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An experimental study of interference effects between closely spaced wires of an X-type hot-wire probe Jerome, Frederick Ernest 1971

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AN EXPERIMENTAL STUDY OF INTERFERENCE EFFECTS BETWEEN CLOSELY SPACED WIRES OF AN X-TYPE HOT-WIRE PROBE  by  FREDERICK ERNEST JEROME B . S c , McMaster U n i v e r s i t y , 1965  . A T h e s i s Submitted  i n Partial Fulfillment  of the Requirements f o r t h e Degree o f Master of Science  i n t h e Department o f P h y s i c s and I n s t i t u t e o f Oceanography  We a c c e p t  t h i s t h e s i s as conforming the r e q u i r e d s t a n d a r d  September, 1971  to  In presenting this thesis in p a r t i a l fulfilment of the  requirements for  an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t f r e e l y available for reference and  study.  I further agree that permission for extensive copying of this thesis for scholarly purposes may by his representatives.  be granted by the Head of my  It is understood that copying or publication  of this thesis for f i n a n c i a l gain shall not written  permission.  Department of  Department or  Physics  The University of B r i t i s h Columbia Vancouver 8, Canada  >  be allowed without my  ABSTRACT  The D i s a type 55A32 X-wire probe has been w i d e l y used i n t u r b u l e n c e measurements.  However, t h e author was unable  to obtain  agreement between t u r b u l e n c e measurements made s i m u l t a n e o u s l y w i t h t h i s type o f X-wire probe and an u l t r a s o n i c anemometer a t " t h e same p o s i t i o n i n the atmospheric n a t u r e o f the disagreement  boundary l a y e r over the ocean. between the two i n s t r u m e n t s  t h a t t h e r e e x i s t e d an unexpected  The  suggested  response o f t h e w i r e s t o the c r o s s  stream wind component normal t o the p l a n e of the X - a r r a y . Wind t u n n e l experiments  confirmed  t h i s response and  a t t r i b u t e d most o f i t t o t h e r m a l c o u p l i n g between t h e two w i r e s o f the a r r a y v i a t h e i r h o t wakes.  The prongs and/or probe body were  a l s o shown t o be c o n t r i b u t o r s t o the anomalous responses  o f the  X-wires. S i m i l a r experiments model 1241-20 X-probe  c a r r i e d out w i t h a Thermo-Systerns  (with a s e n s o r l e n g t h t o s e n s o r s e p a r a t i o n  r a t i o o f 5/8 compared w i t h 0.2 o r l e s s f o r t h e D i s a 55A32 X-wire probe) demonstrated at l e a s t ,  t h a t the i n t e r f e r e n c e e f f e c t s were absent ( o r ,  insignificant). As a consequence o f these f i n d i n g s , the D i s a E l e c t r o n i k A/  company o f H e r l e v , Denmark, m o d i f i e d t h e i r 55A32, 55A38 and 55A39 l i n e s o f X-wire probes unity.  t o make the l e n g t h / s e p a r a t i o n r a t i o  close to  iii  TABLE OF CONTENTS Page  ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF TABLES  v  LIST OF FIGURES  vi  ACKNOWLEDGEMENTS  •  v i i  1  INTRODUCTION  1  2  EXPECTED RESPONSE OF AN X-TYPE HOT-WIRE PROBE  2  2.1  Introduction  2  2.2  S t a t i c C h a r a c t e r i s t i c f o r Flow Normal t o Wire  2  2.3  S t a t i c C h a r a c t e r i s t i c o f an I n c l i n e d Wire  3  2.4  Dynamic Response o f a Hot-Wire Normal t o the  2.5 3  4  Mean Flow  5  Dynamic  6  Response o f the Hot-Wires i n an X - A r r a y  DISCOVERY OF THE PROBLEM  10  3.1  Introduction  10  3.2  T y p i c a l R e s u l t s from the Boundary L a y e r Experiment  12  3.3  The D i s a 55A32 X-Wire Probe  14  3.4  The I n t u i t i v e Case f o r Thermal Wake I n t e r f e r e n c e  14  3.5  Q u e s t i o n s t o be Answered  19  THE WIND TUNNEL EXPERIMENTS  20  4.1  E x p e r i m e n t a l Arrangement  20  4.2  Experimental Procedure  20  4.3  Experimental Results  24  4.4  D i s c u s s i o n o f R e s u l t s and C o n c l u s i o n s  27  iv  Page 4.5  The Thermo-Systems Model 1241 X-Type H o t - F i l m Probe  5  6  33  CONSEQUENCES OF THE INTERFERENCE PROBLEMS  38  5.1  - On S p e c t r a l A n a l y s i s  38  5.2  - On the R e s u l t s o f Other Workers  41  DENOUEMENT  42  BIBLIOGRAPHY  43  APPENDIX - D i s a S p e c i a l I n f o r m a t i o n Note No. 14  45  V  LIST OF TABLES Page I  T y p i c a l Boundary L a y e r R e s u l t s  13  II  Comparison o f C a l c u l a t e d and Measured S p e c t r a l E s t i m a t e s  41  vi  LIST OF FIGURES  Page  1  FIGURE 1.  (a) (b)  Flow Geometry f o r I n c l i n e d Sensor Flow Geometry f o r X - a r r a y o f Hot-Wires  4 4  2.  D e m o n s t r a t i o n o f L i n e a r i t y o f Hot-Wire's Dynamic Response  7  3.  D i s a 55A32 X-Wire Probe  .  15  4.  O r i e n t a t i o n o f 55A32 X-Probe f o r F i e l d Measurements  16  5.  E x p e r i m e n t a l Arrangement i n Wind T u n n e l  21  6.  B l o c k Diagram o f Equipment Used to Measure C h a r a c t e r i s t i c s of X-Probe  Directional 22  7.  v-Response o f "Downstream" Wire o f D i s a 55A32 X-Probe  26  8.  v-Response o f D i s a 55A32 X-Probe  28  9.  w-Response of D i s a 55A32 X-Probe  29  10.  C o n v e n t i o n a l Thermo-Systems Experiments  34  1241-20 Probe Used i n  11.  v-Response o f Thermo-Systems  1241-20 X-Probe  36  12.  w-Response o f Thermo-Systems  1241-20 X-Probe  37  vii  ACKNOWLEDGEMENTS  I w i s h t o e x p r e s s my a p p r e c i a t i o n t o D r . R. W. B u r l i n g f o r h i s d i r e c t i o n during able suggestions The  t h i s study and t o D r . R. W. Stewart f o r v a l u -  made i n my d i s c u s s i o n s w i t h him.  Mechanical Engineering  B r i t i s h Columbia k i n d l y p r o v i d e d Personal  t h e i r wind t u n n e l  for this project.  f i n a n c i a l a s s i s t a n c e came from t h e N a t i o n a l  Research C o u n c i l o f Canada, w h i l e v i d e d by the M e t e o r o l o g i c a l Transport  Department o f the U n i v e r s i t y o f  funds f o r the p r o j e c t were  pro-  Branch o f the Canadian Department o f  and t h e Defense Research Board o f Canada.  CHAPTER I .  INTRODUCTION  The h o t - w i r e anemometer has been used f o r many y e a r s as a r e s e a r c h t o o l i n f l u i d mechanics.  I t i s an i n s t r u m e n t d e s i g n e d f o r measuring  r a p i d l y changing v e l o c i t i e s i n a f l u i d  stream  through the  v a r y i n g c o o l i n g e f f e c t on a v e r y t h i n , e l e c t r i c a l l y The  stream's  heated w i r e  filament.  s m a l l s i z e and r a p i d response o f the s e n s i n g element make the h o t - w i r e  anemometer the b e s t i n s t r u m e n t so f a r developed f o r a n a l y s i s o f the v e l o c i t y m i c r o - s t r u c t u r e of a f l o w i n g f l u i d . of  h o t - w i r e anemometry has r a p i d l y expanded due  R e c e n t l y the to b e t t e r  e l e c t r o n i c s and more i n t e r e s t i n the d e t a i l s o f f l u i d  application  ancillary  flow.  Today,  t u r b u l e n c e measurement w i t h h o t - w i r e anemometers i s r o u t i n e p r o c e d u r e w i t h s p e c i a l X- o r V- a r r a y s o f two l o n g i t u d i n a l and  and,  independent h o t - w i r e s e n s o r s ,  t r a n s v e r s e components o f the f l u c t u a t i o n s i n the  fluid  v e l o c i t y can be measured s i m u l t a n e o u s l y and the c o r r e l a t i o n between them can be  investigated.  D u r i n g the c o u r s e o f the a n a l y s i s o f t u r b u l e n c e d a t a c o l l e c t e d  by  the author i n the atmospheric boundary l a y e r over the ocean from h o t - w i r e s e n s o r s i n an X - c o n f i g u r a t i o n and from a t h r e e - d i m e n s i o n a l u l t r a s o n i c anemometer-thermometer, i t became apparent not g i v i n g  the expected  t h a t the h o t - w i r e s e n s o r s were  response.  The o b j e c t i v e s o f the i n v e s t i g a t i o n d e s c r i b e d h e r e i n were: (i)  to  identify  the  problem,  (ii)  to  determine  (iii)  to  d e s i g n a s e n s o r a r r a y t h a t would e l i m i n a t e the  the s e r i o u s n e s s o f the problem,  and problem.  2. CHAPTER I I .  2.1  EXPECTED RESPONSE OF AN X-TYPE HOT-WIRE PROBE  Introduction C o n s i d e r a r e c t a n g u l a r c o o r d i n a t e system w i t h t h e p o s i t i v e  x - a x i s i n the d i r e c t i o n o f the mean a i r f l o w (which w i l l h o r i z o n t a l i n these d i s c u s s i o n s ) .  always be  L e t the z d i r e c t i o n be v e r t i c a l l y  upward and t h e y d i r e c t i o n be determined by the c o n v e n t i o n f o r r i g h t handed c o o r d i n a t e s .  Then the i n s t a n t a n e o u s v e l o c i t y v e c t o r can be  e x p r e s s e d as i f = ? ( U + u) + j v + kw  (2-1)  where U i s t h e mean wind speed, u, v and w a r e the components o f the much s m a l l e r v e l o c i t y f l u c t u a t i o n and i , j and k a r e the u s u a l u n i t vectors.  2.2  S t a t i c C h a r a c t e r i s t i c f o r Flow Normal t o Wire A t h e o r e t i c a l s o l u t i o n f o r the h e a t t r a n s f e r from a u n i f o r m l y  h e a t e d c y l i n d e r normal  t o a two-dimensional,  f l o w was found by K i n g (1914). i n t h e c o n s t a n t temperature I  2  As a p p l i e d t o a h o t - w i r e s e n s o r o p e r a t e d  mode, K i n g ' s Law can be e x p r e s s e d as  = A' + B'U  to  (2-2)  5  where I i s the h o t - w i r e c u r r e n t , A' and B fluid  incompressible, non-viscous  1  a r e c o n s t a n t s depending on  and w i r e p r o p e r t i e s , and U i s the v e l o c i t y o f the f l u i d ( p e r p e n d i c u l a r  the c y l i n d e r ) .  The i d e a b e h i n d the c o n s t a n t - t e m p e r a t u r e o p e r a t i o n i s  to keep the s e n s i n g element  a t a c o n s t a n t temperature  (and t h e r e f o r e a  c o n s t a n t r e s i s t a n c e ) and t o use t h e square o f the h e a t i n g c u r r e n t as the measure o f the r a t e o f c o o l i n g by heat t r a n s f e r from the w i r e t o t h e wind.  3  Since  the v o l t a g e  temperature o p e r a t i o n , E where A and  B are  2  E across  the w i r e i s p r o p o r t i o n a l to I i n  then  = A + Bl/  (2-3)  5  constants.  I t can be  the h o t - w i r e anemometer i s s t r o n g l y  2.3  constant  seen then t h a t the response o f  non-linear.  S t a t i c C h a r a c t e r i s t i c of an I n c l i n e d Wire If  the f l o w d i r e c t i o n i s n o t normal to a c y l i n d r i c a l s e n s o r  but  r a t h e r makes an a n g l e 0 w i t h the normal t o the s e n s o r as shown i n Fig.  l a , the d i r e c t i o n a l s e n s i t i v i t y of the h o t - w i r e anemometer must  known.  E q u i v a l e n t l y , an " e f f e c t i v e (normal) c o o l i n g v e l o c i t y " s h o u l d  be o b t a i n a b l e  from the a c t u a l mean v e l o c i t y , the geometry and  characteristics  (such  as l e n g t h  to diameter  Normal component o r " c o s i n e 1959;  C o r r s i n , 1963).  h o t - w i r e to the  fluid  law"  (1959) and  ratio).  c o o l i n g i s u s u a l l y assumed  flow depends o n l y on the component o f the For the  0  (Hinze,  cos  the  be  0.  Webster (1962) have suggested what has  widely accepted expression  become the most  f o r the e f f e c t i v e c o o l i n g v e l o c i t y t a k i n g  account t a n g e n t i a l component c o o l i n g as w e l l as normal component cooling, i . e . , C  2  = U (cos 6 + k sin 0). 2  the  fluid  c o n f i g u r a t i o n i n F i g . 1,  e f f e c t i v e c o o l i n g v e l o c i t y , C, would then C =  sensor  T h i s means t h a t the heat t r a n s f e r r e d from  v e l o c i t y normal t o the w i r e .  Hinze  be  2  2  2  (2-4)  into  Sensor Wire  F i g . 1(a). Flow Geometry for Inclined Sensor  Wire ff]  *  Wire #2  F i g . 1(b).  F.low Geometry for X-array of Mot Wires  5.  Champagne (1967) found the temperature to-diameter  t h a t k depends on the parameters t h a t  d i s t r i b u t i o n a l o n g the w i r e , p r i m a r i l y  ratio  I  4, L O  mm-  d * 0.005 and Champagne determined f o r the experiments  cooling.  the l e n g t h -  (1/d) of the w i r e .  F o r the w i r e s used i n the p r e s e n t  by c a l c u l a t i n g  2  0  study,  0  mm.  k = 0.20  for this ratio.  Since 6 =  45°  h e r e i n , then t h e r e i s o n l y a 2% e r r o r i n t r o d u c e d  the e f f e c t i v e c o o l i n g v e l o c i t y assuming normal component  T h i s i s a much s m a l l e r e f f e c t  than the one b e i n g s t u d i e d ,  so normal component c o o l i n g w i t h i t s a t t e n d a n t mathematical w i l l be assumed and K i n g ' s Law E  2.4  govern  2  simplicity  becomes  - A + BC*.  (2-5)  Dynamic Response o f a Hot-Wire Normal t o the Mean Flow C o n s i d e r a h o t - w i r e s e n s o r a l i g n e d p a r a l l e l t o the z - a x i s i n a  t u r b u l e n t a i r f l o w d e s c r i b e d by e q u a t i o n component  (2-1).  Assuming normal  cooling, C - {(U + u )  2  +  v }^ 2  - U ( l + 2u/U •+ u / U 2  = U ( l + u/U  +  2  v /U }^ 2  2  + u /(2U ) + v /(2U ) - u /(2U ) + higher 2  2  2  2  2  2  o r d e r terms} . The  effective  cooling velocity  can be  c o n s i d e r e d t o c o n s i s t of a  mean p a r t C - U + v^/(2U) + h i g h e r o r d e r terms  (2-6)  6.  and a f l u c t u a t i n g p a r t c = u + Hinze  2  (1959) and Pond  intensities, equation  (v -v )/(2U) 2  (1965) have argued  ( u ^ ^ / l l , as h i g h as 0.1,  (2-6) and  + h i g h e r order terms.  (2-7) and  t h a t even f o r t u r b u l e n c e  the second  hot-wire  and h i g h e r o r d e r terms i n  i n the T a y l o r expansion  about C = C can be o m i t t e d w i t h o n l y a 2% e r r o r . low i n t e n s i t y  (2-7)  of K i n g ' s  Law  T h i s means t h a t f o r  t u r b u l e n c e , the dynamic r e s p o n s e , e, o f a s i n g l e  vertical  is essentially linear, i . e . , e -  c  (2-8)  4 EC - -S-r u 4EU^  .  (2-9)  F i g u r e 2 p r o v i d e s e x p e r i m e n t a l j u s t i f i c a t i o n f o r assuming a l i n e a r response  f o r a t u r b u l e n c e i n t e n s i t y near 0.1  boundary l a y e r o v e r the s e a ) .  ( i n the  atmospheric  I t shows u as determined  by  equation  (2-9) p l o t t e d a g a i n s t u as measured s i m u l t a n e o u s l y a t the same p o s i t i o n by a s o n i c anemometer, a l i n e a r response r e p r e s e n t s a 0.8 were determined  second  time average.  instrument.  Note t h a t the z e r o s on the axes  u s i n g the mean wind speed  time l o n g e r than the p e r i o d r e p r e s e n t e d by The mean wind speed 9.2  2.5  (9.2 m/sec) f o r a p e r i o d o f the d a t a i n the  f o r t h i s s h o r t e r i n t e r v a l was  m/sec r e s u l t i n g i n the apparent  the x z - p l a n e .  figure.  s l i g h t l y g r e a t e r than  skewness o f the d a t a i n F i g . 2.  Dynamic Response of the Hot-Wires i n an F i g . l b (page 4) shows two  Each p o i n t  X-array  i n c l i n e d w i r e s i n an X - c o n f i g u r a t i o n i n  The w i r e s are mounted c l o s e t o g e t h e r (but not  on a s i n g l e probe.  They a r e o p e r a t e d  as two  independent  touching)  inclined  wires.  7.  F i g . 2.  Demonstration of Linearity of Hot-Wire's Dynamic Response.  8.  F o r w i r e no. 1, the e f f e c t i v e c o o l i n g flow d e s c r i b e d by e q u a t i o n  C  l  velocity  i n a turbulent  (2-1) i s  = {{(U + u) cos &  i  + w s i n Q^ 2  + v }^ 2  - U cos e ( l + 2u/U + 2(w t a n e p / U i  + 2(uw t a n 9 ^ / U + (v  2  2  sec e )/U ) 2  2  + (w  2  + u /U  tan^^/U  + h i g h e r o r d e r terms}.  As i n t h e case o f the v e r t i c a l w i r e and a t u r b u l e n c e and h i g h e r o r d e r terms can be dropped from  f o r C and c w i t h a r e s u l t i n g e r r o r  related  2  J 2  e  fluctuations  intensity expressions  i n c o f o n l y about 2%.  a c r o s s w i r e no. 1 a r e , t o a good a p p r o x i m a t i o n  t o u and w, i . e . ,  1  _ . UEjp  The v o l t a g e linearly  r  B.(cos e  2  i  = U cos ^ ( l + u/U + (w t a n Q^/U  < 0.1, second  2  2  Q.)^ —L_ (  u  + w t a n 0.) 1  (2-10)  or e  t  = a^u + b w  (2-11)  x  where the d e f i n i t i o n s o f a^ and b^ a r e apparent.  6l  = 45° so t h a t ^ Similarly  =  by  the dynamic response  e  In p r a c t i c e ,  e q u a t i o n f o r w i r e no. 2 i s  B„(cos 6 _ K _ __ —L(u - w t a n 8 ) * 4E U 9  2  Z  (2-12)  or = a u - t> w 2  From e q u a t i o n s  (2-13)  2  (2-11) and (2-13), i t can be seen t h a t  h o t - w i r e s i n an X - a r r a y can be used  two  to measure two components o f  the v e l o c i t y f l u c t u a t i o n v e c t o r - the downstream component and the t r a n s v e r s e component i n the p l a n e o f the "X".  Any response  t o the  t r a n s v e r s e component p e r p e n d i c u l a r to the p l a n e of the "X" i s expected to be a h i g h e r o r d e r e f f e c t .  10.  CHAPTER I I I ,  3.1  DISCOVERY OF THE  PROBLEM  Introduction As p a r t o f the a i r - s e a i n t e r a c t i o n r e s e a r c h program  conducted  by the I n s t i t u t e of Oceanography, the a u t h o r i n t e n d e d t o i n v e s t i g a t e c e r t a i n f e a t u r e s o f the wind t u r b u l e n c e m i c r o s t r u c t u r e i n the boundary l a y e r over the ocean. s t a n d i n g on a t i d a l  flat.  Instruments  were mounted on a tower  Water depth v a r i e d from 0 a t low  t i d e to 14 f t . a t h i g h s p r i n g  atmospheric  spring  tide.  The e x p e r i m e n t a l p l a n was  t o use an X - a r r a y of h o t - w i r e s  i n conjunction with a three-dimensional u l t r a s o n i c  anemometer-thermometer.  I t has been a l o n g - s t a n d i n g p r a c t i c e i n the a i r - s e a i n t e r a c t i o n program to  make simultaneous  q u a n t i t y w i t h two possible.  measurements of a m i c r o m e t e o r o l o g i c a l o r  oceanographic  instruments using d i f f e r e n t p r i n c i p l e s of operation i f  O f t e n the i n s t r u m e n t s used were newly developed o r were b e i n g  used i n an environment  f o r which they were not d e s i g n e d o r  c a l i b r a t i o n s t a b i l i t y was measurement was  suspect.  their  T h e r e f o r e the d u p l i c a t i o n o f  n e c e s s a r y t o "keep t h e i n s t r u m e n t s h o n e s t "  (not t o  mention the graduate s t u d e n t s ) . In  the p a r t i c u l a r f i e l d experiment  b e i n g d e s c r i b e d , the  p r e s e n c e o f the s o n i c anemometer had a more important purpose. w i r e anemometers, h a v i n g a h i g h l y n o n - l i n e a r s t a t i c  Hot-  characteristic  ( s e c t i o n 2.2), present c o n s i d e r a b l e c a l i b r a t i o n d i f f i c u l t i e s .  The  11.  mean wind must be w e l l known and steady f o r a r e l i a b l e dynamic (equations  (2-9),  (2-10) and  (2-12)).  As i f t h a t were n o t enough, t h e i r  s t a b i l i t y o f c a l i b r a t i o n i s s u s p e c t ( W e i l e r , 1966) c o n t a m i n a t i o n o f the w i r e s u r f a c e  calibration  expecially i f  (by s a l t - w a t e r s p r a y , f o r example) i s  a p o s s i b i l i t y and, i n the c o n s t a n t temperature mode o f o p e r a t i o n , the s t a t i c c a l i b r a t i o n seems to d e v i a t e from K i n g ' s Law i s b e t t e r approximated E  2  by  = A + BU * * 0  1  5  a c c o r d i n g t o C o l l i s and W i l l i a m s (1959).  A f u r t h e r problem w i t h X - a r r a y s  of h o t - w i r e s i s t o a c c u r a t e l y reproduce i n the f i e l d used d u r i n g  - the c h a r a c t e r i s t i c  the probe alignment  calibration.  The s o n i c anemometer ( K a i j o D e n k i , Model PAT-311-1), on the o t h e r hand, has minimal c a l i b r a t i o n p r o c e d u r e s - o n l y c e r t a i n adjustments need  t o be i n f r e q u e n t l y checked - and has a l i n e a r response a t  the wind speeds e n c o u n t e r e d . Mitsuta  (1966).  electrical  T h i s anemometer has been d e s c r i b e d by  I t i s u s e f u l f o r measuring o n l y the l a r g e r  scale  (and lower f r e q u e n c y ) t u r b u l e n c e f l u c t u a t i o n s , i n c l u d i n g s c a l e s  which  c o n t r i b u t e t o most of the atmospheric momentum and heat f l u x e s ,  because  it  determines the s p a t i a l average o f the component o f the wind  o v e r each o f t h r e e 20 cm. The i n t e n t i o n was  path l e n g t h s a r r a n g e d i n a s p e c i a l  velocity  geometry.  t o use the s o n i c anemometer measurements t o  p r o v i d e an " i n s i t u " dynamic c a l i b r a t i o n of the h o t - w i r e s .  With u, v ,  and w a l l o b t a i n a b l e from the s o n i c anemometer d a t a , and s i m u l t a n e o u s measurements of the h o t - w i r e v o l t a g e s e^ and e.^ ( e q u a t i o n s (2-11) , (2-13)) a t e s s e n t i a l l y the same p o s i t i o n , then the h o t - w i r e dynamic c o n s t a n t s a., b . , a~ and b„ can be c a l c u l a t e d .  calibration  Since s p e c t r a l  analysis  12.  of quantities l i k e u , w z  average  and uw  z  - were to be o b t a i n e d i n the end,  the p l a n e s o f r e g r e s s i o n o f e ^ f u r t h e r , from e q u a t i o n e The  - the o v e r b a r i n d i c a t i n g a  frequency  and of e ^  2  2 ] L  2  and e^  2  one  time  technique employed  on u , 2  uw  and w . 2  finding  To e l a b o r a t e  (2-11),  - a  2 L  u  2  + 2 3 ^ ^  s p e c t r a o f u , uw, 2  from the no.  + b  and "w^  2 L  w  2  .  (3-1)  from s o n i c anemometer d a t a  1 h o t - w i r e v o l t a g e s i g n a l were computed.  Then  u s i n g the s p e c t r a l e s t i m a t e s from about f i f t e e n t h i r d - o c t a v e bandwidths a t low f r e q u e n c i e s where the s o n i c response  has n o t begun t o f a l l o f f ,  a computer program c a l c u l a t e d t h r e e c o n s t a n t s P, Q and R f o r the p l a n e of " b e s t f i t "  ( i n the l e a s t squares e^  2  - Pu  2  + Quw  sense), i . e . ,  + Rw  2  .  (3-2)  Then, = P  a  and b  1  = R .  T h i s t e c h n i q u e p r o v i d e d a check s i n c e e q u a t i o n and R a r e not independent Q = The  3.2  (3-1) shows t h a t P,  Q  but r a t h e r  2(PR) . J$  c a l i b r a t i o n f o r w i r e No.  2 was  similarly  T y p i c a l R e s u l t s from the Boundary Layer  obtained.  Experiment  Once the dynamic c a l i b r a t i o n s of the h o t - w i r e s had been worked out as d e s c r i b e d i n s e c t i o n 3.1,  a wide v a r i e t y of a u t o s p e c t r a l and  c o s p e c t r a l a n a l y s e s were performed. from one  Table I presents t y p i c a l  results  d a t a r e c o r d f o r t h i r d - o c t a v e bandwidths about t h r e e c e n t r e  13.  frequencies, f.  A subscript h or s indicates whether the subscripted  quantity was determined from hot-wire or sonic anemometer data respectively.  f (sec)" U  (m/sec) s U. (m/sec) h 2  2  2  2  Ws (m/sec) wT n" (m/sec) 2  1.16x10" 1  1.77x10 -1  8.27x10" 1  3.31x10" 1  2.03x10'-1  7.54x10" 1  3.03x10- 1  1.81x10 -1  4.94x10"2  3.48x10" 2  3.33x10 -2  1.41x10" 1  5.34x10" 2  5.19x10--2  4.32x10" 1  1.44x10" 1  9.96x10"-2  -1.24x10" 1  -5.80x10" 2 -5.78x10- 2  -2.84x10 -2  5.68x10" h 6.18x10"2  5.61x10--3  2  2  V (m/sec) s 2  5.19x10" 2  1  2  2  U~W (m/sec) s s . Un7w,n (m/sec) 2  V W (m/sec) s s VsW,h (m/sec)  -1.06x10" 1  2  6.85x10"3  2  2.04x10" 1  2  TABLE I :  -2.78x10 -2  5.13x10--2  Typical Boundary Layer Results  The most dramatic discrepancies occur between w, and w and h s between v w, and v w • The results indicate that the quantity being S ll s s 2  called w^ was contaminated by  2  something correlated with v but only g  weakly, i f at a l l , correlated with u_. Recall from the discussion i n section 2.5 that the response of the wires of an X-array (with the plane of the "X" aligned p a r a l l e l to the xz-coordinate plane) to v fluctuations i s expected to be negligible i n low intensity turbulence.  Furthermore, the shear flow i n the boundary  layer at the f i e l d s i t e i s expected to be essentially horizontally homogeneous.  Consequently v i s not expected to be strongly correlated  14.  with u, w or density fluctuations.  This view i s supported by a  comparison of v w with TTU" i n Table I. s s s s  The l a t t e r correlation i s  typically an order of magnitude greater than the former.  There must  have been a mechanism whereby the hot-wires were directly•responding to v i n such a manner that the analysis procedure attributed the spurious response to a w fluctuation.  In other words, v fluctuations contributed  responses of similar polarity (in e^ and e^) to those caused by w fluctuations.  3.3  The Disa 55A32 X-wire Probe The X-wire probes used i n the f i e l d experiment were Disa  Electronik (of Denmark) type 55A32. wire arrangement are shown i n Fig. 3.  The details of the probe t i p and This type and other Disa types  with similar wire lengths and wire separations have been widely used i n turbulence measurements.  The wires themselves are platinum-plated  tungsten 5 microns i n diameter. The configuration of the wires for the f i e l d measurements described i n this chapter i s shown i n Fig. 4.  3.4  The Intuitive Case for Thermal Wake Interference The main effect of v fluctuations for Ivl < 0.1 U  Wire lengths  =  1.00 ± 0.05 mm  Dia of prong tips  =  0.11 ± 0.01  mm  Separation of wires  =  0.16 ± 0.01  mm  F i g . 3.  Disa 55A32 X-Wire Probe  16.  v  Fig.  ^  Orientation of 55A32 X-probe for f i e l d measurements  \  U  17.  is  t o r o t a t e the i n s t a n t a n e o u s wind v e l o c i t y v e c t o r i n the h o r i z o n t a l  p l a n e by an a n g l e 0 -  tan (v/U) _ 1  r a t h e r than t o a p p r e c i a b l y a l t e r the l e n g t h o f the wind v e c t o r . 1 mm.  l o n g w i r e s s e p a r a t e d by 0.16  mm.  For  i n an X - a r r a y , a wind v e l o c i t y  v e c t o r l y i n g i n the x y - p l a n e but making an a n g l e w i t h the x z - p l a n e o f . _ i 0.16 tan lj~fi 1  3  » o 2 2 . 5c 0  u  w i l l cause an' end o f one w i r e t o l i e d i r e c t l y downwind o f an end the o t h e r w i r e  (see F i g . 4 a g a i n ) .  I f the X-wire a r r a y were  a l i g n e d p r o p e r l y and the mean wind d i r e c t i o n were to remain  of  initially  steady,  then i n s t a n t a n e o u s r o t a t i o n s o f t h i s s i z e i n the h o r i z o n t a l caused  by  v f l u c t u a t i o n s would be e x t r e m e l y r a r e f o r a root-mean-square t u r b u l e n c e i n t e n s i t y of  0.1.  However, the wake o f a w i r e i s expected c o n v e c t e d downstream. system wake. all  Furthermore,  c o n s i s t i n g o f prongs and Hoole  and C a l v e r t  t o broaden as i t i s  the i n f l u e n c e of the w i r e s u p p o r t i n g  the probe body may  (1967), G i l m o r e  f u r t h e r broaden the  (1967) and Norman (1967) have  i n v e s t i g a t e d the d i r e c t i o n a l c h a r a c t e r i s t i c s o f the D i s a Type 55A25  s i n g l e h o t - w i r e probe w i t h the w i r e a l i g n e d normal t o an a i r f l o w . found a 15 - 20% v a r i a t i o n i n the i n d i c a t e d v e l o c i t y as the probe r o t a t e d ± 90° about  They was  the w i r e a x i s from a p o s i t i o n w i t h the probe a x i s  p a r a l l e l t o the f l o w d i r e c t i o n .  They concluded  t h a t prongs and  probe  body were about e q u a l l y r e s p o n s i b l e f o r the f l o w d i s p l a c e m e n t a t the p o s i t i o n o f the w i r e .  Eyre  (1967) made s i m i l a r measurements w i t h  same type o f probe and h i s e x p e r i m e n t a l r e s u l t s agree w e l l w i t h  the  those  18.  r e p o r t e d by the above a u t h o r s .  However, h i s e x p l a n a t i o n o f the  of the d i r e c t i o n a l s e n s i t i v i t y f o r r o t a t i o n about quite d i f f e r e n t .  He a t t r i b u t e s  the w i r e a x i s i s  the whole e f f e c t t o an  v a r i a t i o n o f c o n v e c t i v e heat l o s s from the prongs and a change o f heat c o n d u c t i o n from the w i r e  cause  angular-dependent consequent  ends,  Dahm and Rasmussen (1969) s t u d i e d the dependence o f the directional sensitivity  f o r r o t a t i o n about the w i r e a x i s on  l e n g t h , p r o n g . s p a c i n g and wind speed.  prong  They found t h a t the  interference  e f f e c t s were more s e v e r e a t 10 m/sec than a t 40 m/sec and t h a t  these  e f f e c t s e x h i b i t a s t e e p i n c r e a s e f o r prong s p a c i n g s <2 mm.  and  prong  l e n g t h s <6.5  probe  mm.  Clearly  ( i n h i n d s i g h t ) the 55A32 X-wire  ( F i g . 3) g i v e s the worst o f a l l w o r l d s - f o u r prongs prong s p a c i n g s o f 0.7  mm.  a t b e s t and 0.05  mm.  i n s t e a d of  a t worst  two,  (the w i d t h o f  the a i r gap between the l o n g prong s u p p o r t i n g the o u t e r end o f  one  w i r e and the s h o r t prong s u p p o r t i n g the i n n e r end o f the o t h e r w i r e ) and prong l e n g t h s o f 7 - 8 ram. F i n a l l y , i t can be seen how  t h e r m a l wake i n t e r f e r e n c e between  the w i r e s o f an X - a r r a y would cause v f l u c t u a t i o n s t o g i v e s i m i l a r polarity  responses  end o f s e c t i o n 3.2  ( i n e^ and e^) t o w f l u c t u a t i o n s . t h a t t h i s c o n c l u s i o n was  the d a t a o f T a b l e I.)  ( R e c a l l from the  reached i n o r d e r to e x p l a i n  R e f e r r i n g to the arrangement shown i n F i g u r e 4,  positive v fluctuation rotates U i n a direction w i r e no. 2 l i e downstream o f w i r e no. 1.  t h a t tends to make  The h o t wake o f w i r e no.  f a l l i n g on w i r e no. 2 r e s u l t s i n l e s s c u r r e n t b e i n g s u p p l i e d no.  2 t o m a i n t a i n i t a t a c o n s t a n t temperature  T h e r e f o r e the v o l t a g e a c r o s s w i r e No.  2 drops.  (and  to w i r e  resistance).  1  a  19.  Prong and probe e f f e c t s a s i d e , s u g g e s t s the f o l l o w i n g f o r the X-wires  dynamic responses  for positive v  =  a  2  "V •  U  } C  2  V  1  1  2  i  2  2  (3-3)  *  S i m i l a r l y , f o r negative v f l u c t u a t i o n s , e. = a.u + b.w , e = a u - bw  approximation)  ,  ,  2  (as a f i r s t  reasoning  fluctuations:  e. = a.u + ^w e  t h i s simple-minded  the response e q u a t i o n s are  + c.v , • } .  (3-4)  The c o n s t a n t s are a l l p o s i t i v e .  3.5  Q u e s t i o n s to be Answered The e x p e r i m e n t a l s t u d y of the response t o v f l u c t u a t i o n s  was  directed  toward answering the f o l l o w i n g q u e s t i o n s :  (i)  I s the response q u a l i t a t i v e l y l i k e t h a t suggested by e q u a t i o n s (3-3) and  (3-4)?  (ii)  I f n o t , what form does the response to v take?  (iii)  How  l a r g e must v/U be b e f o r e the s e n s i t i v i t y to v becomes  important (iv)  (say 10% o f the s e n s i t i v i t y to u or w)?  What a l t e r a t i o n s must be made to the w i r e mounting to ensure t h a t  the s e n s i t i v i t y to v i s unimportant?  arrangement  20.  CHAPTER IV.  4.1  E x p e r i m e n t a l Arrangement The X-wire  27 The  THE WIND TUNNEL EXPERIMENTS  probe was  mounted on a t u r n t a b l e i n the 36 i n c h x  i n c h wind t u n n e l o f the Dept. o f M e c h a n i c a l E n g i n e e r i n g , U.B.C. t u r b u l e n c e l e v e l was  about 0.1%.  A s k e t c h o f the arrangement i s  shown i n F i g u r e 5. A b l o c k diagram i n F i g u r e 6.  of the d a t a c o l l e c t i o n equipment i s p r e s e n t e d  Each w i r e of the X - a r r a y was  a c o n s t a n t temperature  by a s e p a r a t e c o n s t a n t temperature  (CTA), D i s a model 55D05.  (to  anemometer  The output v o l t a g e o f an anemometer  the v o l t a g e E i n K i n g ' s Law), was Auxiliary Unit.  heated and m a i n t a i n e d a t  T h i s u n i t was  then a p p l i e d  to a D i s a Model 55D25  employed to p e r f o r m low-pass  filtering  remove the low l e v e l of t u r b u l e n c e n o i s e from the h o t - w i r e  and DC  (i.e.,  signal)  s u p p r e s s i o n i n o r d e r t h a t the DC output o f the anemometer would  n e i t h e r s a t u r a t e the output o f the DC a m p l i f i e r nor d r i v e the pen the c h a r t r e c o r d e r beyond f u l l No attempt was  scale.  made to match the two w i r e s o f the X - a r r a y o r  to  linearize  of  the w i r e s to u, v and w f l u c t u a t i o n s were o f i n t e r e s t .  4.2  the anemometer o u t p u t s s i n c e o n l y the r e l a t i v e  Experimental  on  responses  Procedure  S t a t i c c a l i b r a t i o n s were o b t a i n e d f o r b o t h w i r e s by v a r y i n g the air  speed i n s t e p s and measuring  a f t e r each s t e p .  the DC output o f both anemometers  The dynamic s e n s i t i v i t y  to u f o r any o p e r a t i n g p o i n t  21.  T u n n e l Roof  Axis of Rotation U  •Disa X - w i r e (Type 55A32) Probe  x: •x  Turntable  _  Tunnel f l o o r  ELEVATION  U  y\—  PLAN VIEW F i q . 5-  Experimental Arrangement in Wind Tunnel  fi  Fig. 6  Block Diagram of Equipment Used to Measure D i r e c t i o n a l C h a r a c t e r i s t i c s of X-Probe  23.  (E, U)  c o u l d then be In o r d e r  c a l c u l a t e d as d e s c r i b e d i n s e c t i o n  to determine the s e n s i t i v i t y of the w i r e s  f l u c t u a t i o n s were i n t r o d u c e d turntable  ( F i g u r e 5,  i n the  t u r n t a b l e f i x e d and  by U  and  to v,  quasi  f o l l o w i n g manner. . R o t a t i n g  lower) c l o c k w i s e by an angle  as l e a v i n g the (cos 3-1)  2.5.  8 has  the  the same e f f e c t s  changing the x-component o f the wind  the y-component by U s i n 3.  For s m a l l 3,  the  x-component " f l u c t u a t i o n " i s c o n s i d e r a b l y s m a l l e r than the y-component "fluctuation".  For  example,  (cos 3-1)  = 0.034 s i n 3,  In summary, r o t a t i n g the X - a r r a y  3 =  4°.  by an angle  3 i s equivalent  to i n t r o d u c i n g v » fj s i n  3  (4-1)  and u • U(cos 3 - 1) Clockwise negative  r o t a t i o n s must be  .  (4-2)  taken as p o s i t i v e , c o u n t e r - c l o c k w i s e  i n o r d e r t h a t the s i g n s o f u and v a r e c o n s i s t e n t w i t h  system o f axes a l r e a d y  from behind  was  rotated clockwise  the probe l o o k i n g upwind) by  system i s imagined to r o t a t e w i t h h o r i z o n t a l l y i n the e a r t h ' s t u r n t a b l e by an angle  the  chosen.  " F l u c t u a t i o n s " of w were produced by a s i m i l a r F i r s t the X - a r r a y  as  about the probe a x i s 90°.  the a r r a y  w = U sin y  I f the  (as seen  coordinate  then the xz p l a n e would l i e  frame of r e f e r e n c e .  y i s equivalent  technique.  Then r o t a t i n g the  to i n t r o d u c i n g (4-3)  and u = U(cos y - 1)  •  (4-4)  24.  A g a i n c l o c k w i s e r o t a t i o n s must be a s s i g n e d p o s i t i v e a n g l e s and  counter-  clockwise rotations negative angles. To e s t a b l i s h whether o r n o t the t h e r m a l wake produces e f f e c t s and, i f s o , a t what v a l u e o f v/U the probe was  rotated  cases - the "upstream" wire o f f ( i . e . ,  w i r e o p e r a t i n g ( a t about  o f F i g u r e 5, w i r e No.  the t h e r m a l wake o f w i r e No. Then t o determine  190°C) and the  Note t h a t  "upstream"  f o r n e g a t i v e B and  1 tends to be downstream and i n  2.  the r e l a t i v e s e n s i t i v i t i e s o f the w i r e s to  v and w f l u c t u a t i o n s , B- and y - r o t a t i o n s increments  the e f f e c t s become i m p o r t a n t ,  from 3 ° 0 t o B = -16° i n 2° decrements f o r two  a t ambient t e m p e r a t u r e ) .  the c o n f i g u r a t i o n  significant  from - 10° t o + 1 0 ° .  were r e s p e c t i v e l y made i n 2°  A mean wind speed o f 4.0  m/sec  was  used i n a l l e x p e r i m e n t s .  4.3  Experimental Results In c o n v e r t i n g the d a t a from h o t - w i r e anemometer responses to  $- o r y - r o t a t i o n s it  to d a t a on h o t - w i r e responses  i s n e c e s s a r y to c o r r e c t u = U(cos  or  f o r the i n t r o d u c t i o n S -  u = U(cos y  -  to v or w  fluctuations,  of  1) 1)  upon a B- o r y - r o t a t i o n r e s p e c t i v e l y . y - r o t a t i o n w i l l be d e s c r i b e d h e r e .  The c o r r e c t i o n i n the case o f a  25.  E ^ (y) r e p r e s e n t the v o l t a g e output o f h o t - w i r e anemometer  Let No.  1 when the X - a r r a y has been r o t a t e d by an angle y.  r e p r e s e n t s the output f o r Y - 0° • E (Y) Similarly  From e q u a t i o n ( 2 - 1 1 ) ,  ~ Ej^O) = a u + b w  x  (0)  x  x  .  the change i n the output v o l t a g e of anemometer No.  2 upon a  Y-rotation i s E (y) - E (0) » a u 2  The  2  2  - bw 2  .  c o r r e c t i o n terms t o be s u b t r a c t e d from the v o l t a g e changes to  e l i m i n a t e the u f l u c t u a t i o n s u n a v o i d a b l y i n t r o d u c e d a r e a^u and  a u 2  r e s p e c t i v e l y where u = U(cos Y - 1) • The  c o n s t a n t s a^ and a In  2  a r e determined  from e q u a t i o n s  (2-10) and  (2-12).  summary, the dynamic responses o f the h o t - w i r e anemometers  to v and w f l u c t u a t i o n s w i l l  be  E(B) - E ( 0 ) - aU(cos  g - 1)  (4-5)  E(Y)  y - 1)  (4-6)  and - E ( 0 ) - aU(cos  r e s p e c t i v e l y where the v o l t a g e s and c o n s t a n t s p e r t a i n t o the a p p r o p r i a t e w i r e o f the a r r a y . F i g u r e 7 shows the response of the "downstream" w i r e to v f l u c t u a t i o n s f o r the two (i.e.,  cases o f the "upstream"  a t ambient t e m p e r a t u r e ) .  the upstream  w i r e hot and  cold  Note t h a t the s i t u a t i o n w i t h 6 = 0  w i r e a t the ambient temperature  was  chosen  as the  and  reference  v o l t a g e about which d e v i a t i o n s would be measured f o r b o t h c a s e s .  2  + U p s t r e a m w i r e cold o. U p s t r e a m w i r e hot  4 6 8 10 12 14 16  F i g . 7 v-Response of "Downstream" Wire o f Disa 55A32 X-Probe L  27.  I f the hot wake of the upstream stream w i r e , i t s e f f e c t  w i r e does i n t e r c e p t the down-  i s e x p e c t e d t o be t o d e c r e a s e  (from the  "cold"  wake case) the power r e q u i r e d to m a i n t a i n the downstream w i r e a t a c o n s t a n t temperature.  T h i s t r a n s l a t e s i n t o a decrease i n the h o t - w i r e  c u r r e n t and a d e c r e a s e i n the v o l t a g e a c r o s s the w i r e .  That  this  o c c u r s i s c l e a r l y e v i d e n t i n F i g u r e 7. Two  unexpected  even f o r 3 = 0 t h e r e was  r e s u l t s a r e a l s o i n d i c a t e d by F i g u r e 7.  i . e . , n e i t h e r w i r e t e n d i n g t o be downwind o f the o t h e r ,  some t h e r m a l c o u p l i n g between the two w i r e s .  the upstream w i r e o f f , the response positive.  First,  Secondly, with  t o v f l u c t u a t i o n s was  not  strictly  However the argument t h a t the c o o l i n g depends on the  component would p r e d i c t an i n c r e a s e i n the c o o l i n g r a t e and  normal  consequently  an i n c r e a s e i n t h e v o l t a g e a c r o s s the i n c l i n e d h o t - w i r e as i t undergoes a p o s i t i v e or negative 3 - r o t a t i o n s i n c e e i t h e r r o t a t i o n g r e a t e r l e n g t h o f w i r e normal  "presents" a  to the a i r f l o w .  F i g u r e 8 shows the responses o f the w i r e s to v f l u c t u a t i o n s F i g u r e 9 shows the responses  to w f l u c t u a t i o n s .  r e a s o n a b l y l i n e a r as a n t i c i p a t e d by e q u a t i o n s  are  (2-13), a l t h o u g h  The v - r e s p o n s e  plots  n e a r l y l i n e a r f o r p o s i t i v e v o l t a g e changes (when the r e s p e c t i v e w i r e  tends to be upstream  4.4  The w-response I s  (2-11) and  t h e r e i s a s m a l l break i n the s l o p e near y = 0.  and  o f the o t h e r w i r e ) .  D i s c u s s i o n of R e s u l t s and C o n c l u s i o n s Although  the thermal wake i n t e r f e r e n c e between the two w i r e s o f  the D i s a type 55A32 X-wire  probe  i s a major f a c t o r c o n t r i b u t i n g to the  £(/3)-E(0)-au  A  -,g  (mv.)  -12  8 •- 4 H  -10  -8  o  h  -6  -A  2  -2  o Wire no. 1 + W i r e no.2 H  1  4  6  o - 4  o - 8  o Fig. 8  v-Response of Disa 55A32 X-Probe  1  8  1~>  10  /5'  -10  -8 -20  G  -30 -40  Fie.  9  w-Resoonse  -50  oWire  no.1  -60  + Wire  no.2  o f D i s a 55A32 X-Probe  30 •  anomalous h o t - w i r e r e s u l t s p r e s e n t e d i n T a b l e I , t h e r e i s s t r o n g e v i d e n c e of o t h e r c o n t r i b u t i n g f a c t o r s .  F i g u r e 7 i n d i c a t e s t h a t t h e r e i s thermal  c o u p l i n g between the two w i r e s o f the a r r a y even when i t i s p r o p e r l y a l i g n e d i n t o the wind. t h a t graph  Data were n o t c o l l e c t e d t h a t would have e n a b l e d  to be extended  i n t o the r e g i o n o f p o s i t i v e 8 to  determine  the thermal e f f e c t o f the "downstream" w i r e on the "upstream" Such an e x t e n s i o n would p r o b a b l y a l l o w one c o u p l i n g from c o n v e c t i v e c o u p l i n g .  The  (and t h e r e f o r e a f f e c t o n l y the s t a t i c d e c r e a s e f o r w i r e No.  wire.  to s e p a r a t e the r a d i a t i v e  former would tend to be c o n s t a n t  response) w h i l e the l a t t e r s h o u l d  1 w i t h p o s i t i v e i n c r e a s e i n 8.  Hinze  (1959)  s t a t e s t h a t r a d i a t i o n e f f e c t s i n the heat t r a n s f e r to the ambient a i r are n e g l i g i b l y s m a l l under u s u a l o p e r a t i n g c o n d i t i o n s o f a s i n g l e w i r e where w i r e temperatures While  do not exceed  300°C.  the r a d i a t i v e c o u p l i n g between the two w i r e s remains  matter of c o n j e c t u r e , there i s l i t t l e  doubt  a  t h a t t h e r e are some important  prong and probe e f f e c t s a f f e c t i n g the c o n v e c t i v e c o u p l i n g between the wires at small 6 .  (See F i g u r e 7 ) .  Not o n l y w i l l the prongs  broaden  the h o t - w i r e wakes i n t h e i r v i c i n i t y but they w i l l have t h e i r own wakes due data about  to the u n a v o i d a b l e h e a t i n g o f the prong  (1967) i n d i c a t e  Champagne's  t h a t the j u n c t i o n o f a w i r e and probe  40 C° above the ambient The  tips.  large s e n s i t i v i t y  thermal  tip will  be  temperature. to v f l u c t u a t i o n s r e l a t i v e t o the  to w f l u c t u a t i o n s must a l s o be a prong and/or  probe e f f e c t .  The  sensitivity expected  31.  s e n s i t i v i t y r a t i o f o r the experiment w i l l be derived below assuming normal component cooling and no wake e f f e c t ;  t h i s w i l l be compared  to the r a t i o s calculated from the observed responses for both wires of the Disa 55A32 X-probe. Consider a wire of length 1 i n c l i n e d at 45° to U i n the wind tunnel.  For a g-rotation, the p r o j e c t i o n of the wire's length  on a plane perpendicular to U i s l  - {(1 s i n 4 5 ) 0  x  + (1 s i n 45° s i n g) }*  2  2  2  = 1 s i n 45° (1 + s i n g ) ^ . 2  The response of the wire to the apparent v f l u c t u a t i o n corresponding to an increment dg i n g w i l l be proportional to the r e s u l t i n g increment, dl  x  , i n the component of the wire's length perpendicular to U (according  to the normal component cooling assumption). dl  I.e.,  = 1(1 + s i n g ) s i n 45° s i n g cos g dg 2  x  (4-7)  Note that f o r g beginning at 0, d l i s s t r i c t l y p o s i t i v e . x  S i m i l a r l y f o r a y r o t a t i o n and the same wind speed, 1  » 1 sin(45° + y)  A  and the response to the apparent w fluctuations i s proportional to dl  A  - 1 cos(45° + Y) dY .  (4-8)  Therefore, f o r small g, dg, Y and dY and dg = dy v-sensitivity1 ^ w-sensitivity 1  A  s i n g cos 8 (1 + sin (3p2 z  | s i n 6|  - I 31 .  (4-9)  32  Note t h a t i n the p o s i t i v e p o l a r i t y response r e g i o n o f F i g u r e 8 the responses a r e n e a r l y l i n e a r so t h a t the s e n s i t i v i t y r a t i o w i l l be n e a r l y c o n s t a n t and e q u a l t o the r a t i o o f the s l o p e o f the l i n e a r segment o f the v-response  t o the s l o p e o f the w-response.  f o r w i r e No. 1 i s 0.31 and f o r w i r e No. 2 i s 0.34.  This r a t i o  E q u a t i o n (4-9)  p r e d i c t s a s e n s i t i v i t y r a t i o o f 0.035 f o r 8 = 2° and 0.10 f o r 3 =• 5 . 7 ° . T h e r e f o r e the r a t i o f o r the upstream w i r e i s q u a l i t a t i v e l y and q u a n t i t a t i v e l y q u i t e d i f f e r e n t from the expected.  The v - r e s p o n s e  curve,  a c c o r d i n g t o the t h e o r y p r e s e n t e d above, s h o u l d be concave upwards and g e n e r a l l y a t a c o n s i d e r a b l y lower magnitude over t h e 0 t o 10° range o f 3 .  The e x c e s s i v e l y h i g h response o f a w i r e of the D i s a 55A32 probe  t o v f l u c t u a t i o n s which tend t o p u t t h a t w i r e i n an upstream p r o b a b l y due t o a combination o f two f a c t o r s : s p e e d i n g up r e l a t i v e  position i s  the flow p a s t the w i r e s  t o the u n d i s p l a c e d f l o w as more b l o c k a g e i s p r e s e n t e d  by the r o t a t e d probe and prongs heat, l o s s from the prongs  and the angular-dependent  as proposed by Eyre  convective  (1967) and mentioned  b e f o r e i n s e c t i o n 3.4. The  r e s u l t s o f the wind t u n n e l t e s t i n g suggest m o d i f i c a t i o n s  t h a t s h o u l d be make t o the D i s a type 55A32 X-probe.  The most obvious  and i m p o r t a n t change i s t o move the two w i r e s f u r t h e r a p a r t by s p r e a d i n g the prongs.  A l t h o u g h i n a n a l y t i c a l d i s c u s s i o n s o f the X-wire  array  the w i r e s a r e u s u a l l y assumed t o l i e i n the same p l a n e , t h e r e i s no r e a l j u s t i f i c a t i o n i n a t t e m p t i n g t o d u p l i c a t e the model.  The s m a l l e s t s c a l e  o f t u r b u l e n c e m i c r o s t r u c t u r e t h a t can be s t u d i e d by a h o t - w i r e s e n s o r i s determined  by i t s l e n g t h so t h a t v e r y l i t t l e would be l o s t i n the way o f  r e s o l u t i o n c a p a b i l i t i e s o f an X - a r r a y by s e p a r a t i n g the w i r e s about one  33.  wire  length. Prong e f f e c t s would be reduced by the above change but they  c o u l d be d i m i n i s h e d  f u r t h e r by l e n g t h e n i n g  the prongs - r e c a l l  from  s e c t i o n 3.4 t h a t t h e f i n d i n g s o f Dahm and Rasmussen (1969) i n d i c a t e d t h a t the prong l e n g t h s  4.5  used i n the 55A32 probes a r e b a r e l y  The rhermo-Systerns Model 1241 X-type H o t - F i l m  acceptable.  Probe  Thermo-Systerns I n c . o f S t . P a u l , M i n n e s o t a , produced an " o f f - t h e - s h e l f " l i n e o f X-probes which s a t i s f i e d  the above  c r i t e r i a q u i t e w e l l and had two o t h e r  features.  favourable  design Their  model 1241. probe w i t h no. 20 s e n s o r elements a f f i x e d i s shown i n F i g u r e 10. Each s e n s o r has a 0.8 m i c r o n t h i c k p l a t i n u m  f i l m d e p o s i t e d by  r a d i o f r e q u e n c y s p u t t e r i n g onto a 0.002 i n c h diameter g l a s s r o d . The 0.040 i n c h s e n s i n g  length, c e n t r a l l y  l o c a t e d on the 0.065 i n c h l o n g r o d ,  i s d e f i n e d by g o l d p l a t i n g on the ends o f the r o d . also provides separated length  e l e c t r i c a l contact with  the p l a t i n u m  film.  The rods a r e  by 5/8 o f the s e n s o r l e n g t h and the prongs average 11 mm. i n  (compared w i t h  7.5 mm.  f o r t h e D i s a 55A32 X - p r o b e ) .  Two a d d i t i o n a l f e a t u r e s s h o u l d  d e c r e a s e prong e f f e c t s .  the a r c h i n g s t r u c t u r e o f the two l o n g e r prongs w i l l d i s p l a c e m e n t upstream. attached  The g o l d p l a t i n g  directly  t o reduce  flow  Secondly, the hot s e n s i n g elements a r e not  to the prongs.  prong t i p and the s e n s i n g  tend  First,  The g o l d - p l a t e d  segment w i l l s h a r p l y  g l a s s r o d between the  reduce the h e a t conducted  34.  VIEW  OF  PROBE  (8 x FULL  Quartz rod length Quartz rod diameter Spacing between sensors Diameter of prong tip Sensing length  = = = = -  SIZE)  0.065 ins. 0.002 ins. 0.025 ins. 0 . 0 0 4 5 ins. 0 . 0 4 0 ins.  0.025 ins.  CONVENTIONAL  THERMO-SYSTEMS USED  IN  1241-20  EXPERIMENTS Fig. 10  PROBE  35.  to the prong t i p compared to the Disa 55A32 probe where the hot-wires are d i r e c t l y welded to the prong t i p s . not  The wakes from the prong tips should  produce any. thermal e f f e c t s . Experiments were conducted with the Thermo-Systems probe to determine  the  response of both c y l i n d r i c a l hot-films to v and w f l u c t u a t i o n s .  results are shown i n Figures 11 and 12.  The  The v-response, expecially f o r  f i l m No. 2, i s quite l i k e that predicted by the derivation i n section It i s s t r i c t l y p o s i t i v e and concave upwards. l i n e a r as expected. (the  Disa 55A32 probe). sensitivity (4-9).  The w-response i s very nearly  The highest r a t i o of v- s e n s i t i v i t y  case of f i l m No. 1 and negative 8) i s 0.12  4.4.  to w - s e n s i t i v i t y  (compared with 0.34  f o r the  Except f o r f i l m No. 1 and 8 between 0 and - 6 ° , the  r a t i o i s equal to or smaller than that predicted by equation  The Thermo-Systerns 1241-20 X-type h o t - f i l m probe appears to be  free of the serious thermal wake, probe and prong interference problems that plague the Disa 55A32 X-type hot-wire probe.  E(^)-E(0)-au  o  •  (mv.) •5  O  -4  o Wire  no. 1  + Wire  no. 2  •3  •2  -rG  o  ••1  o +  + -©-  —i—  -10  -8  -6  -4  -2  0  -h  4  F i g . 11 v-Response of Thermo-Systems 1241-20 X-Probe  8  -2 G  -10  2  6  -20 Q  -30 -40  O  -50 -60  o Wire +  Wire  no.1 no.2  F i g . 12 w-Response of Thermo-Systems 1241-20 X-Probe  8  38.  CHAPTER V.  5.1  CONSEQUENCES OF THE INTERFERENCE PROBLEMS  —  On S p e c t r a l A n a l y s i s In the a n a l y s i s  t h a t l e d t o the hot-^wire s p e c t r a l e s t i m a t e s i n  T a b l e I , the h o t - w i r e s were assumed to have the i n s t a n t a n e o u s g i v e n by e q u a t i o n s  (2-11) and  responses  (2-13).  I.e., e^ = a j U +  bjW  and e  2  =  a  2  u  ~ 2 * b  w  The s p e c t r a l a n a l y s i s system s o l v e d t h i s p a i r o f s i m u l t a n e o u s e q u a t i o n s f o r u and w a t every d i g i t i z e d d a t a p o i n t and then computed the s p e c t r a and c o - s p e c t r a . a s d e s c r i b e d by G a r r e t t (1970). In o r d e r t o s i m p l i f y component  the f o l l o w i n g d e r i v a t i o n , assume normal  c o o l i n g with angles of i n c l i n a t i o n  a^ •» b^ and  = b2«  so t h a t a^ = a2«  Assume f u r t h e r t h a t the w i r e responses  Then e^ = a^ (u + w)  and e  (u + w) .  ** i a  2  8^ and 82 b o t h 4 5 ° .  Therefore u = (e  + e )/2a  1  ,  w = (ej^ - e ) / 2 a  1  ,  1  2  2  Then  are i d e n t i c a l  39.  (e w^=  + e ^ M a  l  (e  ,  2  (5-1)  - e )<74a2  (5-2)  2  L  and uw = ( e + e ) ( e - e ) /4a L  2  L  2  2  .  (5-3)  However, the wires of the Disa 55A32 X-probe have a s i g n i f i c a n t response to v f l u c t u a t i o n s .  As a f i r s t approximation, this response  w i l l be taken as l i n e a r so that e^ = a^u +  + c^v  bjW  and e  2  =  a  2  " 2  U  b  ~ 2  W  C  V  *  Figure 8 indicates that the response to v i s very nearly l i n e a r f o r |B|<4°. Making the same assumptions as before and taking c^/bj  a  c  2^2  - t h e i r values were observed i n the experiment to be 0.31 and 0.34 i n section 4.4 - the response equations become e  x  = a  e  2  = a^ (u - w - 0.32 v) .  x  (u + w + 0.32  v)  and  In t h i s case, e^ + e_, =  2a^  and e  L  - e  2  - 2a  (w + 0.32  1  v)  so that  _T___/4a  2 =  u 2  ^  ( 5  _  4 )  ~  40.  (e  L  - e )<74a 2  2  = w " + 0.64 vw + 0.10 v " 2  (5-5)  2  and (e^ + e ) ( e 2  Comparing e q u a t i o n s (5-4),  x  - e )/4a  2  2  = uw + 0.32 uv .  (5-1), (5-2) and (5-3) w i t h e q u a t i o n s  (5-5) and (5-6) r e s p e c t i v e l y g i v e s (as f i r s t  to the s o r t o f e r r o r s i n t r o d u c t e d 2=  V w, h  2  = w  (5-6)  approximations  by the anomalous X-wire  responses)  2  V 2  + 0.64 v w + 0.10 v s s s  (5-7)  2  s  and u^w^ = u^w + 0 . 3 2 u v s s s s where the s u b s c r i p t s h and s have the same i n t e r p r e t a t i o n as i n T a b l e I. Because o f the h o r i z o n t a l homogeneity ( s e c t i o n 3.2) i n the atmospheric boundary l a y e r o v e r the ocean, v w and u v a r e expected t o be s m a l l . s s s s . T h e r e f o r e the major e r r o r i n t r o d u c e d i n the h o t - w i r e s p e c t r a l e s t i m a t e s is  the 0.10 v  2  s  term i n w,  2  h  .  Note a l s o  v w, = v w + 0.32 v s h s s s 2  that .  (5-8)  T a b l e I I shows how the measured v a l u e s o f w, h  2  much b e t t e r sides  and v w, a r e i n s h  agreement w i t h the v a l u e s c a l c u l a t e d from the r i g h t - h a n d  o f e q u a t i o n s (5-7) and (5-8) than w i t h w  2  s  and v w respectively. s s  No s p e c i a l s i g n i f i c a n c e s h o u l d be p l a c e d on the disagreement still  that  e x i s t s between the measured and c a l c u l a t e d v a l u e s because  many assumptions and because  o f the  t h a t were made i n d e r i v i n g e q u a t i o n s (5-7) and (5-8)  the s e n s i t i v i t y  r a t i o s f o r the probe used i n the f i e l d  measurements may have been l a r g e r than 0.32.  41.  5.19x10"  f (sec ) - 1  w  (m/sec) s w (meas.) (m/sec) n w^ (calc.) (m/sec) 2  4.94xl0  2  2  2  2  2  2  2  g  v w, (calc.) (m/sec) s n  5.2  1.16x10"  -2  3.48xl0~  2  1  1.77X10"  1  2  3.33xl0"  2  -2  5.19xl0"  2  2  4.69xl0"  2  _,+  5.61x10"  1.41x10"  5.34xl0  9.70xl0  -2  4.96xl0"  6.85xl0  -3  5.68xl0  1  v w (m/sec) ss v w^(meas.) ..(m/sec)  TABLE I I :  2  2.04x10"  1  6.18x10"  1.45x10"  1  4.66xl0"  2  2  3  5.13xl0"  2  3.75xl0~  2  Comparison of Calculated and Measured Spectral Estimates  On the Results of Other Workers Although the Disa 55A32 X-wire probe had not been used by the  I n s t i t u t e of Oceanography at the University of B r i t i s h Columbia p r i o r to the present work, i t has been widely used elsewhere i n the study of boundary l a y e r s , mixing regions, j e t s , e t c . where i t has been necessary to measure the downstream and one-cross stream component of the v e l o c i t y flucutuation.  I t i s clear that a l l measurements, regardless of  whether the turbulence i n t e n s i t y i s low or not, made with this type of probe are now suspect.  In p a r t i c u l a r , measurements of shear stress  and energies i n the transverse component of the f l u c t u a t i o n i n the plane of the X-array w i l l be over-estimated. Furthermore, many experimenters neglect to describe the probe they use and t h i s , i n the l i g h t of the present findings, becomes a meaningful omission.  42.  CHAPTER V I . D.E.  G u i t t o n and  R.P.  DENOUEMENT  P a t e l (Jerome, G u i t t o n and  Patel,  1971)  have c a r r i e d the type of r e s e a r c h d e s c r i b e d i n t h i s t h e s i s f u r t h e r t o determine the dependence of the r a t i o of v - s e n s i t i v i t y  to w - s e n s i t i v i t y  o f the D i s a 55A32 X-wire probe on the Reynold's number o f the  flow.  T h e i r d a t a are i n e x c e l l e n t agreement w i t h an e x p r e s s i o n they  derived,  i.e., •  v-sensitivity w-sensitivity  g  R  e  - l . l  (  1  +  1  >  3  1  ^ 0 . ^ - .  T r a n s l a t e d i n t o wind speed dependence, the r a t i o was 2 m/sec d e c r e a s i n g  to about 0.1  ,  about u n i t y a t  a t 20 m/sec.  As a r e s u l t of problems w i t h  the D i s a 55A32 X-wire probe  t h a t were demonstrated by Jerome, G u i t t o n and P a t e l (1971), D i s a E l e c t r o n i k A/S  m o d i f i e d t h e i r t h r e e types of X-wire probes  55A32, 55A38 and 1 mm.  (types  55A39) by i n c r e a s i n g the s e p a r a t i o n of the w i r e s  ( i . e . , about one w i r e  length).  The  to  s p e c i a l i n f o r m a t i o n note w i t h  which DISA i n t r o d u c e d the m o d i f i e d probes i s reproduced  i n the Appendix.  43.  BIBLIOGRAPHY Champagne, F. H., C. A. S l e l c h e r and 0. H. Wehrmann, 1967: T u r b u l e n c e Measurements w i t h I n c l i n e d Hot-Wires. J . F l u i d Mech., 28, P a r t I . C o l l i s , D. C. and M. J . W i l l i a m s , 1959: Two-Dimensional C o n v e c t i o n from Heated Wires a t Low Reynolds Numbers. J . F l u i d Mech., 6_, page 357. C o r r s i n , S., 1963. E n c y c l o p e d i a o f P h y s i c s , V o l . V I I I / 2 , B e r l i n , S p r i n g e r - V e r l a g OHG, page 555. Dahm, M. and C. G. Rasmussen, 1969: E f f e c t of Wire Mounting System on Hot-Wire Probe C h a r a c t e r i s t i c s . DISA I n f o r m a t i o n No. 7, page 19. E y r e , D., 1967: End C o n d u c t i o n and Angle o f I n c i d e n c e E f f e c t s i n S i n g l e Hot-Wire Anemometer Probes. IRG Report 1521 (W), U n i t e d Kingdom Atomic Energy A u t h o r i t y . G a r r e t t , J . F., 1970: F i e l d O b s e r v a t i o n s o f Frequency Domain S t a t i s t i c s and N o n l i n e a r E f f e c t s i n Wind-Generated Ocean Waves, Ph. D. d i s s e r t a t i o n , U n i v e r s i t y o f B r i t i s h Columbia. G i l m o r e , D. C., 1967: The Probe I n t e r f e r e n c e E f f e c t o f HotWire Anemometers. Report No. 67-3, Mech. Eng. Res. Lab., M c G i l l U n i v e r s i t y , M o n t r e a l . H i n z e , J . 0., 1959: T u r b u l e n c e .  New York, M c G r a w - H i l l , 586 pp.  Hoole, B. J . , and J . R. C a l v e r t , 1967: The Use o f a Hot-Wire Anemometer i n T u r b u l e n t Flow. J . o f R o y a l Aero, S o c , 71, page 213. Jerome,  F. E., D. E. G u i t t o n and R. P. P a t e l , 1971: E x p e r i m e n t a l Study of Thermal Wake I n t e r f e r e n c e Between C l o s e l y Spaced Wires o f an X-type Hot-Wire Probe. Aero. Quart., 22^, page 119.  K i n g , L. V., 1914: On t h e C o n v e c t i o n o f Heat From Small C y l i n d e r s i n a Stream o f F l u i d . P r o c . Roy. S o c , (London), 214A, page 373. M i t s u t a , Y., 1966: Sonic Anemometer-Thermometer f o r G e n e r a l Use. J . Meteor. Soc. Japan, 44, page 12. Norman, B., 1967: Hot-Wire Anemometer C a l i b r a t i o n a t High Subsonic Speeds. DISA I n f o r m a t i o n No. 5, page 5.  44.  Pond, S. , 1965: T u r b u l e n c e S p e c t r a i n t h e Atmospheric Boundary L a y e r Over t h e Sea. I n s t i t u t e o f Oceanography, U n i v e r s i t y o f B r i t i s h Columbia, Report No. 19. Webster, C.A.G., 1962: A Note on t h e S e n s i t i v i t y t o Yaw of a Hot-Wire Anemometer. J . F l u i d Mech., 13, page 307. W e i l e r , H. S., 1966: D i r e c t Measurements o f S t r e s s and S p e c t r a o f T u r b u l e n c e i n the Boundary L a y e r Over the Sea. Ph. D. d i s s e r t a t i o n , U n i v e r s i t y of B r i t i s h Columbia.  45.  APPENDIX  T h e r m a l W a k e Interference b e t w e e n the W i r e s of X - t y p e H o t - w i r e P r o b e s •  S p e c i a l  Fig.  I n f o r m a t i o n  1.  INTRODUCTION  F o r c o n v e n i e n c e t h i s r e l a t i o n is w r i t t e n as  X - t y p e h o t - w i r e probes w i t h their t w o wires a l m o s t in t h e same plane are quite sensitive t o m o v e m e n t s o f the veloci-  c = au + bv + cw  (4)  t y v e c t o r o u t o f t h a t p l a n e . T h i s p i t c h i n g m o t i o n m a y cause the h o t w a k e p r o d u c e d b y the u p s t r e a m wire t o affect  por-  tions o f the downstream wire, reducing the electrical power r e q u i r e d t o keep it at a c o n s t a n t t e m p e r a t u r e . R e c e n t i n vestigations  o f the behavior o f conventional D I S A X-probes,  w h e r e t h e t w o wires are o n l y 0.2 m m apart, s h o w e d  these  T a k i n g into a c c o u n t the sensitivity coefficients tion o f v  from  - e ) , where  (e1  and e  2  s t a n t a n e o u s signals f r o m measured a n d actual v  2  2  i n the cvaluaare t h e i n -  the t w o wires, the relation between i n a t w o - d i m e n s i o n a l f l o w is  t y p e s t o h a v e v e r y s i g n i f i c a n t s e n s i t i v i t y t o s m a l l angles o f . p i t c h at l o w R e y n o l d s n u m b e r s ( R e < 5). H o w e v e r , this sensitivity cancels o u t at R e > 10.  v  =v  2  meas THE  IMPORTANCE  ANALYSIS  O F TURBULENCE  (ej  respectively  uv  dU  +  ^  8a  da +  f £  8V  2  measured and  mcas  = uv  act  c  (1  2a  vlwl uv  4 ab  uv  (6)  80  ) u  +( — - — ) v +( — U  8a  u  and D  .  (2) F o r nonlinear response E  e =(  ) ( C j - e ) the equation between  b y d e t e r m i n i n g the ratios — a  dfl  or 8E  2  T h e i m p o r t a n c e o f the sensitivity t o p i t c h can b e expressed  changes  8v  + c  signals  (1)  9 a n d tt a r e t h e p i t c h a n d y a w a n g l e s ,  ^  v  aged p r o d u c t o f t h e i n s t a n t a n e o u s  (see a l s o F i g . 1).  dE =  (5)  a c t u a l u v is  E = E(U, 0, a)  small  4 d - ) 2  W h e n o b t a i n i n g t h e s h e a r stress u v b y t a k i n g t h e t i m e a v e r -  DATA  t h e w i r e s i n a n X - w i r e a r r a y m a y g e n e r a l l y b e w r i t t e n as  For  -A 4b  act  O F PITCH SENSITIVITY IN  If t h e p i t c h s e n s i t i v i t y is i n c l u d e d , t h e r e s p o n s e o f o n e o f  where  (i +  2  TT; )  W  8U  (3)  2  = A + . B ( U )  (7)  n  the sensitivity coefficients  a a n d b are  i  a = - - n B(U) 2E 1  w h e r e the b r a c k e t e d terms are the sensitivity  coefficients.  n  '  1  (8)  This note summarizes the results of recent experiments by Jerome, Guitton, and Patel which are given in the following: Jerome, RE., Gnitlon, IX and Paid, R.I'.  "Experimental  Guitlon, D. and Patel, R.P. "An experimental stud  study of the thermal wake interference between closely  thermal wake interference between closely spaced wires of  spaced wires of a X-typc hot wire probe (1969)  a X-type hot wire probe", McGill University, M . U . R . L .  (To be published.)  Report 69-7 (1969).  a9  1.6 1.4  e = au + bv + cw o - upstream wire cold 1^ • - upstream wire hot j  1.2 1.0  •  - Present investigation  9  - (Approximate) U.B.C. result  _ ,(  ^  6.8 o >  _  _. Q8  CM LU  0.6  6.7  0.4 Q2 0.0 0 Re  10  _ Ud  6.6  12 14  Fig. 2. Ratio of pitch to yaw sensitivity X-wires vs. Reynolds number.  for  conventional  16 20  24  28  Fig. 3.  Pitch response of modified •without a thermal wake.  X-toire probe with end  -1/2  and  to R e  a  cot  a  (9)  if l o n g i t u d i n a l c o o l i n g effects, w h i c h are o f s e c o n d  order,  in a t u r b u l e n t f l o w ,  to that taken f r o m a static NEW  DISA  X-TYPE  which might  appears  exist  to b e similar  calibration.  PROBES  the d i r e c t i o n perpendicular t o t h e plane o f t h e X , J e r o m e ,  T h e v a l u e o f c is 1  . T h e d y n a m i c p i t c h sensitivity,  for measurements  B y m o v i n g t h e wires apart b y a p p r o x . o n e w i r e l e n g t h i n  are. neglected.  G u i t t o n , a n d Patel observed  SE  DISA  o f these results (10)  U se  by  n o wake interference.  has i m p r o v e d t h e d e s i g n  increasing t h e distance b e t w e e n  O n a basis  o f its X - p r o b e s  t h e w i r e s t o 1.0 m m  instead o f t h e present 0 . 2 m m .  c, a c c o u n t i n g f o r t h e t h e r m a l w a k e i n t e r f e r e n c e ,  can be o b -  tained b y measuring t h e slopes o f t h e A E versus  0 p l o t s at  0  12  0 Degrees  = 0.  These modifications 55A39.  Type  include probe types  55A32,  numbers will n o t b e changed.  tinguish between  the n e w t y p e s w i t h w i d e l y  and t h e conventional types,  55A38  In o r d e r t o spaced  and dis-  wires  all n e w X - p r o b e s are m a r k e d  w i t h t h e c o l o r code, w h i c h w a s i n t r o d u c e d at t h e e n d o f 1969. CONVENTIONAL  DISA  X-TYPE  PROBES  E x p e r i m e n t s carried o u t b y J e r o m e , G u i t t o n a n d  Reynolds  (c/b) varies s t r o n g l y  n u m b e r . In t h e r a n g e o f R e f r o m  r a t i o n (c/b) decreases  from  ly b y t h e d e p e n d e n c e  o f the y a w sensitivity  approx.  engraved  body.)  Patel  ( 1 9 6 9 ) have s h o w n that t h e ratio o f t h e static p i t c h sitivity t o y a w sensitivity  (Conventional X-probes had type numbers  on the probe sen-  with the  T h e c o l o r c o d e , c o n s i s t i n g o f t h r e e d o t s , w i l l be:  1 t o 10 the  1 to 0.1 e x p l a i n e d  part-  b o n R e and  partly b y the width o f the thermal wake being proportional  55A32: red  organge - red  5 5 A 3 8 : red  orange - grey  5 5 A 3 9 : red  orange - w h i t e  read f r o m t h e sensor e n d  D I S A E L E K T R O N I K A/S . D K 2730 H E R L E V . D E N M A R K Telephone: Copenhagen  Printed  in D e n m a r k  by  D I S A ,  February  1970  (01) 94 52  11 . Telegrams:  DISAW0RKS.  Copenhagen . Telex:  5849  

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