 ) CONTINUE RETURN 1 CALL ERROR('TITLES ') RETURN 1  11 4  C C  1  END SUBROUTINE NEWF(*,*) IMPLICIT LOGICAL*1(C),INTEGER*2(H) LOGICAL*1 CMND(19)/'ASSIGN 0=DATA EQUIVALENCE ( C F I L E ( 1 ) , C M N D ( 1 0 ) ) FORMAT('ENTER NEW  '/,CFILE(10)  DATAFILE NAME')  PRINT 1 CALL A S K ( C F I L E , L E N ) I F (LEN.EQ.O) RETURN2 CALL FTNCMD(CMND,19) RETURN1 END c  SUBROUTINE ERROR(CMSG) c  IMPLICIT LOGICAL*1(C) INTEGER*2(H) DIMENSION CMSG(10) r  1  C C  1  FORMAT ('I/O ERROR OCURRED IN ROUTINE  ',1fJAl)  PRINT 1,(CMSG(I),1=1,10) RETURN END SUBROUTINE DRAW(N,*) IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,HBUF(500 FORMAT('THERE I S NO RECORD  ',14)  I F (N.LT.1) GOTO 990 LNUM=(N+1)*1000 CALL READ(HBUF,HL,2,LNUM,7,&990) NREC=N CALL VECTOR(500) CALL L A B E L ( N D I R ( I N D E X , 1 ) , ' . ' , N ) RETURN1 C 990  PRINT 1,N RETURN 1 END  BAD NUMBER  c  C  SUBROUTINE VECTOR(N) IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,HBUF(500 LOGICAL*1 C F I R S T / . F A L S E . / REAL X ( 5 0 0 ) , Y ( 5 0 0 )  11 5  50  100 150  I F ( C F I R S T ) GOTO 100 DO 50 1=1,500 X(I)=FLOAT(l) CALL START CFIRST=.TRUE. DO 150 1=1,N Y(I)=HBUF(I) CALL I G C T N S ( ' S P E C ) CALL IGVEC(N,X,Y) CALL IGENDS('SPEC') LASTR=N RETURN END  c  SUBROUTINE  LABEL(N1,CHAR,N2)  c  IMPLICIT LOGICAL*1(C),INTEGER*2(H) CALL IGCTNS('CNUM') CALL IGFMTH(N1,'I') CALL IGFMTH(CHAR,'A') CALL IGFMTH(N2,'I') CALL IGTXTH(',<E>') CALL IGENDS('CNUM') CALL IGDRON('TERM') RETURN END c  SUBROUTINE MOD(CMND,*) C IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,HBUF(500 LOGICAL*1 CMND(10) DATA RATIO/.33/ 1 C 100  C 200  C 250  FORMAT('PEAK AT ',13,' WIDTH ',15,' HEIGHT ',15) IF  (NREC.EQ.0)  RETURN1  GET COMMAND ITYPE=NUMGET(CMND) JMP=ITBLC(CMND(2),'SRAPET####') GOTO ( 2 0 0 , 2 5 0 , 3 0 0 , 3 5 0 , 4 0 0 , 5 0 0 ) , J M P CALL VECTOR(LASTR) CALL L A B E L ( N D I R ( I N D E X , 1 ) , ' / ' , N R E C ) RETURN1 /SMOOTH CALL SMOOTH(HBUF,LASTR,ITYPE) CALL VECTOR(LASTR) CALL L A B E L ( N R E C , ' S ' , I T Y P E ) RETURN1 /ROTATE CALL ROTATE(HBUF,500,ITYPE) CALL V E C T 0 R ( N D I R ( I N D E X , 3 ) )  1 16  c  300  C 350  c  400  C 500  550  NREC=ITYPE CALL T I C S CALL L A B E L ( N D I R ( I N D E X , 1 ) , ' R ' , I T Y P E ) RETURN 1 /ABEL CALL PEAK(HBUF,500,LASTR,NPK,NHT,NWD) CALL ABEL(HBUF,500,NPK,ITYPE) CALL VECTOR(NPK) CALL L A B E L ( N R E C , ' A ' , I T Y P E ) RETURN1 /PEAK I F (ITYPE.EQ.O) ITYPE=LASTR CALL PEAK(HBUF,500,1TYPE,NPK,NHT,NWD) PRINT 1,NPK,NWD,NHT RETURN1 /ERASE CALL E R A S E ( 0 ) CMND(2)=CMND(3) GOTO 100 /TEMP CALL PEAK(HBUF,500,LASTR,NPK,IMAX,NWD) RMAX=FLOAT(IMAX) I F ( I T Y P E . N E . 0 ) RATI0=100./ITYPE DO 550 1=1,LASTR HBUF(I)=INT(11600./(I."RATIO*ZLOG(HBUF(I)/RMAX))) CALL VECTOR(LASTR) CALL T I C S CALL L A B E L ( N D I R ( I N D E X , 1 ) , ' T ' , N R E C ) RETURN1 END  c  C  50  SUBROUTINE T I C S IMPLICIT LOGICAL*1(C),INTEGER*2(H) CALL IGCTNS('SPEC') CALL IGMA(0.,50.) DO 50 1=1,9 CALL IGMR(9.09,-1000.) CALL I G D R ( 0 . , 1 0 0 0 . ) CONTINUE CALL IGENDS('SPEC') RETURN END  c  C  C C  FUNCTION ZLOG(X) ZLOG=1E5 I F ( X . L E . 0 ) RETURN ZLOG=ALOG(X) RETURN END SUBROUTINE  ERASE(N,*)  1 17  IMPLICIT L0GICAL*1(C),INTEGER*2(H) CALL IGBGNS('SPEC') CALL I G E N D S ( ' S P E C ) CALL IGBGNS('CNUM') CALL IGENDS('CNUM') I F (N.NE.O) CALL DRAW(N) RETURN 1 END c  SUBROUTINE RSCL(CMND,*) c  IMPLICIT LOGICAL*!(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR LOGICAL*1 CMND(10)  50 100 C C  C C  C  70  N1=NUMGET(CMND) N2=NUMG2(CMND) I F (N2.NE.0) GOTO 50 I F (N1.NE.0) CALL SCL(NI ,& 100) N1 = 1 N2=LASTR XR=N1+(N2-N1)/500. XL=2.*N1-XR CALL IGTRAN('XAXE','WIND',XL,XR,-1.,1.) CALL IGDRON('TERM') RETURN 1 END SUBROUTINE S C L ( N , * ) IMPLICIT LOGICAL*1(C),INTEGER*2(H) I F (N.GT.0) CALL IGTRAN('SPEC','WIND',-1.,1.,-10./N,10. I F (N.LT.0) CALL I G T R A N ( ' S P E C ,'WIND' ,- 1 .,1.,-100., 100. RETURN 1 END SUBROUTINE START IMPLICIT LOGICAL*1(C),INTEGER*2(H) REAL X 0 ( 1 4 ) / 0 . , 5 0 0 . , 5 0 0 . , 5 0 0 . , 4 0 0 . , 4 0 0 . , 3 0 0 . , 3 0 0 . , 2 0 0 . , +100.,100.,0.,0./ REAL Y 0 ( 1 4 ) / 0 . , 0 . , - 1 0 . , 1 0 . , - 1 0 . , 1 0 . , - 1 0 . , 1 0 . , - 1 0 . , 1 0 . , +10.,-10.,10./ CALL SETUP DRAW BACKGROUND CALL IGTRAN('MAIN','WIND',0.,500.,-50.,500.) CALL I G V E C ( 1 4 , ' ( M D ) ' , Y 0 , X 0 ) CALL IGBGNS('XAXE') CALL I G V E C ( 1 4 , ' ( M D ) ' , X 0 , Y 0 ) DO 70 1=1,4 CALL I G M A ( 1 0 0 . * I , 1 0 . ) CALL IGFMTH(100*1,'I *) CONTINUE  118  • I N I T I A L I Z E PICTURES IGBGNS( SPEC' ) IGENDS( SPEC' ) IGENDS('XAXE') IGBGNS('CNUM') IGENDS('CNUM') IGTRAN('CNUM', MOVE',10. , 4 9 0 . ) DEFAULT SCALE CALL S C L ( - 1) RETURN END CALL CALL CALL CALL CALL CALL  SUBROUTINE VIEW(*) IMPLICIT LOGICAL*1(C),INTEGER*2(H) COMMON INDEX,LAST,NDIR(20,3),NPLOTS,NREC,LASTR,HBUF(500 DIMENSION CMND(10)  5  10 20 30 50 60  CALL DRAW(1) CALL E R A S E ( 0 ) CALL RSCL('R 1 50 ') NREC=1 DO 50 I=INDEX,LAST CALL G E T ( N D I R ( I , 1 ) ) CALL MOD('/R 265 ') CALL ASK(CMND,LEN) JMP=ITBLC(CMND(1),' RE/S#####') GOTO(50,10,20,30,60),JMP RETURN1 CALL RSCL(CMND,&5) CALL ERASE(0,5.50) CALL MOD(CMND,&5) CONTINUE RETURN 1 END  c  SUBROUTINE ROTATE(HB1,LEN,N) C IMPLICIT LOGICAL*1(C),INTEGER*2(H) DIMENSION H B U F ( 5 0 0 ) , H B 1 ( L E N ) COMMON INDEX,LAST,NDIR(20,3)  50 990 C C  NREPS=NDIR(INDEX,3) REWIND 7 CALL READ(HBUF,HL,0,LNUM,7,&990) DO 50 1=1,NREPS CALL READ(HBUF,HL,0,LNUM,7,&990) HB1(I)=HBUF(N) RETURN END SUBROUTINE F I X ( N D E V ) IMPLICIT LOGICAL*1(C),INTEGER*2(H)  119  DIMENSION HBUF(500) 100  150 200 990  REWIND NDEV CALL READ(HBUF,HL,0,LNUM,NDEV,&990) I F (HL.NE.1000) GOTO 200 DO 150 1=1,500 N=HBUF(I) I F (N.LT.O) N=65536+N HBUF(l)=N/2 CALL WRITE(HBUF,HL,2,LNUM,NDEV,&990) GOTO 100 RETURN END  c  C 1 50 100  SUBROUTINE  XHAIRS  LOGICAL*1 CHECK FORMAT('CHANNEL #',F4.0,' CALL IGCTNS('SPEC') CALL I G X Y I N ( X , Y , & 1 0 0 ) PRINT 1,X,Y I F ( C H E C K ( ' Y ' ) ) GOTO 50 CALL I G E N D S ( ' S P E C ) RETURN END  HEIGHT I S ',F6.0/'&AGAIN?')  1 20  j.  c  C  PROGRAM ASPEC  (23/V/81)  c  IMPLICIT LOGICAL*1(C),INTEGER*2(H) CALL FTNCMD('DEFAULT 0=DATA',14) CALL FTNCMD('DEFAULT 1=*PRINT*;') DIMENSION C B U F ( 3 0 ) , H B U F ( 5 0 0 ) , H M A T ( 1 0 0 , 4 0 ) , I T ( 3 ) , E N ( 2 ) DATA T430/16.8/,TNE/l.04E5/,CHAR/'A'/ 1 2 3 C 100 C  C 150 200 C  250 C 300 C 310 320 C  350  FORMAT(' ' ,1 OX,3 0A1//1 OX,'EN(WIDTH) +'T(CONT) T(430)'/) FORMAT(' ' , 8 X , 2 E 1 0 . 3 , 3 I 1 0 ) FORMAT(';')  EN(CONT)  T(WIDTH)  NEXT RUN CALL RUNIS(CBUF,NLINES,CHAR,&990) CALL T I T L E ( 1 , ' * * * A S P E C * * * ' , 1 1 ) WRITE(1,1) CBUF CHAMBER PRESSURE P=1+NUMGET(CBUF(25))/49. ALOGP=ALOG(P) NCTR=250 FIND THE L I N E CALL READ(HBUF,HL,0,LNUM,0,&990) DO 150 1=220,280 I F ( H B U F ( I ) . G T . H B U F ( N C T R ) ) NCTR=I NLOW=NCTR-2l DO 200 1=1,40 HMAT(1,I)=HBUF(NLOW+I) READ AND STORE DATA DO 250 J=2,NLINES CALL READ(HBUF,HL,0,LNUM,0,&990) DO 250 1=1,40 HMAT(J,I)=HBUF(NLOW+I) ABEL UNFOLD DO 300 1=1,40 CALL FSA(HMAT(1,1),NLINES,MAX) MAX=MAX-1 DO 450 J=1,MAX BACKGROUND BACK=HMAT(J,1) DO 310 1=2,5 BACK=BACK+HMAT(J,I) DO 320 1=36,40 BACK=BACK+HMAT(J,I) BACK=BACK/10. L I N E AREA AREA=HMAT(J,6) MAXHT=HMAT(J,2 0) DO 350 1=7,35 I F (HMAT(J,I).GT.MAXHT) MAXHT=HMAT(J,I) AREA=AREA+HMAT(J,I) AREA=AREA-BACK*30. t  121  C  L I N E WIDTH WIDTH=1E-2 NHALF=INT((MAXHT+BACK)/2.) I F (NHALF.GE.MAXHT) GOTO 400  380 390  1 = 10  1=1+1  I F ( H M A T ( J , I ) . L T . N H A L F ) GOTO 380 FIRST=I-(HMAT(J,I)-NHALF)*1./(HMAT(J,I)-HMAT(J,I-1))  1=1+1  I F (HMAT(J,I).GT.NHALF) GOTO 390 WIDTH=I-FIRST (NHALF-HMAT(J,I))*1./(HMAT(J,I)-HMAT(J,IINSTRUMENT WIDTH=2.5 WIDTH=WIDTH-2.5 ZERO CHECKS; I F (BACK.LE.0) BACK=1E~2 I F (AREA.LE.0) AREA=1E~2 I F (WIDTH.LE.0.) WIDTH=1E~2 DO CALCULATIONS DEN3=24.81+ALOGP-ALOG(AREA) T=T430/DEN3 DEN3=DEN3-ALOG(T) T=T430/DEN3 IT(3)=INT(T*1E4) -  C C 400 C  DEN1=61.45+ALOGP-ALOG(T) EN(1)=1.52E22*WIDTH/T**.1667 IT(1)=INT(TNE/(DEN1 - A L O G ( E N ( 1 ) ) ) ) EN(2)=1.40E21*SQRT(BACK)*T**.25 IT(2)=INT(TNE/(DEN1-ALOG(EN(2)))) 450 C 990  WRITE(1,2) EN,IT GOTO 100 WRITE(1,3) STOP END  EOF OR ERROR  122  APPENDIX D  GAS FLOW IN THE SYSTEM In o r d e r understood, and  t o ensure the  the t o t a l  temperature  that  various  the  pressure  mass f l o w have gas flow w i t h  gas  been  adiabatic  is  quickly  forced  viscous  losses  stationary with  For  or  occurring  atomic  *« = 3.7 • 1 0~  conservation  through  the system  for a  out  when  mass 5  room  l o s s mechanisms have been  a c c e l e r a t i o n s o c c u r r i n g when into  an a d i a b a t i c  completely  t h e a r c c u r r e n t o f f , a n d compared  the  gas  2  which  acceleration  flows  along  a  i s a v i s c o u s i d e a l gas  m=39.95amu  Nsnr  the gas  o f a s m a l l a p e r t u r e , and  w a l l . We assume t h a t a r g o n  r=5/3,  viscosity  drops  is  calculated  w i t h m e a s u r e d v a l u e s . Two p r e s s u r e considered;  flow  (6.63«10~  2 6  kg) a n d  i s constant. in a  straight  line  the  equations are  pvA  (D-1)  = m  (D-2)  (D-3) where  the  cross-sectional  (x),  t h e mass f l o w  gas  density,velocity  area A i s a f u n c t i o n of p o s i t i o n  rate m i s constant and  a n d p,v a n d P a r e t h e  p r e s s u r e , a n d do n o t change  with  123  time.  I f we s t a r t  density  p  i n a pipe  a n d move t h r o u g h  0  equations  function  f  o  )  1  '  ^  2  o  f(x)=x -x°  a t (£. )  flow  v  1  '  6  "  2  and A  ^  ( » - « >  2  t h e maximum  mass when  the o u t l e t pressure  drag  i n the supply  o f 0.1055 a t  flow  possible  t h e f l o w becomes will  not  a  slow  isothermal.  a pipe  l i n e s and the heat  pressure  dP/dx=F/rrr l, 2  change  The v i s c o u s  increase  drag  exchanger  which on  will  thus  substituting  by  a  be  gas f l o w i n g  of radius r and length 1 a t average  i s F = 8 r r n v l a n d must be o v e r c o m e  so  -  5A P o  o  causes  considered through  0  rate.  Viscous tubing  )  = 0.75 o r P = 0 . 4 9 P ,  0 , 4  s o n i c , and d e c r e a s i n g the  P  a n o z z l e o f much s m a l l e r a r e a  h a s a maximum v a l u e  3  x=0.75, w h i c h means t h a t occurs  a t pressure  D-1 t o 3 c a n be s o l v e d t o g i v e  (  The  of large area  pressure  velocity gradient  dP/dx=-8,»v/r . Now v=m/trr /> a n d />=P(m/kT) 2  2  we g e t dP_ dx  p  =  -8pm kT u  m  or d  ^ and  f o r a pipe  2->  rr>  (  -16ymkT  } =  2  viscous  ( D _ 5 )  TTT m of radius r and length 1  A(P ) = ^ The  ^T"  drag  1 l r " m = Rm  (D~6)  4  factors R f o r the supply  exchanger and the a r c v e s s e l  a r e given  t u b i n g , t h e heat  i n Figure  III-2,  124  which  shows t h e gas heat  s y s t e m s c h e m a t i c a l l y . The  through  the  exchanger  supply  t u b i n g s m a l l , and  is  significant,  through  pressure  drop  through  the  t h e a r c chamber  completely  negligible. The  pressure  calculated. drag  t o P,  into  the  The  drops  through  supply  pressure  at the n o z z l e , nozzle  the  and  P  the  system  t o a b o u t 200  adiabatic  ms~ .  pressure)  drag  t h e w a l l , a s we  on  chamber  pressure  pressure  and  exhaust  heat  inlet  pressures  a t the e x i t exit  Equation Given mass  flow  thus  l e s s than  the  flow the  III  rate  finally the  at  at lower  through  the  first  adiabatically  the an  a viscous loss the  pressures  i s c a l c u l a t e d by a s s u m i n g t h a t decelerates  nozzle  exit.  becomes s o n i c a t t h e e x i t ,  t h e r e , and  The  flow rate i n through  a deceleration  flow  C.  to the  out  the  viscous  section  or equal  and  enters  i s below  l o s s e s i n the heat exchanger are  the  the  which  pressure  flow  t o r e s t , and  At  after  applying  D-4. a measured s u p p l y rate  through  d i f f e r e n t p o i n t s , and begin  i n chapter  a c c e l e r a t i o n i n t o the t u b i n g , then  s e t s the p r e s s u r e  the  see  exchanger equals  i n t h e t u b i n g and high  is  jet  i s v e r y q u i c k l y s l o w e d down by  rises until  n o z z l e . The  adiabatic  and  viscous  t o a b o u t 0.49'P, When t h e  1  be  acceleration  t h e chamber i t e x p a n d s ( i f t h e chamber p r e s s u r e nozzle  now  i s r e d u c e d by  0  reduces the pressure  a c c e l e r a t e s t h e gas  can  pressure  the  calculate  the  the p r e s s u r e s  at  w i t h measured v a l u e s .  We  system  compare t h e s e  by a s s u m i n g t h a t t h e  we  flow through  can and  the  inlet  nozzle  is  125  sonic  and  calculating  t h e mass f l o w t h r o u g h  us a mass f l o w t o u s e i n c a l c u l a t i n g drops and  through  the  the supply  line  it.  This  the remaining  s y s t e m , a n d we g e t t h e chamber mass  pressure then  c a l c u l a t e t h e mass f l o w r a t e t h r o u g h  the nozzle taking  these  into  account.  h a s no e f f e c t e x c e p t  very  low s u p p l y  The chamber p r e s s u r e pressures,  correction  for  so a t normal p r e s s u r e s  supply  line  c a l c u l a t i o n converges very q u i c k l y . inlet  nozzle  departs  slightly  i t e r a t i o n s are required before D-1  lists  rates  the p r e d i c t e d  at different  and  agrees  flowmeter a  indicated as  are  At  from  low  pressures  sonic,  and  measured  pressures  with  but  venturi is  and  fit  so  gauge.  The  pressure  and  the v i s c o u s drag  40%  from  10% e r r o r i n t h e  Table flow  much  more  accurate  system, than  were m e a s u r e d  the with  n o z z l e and t u b i n g d i m e n s i o n s a r e  flow  rate  t o about  measurements.  pressure,  and  i t  5%, The  approximate  c o e f f i c i e n t was d e t e r m i n e d by  t o t h e m e a s u r e d chamber  about  or 4  and  manometer  dimensions of the heat exchanger t u b i n g a r e very and  the  3  the s o l u t i o n converges.  i n F i g u r e I I I - 2 and a r e o n l y a c c u r a t e the  the  l o s s e s a p p l i e s , and t h e  i n t h e l i n e , and t h e p r e s s u r e s  mechanical  only  at  s u p p l y p r e s s u r e s . The f l o w r a t e s i n t h i s  t a b l e were m e a s u r e d w i t h a which  flow  pressure  rate,  small  losses for this  gives  differs  best by  t h e n o m i n a l v a l u e , w h i c h c o u l d be due t o a estimated  average  radius.  f o u n d i n t h e t a b l e t o w i t h i n 5%, a s i t s h o u l d  Agreement be.  is  T a b l e D-1. Gas f l o w  r a t e s and  pressures  P (kPa) m e a s u r e d ±5  200  300  500  700  P,(kPa) calculated  197  297  497  697  m(gs" ) calculated  0.55  0.92  1.54  2.15  m e a s u r e d ±0.03  0.60  0.93  1.52  2.14  P (kPa) calculated  138  153  212  288  m e a s u r e d ±5  133  154  222  288  P (kPa) calculated  130  133  177  218  P„(kPa) calculated  90  54  81  114  0  1  2  3  127  APPENDIX E  THE VISCOUS DECAY OF A VORTEX In  section  vortex motion differential  III-C  i n s i d e a tube of r a d i u s  the viscous  a leads  decay of  to the p a r t i a l  equation  = -U- M r  223t with  i t i s shown t h a t  boundary  3  9r  3  conditions  ^]  3r  i r  (E-1 )  J  u(a)=0,  = 0.  If  we  assume  3r'o u(r,t)=R(r)f(t)  with  f(t)=e'  3OJ  it and  we c a n d i v i d e  =  "  " —  a W  we g e t  a t  y  pr  3  3 ir"  C r 3  o 3OK 37^  o u t f ( t ) and expand  the r a d i a l  derivative  to get R  This  equation  +  ^ i i d R -JidfR apr d r ap ^ +  i s satisfied  0  =  (E-2)  2  by t h e f u n c t i o n  R(r) = £ J ^ i T S ^ ) The  Bessel  boundary  function  condition  (E-3)  J , h a s z e r o e s a t {* }. n  u ( a ) = 0 , R ( r ) must a l s o  so t o s a t i s f y t h e be o f t h e f o r m  R(r) = £ JjCx^/a) E q u a t i o n s E-3 a n d E-4 t o g e t h e r of  o  restrict  to  a  = yx /pa = x /x , 2  n  2  2  (E-4) the  allowed  values  128  where T = p a / i » . 2  Now we have a s e t o f s o l u t i o n s  o)(r,t) = i j C x r / a ) - e ' n x  1  and  any  linear  combination  initial  distribution  solution  to Equation  of  o f t h e form  t / T  n  of these, corresponding  angular  velocity,  is  a  t o some valid  E - 1 . The f u n c t i o n J , ( x ) / x  i s plotted in  F i g u r e E-1 o v e r  t h e r a n g e 0<x<20, w h i c h c o v e r s  the f i r s t s i x  zeroes.  zeroes  and  These  a r e : 3.83, 7.02, 10.17,  13.32, 16.47  19.62.  F i g u r e E - 1 . The f u n c t i o n J , ( x ) / x v s x  To  study  distribution  the  evolution  we n e e d t o e x p r e s s  of  an  initial  i t i n t h e form  velocity  129  130  U  One  (r,0) = ^ n  likely  ij(xr/a)  distribution  i s a s o l i d body r o t a t i o n  which f a l l s o f f t o z e r o v e r y possibility  i s an  close  to  the  these  harmonics  types with  have  the  been  aid  of  composed a  0  Another  a n n u l a r j e t type d i s t r i b u t i o n w i t h u=u  near the w a l l and «=0 i n the c e n t e r . I n i t i a l both  wall.  o(r)=o  conditions  0  of  from the f i r s t s i x  computer.  The  initial  d i s t r i b u t i o n s a r e shown i n F i g u r e s E-2 and 3, a l o n g w i t h the distributions elapsed axial  after  0.125,  0.25  (corresponding to roughly  and 50,  0.50 100  seconds and  200 mm  have of  t r a v e l ) . The v a l u e s of the harmonic c o e f f i c i e n t s  {A }  a r e i n d i c a t e d on each f i g u r e . I t can be seen t h a t a f t e r  0.5  second  has  elapsed  these  n  d i s t r i b u t i o n s are very s i m i l a r ,  both h a v i n g decayed n e a r l y t o the fundamental mode.  

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