A Comparison of the Transient and Heated-Coating Methods for the Measurement of Local Heat Transfer Coefficients on a Pin Fin

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1 ES ^^C THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47 St., New York, N.Y The Society shall not be responsible for statements or opinions advanced in papers or in discussion at meetings of the Society or of its Divisions or Sections, or printed in its publications. Discussion is printed only if the paper is published in an ASME Journal. Papers are available from ASME for fifteen months after the meeting. Printed in USA. Copyright 1988 by ASME 88-GT-180 A Comparison of the Transient and Heated-Coating Methods for the Measurement of Local Heat Transfer Coefficients on a Pin Fin J. W. BAUGHN* P. T. IRELAND** T. V. JONES** N. SANIEI* *Department of Mechanical Engineering University of California, Davis **St. Annes College and Department of Engineering Science Oxford University, U.K. OX26HS ABSTRACT Measurements of the local heat transfer coefficients on a pin fin (i.e., a short cylinder in crossflow) in a duct have been made using two methods, both of which employ liquid crystals to map an isotherm on the surface. The transient method uses the liquid crystal to determine the transient response of the surface temperature to a change in the fluid temperature. The local heat transfer coefficient is determined from the surface response time and the thermal properties of the substrate. The heated-coating method uses an electrically heated coating (vacuum-deposited gold in this case) to provide a uniform heat flux while the liquid crystal is used to locate an isotherm on the surface. The two methods compare well, especially the value obtained near the center stagnation point of the pin fin where the difference in the thermal boundary condition of the two methods has little effect. They are close but differ somewhat in other regions. NOMENCLATURE A area of gold coating c specific heat of substrate D diameter of pin fin f gold coating nonuniformity factor F g Frossling number Nu/,/Re h heat transfer coefficient H pin fin and pedestal height I gold coating current kw thermal conductivity of substrate k a thermal conductivity of air Nu local Nusselt number based on D q c convective heat flux q L heat flux loss due to conduction Re Reynolds number based on D and UcL t time T a air temperature T i initial wall temperature T Lc liquid crystal temperature Twwall surface temperature at time t U velocity at position y U cl centerline velocity V voltage across gold coating y distance from duct wall z distance from pin centerline E emissivity of liquid crystal surface P density of plastic substrate o Stefan Boltzmann constant 8 angle around pin fin or cylinder as measured from the front INTRODUCTION The measurement of local heat transfer coefficients for complex geometries with their correspondingly complex flows is important in many applications. For example, in gas turbines local heat transfer coefficients are needed for designing blade coolant passages and in electronic and computer packages local heat transfer coefficients are needed to design cooling systems to prevent chip overheating. Measurements of the local heat transfer coefficient provide both needed design data and a check on computational models for the prediction of heat transfer for such complex flows. Two experimental techniques which have been used for the global measurement of local heat transfer coefficients over a surface are the transient method (Ireland and Jones, 1985) and the heated-coating method (Baughn et al. 1985). Other techniques for local measurements include the heat flux sensor method (Baughn et al. 1987) which uses a sensor at selected Presented at the Gas Turbine and Aeroengine Congress Amsterdam, The Netherlands June 6-9, 1988

2 positions and the napthalene method (Sparrow et al. 1984) which makes global measurements of mass transfer which are then related to heat transfer by analogy. Direct comparisons of different methods under identical flow conditions are important. A recent comparison of the transient method and the heated-coating method for heat transfer to the curved wall of a wind tunnel by Jones and Hippensteele (1987) has shown that these two methods produce consistent results for similar flows, although there were large differences in the measurements due to their differing thermal boundary conditions. Flow from B=60 mm heater Y I H=120 mm This paper deals with a comparison of the transient and the heated-coating methods for the case of flow around a pin fin in a duct where a centerline stagnation point exists. At the stagnation point the heat transfer coefficient should be independent of the thermal boundary condition. Significant improvements in these two methods have recently been made by adapting liquid crystals for the surface temperature 2asurement. For example, Ireland and Jones (1986) ave used the transient method with a chiral nematic (thermochromic) liquid crystal on the surface of a plastic (Perspex) substrate. These were also the methods used by Jones and hippensteele (1987). Baughn et al. (1986a) has used the heated-coating method by applying the same liquid crystal directly on the surface of an ultra-thin (vacuum deposited) electrically heated gold coating. An apparatus which was previously used for a study of pin fin heat transfer using the transient method (see Ireland and Jones, 1986) was selected for the present comparison for several reasons: it provides an interesting and important complex flow; a full set of transient data existed; and a heated-coating pin fin could be easily substituted in the existing apparatus for the transient method pin fin previously used. Flow around a pin fin (or pedestal, i.e., a short cylinder mounted across a duct with flow in the duct) is a complex three-dimensional flow with flow separation and vortices. It is a geometry of interest in such areas as internal blade cooling in gas turbines and T electronic cooling systems. ) 0 EXPERIMENTAL APPARATUS A basic diagram of the duct used in this study is shown in Fig. 1. The duct was 0.6 meters wide and 0.12 meters high. Diagrams of the pin fin design for the transient method and for the heated-coating method are shown in Fig. 2a and 2b respectively. The pin fin diameter was 6.0 cm which corresponds to an L/D of 2.0. It was mounted 1.88 meters downstream of a bypass section giving an upstream development length of approximately 16 duct heights. Upstream of the bypass section there were heater and diffuser sections. When used with the transient method the flow is initially stabilized in the by-pass line with no flow in the test duct. In this case the heaters are used to raise the flow air temperature to C, while the apparatus remains at ambient temperature. The test is begun by simultaneously closing the bypass valve and opening the in-line valve. Details on the experimental procedure for the transient method with this apparatus are given by Ireland (1987). When used with the heated-coating method, the flow is unheated and is stabilized directly in the main duct containing the pin fin. The flow rate was adjusted so that the pin fin Reynolds number based on the pin By-pass line - - Flow during by-pass stage - Flow during test stage Fig. 1 Diagram of the Apparatus T Plastic [[Jolts fl I'in Fin Liquid Crystal Fig. 2a Diagram of Transient Method Styrofoam / beads Electrodes Thin walled plastic tube pump with liquid a Q g Fig. 2b Diagram of Heated coating method. diameter and the center velocity was 18,000 since a complete set of data using the transient method was available at this Reynolds number. The air velocity distribution was measured just upstream of the pin fin with a pitot tube and the air temperature distribution was measured near the same location with a calibrated thermocouple. TRANSIENT METHOD The transient method has a long history and a complete review is beyond the scope of this paper. It was used for many years at high temperatures in shock tunnels for the measurement of heat flux (Schultz and Jones, 1973). In these applications the surface was usually a ceramic and the surface temperature was measured with a film resistance thermometer (usually platinum). Although some early external thermal paint measurements are reviewed in Schultz and Jones (1973)

3 and Jones (1977), the use of the transient technique at lower temperatures for internal flows has been developed more recently. Clifford, et al. (1983) first used phase change paints on acrylic (Perspex) models to study heat transfer within gas turbine blade cooling passages. More recently Ireland and Jones (1985 and 1986) have used liquid crystals on the surface as the temperature sensor. The technique can be used for very complex geometries including curved ducts (Metzger and Larson, 1986) and complex gas turbine blade cooling passages (Clifford et al and Saabas et al. 1987). The basic principles and the data reduction for this method are described by Ireland and Jones (1985, 1986) and Ireland (1987) so only a brief review is given here. The transient method uses the surface temperature transient in response to a fluid temperature change as a measure of the surface heat flux and the corresponding heat transfer coefficient. For example, if a step change in the fluid temperature is induced, the surface temperature for a semi-infinite ')ody with one-dimensional heat transfer is given by: 2 (Tw - Ti)/(T a - T i ) = 1 - e 7 erfc (y ) (1) 7 =h,/t / k When the surface has a low thermal diffusivity (e.g., plastic), this one-dimensional assumption is often a good approximation since the surface temperature response is limited to a thin layer near the surface and lateral conduction can be shown to be small (Dunne, 1983). In the present work, although the inlet fluid temperature is very close to a step change, the actual air temperature transient is measured and used in the data reduction. Although both thermal paints and melting point coatings (see Clifford et al and Metzger et al respectively) and liquid crystals (Ireland and Jones, 1986) have been used for the surface temperature measurement, liquid crystals have been found to be particularly suitable since their response is repeatable and their color play can be easily recorded with a video system (Ireland and Jones, 1986). In the present study the pin fin and duct walls are Perspex and the liquid crystal is silk-screen printed on the inside surface duct walls and on the pin fin (see Fig. 2a). The video recording provides the time and location of the color play on the surface. In the present study the initial surface temperature is near 20 C, the flow temperature is approximately 70 C, and three liquid crystals were used simultaneously in a single coating. The crystal color band (e.g., the range of temperature over which the colors occur) was approximately 1 C and occurred at temperatures of 31, 35 and 4 C. Fig. 3 shows the location of the liquid crystal colors at a particular time as sketched from a video frame. The line of constant color on this sketch would represent an isotherm and is a line of constant heat transfer coefficient. The uncertainty in the measurement of the heat transfer coefficient with the transient method has been estimated for these results using standard uncertainty methods (Kline and McKlintock, 1953), with odds of 20:1. The individual contributions of each measurand to the total uncertainty are given in Table 1. The total uncertainty is estimated as 7.2%. The uncertainty in the Reynolds number was estimated to be l iquil Crystal temperature above color play temperatures. Duct Cente Position of c color play uquiu crystai temperature below color play temperatures. Fig. 3 Sketch of the pin fin from video frame showing location of the liquid crystal color for the transient method (viewed from the side 8=90 ) approximately 1%, which is much lower than that of the heat transfer coefficient, so the total uncertainty in the Frossling number is essentially the same as that of the Nusselt number (and the heat transfer coefficient). The uncertainty in the position around the pin fin is estimated to be +/-5 on the front and rear and +1-2 on the side and the uncertainty in the position along the pin fin (z) is estimated to be +/- 1.0 mm. Table 1 Uncertainty Analysis- Contribution of Individual Measurands x. 1 sxi sxi anu x100 A. Transient Method Nu i ax t 12 sec 0.1 pck T Lc -T a14 K T i -T a41.5 K B. Heated-Coating Method Nu uncertainty = 7.2% 6 Amps 0.01 V 7.6 Volts A m f T Lc -Ta1 K Ta C 2.0 Nu uncertainty = 4.7% 3

4 HEATED-COATING METHOD The heated-coating method also has a long history and again space does not allow a complete review here. It has recently been described by Baughn et al. (1985) and Baughn et al. (1986a), so only a brief description is included here. In the heated-coating method a very thin conductive coating (vacuum deposited gold in this case) on the surface of a plastic substrate (a thin polyester sheet mounted to a plastic tube in this case) is electrically heated. Conduction in the plastic substrate is generally quite small (less than 1%) of the surface heating so that the surface boundary condition is very close to a uniform heat flux. An early example of this is the copper coating used in a flat duct by Hatton and Woolley (1972). Several methods for measuring the surface temperature have been used including thermocouples (Baughn et al. 1985) and the resistance of the coating itself (Oker and Merte, 1981). In recent developments Hippensteele et al. (1983, 1985 and 1987), Simonich and Moffat (1982) and Baughn et. al. (1986a) have used liquid crystals to map the surface isotherms. Since the heat flux can be adjusted by changing the electrical voltage on the electrodes, the surface temperatures can be increased or decreased. When this is done an isotherm on the surface corresponds to a line of constant heat transfer coefficient. The local heat transfer coefficient at the position of the color play is then given by h = q c / ( T lc - T a ) (2) where q c is given by q c = f I V / A - e o ( T T ) - ql (3) and f is the ratio of the local electrical heating to the average heating and accounts for nonuniformity in the coating. The radiation correction assumes the surrounding walls have a large area and are at the ambient temperature. In the present study, a narrow band liquid crystal with a color play of 0.7 C at approximately 42 C is used. The ambient temperature was approximately 25 C. The position of the color play is moved on the surface by adjusting the electrical heating. A typical photograph showing the color distribution for a particular power setting is shown in Fig. 4. A line of constant color represents both an isotherm and a line of constant heat transfer coefficient, the value being given by equation 2. The uncertainty in the measurement of the heat transfer coefficient has been estimated for these measurements at 4.7%. The individual contributions of the measurands are shown in Table 1. Since at these low values of the heat transfer coefficient the thermal radiation correction can be as high as 3-7%, the uncertainty caused by the emissivity may be significant. Measurements of the emissivity were made by inserting the pin fin in a vacuum chamber. For the thin silk-screened liquid crystal coating used here the emissivity was found to be 0.5 with an uncertainty of 0.1. A thicker brushed-on coating of liquid crystal had an emissivity of 0.9. As shown in Table 1, the uncertainty in emissivity is the largest contributor to the total uncertainty. Another important source of uncertainty is f (the nonuniformity in the coating). For a small carefully selected sheet such as used here the nonuniformity may by as low as 2% as given here. In general, it may be much higher (up to 6%). Liquid Crystal temperature below color play temperatures. Duct Centerl Position of crys color play Liquid Crystal temperature above color play temperatures. Fig. 4 Sketch of the pin fin from a 35 mm photograph showing location of the liquid crystal colors for the heated-coating method (viewed from the side, a=90 ) The uncertainty in the Reynolds number is estimated at 1% which contributes little to the total uncertainty in the Frossling number. The uncertainty in position is the same as that for the transient method.. RESULTS The velocity and temperature profiles upstream of the pin fin are shown in Fig. 5a and 5b respectively. Although the velocity profiles are the same, the upstream air temperature distributions are quite different. The air has been heated for the transient method and has a distribution across the channel; while it is at ambient temperature and is uniform for the heated-coating method. The distribution for the transient method is caused by heat transfer to the upstream duct walls, while in the heated-coating method the walls are at ambient temperature (the same as the air) and act as an adiabatic boundary condition. Only the pin fin surface is heated for the heated-coating method results reported here. The heat transfer coefficient distribution around the pin (given in terms of the Frossling number based on the centerline velocity, pin fin diameter, and centerline temperature) is shown in Fig. 6 for the centerline (z/d= 0.0) and in Fig. 7 for a position further out along the pin fin (z/d= 0.75). In both methods and for both of these distributions the heat transfer coefficient is based on the centerline air temperature measured just upstream of the pin fin. The Reynolds number is based on the centerline velocity near the same position. For the centerline position (z/d= 0.0) the results from both methods are very similar and agree well within the estimated uncertainties at the stagnation point. Further out on the pin fin (z/d= 0.75) the heat transfer coefficients over the front of the pin fin for the heated-coating method are higher than those for the transient method. This is a consequence of the

5 difference in the temperature distribution across the duct for the transient method and heated-coating method. The heat transfer coefficients are based on the centerline air temperature and the wall boundary conditions are different in both cases. As a result, as we approach the duct wall, the two methods diverge. This is shown in Fig. 8 where the Frossling number distribution along the leading edge of the pin fin is compared the front side of the cylinder (Kraabel, 1982). The stagnation line values for the infinite cylinder are nearly identical in Fig. 9 for both thermal boundary conditions as expected. However, the distribution of the heat transfer coefficient around the cylinder is quite different for the two different boundary conditions. The cylinder with a constant heat flux boundary condition has a higher heat transfer coefficient on the front. At the rear of the cylinder the heat transfer coefficient for the uniform temperature boundary condition increases rapidly and becomes greater than that for the uniform heat flux boundary condition on the far back side. This behavior has also been observed by Papell (1981). I Re = 18,000 L/D = 2 z/d = U/Ucl Fig. 5a Typical Upstream Velocity Distribution d 2 } Dcoating T a ( C) Fig. 5b Typical Upstream Temperature Distribution DISCUSSION In order to discuss the above results, it is helpful to first discuss the effect of the cylinder wall thermal boundary condition on the heat transfer coefficient distribution around an infinite cylinder. The effect of the thermal boundary condition has been studied by Papell (1981) and more recently by Baughn and Saniei (paper in preparation). Baughn and Saniei plan to compare results using the heated-coating method (with a uniform heat flux boundary condition) to some results of the heat flux sensor method (with a uniform wall temperature boundary condition) given by Kraabel et al. (1982) for a long cylinder in a low turbulence and low blockage wind tunnel. The heated-coating results were obtained by putting extensions on the pin fin used in the present study and using it in the same wind tunnel as Kraabel et al. (1982). In order to assist in understanding some of the results of the present study, these measurements are shown in Fig. 9. Although these measurements were at a Reynolds number of 34,000 (higher than the 18,000 used in this study) there is very little effect of the Reynolds number on Oo o transient method, pin fin heated coating method, pin fin Fig. 6 Comparison of transient and heated-coating methods for a pin fin at the centerline (Z/D=O) Re = 18,000 z/d = g o transient method, pin fin heated coating method, pin fin a Fig. 7 Comparisons of transient and heated-coating methods for a pin fin at Z/D = 0.75 i 5

6 2.0 Heated-coating method 1.6 Re = 18,000 L/D = e - - dl 0.6 o transient method, pin fin heated-coating method, pin fin o L/D=2, z/d=0, Re=18,000 o L/D=20, z/d=0, Re=34,000 0.^ 7 0_2 n Fh P, R z/d Fig. 8 Comparison of Transient and Heated-Coating Methods along the Leading Edge of the Pin Fin Fig. 10 Comparison of Heated-Coating Results for a Pin Fin (L/D=2, z/d=0) ) to Heated-Coating Results for a Long Cylinder (L/D=20) 1.0 o heated-coating method, Re=18,000 * uniform temp (Kraabel et al. 1982), Re=34,000, low Turbulence L 0.6 L/D = 20 z/d = B 8 o transient method L/D =2, Re=18,000 * uniform temp. L/D=20, Re=34, t 0 2 Fig. 9 The Effect of the Thermal Boundary Condition on Fig. 11 Comparison of Transient Results for a Pin Fin Heat Transfer from a Long Cylinder (L/D = 20) (L/D=2, z/d=0) to Uniform Temperature Results for a Long Cylinder (L/D=20) If we compare the results for the infinite cylinder with two different thermal boundary conditions (i.e. fin is compared with the uniform temperature data of Fig. 9) to the Pin Fin results using the two different Kraabel et al. (1982) in Fig. 11. methods (i.e. Fig. 6) we see a somewhat similar behavior. (Note that the heated-coating method Both methods show slightly higher Frossling numbers provides a uniform heat flux boundary condition and the on the front for the pin fin in a duct than for the transient method approximates a uniform wall infinite cylinder (see Fig. 10 and Fig. 11). This may temperature boundary condition.) The heated coating be a consequence of the higher levels of turbulence for method for the pin fin is compared to the infinite the duct flow, which can have a strong effect on the cylinder in Fig. 10. The transient method for the pin heat transfer coefficients (Baughn, 1986b). 6

7 Both methods also appear to show a slight rearward shift of the separation point (Fig. 10 and 11). This could be caused by blockage, or by the higher turbulence level in the duct of the pin fin, or an acceleration of the flow around the cylinder caused by the end wall effects, or a combination of these effects. The transient method results for the pin fin do not show quite as sharp a drop in Frossling number near separation for the pin fin as that for the infinite cylinder with a uniform wall temperature (see Fig. 11). This may be partly caused by the difference in the boundary condition between the transient method and the uniform wall temperature. In regions with much lower heat transfer coefficients, the transient method does not quite simulate a uniform wall temperature boundary condition, since by the time the liquid crystal reaches its color play temperature at this position, the temperature at positions of higher heat transfer coefficient (i.e., the stagnation point) have reached higher temperatures. The crossover in Frossling number observed for the infinite cylinder (e.g., a higher Frossling number on the front and then lower Frossling number on the back for the uniform heat flux condition when compared to the uniform wall temperature results) is not as evident for the pin fin results. CONCLUSIONS Heat transfer results for the transient and the heated-coating methods have been compared for a pin fin in a duct and found to compare well in absolute value in the stagnation region. Differences observed away from the stagnation point are consistent with the effect of the different thermal boundary conditions imposed by the two methods. This comparison increases the confidence in both of these powerful methods. The transient method (which approximates a uniform temperature boundary condition) is very useful for handling very complex geometries. The heated-coating method (which provides a uniform heat flux boundary condition) is restricted to geometries with curvature in one direction, but provides relatively low uncertainty absolute results which are useful for comparison to computational results. The heat transfer results for the pin fin in a duct were found to be slightly higher than those of an infinite cylinder in low turbulence flow. The differences were hypothesized to be the result of higher turbulence levels in the duct and the complex three-dimensional flow associated with a pin fin. ACKNOWLEDGEMENT The authors gratefully acknowledge the support of the University of California UERG program, the S.E.R.C., the Ministry of Defence (procurement executive) and Rolls Royce Ltd, and kind permission of Rolls Royce to publish the work. The technical support of Mr. P. Timms is also gratefully acknowledged. Note: Authors are listed in alphabetical order REFERENCES Baughn, J. W., Takahashi, R. K., Hoffman. M. A., and McKillop, A. A., 1985, "Local Heat Transfer Coefficient Measurements Using an Electrically Heated Thin Gold- Coated Sheet," ASME Journal of Heat Transfer, Vol. 107, pp Baughn, J. W., Hoffman, M. A., and Makel, D. B., 1986a, "Improvements in a New Technique for Measuring Local Heat Transfer Coefficients," Review of Scientific Instruments, Vol. 57, pp Baughn, J. W., Elderkin, A. A., and McKillop, A. 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