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An experimental study of interference effects between closely spaced wires of an X-type hot-wire probe 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.Sc, McMaster U n i v e r s i t y , 1965 . A Thesis Submitted i n P a r t i a l F u l f i l l m e n t of the Requirements f o r the Degree of Master of Science i n the Department of Physics and I n s t i t u t e of Oceanography We accept t h i s thesis as conforming to the required standard September, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia Vancouver 8, Canada > ABSTRACT The Disa type 55A32 X-wire probe has been widely used i n turbulence measurements. However, the author was unable to obtain agreement between turbulence measurements made simultaneously with t h i s type of X-wire probe and an u l t r a s o n i c anemometer at"the same p o s i t i o n i n the atmospheric boundary layer over the ocean. The nature of the disagreement between the two instruments suggested that there existed an unexpected response of the wires to the cross stream wind component normal to the plane of the X-array. Wind tunnel experiments confirmed t h i s response and at t r i b u t e d most of i t to thermal coupling between the two wires of the array v i a t h e i r hot wakes. The prongs and/or probe body were also shown to be contributors to the anomalous responses of the X-wires. Si m i l a r experiments c a r r i e d out with a Thermo-Systerns model 1241-20 X-probe (with a sensor length to sensor separation r a t i o of 5/8 compared with 0.2 or less f o r the Disa 55A32 X-wire probe) demonstrated that the int e r f e r e n c e e f f e c t s were absent (or, at l e a s t , i n s i g n i f i c a n t ) . As a consequence of these f i n d i n g s , the Disa E l e c t r o n i k A/ company of Herlev, Denmark, modified t h e i r 55A32, 55A38 and 55A39 l i n e s of X-wire probes to make the length/separation r a t i o close to unity. i i i TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v LIST OF FIGURES v i 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 to Wire 2 2.3 S t a t i c C h a r a c t e r i s t i c of an Inclined Wire 3 2.4 Dynamic Response of a Hot-Wire Normal to the Mean Flow 5 2.5 Dynamic Response of the Hot-Wires i n an X-Array 6 3 DISCOVERY OF THE PROBLEM 10 3.1 Introduction 10 3.2 T y p i c a l Results from the Boundary Layer Experiment 12 3.3 The Disa 55A32 X-Wire Probe 14 3.4 The I n t u i t i v e Case f o r Thermal Wake Interference 14 3.5 Questions to be Answered 19 4 THE WIND TUNNEL EXPERIMENTS 20 4.1 Experimental Arrangement 20 4.2 Experimental Procedure 20 4.3 Experimental Results 24 4.4 Discussion of Results and Conclusions 27 i v Page 4.5 The Thermo-Systems Model 1241 X-Type Hot-Film Probe 33 5 CONSEQUENCES OF THE INTERFERENCE PROBLEMS 38 5.1 - On Spectral Analysis 38 5.2 - On the Results of Other Workers 41 6 DENOUEMENT 42 BIBLIOGRAPHY 43 APPENDIX - Disa Special Information Note No. 14 45 V LIST OF TABLES Page I T y p i c a l Boundary Layer Results 13 II Comparison of Calculated and Measured Spectral Estimates 41 v i LIST OF FIGURES 1 Page FIGURE 1. (a) Flow Geometry f o r In c l i n e d Sensor 4 (b) Flow Geometry f o r X-array of Hot-Wires 4 2. Demonstration of L i n e a r i t y of Hot-Wire's Dynamic Response 7 3. Disa 55A32 X-Wire Probe . 15 4. Ori e n t a t i o n of 55A32 X-Probe f o r F i e l d Measurements 16 5. Experimental Arrangement i n Wind Tunnel 21 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 22 7. v-Response of "Downstream" Wire of Disa 55A32 X-Probe 26 8. v-Response of Disa 55A32 X-Probe 28 9. w-Response of Disa 55A32 X-Probe 29 10. Conventional Thermo-Systems 1241-20 Probe Used i n Experiments 34 11. v-Response of Thermo-Systems 1241-20 X-Probe 36 12. w-Response of Thermo-Systems 1241-20 X-Probe 37 v i i ACKNOWLEDGEMENTS I wish to express my appreciation to Dr. R. W. Burling f o r h i s d i r e c t i o n during t h i s study and to Dr. R. W. Stewart f o r v a l u - able suggestions made i n my discussions with him. The Mechanical Engineering Department of the U n i v e r s i t y of B r i t i s h Columbia k i n d l y provided t h e i r wind tunnel f o r t h i s p r o j ect. Personal f i n a n c i a l assistance came from the National Research Council of Canada, while funds for the project were pro- vided by the Meteorological Branch of the Canadian Department of Transport and the Defense Research Board of Canada. CHAPTER I. INTRODUCTION The hot-wire anemometer has been used f o r many years as a research t o o l i n f l u i d mechanics. I t i s an instrument designed 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 stream's varying cooling e f f e c t on a very t h i n , e l e c t r i c a l l y heated wire filament. The small s i z e and rapid response of the sensing element make the hot-wire anemometer the best instrument so f a r developed f o r analysis of the v e l o c i t y micro-structure of a flowing f l u i d . Recently the a p p l i c a t i o n of hot-wire anemometry has r a p i d l y expanded due to better a n c i l l a r y 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 of f l u i d flow. Today, turbulence measurement with hot-wire anemometers i s routine procedure and, with s p e c i a l X- or V- arrays of two independent hot-wire sensors, l o n g i t u d i n a l and transverse components of the f l u c t u a t i o n s i n the f l u i d v e l o c i t y can be measured simultaneously and the c o r r e l a t i o n between them can be i n v e s t i g a t e d . During the course of the a n a l y s i s of turbulence data c o l l e c t e d by the author i n the atmospheric boundary layer over the ocean from hot-wire sensors i n an X-configuration and from a three-dimensional u l t r a s o n i c anemometer-thermometer, i t became apparent that the hot-wire sensors were not g i v i n g the expected response. The objectives of the i n v e s t i g a t i o n described herein were: (i ) to i d e n t i f y the problem, ( i i ) to determine the seriousness of the problem, and ( i i i ) to design a sensor array that would eliminate the problem. 2. CHAPTER I I . EXPECTED RESPONSE OF AN X-TYPE HOT-WIRE PROBE 2.1 Introduction Consider a rectangular coordinate system with the p o s i t i v e x-axis i n the d i r e c t i o n of the mean a i r flow (which w i l l always be h o r i z o n t a l i n these d i s c u s s i o n s ) . Let the z d i r e c t i o n be v e r t i c a l l y upward and the y d i r e c t i o n be determined by the convention f o r r i g h t - handed coordinates. Then the instantaneous v e l o c i t y vector can be expressed as if = ?(U + u) + j v + kw (2-1) where U i s the mean wind speed, u, v and w are the components of the much smaller v e l o c i t y f l u c t u a t i o n and i , j and k are the usual 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 to 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 heat t r a n s f e r from a uniformly heated c y l i n d e r normal to a two-dimensional, incompressible, non-viscous flow was found by King (1914). As applied to a hot-wire sensor operated i n the constant temperature mode, King's Law can be expressed as I 2 = A' + B'U 5 (2-2) where I i s the hot-wire current, A' and B 1 are constants depending on f l u i d and wire properties, and U i s the v e l o c i t y of the f l u i d (perpendicular to the c y l i n d e r ) . The idea behind the constant-temperature operation i s to keep the sensing element at a constant temperature (and therefore a constant resistance) and to use the square of the heating current as the measure of the rate of cooling by heat t r a n s f e r from the wire to the wind. 3 Since the voltage E across the wire i s proportional to I i n constant temperature operation, then E 2 = A + Bl/ 5 (2-3) where A and B are constants. I t can be seen then that the response of the hot-wire anemometer i s strongly non-linear. 2.3 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 flow d i r e c t i o n i s not normal to a c y l i n d r i c a l sensor but rather makes an angle 0 with the normal to the sensor as shown i n F i g . 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 hot-wire anemometer must be known. Equivalently, an " e f f e c t i v e (normal) cooling v e l o c i t y " should be obtainable from the actual mean v e l o c i t y , the geometry and sensor c h a r a c t e r i s t i c s (such as length to diameter r a t i o ) . Normal component or "cosine law" cooling i s usually assumed (Hinze, 1959; C o r r s i n , 1963). This means that the heat transferred from the hot-wire to the f l u i d flow depends only on the component of the f l u i d v e l o c i t y normal to the wire. For the configuration i n F i g . 1, the e f f e c t i v e cooling v e l o c i t y , C, would then be C = 0 cos 0. Hinze (1959) and Webster (1962) have suggested what has become the most widely accepted expression for the e f f e c t i v e cooling v e l o c i t y taking i n t o account tan g e n t i a l component cooling as well as normal component cooling, i . e . , C 2 = U 2 ( c o s 2 6 + k 2 s i n 2 0 ) . (2-4) Sensor Wire Fig. 1(a). Flow Geometry for Inclined Sensor Wire ff] * Wire #2 Fig. 1(b). F.low Geometry for X-array of Mot Wires 5. Champagne (1967) found that k depends on the parameters that govern the temperature d i s t r i b u t i o n along the wire, p r i m a r i l y the length- to-diameter r a t i o (1/d) of the wire. For the wires used i n the present study, I 4, L O mm- 2 0 0 d * 0.005 mm. and Champagne determined k = 0.20 for t h i s r a t i o . Since 6 = 45° f o r the experiments herein, then there i s only a 2% er r o r introduced by c a l c u l a t i n g the e f f e c t i v e cooling v e l o c i t y assuming normal component cooli n g . This i s a much smaller e f f e c t than the one being studied, so normal component cooling with i t s attendant mathematical s i m p l i c i t y w i l l be assumed and King's Law becomes E 2 - A + BC*. (2-5) 2.4 Dynamic Response of a Hot-Wire Normal to the Mean Flow Consider a hot-wire sensor aligned p a r a l l e l to the z-axis i n a turbulent a i r flow described by equation (2-1). Assuming normal component cooling, C - {(U + u ) 2 + v 2 } ^ - U ( l + 2u/U •+ u 2/U 2 + v 2/U 2}^ = U ( l + u/U + u 2/(2U 2) + v 2/(2U 2) - u 2/(2U 2) + higher order terms} . The e f f e c t i v e cooling v e l o c i t y can be considered to c o n s i s t of a mean part C - U + v^/(2U) + higher order terms (2-6) 6. and a f l u c t u a t i n g part c = u + (v 2-v 2)/(2U) + higher order terms. (2-7) Hinze (1959) and Pond (1965) have argued that even f o r turbulence i n t e n s i t i e s , ( u ^ ^ / l l , as high as 0.1, the second and higher order terms i n equation (2-6) and (2-7) and i n the Taylor expansion of King's Law about C = C can be omitted with only a 2% e r r o r . This means that f o r low i n t e n s i t y turbulence, the dynamic response, e, of a s i n g l e v e r t i c a l hot-wire i s e s s e n t i a l l y l i n e a r , i . e . , e - c (2-8) 4 EC - - S - r u . (2-9) 4EU^ Figure 2 provides experimental 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 turbulence i n t e n s i t y near 0.1 ( i n the atmospheric boundary layer over the sea). I t shows u as determined by equation (2-9) p l o t t e d against u as measured simultaneously at the same p o s i t i o n by a sonic anemometer, a l i n e a r response instrument. Each point represents a 0.8 second time average. Note that the zeros on the axes were determined using the mean wind speed (9.2 m/sec) f o r a period of time longer than the period represented by the data i n the f i g u r e . The mean wind speed f o r t h i s shorter i n t e r v a l was s l i g h t l y greater than 9.2 m/sec r e s u l t i n g i n the apparent skewness of the data i n F i g . 2. 2.5 Dynamic Response of the Hot-Wires i n an X-array F i g . lb (page 4) shows two i n c l i n e d wires i n an X-configuration i n the xz-plane. The wires are mounted close together (but not touching) on a s i n g l e probe. They are operated as two independent i n c l i n e d wires. 7. Fig. 2. Demonstration of Linearity of Hot-Wire's Dynamic Response. 8. For wire no. 1, the e f f e c t i v e cooling v e l o c i t y i n a turbulent flow described by equation (2-1) i s Cl = {{(U + u) cos &i + w s i n Q^ 2 + v 2 } ^ - U cos e i ( l + 2u/U + 2(w tan ep/U + u 2/U 2 + 2(uw tan 9^/U 2 + (w2 t a n ^ ^ / U 2 + ( v 2 s e c 2 e i ) / U 2 ) J 2 = U cos e ^ ( l + u/U + (w tan Q^/U + higher order terms}. As i n the case of the v e r t i c a l wire and a turbulence i n t e n s i t y < 0.1, second and higher order terms can be dropped from expressions f o r C and c with a r e s u l t i n g e r r o r i n c of only about 2%. The voltage f l u c t u a t i o n s across wire no. 1 are, to a good approximation l i n e a r l y r e l a t e d to u and w, i . e . , r B.(cos Q.)^ e _ . — L _ ( u + w tan 0.) (2-10) 1  UEjp 2 1 or e t = a^u + b xw (2-11) where the d e f i n i t i o n s of a^ and b^ are apparent. In p r a c t i c e , 6 l  = 45° so that ^ = by S i m i l a r l y the dynamic response equation f o r wire no. 2 i s B„(cos 6_K e _ __ —L- (u - w tan 8 9) (2-12) * 4E U 2 Z or = a 2u - t>2w (2-13) From equations (2-11) and (2-13), i t can be seen that two hot-wires i n an X-array can be used to measure two components of the v e l o c i t y f l u c t u a t i o n vector - the downstream component and the transverse component i n the plane of the "X". Any response to the transverse component perpendicular to the plane of the "X" i s expected to be a higher order e f f e c t . 10. CHAPTER I I I , DISCOVERY OF THE PROBLEM 3.1 Introduction As part of the a i r - s e a i n t e r a c t i o n research program conducted by the I n s t i t u t e of Oceanography, the author intended to i n v e s t i g a t e c e r t a i n features of the wind turbulence microstructure i n the atmospheric boundary la y e r over the ocean. Instruments were mounted on a tower standing on a t i d a l f l a t . Water depth v a r i e d from 0 at low spring t i d e to 14 f t . at high spring t i d e . The experimental plan was to use an X-array of hot-wires i n conjunction with a three-dimensional u l t r a s o n i c anemometer-thermometer. I t has been a long-standing 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 measurements of a micrometeorological or oceanographic quantity with two 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 p o s s i b l e . Often the instruments used were newly developed or were being used i n an environment f o r which they were not designed or t h e i r c a l i b r a t i o n s t a b i l i t y was suspect. Therefore the d u p l i c a t i o n of measurement was necessary to "keep the instruments honest" (not to mention the graduate students). In the p a r t i c u l a r f i e l d experiment being described, the presence of the sonic anemometer had a more important purpose. Hot- wire anemometers, having a highly non-linear s t a t i c c h a r a c t e r i s t i c (section 2.2), present considerable 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 for a r e l i a b l e dynamic c a l i b r a t i o n (equations (2-9), (2-10) and (2-12)). As i f that were not enough, t h e i r s t a b i l i t y of c a l i b r a t i o n i s suspect (Weiler, 1966) e x p e c i a l l y i f contamination of the wire surface (by salt-water spray, f o r example) i s a p o s s i b i l i t y and, i n the constant temperature mode of operation, the s t a t i c c a l i b r a t i o n seems to deviate from King's Law - the c h a r a c t e r i s t i c i s b e t t e r approximated by E 2 = A + BU 0* 1* 5 according to C o l l i s and Williams (1959). A further problem with X-arrays of hot-wires i s to accurately reproduce i n the f i e l d the probe alignment used during c a l i b r a t i o n . The sonic anemometer (Kaijo Denki, Model PAT-311-1), on the other hand, has minimal c a l i b r a t i o n procedures - only c e r t a i n e l e c t r i c a l adjustments need to be infreq u e n t l y checked - and has a l i n e a r response at the wind speeds encountered. This anemometer has been described by Mitsuta (1966). I t i s u s e f u l f o r measuring only the l a r g e r scale (and lower frequency) turbulence f l u c t u a t i o n s , i n c l u d i n g scales which contribute to most of the atmospheric momentum and heat f l u x e s , because i t determines the s p a t i a l average of the component of the wind v e l o c i t y over each of three 20 cm. path lengths arranged i n a s p e c i a l geometry. The i n t e n t i o n was to use the sonic anemometer measurements to provide an " i n s i t u " dynamic c a l i b r a t i o n of the hot-wires. With u, v, and w a l l obtainable from the sonic anemometer data, and simultaneous measurements of the hot-wire voltages e^ and e.^ (equations (2-11) , (2-13)) at e s s e n t i a l l y the same p o s i t i o n , then the hot-wire dynamic c a l i b r a t i o n constants a., b., a~ and b„ can be c a l c u l a t e d . Since s p e c t r a l analysis 12. of q u a n t i t i e s l i k e u z , wz and uw - the overbar i n d i c a t i n g a time average - were to be obtained i n the end, one technique employed f i n d i n g the planes of regression of e^ 2 and e^2 on u 2 , uw and w2. To elaborate f u r t h e r , from equation (2-11), e ] L 2 - a L 2 u 2 + 2 3 ^ ^ + b L 2w 2 . (3-1) The frequency spectra of u 2 , uw, and "ŵ  from sonic anemometer data and of e^ 2 from the no. 1 hot-wire voltage s i g n a l were computed. Then using the s p e c t r a l estimates from about f i f t e e n third-octave bandwidths at low frequencies where the sonic response has not begun to f a l l o f f , a computer program ca l c u l a t e d three constants P, Q and R f o r the plane of "best f i t " ( i n the l e a s t squares sense), i . e . , e^ 2 - Pu 2 + Quw + Rw2 . (3-2) Then, = P a and b 1 = R . This technique provided a check since equation (3-1) shows that P, Q and R are not independent but rather Q = 2(PR) J $. The c a l i b r a t i o n f o r wire No. 2 was s i m i l a r l y obtained. 3.2 T y p i c a l Results from the Boundary Layer Experiment Once the dynamic c a l i b r a t i o n s of the hot-wires had been worked out as described i n s e c t i o n 3.1, a wide v a r i e t y of autospectral and c o s p e c t r a l analyses were performed. Table I presents t y p i c a l r e s u l t s from one data record for third-octave bandwidths about three centre 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)" 1 5.19x10" 2 1.16x10" 1 1.77x10 -1 U 2 (m/sec)2 s 8.27x10" 1 3.31x10" 1 2.03x10' -1 U. 2 (m/sec)2 h 7.54x10" 1 3.03x10- 1 1.81x10 -1 W 2 (m/sec)2 s 4.94x10" 2 3.48x10" 2 3.33x10 -2 wT2" (m/sec)2 n 1.41x10" 1 5.34x10" 2 5.19x10--2 V 2 (m/sec)2 s 4.32x10" 1 1.44x10" 1 9.96x10" -2 U~W (m/sec)2 s s -1.24x10" 1 -5.80x10" 2 -2.84x10 -2 . U7w, (m/sec)2 n n -1.06x10" 1 -5.78x10-2 -2.78x10 -2 V W (m/sec)2 6.85x10" 3 5.68x10" h 5.61x10--3 s s V W, (m/sec)2 s h 2.04x10" 1 6.18x10" 2 5.13x10--2 TABLE I: Typical Boundary Layer Results The most dramatic discrepancies occur between w, 2 and w 2 and h s between v w, and v w • The results indicate that the quantity being S l l s s called ŵ  was contaminated by something correlated with v g but only weakly, i f at a l l , correlated with u_. Recall from the discussion in section 2.5 that the response of the wires of an X-array (with the plane of the "X" aligned parallel to the xz-coordinate plane) to v fluctuations i s expected to be negligible in low intensity turbulence. Furthermore, the shear flow in the boundary layer at the f i e l d site is 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" in Table I. The latter correlation i s s s s 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 in 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. The details of the probe tip and wire arrangement are shown in Fig. 3. This type and other Disa types with similar wire lengths and wire separations have been widely used in turbulence measurements. The wires themselves are platinum-plated tungsten 5 microns in diameter. The configuration of the wires for the f i e l d measurements described in this chapter i s shown in 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 Fig. 3. Disa 55A32 X-Wire Probe 16. v ^ \ U Fig. Orientation of 55A32 X-probe for f i e l d measurements 17. i s to rotate the instantaneous wind v e l o c i t y vector i n the h o r i z o n t a l plane by an angle 0 - tan _ 1(v/U) rather than to appreciably a l t e r the length of the wind vector. For 1 mm. long wires separated by 0.16 mm. i n an X-array, a wind v e l o c i t y vector l y i n g i n the xy-plane but making an angle with the xz-plane of . _ i 0.16 0 » co tan 1 lj~fi 3 22.5 u w i l l cause an' end of one wire to l i e d i r e c t l y downwind of an end of the other wire (see F i g . 4 again). I f the X-wire array were i n i t i a l l y aligned properly and the mean wind d i r e c t i o n were to remain steady, then instantaneous rotations of 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 extremely rare f o r a root-mean-square turbulence i n t e n s i t y of 0.1. However, the wake of a wire i s expected to broaden as i t i s convected downstream. Furthermore, the influence of the wire supporting system c o n s i s t i n g of prongs and the probe body may fur t h e r broaden the wake. Hoole and Calvert (1967), Gilmore (1967) and Norman (1967) have a l l 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 of the Disa Type 55A25 s i n g l e hot-wire probe with the wire aligned normal to an a i r flow. They found a 15 - 20% v a r i a t i o n i n the ind i c a t e d v e l o c i t y as the probe was rotated ± 90° about the wire axis from a p o s i t i o n with the probe axis p a r a l l e l to the flow d i r e c t i o n . They concluded that prongs and probe body were about equally responsible f o r the flow displacement at the p o s i t i o n of the wire. Eyre (1967) made s i m i l a r measurements with the same type of probe and h i s experimental r e s u l t s agree w e l l with those 18. reported by the above authors. However, h i s explanation of the cause 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 the wire axis i s quite d i f f e r e n t . He a t t r i b u t e s the whole e f f e c t to an angular-dependent v a r i a t i o n of convective heat l o s s from the prongs and a consequent change of heat conduction from the wire ends, Dahm and Rasmussen (1969) studied the dependence 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 the wire axis on prong length, prong.spacing and wind speed. They found that the interference e f f e c t s were more severe at 10 m/sec than at 40 m/sec and that these e f f e c t s e x h i b i t a steep increase f o r prong spacings <2 mm. and prong lengths <6.5 mm. C l e a r l y ( i n hindsight) the 55A32 X-wire probe ( F i g . 3) gives the worst of a l l worlds - four prongs instead of two, prong spacings of 0.7 mm. at best and 0.05 mm. at worst (the width of the a i r gap between the long prong supporting the outer end of one wire and the short prong supporting the inner end of the other wire) and prong lengths of 7 - 8 ram. F i n a l l y , i t can be seen how thermal wake interference between the wires of an X-array would cause v f l u c t u a t i o n s to give s i m i l a r p o l a r i t y responses ( i n e^ and e^) to w f l u c t u a t i o n s . (Recall from the end of s e c t i o n 3.2 that t h i s conclusion was reached i n order to explain the data of Table I.) Referring to the arrangement shown i n Figure 4, a p o s i t i v e v f l u c t u a t i o n rotates U i n a d i r e c t i o n that tends to make wire no. 2 l i e downstream of wire no. 1. The hot wake of wire no. 1 f a l l i n g on wire no. 2 r e s u l t s i n l e s s current being supplied to wire no. 2 to maintain i t at a constant temperature (and r e s i s t a n c e ) . Therefore the voltage across wire No. 2 drops. 19. Prong and probe e f f e c t s aside, t h i s simple-minded reasoning suggests the following dynamic responses (as a f i r s t approximation) for the X-wires for p o s i t i v e v f l u c t u a t i o n s : e. = a.u + ^w , , } (3-3) e2 = a 2 U " V • C 2 V * 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 , the response equations are e. = a.u + b.w + c.v , 1 1 , i • } (3-4) e 2 = a 2u - b2w . The constants are a l l p o s i t i v e . 3.5 Questions to be Answered The experimental study of the response to v f l u c t u a t i o n s was d i r e c t e d toward answering the following questions: ( i ) Is the response q u a l i t a t i v e l y l i k e that suggested by equations (3-3) and (3-4)? ( i i ) I f not, what form does the response to v take? ( i i i ) How large must v/U be before the s e n s i t i v i t y to v becomes important (say 10% of the s e n s i t i v i t y to u or w)? (iv) What a l t e r a t i o n s must be made to the wire mounting arrangement to ensure that the s e n s i t i v i t y to v i s unimportant? 20. CHAPTER IV. THE WIND TUNNEL EXPERIMENTS 4.1 Experimental Arrangement The X-wire probe was mounted on a turntable i n the 36 inch x 27 inch wind tunnel of the Dept. of Mechanical Engineering, U.B.C. The turbulence l e v e l was about 0.1%. A sketch of the arrangement i s shown i n Figure 5. A block diagram of the data c o l l e c t i o n equipment i s presented i n Figure 6. Each wire of the X-array was heated and maintained at a constant temperature by a separate constant temperature anemometer (CTA), Disa model 55D05. The output voltage of an anemometer ( i . e . , the voltage E i n King's Law), was then applied to a Disa Model 55D25 A u x i l i a r y Unit. This unit was employed to perform low-pass f i l t e r i n g (to remove the low l e v e l of turbulence noise from the hot-wire signal) and DC suppression i n order that the DC output of the anemometer would neither saturate the output of the DC a m p l i f i e r nor drive the pen on the chart recorder beyond f u l l s c a l e . No attempt was made to match the two wires of the X-array or to l i n e a r i z e the anemometer outputs since only the r e l a t i v e responses of the wires to u, v and w f l u c t u a t i o n s were of i n t e r e s t . 4.2 Experimental Procedure S t a t i c c a l i b r a t i o n s were obtained f o r both wires by varying the a i r speed i n steps and measuring the DC output of both anemometers a f t e r each step. The dynamic s e n s i t i v i t y to u f o r any operating point 21. Tunnel Roof A x i s of Ro t a t i o n U Turntable •Disa X-wire (Type 55A32) Probe x: •x _ Tunnel f l o o r ELEVATION U y\— PLAN VIEW Fiq. 5- Experimental Arrangement in Wind Tunnel fi F i g . 6 Block Diagram of Equipment Used to Measure D i r e c t i o n a l Characteristics of X-Probe 23. (E, U) could then be c a l c u l a t e d as described i n section 2.5. In order to determine the s e n s i t i v i t y of the wires to v, quasi f l u c t u a t i o n s were introduced i n the following manner. . Rotating the turntable (Figure 5, lower) clockwise by an angle 8 has the same e f f e c t s as leaving the turntable f i x e d and changing the x-component of the wind by U (cos 3-1) and the y-component by U s i n 3. For small 3, the x-component " f l u c t u a t i o n " i s considerably smaller than the y-component " f l u c t u a t i o n " . For example, (cos 3-1) = 0.034 s i n 3, 3 = 4°. In summary, r o t a t i n g the X-array by an angle 3 i s equivalent to introducing v » fj s i n 3 (4-1) and u • U(cos 3 - 1) . (4-2) Clockwise rotations must be taken as p o s i t i v e , counter-clockwise as negative i n order that the signs of u and v are consistent with the system of axes already chosen. "Fluctuations" of w were produced by a s i m i l a r technique. F i r s t the X-array was rotated clockwise about the probe axis (as seen from behind the probe looking upwind) by 90°. I f the coordinate system i s imagined to rotate with the array then the xz plane would l i e h o r i z o n t a l l y i n the earth's frame of reference. Then r o t a t i n g the turntable by an angle y i s equivalent to introducing w = U s i n y (4-3) and u = U(cos y - 1) • (4-4) 24. Again clockwise r o t a t i o n s must be assigned p o s i t i v e angles and counter- clockwise rotations negative angles. To e s t a b l i s h whether or not the thermal wake produces s i g n i f i c a n t e f f e c t s and, i f so, at what value of v/U the e f f e c t s become important, the probe was rotated from 3 ° 0 to B = -16° i n 2° decrements f o r two cases - the "upstream" wire operating (at about 190°C) and the "upstream" wire o f f ( i . e . , at ambient temperature). Note that f o r negative B and the configuration of Figure 5, wire No. 1 tends to be downstream and i n the thermal wake of wire No. 2. Then to determine the r e l a t i v e s e n s i t i v i t i e s of the wires to v and w f l u c t u a t i o n s , B- and y-rotations were r e s p e c t i v e l y made i n 2° increments from - 10° to +10°. A mean wind speed of 4.0 m/sec was used i n a l l experiments. 4.3 Experimental Results In converting the data from hot-wire anemometer responses to $- or y-rotations to data on hot-wire responses to v or w f l u c t u a t i o n s , i t i s necessary to correct for the in t r o d u c t i o n of u = U(cos S - 1) or u = U(cos y - 1) upon a B- or y - r o t a t i o n r e s p e c t i v e l y . The c o r r e c t i o n i n the case of a y - r o t a t i o n w i l l be described here. 25. Let E ^ (y) represent the voltage output of hot-wire anemometer No. 1 when the X-array has been rotated by an angle y. (0) represents the output f o r Y - 0° • From equation (2-11), E x ( Y ) ~ Ej^O) = a xu + b xw . S i m i l a r l y the change i n the output voltage of anemometer No. 2 upon a Y-rotation i s E 2 ( y ) - E 2 ( 0 ) » a 2 u - b 2w . The c o r r e c t i o n terms to be subtracted from the voltage changes to eliminate the u f l u c t u a t i o n s unavoidably introduced are a^u and a 2u r e s p e c t i v e l y where u = U(cos Y - 1) • The constants a^ and a 2 are determined from equations (2-10) and (2-12). In summary, the dynamic responses of the hot-wire 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) and E(Y) - E(0) - aU(cos y - 1) (4-6) r e s p e c t i v e l y where the voltages and constants p e r t a i n to the appropriate wire of the array. Figure 7 shows the response of the "downstream" wire to v f l u c t u a t i o n s f or the two cases of the "upstream" wire hot and cold ( i . e . , at ambient temperature). Note that the s i t u a t i o n with 6 = 0 and the upstream wire at the ambient temperature was chosen as the reference voltage about which deviations would be measured for both cases. + Upstream w i r e cold o. Upstream wire hot 2 4 6 8 10 12 14 16 F i g . 7 v-Response of "Downstream" Wire of Disa 55A32 X-Probe L 27. If the hot wake of the upstream wire does i n t e r c e p t the down- stream wire, i t s e f f e c t i s expected to be to decrease (from the " c o l d " wake case) the power required to maintain the downstream wire at a constant temperature. This translates i n t o a decrease i n the hot-wire current and a decrease i n the voltage across the wire. That t h i s occurs i s c l e a r l y evident i n Figure 7. Two unexpected r e s u l t s are also i n d i c a t e d by Figure 7. F i r s t , even f o r 3 = 0 i . e . , neither wire tending to be downwind of the other, there was some thermal coupling between the two wires. Secondly, with the upstream wire o f f , the response to v f l u c t u a t i o n s was not s t r i c t l y p o s i t i v e . However the argument that the cooling depends on the normal component would p r e d i c t an increase i n the cooling rate and consequently an increase i n thevoltage across the i n c l i n e d hot-wire as i t undergoes a p o s i t i v e or negative 3-rotation since e i t h e r r o t a t i o n "presents" a greater length of wire normal to the a i r flow. Figure 8 shows the responses of the wires to v f l u c t u a t i o n s and Figure 9 shows the responses to w f l u c t u a t i o n s . The w-response Is reasonably l i n e a r as a n t i c i p a t e d by equations (2-11) and (2-13), although there i s a small break i n the slope near y = 0. The v-response pl o t s are nearly l i n e a r f o r p o s i t i v e voltage changes (when the respective wire tends to be upstream of the other wire). 4.4 Discussion of Results and Conclusions Although the thermal wake interference between the two wires of the Disa 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 A £ ( / 3 ) - E ( 0 ) - a u -,g (mv.) -12 H h 8 •- 4 o o Wire no. 1 + Wire no.2 H 1 1 1~> /5' -10 -8 -6 -A -2 o o 2 4 6 8 10 o - 4 - 8 F i g . 8 v-Response of Disa 55A32 X-Probe -10 -8 G - 2 0 -30 -40 - 5 0 -60 o W i r e no.1 + W i r e no.2 F i e . 9 w-Resoonse of Disa 55A32 X-Probe 30 • anomalous hot-wire r e s u l t s presented i n Table I, there i s strong evidence of other c o n t r i b u t i n g f a c t o r s . Figure 7 in d i c a t e s that there i s thermal coupling between the two wires of the array even when i t i s properly aligned i n t o the wind. Data were not c o l l e c t e d that would have enabled that graph to be extended i n t o the region of p o s i t i v e 8 to determine the thermal e f f e c t of the "downstream" wire on the "upstream" wire. Such an extension would probably allow one to separate the r a d i a t i v e coupling from convective coupling. The former would tend to be constant (and therefore a f f e c t only the s t a t i c response) while the l a t t e r should decrease f o r wire No. 1 with p o s i t i v e increase i n 8. Hinze (1959) states that 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 small under usual operating conditions of a s i n g l e wire where wire temperatures do not exceed 300°C. While the r a d i a t i v e coupling between the two wires remains a matter of conjecture, there i s l i t t l e doubt that there are some important prong and probe e f f e c t s a f f e c t i n g the convective coupling between the wires at small 6 . (See Figure 7). Not only w i l l the prongs broaden the hot-wire 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 thermal wakes due to the unavoidable heating of the prong t i p s . Champagne's data (1967) i n d i c a t e that the junction of a wire and probe t i p w i l l be about 40 C° above the ambient temperature. The large s e n s i t i v i t y to v f l u c t u a t i o n s r e l a t i v e to the s e n s i t i v i t y to w f l u c t u a t i o n s must also be a prong and/or probe e f f e c t . The expected 31. sensitivity ratio for the experiment w i l l be derived below assuming normal component cooling and no wake effect; this w i l l be compared to the ratios calculated from the observed responses for both wires of the Disa 55A32 X-probe. Consider a wire of length 1 inclined at 45° to U in the wind tunnel. For a g-rotation, the projection of the wire's length on a plane perpendicular to U i s l x - {(1 sin 4 5 0 ) 2 + (1 sin 45° sin g)2}*2 = 1 sin 45° (1 + s i n 2 g ) ^ . The response of the wire to the apparent v fluctuation corresponding to an increment dg i n g w i l l be proportional to the resulting increment, d l x , in the component of the wire's length perpendicular to U (according to the normal component cooling assumption). I.e., d l x = 1(1 + sin 2g)sin 45° sin g cos g dg (4-7) Note that for g beginning at 0, d l x i s s t r i c t l y positive. Similarly for a y r o t a t i o n and the same wind speed, 1 A » 1 sin(45° + y) and the response to the apparent w fluctuations i s proportional to d l A - 1 cos(45° + Y) dY . (4-8) Therefore, for small g, dg, Y and dY and dg = dy v-sensitivity1 ^ w-sensitivity 1 sin g cos 8 (1 + sin z(3p2 A | sin 6| - I 31 . (4-9) 32 Note that i n the p o s i t i v e p o l a r i t y response region of Figure 8 the responses are nearly l i n e a r so that the s e n s i t i v i t y r a t i o w i l l be nearly constant and equal to the r a t i o of the slope of the l i n e a r segment of the v-response to the slope of the w-response. This r a t i o f o r wire No. 1 i s 0.31 and f o r wire No. 2 i s 0.34. Equation (4-9) pre d i c t s a s e n s i t i v i t y r a t i o of 0.035 for 8 = 2° and 0.10 f o r 3 =• 5.7°. Therefore the r a t i o f o r the upstream wire 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 quite d i f f e r e n t from the expected. The v-response curve, according to the theory presented above, should be concave upwards and generally at a considerably lower magnitude over the 0 to 10° range of 3 . The excessively high response of a wire of the Disa 55A32 probe to v f l u c t u a t i o n s which tend to put that wire i n an upstream p o s i t i o n i s probably due to a combination of two f a c t o r s : the flow past the wires speeding up r e l a t i v e to the undisplaced flow as more blockage i s presented by the rotated probe and prongs and the angular-dependent convective heat, loss from the prongs as proposed by Eyre (1967) and mentioned before i n se c t i o n 3.4. The r e s u l t s of the wind tunnel t e s t i n g suggest modifications that should be make to the Disa type 55A32 X-probe. The most obvious and important change i s to move the two wires further apart by spreading the prongs. Although i n a n a l y t i c a l discussions of the X-wire array the wires are usually assumed to l i e i n the same plane, there i s no r e a l j u s t i f i c a t i o n i n attempting to duplicate the model. The smallest scale of turbulence microstructure that can be studied by a hot-wire sensor i s determined by i t s length so that very l i t t l e would be l o s t i n the way of re s o l u t i o n c a p a b i l i t i e s of an X-array by separating the wires about one 33. wire length. Prong e f f e c t s would be reduced by the above change but they could be diminished further by lengthening the prongs - r e c a l l from se c t i o n 3.4 that the findings of Dahm and Rasmussen (1969) indicated that the prong lengths used i n the 55A32 probes are barely acceptable. 4.5 The rhermo-Systerns Model 1241 X-type Hot-Film Probe Thermo-Systerns Inc. of St. Paul, Minnesota, produced an " o f f - t h e - s h e l f " l i n e of X-probes which s a t i s f i e d the above design c r i t e r i a quite w e l l and had two other favourable features. Their model 1241. probe with no. 20 sensor elements a f f i x e d i s shown i n Figure 10. Each sensor has a 0.8 micron thick platinum f i l m deposited by radio frequency sputtering onto a 0.002 inch diameter glass rod. The 0.040 inch sensing length, c e n t r a l l y located on the 0.065 inch long rod, i s defined by gold p l a t i n g on the ends of the rod. The gold p l a t i n g also provides e l e c t r i c a l contact with the platinum f i l m . The rods are separated by 5/8 of the sensor length and the prongs average 11 mm. i n length (compared with 7.5 mm. f o r the Disa 55A32 X-probe). Two a d d i t i o n a l features should decrease prong e f f e c t s . F i r s t , the arching structure of the two longer prongs w i l l tend to reduce flow displacement upstream. Secondly, the hot sensing elements are not attached d i r e c t l y to the prongs. The gold-plated glass rod between the prong t i p and the sensing segment w i l l sharply reduce the heat conducted 34. VIEW OF PROBE (8 x FULL SIZE) Quartz rod length = 0.065 ins. Quartz rod diameter = 0.002 ins. Spacing between sensors = 0.025 ins. Diameter of prong tip = 0.0045 ins. Sensing length - 0.040 ins. 0.025 ins. CONVENTIONAL THERMO-SYSTEMS 1241-20 PROBE USED IN EXPERIMENTS Fig. 10 35. to the prong tip compared to the Disa 55A32 probe where the hot-wires are directly welded to the prong tips. The wakes from the prong tips should not produce any. thermal effects. Experiments were conducted with the Thermo-Systems probe to determine the response of both cylindrical hot-films to v and w fluctuations. The results are shown in Figures 11 and 12. The v-response, expecially for film No. 2, i s quite like that predicted by the derivation in section 4.4. It i s s t r i c t l y positive and concave upwards. The w-response is very nearly linear as expected. The highest ratio of v- sensitivity to w-sensitivity (the case of film No. 1 and negative 8) i s 0.12 (compared with 0.34 for the Disa 55A32 probe). Except for film No. 1 and 8 between 0 and -6°, the sensitivity ratio i s equal to or smaller than that predicted by equation (4-9). The Thermo-Systerns 1241-20 X-type hot-film 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. o O -r- G + — i — •5 -4 •3 •2 ••1 E ( ^ ) - E ( 0 ) - a u • (mv.) o W i r e no. 1 + W i r e no. 2 o o + -©- -h -10 -8 -6 -4 -2 0 4 8 F i g . 11 v-Response of Thermo-Systems 1241-20 X-Probe -2 G 2 Q O -10 -20 -30 -40 -50 o W i r e no.1 -60  +  W i r e no.2 6 8 F i g . 12 w-Response of Thermo-Systems 1241-20 X-Probe 38. CHAPTER V. CONSEQUENCES OF THE INTERFERENCE PROBLEMS — 5.1 On Spectral Analysis In the analysis that l e d to the hot-^wire s p e c t r a l estimates i n Table I, the hot-wires were assumed to have the instantaneous responses given by equations (2-11) and (2-13). I.e., e^ = a j U + b j W and e2 = a 2 u ~ b 2 w * The s p e c t r a l analysis system solved t h i s p a i r of simultaneous equations f or u and w at every d i g i t i z e d data point and then computed the spectra and co-spectra.as described by Garrett (1970). In order to s i m p l i f y the following d e r i v a t i o n , assume normal component cooling with angles of i n c l i n a t i o n 8^ and 82 both 45°. Then a^ •» b^ and = b2« Assume further that the wire responses are i d e n t i c a l so that a^ = a2« Then e^ = a^ (u + w) and Therefore e 2 ** ai (u + w) . u = (e1 + e 2 ) / 2 a 1 , w = (ej^ - e 2 ) / 2 a 1 , 39. (el + e ^ M a 2 , (5-1) w^= (e L - e2)<74a2 (5-2) and uw = (e L + e 2) (e L - e 2) /4a 2 . (5-3) However, the wires of the Disa 55A32 X-probe have a significant response to v fluctuations. As a f i r s t approximation, this response w i l l be taken as linear so that e^ = a^u + b j W + c^v and e2 = a 2 U " b 2 W ~ C 2 V * Figure 8 indicates that the response to v is very nearly linear for |B|<4°. Making the same assumptions as before and taking c^/bj a c2^2 ~ - their values were observed in the experiment to be 0.31 and 0.34 in section 4.4 - the response equations become e x = a x (u + w + 0.32 v) and In this case, and e 2 = a^ (u - w - 0.32 v) . e^ + e_, = 2 a ^ e L - e 2 - 2a 1 (w + 0.32 v) so that _T___/4a 2 = u 2 ^ ( 5 _ 4 ) 40. ( e L - e 2)<74a 2 = w2" + 0.64 vw + 0.10 v 2" (5-5) and (e^ + e 2 ) ( e x - e 2 ) / 4 a 2 = uw + 0.32 uv . (5-6) Comparing equations (5-1), (5-2) and (5-3) with equations (5-4), (5-5) and (5-6) r e s p e c t i v e l y gives (as f i r s t approximations to the so r t of err o r s introducted by the anomalous X-wire responses) 2 2 V  =  V w, 2 = w 2 + 0.64 v w + 0.10 v 2 (5-7) h s s s s and u^w^ = u^w +0.32 u v s s s s where the subscripts h and s have the same i n t e r p r e t a t i o n as i n Table I. Because of 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 over the ocean, v w and u v are expected to be small. s s s s . Therefore the major e r r o r introduced i n the hot-wire s p e c t r a l estimates i s the 0.10 v 2 term i n w, 2 . Note also that s h v w, = v w + 0.32 v 2 . (5-8) s h s s s Table I I shows how the measured values of w, 2 and v w, are i n h s h much better agreement with the values c a l c u l a t e d from the right-hand sides of equations (5-7) and (5-8) than with w 2 and v w r e s p e c t i v e l y . s s s No s p e c i a l s i g n i f i c a n c e should be placed on the disagreement that s t i l l e x i s t s between the measured and cal c u l a t e d values because of the many assumptions that were made i n der i v i n g equations (5-7) and (5-8) and because 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. f (sec - 1) w 2 (m/sec)2 s w 2(meas.) (m/sec)2  n w^ 2(calc.) (m/sec)2 v w (m/sec)2 s s vgw^(meas.) ..(m/sec)2 v w, (calc.) (m/sec)2 s n 5.19x10"2 4.94xl0 - 2 1.41x10"1 9.70xl0 - 2 6.85xl0 - 3 2.04x10"1 1.45x10"1 1.16x10"1 3.48xl0~2 5.34xl0 - 2 4.96xl0"2 5.68xl0 _ , + 6.18x10"2 4.66xl0"2 1.77X10"1 3.33xl0"2 5.19xl0"2 4.69xl0"2 5.61x10"3 5.13xl0"2 3.75xl0~2 TABLE II: Comparison of Calculated and Measured Spectral Estimates 5.2 On the Results of Other Workers Although the Disa 55A32 X-wire probe had not been used by the Institute of Oceanography at the University of British Columbia prior to the present work, i t has been widely used elsewhere in the study of boundary layers, mixing regions, jets, etc. where i t has been necessary to measure the downstream and one-cross stream component of the velocity flucutuation. It i s clear that a l l measurements, regardless of whether the turbulence intensity i s low or not, made with this type of probe are now suspect. In particular, measurements of shear stress and energies in the transverse component of the fluctuation in the plane of the X-array w i l l be over-estimated. Furthermore, many experimenters neglect to describe the probe they use and this, in the light of the present findings, becomes a meaningful omission. 42. CHAPTER VI. DENOUEMENT D.E. Guitton and R.P. P a t e l (Jerome, Guitton and P a t e l , 1971) have c a r r i e d the type of research described i n t h i s t hesis f u r t h e r to 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 of the Disa 55A32 X-wire probe on the Reynold's number of the flow. Their data are i n e x c e l l e n t agreement with an expression they derived, i . e . , • v - s e n s i t i v i t y g R e - l . l ( 1 + 1 > 3 1 ^ 0 . ^ - . , w - s e n s i t i v i t y Translated i n t o wind speed dependence, the r a t i o was about unity at 2 m/sec decreasing to about 0.1 at 20 m/sec. As a r e s u l t of problems with the Disa 55A32 X-wire probe that were demonstrated by Jerome, Guitton and P a t e l (1971), Disa E l e c t r o n i k A/S modified t h e i r three types of X-wire probes (types 55A32, 55A38 and 55A39) by increasing the separation of the wires to 1 mm. ( i . e . , about one wire length). The s p e c i a l information note with which DISA introduced the modified probes i s reproduced i n the Appendix. 43. BIBLIOGRAPHY Champagne, F. H., C. A. Sl e l c h e r and 0. H. Wehrmann, 1967: Turbulence Measurements with Inclined Hot-Wires. J . F l u i d Mech., 28, Part I. C o l l i s , D. C. and M. J . Williams, 1959: Two-Dimensional Convection from Heated Wires at Low Reynolds Numbers. J . F l u i d Mech., 6_, page 357. Corrs i n , S., 1963. Encyclopedia of Physics, V ol. VIII/2, B e r l i n , Springer-Verlag 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 Information No. 7, page 19. Eyre, D., 1967: End Conduction and Angle of Incidence E f f e c t s i n Single Hot-Wire Anemometer Probes. IRG Report 1521 (W), United Kingdom Atomic Energy Authority. Garrett, J . F., 1970: F i e l d Observations of Frequency Domain S t a t i s t i c s and Nonlinear 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 of B r i t i s h Columbia. Gilmore, D. C., 1967: The Probe Interference E f f e c t of Hot- Wire 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 , Montreal. Hinze, J . 0., 1959: Turbulence. New York, McGraw-Hill, 586 pp. Hoole, B. J . , and J . R. Calvert, 1967: The Use of a Hot-Wire Anemometer i n Turbulent Flow. J . of Royal Aero, S o c , 71, page 213. Jerome, F. E., D. E. Guitton and R. P. P a t e l , 1971: Experimental Study of Thermal Wake Interference Between Closely Spaced Wires of an X-type Hot-Wire Probe. Aero. Quart., 22̂ , page 119. King, L. V., 1914: On the Convection of Heat From Small Cylinders i n a Stream of F l u i d . Proc. Roy. S o c , (London), 214A, page 373. Mitsuta, Y., 1966: Sonic Anemometer-Thermometer f o r General 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 at High Subsonic Speeds. DISA Information No. 5, page 5. 44. Pond, S. , 1965: Turbulence Spectra i n the Atmospheric Boundary Layer Over the Sea. I n s t i t u t e of Oceanography, U n i v e r s i t y of B r i t i s h Columbia, Report No. 19. Webster, C.A.G., 1962: A Note on the S e n s i t i v i t y to Yaw of a Hot-Wire Anemometer. J . F l u i d Mech., 13, page 307. Weiler, H. S., 1966: D i r e c t Measurements of Stress and Spectra of Turbulence i n the Boundary Layer 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 ype Ho t -w i r e P robe s • S p e c i a l I n f o r m a t i o n Fig. 1. I N T R O D U C T I O N X - t y p e h o t - w i r e p r o b e s w i t h t h e i r t w o wires a l m o s t in t h e s a m e p l a n e are q u i t e sensit ive t o m o v e m e n t s o f t h e v e l o c i - 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 t h e h o t w a k e p r o d u c e d b y t h e u p s t r e a m w i r e t o affect p o r - t i o n s o f t h e d o w n s t r e a m w i r e , r e d u c i n g t h e e l e c t r i c a l p o w e r r e q u i r e d t o k e e p 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 - v e s t i g a t i o n s o f t h e b e h a v i o r o f c o n v e n t i o n a l D I S A X - p r o b e s , w h e r e t h e t w o w i r e s are o n l y 0.2 m m a p a r t , s h o w e d these 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 to 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 , t h i s s e n s i t i v i t y c a n c e l s o u t at R e > 10. T H E I M P O R T A N C E O F P I T C H S E N S I T I V I T Y I N A N A L Y S I S O F T U R B U L E N C E D A T A 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 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 E = E(U, 0, a) (1) w h e r e 9 a n d tt are t h e p i t c h a n d y a w angles, r e s p e c t i v e l y (see also F i g . 1). For s m a l l c h a n g e s d E = ^ 8v or 8E d U + ^ da + f £ dfl 8a 80 e = ( 8V ) u + ( — - — ) v + ( — TT; ) W U 8a u 8U i (2) (3) w h e r e the b r a c k e t e d t e r m s are the s e n s i t i v i t y c o e f f i c i e n t s . 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 c = a u + b v + c w (4) T a k i n g i n t o a c c o u n t t h e s e n s i t i v i t y c o e f f i c i e n t s i n t h e c v a l u a - t i o n o f v f r o m (e 1  - e 2 ) , w h e r e a n d e 2 are t h e i n - s t a n t a n e o u s signals f r o m t h e t w o w i r e s , t h e r e l a t i o n b e t w e e n m e a s u r e d a n d a c t u a l v 2 in a t w o - d i m e n s i o n a l f l o w is v 2 = v 2 ( i + -A 4 d - ) meas act 4 b v2 (5) 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 aver- 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 signals (ej + c 2 ) ( C j - e 2 ) the e q u a t i o n b e t w e e n m e a s u r e d a n d a c t u a l u v is uv = u v (1 mcas act c v l w l (6) 2 a u v 4 ab u v T h e i m p o r t a n c e o f t h e s e n s i t i v i t y t o p i t c h c a n b e e x p r e s s e d b y d e t e r m i n i n g t h e r a t i o s — a n d . a D F o r n o n l i n e a r r e s p o n s e E 2 = A + . B ( U ) n (7) t h e s e n s i t i v i t y c o e f f i c i e n t s a a n d b are a = - 1 - n B ( U ) n ' 1 2 E (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 study of the 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). 1.6 1.4 1.2 1.0 _ _. Q8 0.6 0.4 Q2 0.0 0 e = au + bv + cw • - Present investigation 9 - (Approximate) U.B.C. result 10 12 14 Re _ Ud a9 6.8 o > CM LU 6.7 6.6 o - upstream wire cold 1̂  _ , (  ^ • - upstream wire hot j 12 16 20 0 Degrees 24 28 Fig. 2. Ratio of pitch to yaw sensitivity for conventional X-wires vs. Reynolds number. Fig. 3. Pitch response of modified X-toire probe with end •without a thermal wake. and a c o t a ( 9 ) i f 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 o r d e r , a r e . n e g l e c t e d . T h e v a l u e o f c is 1 SE U se ( 1 0 ) 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 , c a n b e o b - t a i n e d b y m e a s u r i n g t h e s l o p e s o f t h e A E v e r s u s 0 p l o t s at 0 = 0. C O N V E N T I O N A L D I S A X - T Y P E P R O B E S E x p e r i m e n t s c a r r i e d o u t b y J e r o m e , G u i t t o n a n d P a t e l ( 1 9 6 9 ) h a v e s h o w n t h a t t h e r a t i o o f t h e s t a t i c p i t c h s e n - s i t i v i t y t o y a w s e n s i t i v i t y ( c / b ) varies s t r o n g l y w i t h t h e R e y n o l d s n u m b e r . In t h e range o f R e f r o m 1 t o 10 t h e r a t i o n ( c / b ) d e c r e a s e s f r o m a p p r o x . 1 to 0.1 e x p l a i n e d p a r t - l y b y t h e d e p e n d e n c e o f t h e y a w s e n s i t i v i t y b o n R e a n d p a r t l y b y t h e w i d t h o f t h e t h e r m a l w a k e b e i n g p r o p o r t i o n a l -1 /2 t o R e . T h e d y n a m i c p i t c h s e n s i t i v i t y , w h i c h m i g h t e x i s t f o r m e a s u r e m e n t s in a t u r b u l e n t f l o w , a p p e a r s t o b e s i m i l a r t o t h a t t a k e n f r o m a s t a t i c c a l i b r a t i o n . N E W D I S A X - T Y P E P R O B E S B y m o v i n g t h e wires a p a r t b y a p p r o x . o n e w i r e l e n g t h i n t h e d i r e c t i o n p e r p e n d i c u l a r t o t h e p l a n e o f t h e X , J e r o m e , G u i t t o n , a n d P a t e l o b s e r v e d n o w a k e i n t e r f e r e n c e . O n a basis o f these results DISA has i m p r o v e d t h e d e s i g n o f its X - p r o b e s b y i n c r e a s i n g t h e d i s t a n c e b e t w e e n t h e w i r e s t o 1.0 m m i n s t e a d o f t h e present 0.2 m m . T h e s e m o d i f i c a t i o n s i n c l u d e p r o b e t y p e s 5 5 A 3 2 , 5 5 A 3 8 a n d 5 5 A 3 9 . T y p e n u m b e r s w i l l n o t b e c h a n g e d . In o r d e r t o d i s - t i n g u i s h b e t w e e n the n e w t y p e s w i t h w i d e l y s p a c e d w i r e s a n d t h e c o n v e n t i o n a l t y p e s , al l 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 c o d e , 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 1 9 6 9 . ( C o n v e n t i o n a l X - p r o b e s h a d t y p e n u m b e r s e n g r a v e d o n t h e p r o b e b o d y . ) 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: 5 5 A 3 2 : r e d 5 5 A 3 8 : r e d 5 5 A 3 9 : r e d o r g a n g e - r e d o r a n g e - g r e y o r a n g e - w h i t e r e a d f r o m t h e s e n s o r e n d DISA ELEKTRON IK A/S . DK 2730 H E R L E V . D E N M A R K Telephone: Copenhagen (01) 94 52 11 . Telegrams: DISAW0RKS. Copenhagen . Telex: 5849 Printed in D e n m a r k by D I S A , February 1970

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