An improved method for measuring velocity and ... - Springer Link

Experiments in Fluids 22 (1996) 174—182 ( Springer-Verlag 1996

An improved method for measuring velocity and concentration by thermo-anemometry in turbulent helium-air mixtures J.-L. Harion, M. Favre-Marinet, B. Camano

174 Abstract A hot wire/film probe is used with new operating conditions for measurements of velocity and concentration in helium/air mixtures. With the upstream wire much more overheated than the downstream film, the sensing elements behave almost independently and the calibration map is composed of clearly distinct iso-velocity and iso-concentration curves. This behaviour is largely explained by the difference in the heated elements’ diameters. Tests of the probe in a turbulent boundary layer with large density variations indicate very satisfactory measurements. The domain of use for the probe is considerably extended with these new operating conditions.

List of symbols a c d e E k Kn L l Pe Nu R

overheat ratio mass fraction of helium sensing element diameter injection slot width anemometer voltage mixture thermal conductivity Knudsen number, (\l/d) length of a sensing element mean free path of gas molecules Peclet number Nusselt number electrical resistance of a sensing element

Re h u q U T x X y y` a a !# h m l D U ( ) f ( ) */+ ( ) w ( ) g ( )` ( )@ ( ) =

momentum thickness Reynolds number, (\U h/l ) = w friction velocity upstream fluid velocity temperature distance from the injection slot molar fraction of air distance to the wall distance to the wall in wall units, (\yu /l ) q w mixture thermal diffusivity accommodation factor boundary layer momentum thickness lengthscale of the wire thermal field in the upstream direction mixture kinematic viscosity distance between sensing elements heat flux exchanged by a sensing element relative to the film relative to injection relative to the wire relative to the gas inner variables turbulent fluctuation relative to external flow

1 Introduction Received: 8 January 1996 /Accepted: 29 May 1996 J. -L. Harion Laboratoire d’Energe´ tique Industrielle, Ecole Nationale Supe´ rieure des Mines de Douai, 941 rue Charles Bourseul, B.P. 838, F-59508 Douai Cedex, France M. Favre-Marinet Laboratoire des Ecoulements Ge´ ophysiques et Industriels, Institut de Me´ canique de Grenoble, B.P. 53X, F-38041 Grenoble Cedex, France, INPG, UJF, CNRS B. Camano Instituto de Pesquisas Hidraulicas, Universidade Federal de Rio Grande do Sul Porto Alegre, Brasil Correspondence to: M. Favre-Marinet The authors gratefully acknowledge financial support from the HERMES R&D Program through the Centre d’Etudes Spatiales and Dassault-Aviation

Variable density turbulent flows are present in many industrial or environmental applications and they have been therefore an active research subject during the last decades (see for example, Pitts 1991a, b; Chassaing et al. 1994). Helium—air flows have been especially studied, because these gases are very convenient for generating large density differences in low speed flows. However, measuring simultaneously velocity and concentration in such flows of gas mixtures is a very challenging problem and requires special instrumentation. Combined hot wire/hot film probes have significant advantages (e.g., low cost, good time response) over other techniques, but must be specially adapted for these types of flows. Measurements of density may be performed by aspirating probes, first developed by Zawacki and Weinstein (1968) and later on by Brown and Rebollo (1972) to study the inhomogeneous turbulent mixing layer. In this technique, a hotwire placed inside a thin tube is exposed to a mixture flow extracted from the measurement point. When the probe is operated at sonic conditions, the hot-wire is sensitive only to density variations. This instrumentation has been

successfully used in free turbulent flows of gas mixtures but is not well suited to wall flows due to the large size of the probe. Moreover, it is not possible to combine a hot-wire with an aspirating probe in order to measure simultaneously density and velocity fluctuations because a minimum distance (+2 mm) between the two probes is required to ensure that the velocity field near the hot-wire is not perturbed by the aspirating probe. In most practical laboratory conditions, density and velocity fluctuations are uncorrelated over such a distance and the measurement of joint statistical quantities of these two variables is impossible with this arrangement. Way and Libby (1970, referenced WL hereafter) proposed for the first time a technique based on a hot wire—film combination aimed at measuring velocity and concentration simultaneously. Their probe consisted of two heated elements very close to each other (typically 25 lm). WL have shown that flow velocity and concentration are unambiguously determined from the hot wire—film responses if the overheat ratios of the two sensing elements and their relative distance are carefully chosen so that the associated thermal fields interfere. However, they found a lack of accuracy for low velocities and high concentrations of helium. Way and Libby (1971) successfully performed measurements with this probe in a turbulent helium—air jet, for mass fractions of helium, c, less than 0.3. Stanford and Libby (1974) extended this technique by using a three sensor probe for measurements of two velocity components and concentration. A similar probe was used by LaRue and Libby (1977, 1980) to study the turbulent boundary layer with slot injection of helium. More recently, Sirivat and Warhaft (1982) and later, Panchapakesan and Lumley (1993) used interference probes consisting of almost parallel hot wires very close to each other (5 lm). Detailed turbulence measurements in the far field of helium jets (c\0.06) were reported by these latter authors. Most of the previous studies are restricted to a limited range of concentration of helium and the lack of accuracy when operating an interfering probe out of this range may be a serious drawback to the investigation of flows where mixing occurs between pure helium and pure air. We have undertaken a research project on the effects of large density gradients on turbulent transport properties (Harion 1994). In most experiments, density differences were generated by injecting helium into air, which required measurements over a very large range of c. Accordingly, the use of a WL-type probe was not appropriate for these studies. The purpose of the present paper is to analyze the principles of a hot wire/film probe and to examine its behaviour for various configurations of overheat ratios with the aim of improving measurement accuracy over a large range of velocity and concentration.

2 The interfering probe Classical thermo-anemometry considers the response E of a single hot-wire placed in a low-speed uniform flow of given composition as a function of the probe geometry, the flow velocity U, the overheat ratio a (or the wire temperature T ), w the fluid temperature T and the fluid physical properties. In g usual applications, heat transfer is governed by convection between the wire and the fluid. As a result, the probe response

follows King’s law (n+0.45):

E2\A(X )]B(X )U n

(1)

where in a mixture the coefficients A and B depend on the molar fraction X of a component (in the present paper, X denotes the molar fraction of air in helium/air mixture) and on the wire and fluid temperatures. By using a single hot-wire at two successive different overheat ratios a and a for the 1 2 same flow conditions, it would seem possible at first glance to deconvolute U and X from the two corresponding hot-wire responses E and E . This method was successfully used by a1 a2 Chassaing (1977) in CO —air mixtures, because the sensitivity 2 to the concentration is reduced to zero for an overheat ratio of 1.4. On the contrary, it has been verified that the calibration curves obtained in helium/air flows for several values of X overlap in the plane (E , E ) and that it is quite impossible a1 a2 to separate the effects of U and X in the probe response. A similar observation was made by WL when the sensing elements of their hot-wire/film probe were separated by too a large distance from each other (1.3 mm, see Fig. 3 of their paper). It is therefore necessary to use a special instrumentation in helium/air flows. The interfering probe used in the present study is similar to that of WL and takes advantage of the same principles. It consists of two orthogonal sensing elements determining a plane perpendicular to the flow direction (Fig. 1). A thin wire of 2.5 lm diameter (6 lm in some experiments) is placed upstream of a film sensor of much larger diameter (d +70 lm). These two heated elements are separated by f such a small distance (D+25 lm) that the associated thermal fields interfere under certain conditions. The length L of both sensing elements is 500 lm. The body of the probe is aligned with the flow direction (x-axis). WL used a similar probe with the film temperature T much f larger than the wire temperature T . In this case, the influence w of the wire on the film response is small because the heat transfer from the film to the fluid is only slightly reduced due to the hot wake of the wire. On the contrary, the heat exchanged by the wire is related to its overheat ratio a but also w to the local thermal field, which can be largely affected by the downstream film overheat ratio a . More precisely, the temperf ature field associated with the film overheating extends in the upstream direction over a length m determined, as a first approximation, by the balance between longitudinal convection and diffusion, when radiation effects are neglected:

T [T T [T g\a f g U f m m2

a so that m+ U

(2)

where a, the fluid thermal diffusivity, is dependent on the molar fraction X. For the present geometry, the lengthscale m is then given approximately by

m a d 3 f+ + D Ud D Pe f

(3)

where

Pe\Ud /a f For the experimental conditions of interest in this study, the flow in the vicinity of the film evolves between two extreme

175

Fig. 1. Sketch of the film/wire probe

176 regimes: (i) moderately high-speed flow of pure air (U\15 m/s, Pe\17.5) (ii) low-speed flow of pure helium (U\0.5 m/s, Pe\0.08) Note that the Peclet number varies by a factor greater than 200 between these two cases. For the first conditions, m/D is quite small and interference effects are expected to be very weak, whereas in the second case, m/D is very large and the upstream wire is completely embedded in the film’s thermal field. In this latter case and for intermediate regimes, reduction of the heat flux from the wire is strongly dependent on these interference effects and consequently, the wire response depends on the flow regime and on the temperatures T and T chosen for f w the experiments. Different sets of (T , T ) pairs lead to very f w different (E , E ) calibration maps. f w The probe was calibrated in the potential core of a round jet (diameter 25 mm, velocity U ) of helium/air mixture at ambient temperature T . The flow rate and composition of g mixture were controlled by sets of sonic throat orifices of different sizes placed upstream of the settling chamber. Figure 2a shows a calibration map obtained with the film substantially more overheated than the wire (T \300 °C, T \75 °C). For f w a wide range of flow conditions, the iso-concentration and iso-velocity curves are clearly distinct and the calibration data can be used to deconvolute U and X from the voltages (E , E ). f w However, the high value of T leads to fluid temperatures in the f vicinity of the wire close to or even larger than T for low X-low w speed flows (small Pe). The heat transfer is then from the fluid to the wire and E goes to zero for these conditions. On the w other hand, the calibration map tends towards the result for a single hot-wire (overlap of iso-concentration curves) for high X-high speed flows (large Pe) and accuracy is reduced for these flow conditions. The choice of the two operating overheat ratios is very delicate: an increase of the difference T [T gives rise to f w enhancement of the first effect and a reduction of the second. The inverse holds true for a decrease of T [T . A good f w compromise was obtained after many trials using T \200 °C f and T \100 °C (Fig. 2b). The iso-concentration curves are w then satisfactorily separated, except in the extreme lower right part of the map, where accuracy is likely to be poor. The probe operated in the above conditions results in thermal interference between the heated elements, leading to extreme sensitivity of the calibration map to the distance D between elements. This is a major drawback for practical use of the probe. Consequently, the same probe has been used with a quite different choice of overheats.

Fig. 2a, b. Interference probe calibration data: d +2.5 lm, w d +70 lm, D+25 lm. a T \75 °C, T \300 °C; b T \100 °C, f w f w T \200 °C; m X \0; j, 0.1; ], 0.2; W, 0.4; K, 0.6; d, 0.8; 3, 1. f !*3 Dashed lines denote iso-velocity contours

3 A new method of using the hot wire/film probe A new set of overheat conditions was used for the present work (Harion et al. 1995) in which the upstream wire is the hottest element. Figure 3 shows the calibration map obtained for T \100 °C and T \250 °C. In this case, the iso-concentration f w curves are clearly distinct and are linear over the whole Xrange. This behavior persists up to the highest velocities and provides the possibility of measurements over a very large range of velocity and concentration. Although the flow and heat transfer problem is quite complex, a simplified analysis of the probe response may be made by neglecting the interference effects between the two sensing elements. With this assumption, the heat flux U exi changed by the hot-wire/film of length L (i\w or f ) and i electrical resistance R may be written: i

E2 U \ i \Nu nk(X )L (T [T ) i R i i i g i

(4)

where k is the mixture thermal conductivity. It is well known that non-continuum effects can affect dramatically heat transfer near a wall, especially for helium flows (see for example Pitts and McCaffrey 1986), resulting in

177

Fig. 3. Double probe calibration data: d +6 lm, d +70 lm, w f D+25 lm, T \250 °C, T \100 °C; same symbols as in Fig. 2 w f

an effective Nusselt number, Nu, different from the continuum value, Nu . These effects may be taken into account by using c the Knudsen number, Kn and a thermal accommodation factor, a to obtain a relationship between Nu and Nu . !# c Knowing Kn and a , it would then be possible to derive Nu !# from Nu , which satisfies a classical heat transfer law of the c form: Nu \A]BRen, the constants A and B being independent c of X. Andrews et al. (1972) pointed out, however, the wide disagreement on the value a , which is found in the literature, !# for given flow conditions. Moreover, the velocity field near the wire is strongly influenced by the large-diameter downstream film. Determining the effective Nusselt number from King’s law for both sensing elements is a very challenging problem even without thermal interference effects. Consequently the heat transfer laws were determined experimentally by heating successively the wire or the film alone. The resulting Nusselt number behavior shown on Fig. 4 follows a power-law with molar fraction-dependent coefficients:

Nu \A (X )]B (X ) Ren i i i i

Fig. 4. Experimental Nusselt number for the wire and film without thermal interference effects. Same conditions as in Fig. 3; same symbols as in Fig. 2

(5)

It is worth noting that the Nu for a given velocity is signifw icantly lower than Nu because velocities near the wire are f strongly reduced by the presence of the downstream large diameter fiber and also because slip effects are more important on the wire. Eliminating the velocity U from the Eq. (5) written for i\w and f results in the equation for the iso-concentration curves:

E2\m(X )E2 ]p(X ) w f

(6)

with

AB

B R (T [T ) L d 0.45 f g f f m(X )\ f (X ) f B R (T [T ) L d g w w w w w A B d 0.45 f p(X )\A R nk(X )L (T [T ) 1[ w f f f f f g A B d f w w

A

AB B

A similar equation was established by WL, who noted that p(X ) is a sensitive function of concentration and that the E2 -factor is almost independent of X. The present calibration w gives essentially the same result (Fig. 3). The above calculation

shows that without thermal interference effects, the isoconcentration curves are nearly parallel straight lines in the plane E2 , E2 , shifted from each other by the effect of f w concentration. It also demonstrates the influence of the film to wire diameter ratio. When the sensing elements have the same diameter, A /A and B /B tend to one, p(X ) tends to zero and w f f w all the iso-concentration curves collapse on to a single straight line. This explains the result obtained with a single hot-wire operated at two successive different overheat ratios. On the contrary, the voltage shift between two iso-concentration curves increases with increasing diameter ratio. The good qualitative agreement between the contours of constant concentration obtained by heating both sensing elements and the tendencies shown by Eq. (6) suggests that interference effects are of secondary importance with this overheat configuration. In this method, the influence of the wire thermal wake plays a minor role in the probe response and the primary effect is due to the difference in the two sensors diameters.

178

Fig. 5a–c. Influence of overheat ratios on the shape of the wire/film calibration map. a without interference; b with strong influence of the upstream wire on the film; c with strong influence of the downstream film on the wire

Figure 5 summarizes in a qualitative way the variation of calibration map when the operating overheating of the sensing elements is varied. Increasing the wire temperature leads to a curvature of the iso-concentration for low velocities (Fig. 5b), indicating a stronger influence of the hot wire on the downstream film. Inversion of the sign of T [T gives rise to f w a strong reduction in the front hot-wire’s response for a flow of helium and accordingly the relative position of the iso-concentration is completely inverted compared to the preceding case (Fig. 5c). Moreover, in this last case, interference effects are of primary importance in the probe response and the iso-concentration curves are strongly distorted in the lowconcentration-low velocity domain.

4 Data reduction and test of probe accuracy 4.1 Data reduction Following the method of Panchapakesan and Lumley (1993), a linear transformation of coordinates (E , E [E* , E* ) was w f w f applied to calibration data in order to obtain an almost rectangular domain. Using axes defined by vectors such as &" &" P P , P P (Fig. 6) results in a map more convenient than the 1 2 1 3 original one for generating a Cartesian grid with good accuracy. A look-up table was built using standard techniques (Lueptow et al. 1988; Stanford and Libby 1974; Way and Libby 1971). Several interpolation schemes were tried in the different steps of the data reduction and tested on the calibration data themselves. From each voltage pair E , E , differences DU, DX w f were computed between the original velocity/concentration values and the corresponding ones deduced from the look-up table. The best result was obtained with interpolation by cubic spline functions, for which the r.m.s errors pD , pD were about U X 0.9 cm/s and 0.0009 respectively. An even better result was

Fig. 6a, b. Calibration data. a Domain (E , E ); b domain transw f formed by a linear change of coordinates (E * , E * ); same symbols as w f in Fig. 2

achieved using a neural network method (Harion et al. 1994): pD +0.5 cm/s, pD +0.0004. U X The probe was used in a wind-tunnel designed for studying turbulent boundary layers with large density gradients (Harion 1994). The density differences were generated by injecting different air—helium mixtures parallel to the wall in a way similar to that of LaRue and Libby (Fig. 7; for more details, see Riva et al. 1994). The injection slot (width e\3 mm, spanwise length 300 mm) was located at a distance of 577 mm from the leading edge of the upper plate. The double probe was positioned in the boundary layer, the wire being aligned in the spanwise direction and the film in the transverse direction.

4.2 Mean velocity measurements The probe was first tested in the turbulent boundary layer developing on the upper plate of the working section for two values of the external velocity (U \5.8 m/s; 11.6 m/s) and for = constant molar fraction (X \0.8). The corresponding values = of the Reynolds number Re based on momentum thickness h were respectively 800 and 1140. Measurements were performed in the section defined by x\1 mm, so as to approach very closely the plane of the wall. Only the upper parts of the

Fig. 7. Sketch of the boundary layer with density differences

profiles (y[e) are considered. The mean velocity-profiles are normalized by the friction velocity u deduced from adjustq ment of the universal log-law of the wall, whereas y` is computed using the distance to the upper plate: y`\(y[e)u /l. The sensing length of the film (L\500 lm) is q about 9 in wall units for Re \800 and the spatial resolution of h the probe may affect the measurements very near the wall, nevertheless the present results are in very good agreement with those obtained with a single hot-wire in air flow generated with the same conditions (Fig. 8). The quasi-absence of a logarithmic region in Fig. 8a seems to indicate that the boundary layer has not reached an asymptotic state at the end of the plate for the case of the lowest external velocity. Figure 8b shows close agreement with results obtained by Purtell et al. (1981) for a slightly greater value of Re . The shape factor and h friction coefficient deduced from these measurements agree within 7—10% with classical results (White 1974).

4.3 Mean density measurements As is shown in Fig. 7, injection of helium into an external flow of a mixture rich in air gives rise to a mixing layer embedded in the much larger boundary layer issuing from the upper plate. The injection bulk velocity U was 2 m/s. Mean density as */+ given by the double probe was found to be in close agreement with the results obtained with an aspirating probe (sonic throat diameter\100 lm) at various downstream stations. For example, at a distance from the injection slot where density differences are very large (x\25 mm, x/e\8.3), the corresponding mean density profiles match quite well (Fig. 9). It is worth emphasizing that the two probes operate by quite different principles, which allows reasonable confidence in the present measurements. Figure 9 also shows that the different reduction schemes give only small variations in the resulting mean density.

179

Fig. 8a, b. Semi-logarithmic plot of mean velocity profiles in the homogeneous region (x\1 mm, X \0.8). a U \5.8 m/s, Re \800; = = h n, single hot-wire; ], double probe, T \250 °C, T \100 °C; —— w f Re \465, Purtell et al. (1981); b U \11.6 m/s; ], Re \1140 double h = h probe; —— Re \1340, Purtell et al; - - - - 5.62 log y`]5 h

4.4 Probe time-response The dynamic behavior of the double probe was first tested in the homogeneous flow of Sect. 4.2 (X\0.8). At x\1 mm, the rms fluctuations of velocity compare well with the results of Purtell et al. (Fig. 10). It should be noted that the results obtained with the probe in the interference mode (T \175 °C, f T \75 °C) are significantly overestimated, especially near w y`+100 (Fig. 10a). This may be due to the shape of the calibration map and to the method of polynomial interpolation used for data reduction in this case. For the case of the highest Re , the double probe used with the new overheat configurah tion seems to underestimate the r.m.s velocity fluctuations (Fig. 10b). This point will be discussed below.

Fig. 9. Mean density profiles at x/e\8.3, U \5.8 m/s, X \0.8, = = injection of helium at U \2 m/s: K, aspirating probe; double */+ probe: ] linear interpolation, ] polynomial regression, L neural network

180

Fig. 11. Distribution of r.m.s density fluctuations at x\1 mm: ] double probe, T \250 °C, T \100 °C, d interfering probe, w f T \75 °C, T \175 °C, L LaRue and Libby (1977) w f

Fig. 12. Hot-wire/film voltage spectra in the homogeneous region: T \250 °C, T \100 °C, x\[10 mm, y/d\0.24 (d: overall boundary w f layer thickness), U \11.6 m/s, X \0.8 = = Fig. 10a, b. R.m.s velocity profiles in inner variables in the homogeneous region (x\1 mm). a U \5.8 m/s; ], double probe, = T \250 °C, T \100 °C, Re \800; ], interfering probe, T \75 °C, w f h w T \175 °C, Re \680; b U \11.6 m/s; K, double probe, Re \1140; f h = h Purtell et al. (1981) —, Re \465, 1340 h

Figure 11 shows that the measurements of density fluctuations are affected by a bias effect in the homogeneous flow region (x/e\0.33, y/e[1.3). Hence, the probe gives an apparent intensity of o@ (+2%), which increases with turbulent intensity as the wall is approached. This seems to be due to the larger time-response of the film, as is shown by spectra of the voltages (E , E ) in Fig. 12. The film voltage f w spectrum deviates from the wire’s counterpart for frequencies higher than 100 Hz. The reduction reaches 3 dBR at 250 Hz. When the probe is exposed to high frequency velocity fluctuations in the homogeneous flow, the variations of E are f then lower than expected whereas E is not affected by such w reduction. Data points are consequently scattered around the iso-concentration curve X\0.8, resulting in erroneous density

fluctuations. The corresponding density spectrum (Fig. 13a) shows that density fluctuations are mainly overestimated for frequencies in the range [60 —500 Hz]. The behavior of the velocity spectrum (Fig. 13b) seems little affected by the large film time-response, however reduction of E -variations should f result in a related reduction of velocity fluctuations. This may explain why Ju@2/u is underestimated in the case of the q highest Re , which corresponds to energy containing struch tures of higher frequency than in the other case. The reduction Ju@2/u may also be due to the spatial resolution of q the probe, which integrates the velocity fluctuations over the length of the sensing elements (L`+17 in this case). It is worth noting that the same bias effect occurs when using the probe in the interference mode (T \175 °C, T \75 °C, Fig. f w 11). It is therefore unlikely that the rather poor frequency response of the probe is due to lower film overheating. On the other hand, such a bias effect was not observed by LaRue and Libby (1977) at their first measurement section (x\0) with a fiber probe diameter (25 lm) smaller than that used here. These two remarks suggest that the damping of the film’s

181

Fig. 13a, b. Effect of the probe time-response on spectra in the homogeneous region. a Density spectrum; b velocity spectrum; same conditions as in Fig. 12

voltage may be due to the large diameter of the fiber body which supports the film and to the resulting thermal inertia, but not to the overheat configuration. It is very difficult to estimate the errors resulting from this bias effect in the downstream flow development where large density fluctuations are present. Yet, it must be remarked that the apparent r.m.s of o@ detected in homogeneous flow is much smaller than typical values in the mixing layer (Jo@2/o +20% = at x/e\8). In addition, at a section where density fluctuations are less important (x/e\34), the present measurements are in very good agreement with those of LaRue and Libby (Fig. 14). It seems therefore that the rather low cut-off frequency of the probe does not lead to significant errors in the measured first moments of turbulent fluctuations for the present flow.

5 Conclusion It has been shown that a hot film/wire probe used with new operating conditions is suitable for measurements of velocity and concentration in air/helium mixtures. The overheat arrangement used by previous authors corresponds to a much hotter downstream element and to strong interference effects between the two sensors. In the new method, the upstream wire is the hottest element, resulting in much smaller interference effects. This arrangement has several advantages. Firstly, the shape of the calibration map is well conditioned for separating velocity/concentration in a wide range of these variables; moreover it is very convenient for data reduction using a linear

Fig. 14. Distributions of r.m.s velocity and density fluctuations at x/e\34. Comparison with LaRue and Libby results. Present measurements ]U \5.8 m/s, U \2 m/s; ]U \11.6 m/s, = */+ = U \4 m/s; K LaRue and Libby (1977), injection of helium */+

transformation. Secondly, minimizing interference effects makes the probe response rather insensitive to the distance between elements, contrary to the earlier arrangement where this parameter was crucial to the operation of the probe. As this distance is difficult to set and control, the new arrangement is obviously more convenient for practical use. Neglecting completely the interference effects, a very simple calculation shows that the calibration map of the probe is composed of straight lines in the plane E2 , E2 , in good qualf w itative agreement with experimental data. It also demonstrates that separation of the iso-concentration curves is chiefly due to the large diameter ratio of the two sensing elements. Tests of the probe in a turbulent boundary layer with large density variations indicate very satisfactory measurements; however high-frequency fluctuations (higher than 300 Hz) cannot be determined accurately by a probe of such dimensions. The resulting bias effect is attributed to the large fiber diameter (70 lm). It seems then possible to improve this probe by reducing the diameters of both sensing elements. Measurements of LaRue and Libby indicate that a fiber diameter of 25 lm gives consistent results in the homogeneous region of the flow. Consequently, a probe built with diameters of 2—3 lm for the wire and 20—30 lm for the fiber and used with the new overheat arrangement should optimize the timeresponse and the shape of the calibration map. An additional improvement of this instrumentation should be possible by modifying the geometric configuration of the

probe. The present arrangement consisting of two orthogonal sensing elements is not very well suited for wall measurements. A better arrangement seems possible by setting a small angle (+20°) between the two sensors so as to perform measurements closer to the wall. As the main effect is due to the diameter ratio, the principle of operation should not be affected by this modification.

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