Measurements of the Effect of Free-Stream Turbulence Length Scale on Heat Transfer

Transcription

1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47 St., New York. N.Y GT-244 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. M Discussion is printed only if the paper Is published in an ASME Journal. Papers are available 9[ from ASME for fifteen months after the meeting. Printed in SA. Copyright 992 by ASME Measurements of the Effect of Free-Stream Turbulence Length Scale on Heat Transfer R. W. MOSS and M. L. G. OLDFIELD Department of Engineering Science niversity of Oxford ABSTRACT The effects of free-stream turbulence scale on heat transfer through a turbulent flat plate boundary layer have been measured. A variety of turbulence spectra were produced by parallel bar grids. The design of these was guided by previous measurements of combustion chamber turbulence. Heat transfer was measured transiently using thin film gauges. The heat transfer to the plate was found to be a function of turbulence integral length scale as well as intensity, and is of relevance to gas turbine heat transfer where aerofoils are subject to high turbulence levels from the combustor. Enhancement factors of up to 4% were experienced and the results extend conclusions drawn by other workers to higher turbulence levels and scales. ' Fluctuating component of streamwise velocity. X, Correlating parameter (Equation ). Xd, Correlating parameter (Equation 2). X,, Correlating parameter (Equation 4). Xi, Correlating parameter (Equation 6). x Distance in streamwise direction from leading edge. xgdistance from grid to plate leading edge. y Distance above plate surface % boundary layer thickness. 6 Boundary layer momentum thickness. AxIntegral length scale in the streamwise direction. z Time lag in correlations. v Kinematic viscosity. NOMENCLATRE. Cf Skin friction coefficient Cffl Skin friction coefficient without freestream turbulence. d Bar diameter. h Heat transfer coefficient q/(t i, - TPA,,) Le Dissipation length scale. M Mach number. Nu Nusselt number hx/k Nu, Nusselt number with no grid. PSD Power spectral density. 9 Heat flux measured by thin film gauges. R(i) Autocorrelation of velocity fluctuations u' at time lag 'r. Rex Reynolds number based on distance along plate. Ree Reynolds number based on boundary layer momentum thickness. T Temperature. Tu Turbulence intensity u x (% t Time Mean streamwise velocity. INTRODCTION. The effects of free-stream turbulence length scale are highly relevant to the prediction of heat transfer around gas turbine aerofoils. In this environment the turbulence intensity is often sufficiently high (Moss and Oldfield, 99) that heat transfer coefficients are raised significantly above the level expected for a turbulent boundary layer. In the past, measurements of the effect of turbulence on boundary layers have concentrated on the effects of turbulence intensity on the skin friction coefficient; only a few workers have taken measurements of the heat transfer effect and of the influence of length scale as well as intensity. Hancock (98) and Hancock and Bradshaw (983) measured the effect of length scale and turbulence intensity on the skin friction coefficient on a flat plate, and found that the data could be collapsed onto an empirical curve by plotting enhancement factors C,/C,J against the parameter: a 7)' Xd d =, +2) ( ) 995 Presented at the International Gas Turbine and Aeroengine Congress and Exposition Cologne, Germany June -4, 992

2 Bypass flow before run. Bypass duct Hot air outlet To fans via diffuser J/ Hot wire probe Air intake from bell-mouth / Turbulence gri ;^'" IE ; 5 mm i-arl.p: Diffusing section Gauges on Macor Sliding door Grid box flat platespacer Flap valve \\- Hot air supply (various lengths) closed position. Figure. Wind tunnel working section showing flat plate. Castro (984) also measured turbulent skin friction enhancement at low Reynolds numbers. Blair (98) measured heat transfer coefficients on a flat plate in a low speed tunnel, and correlated the enhancement against a similar parameter to that used by Hancock, but with the addition of a term to allow for effects at low Reynolds numbers. He found that his results agreed well with Hancock's correlation if a Reynolds' analogy factor was assumed: ANuDC = B t Nu Cjo with B =.3. Both Hancock's and Blair's results were taken using relatively low levels (Tu < 7%) of mainly isotropic turbulence. The present work is geared to turbulence levels relevant to that incident on an high pressure nozzle guide vane immediately downstream of a combustor. These levels (Moss and Oldfield, 99) are as high as % and the turbulence is unlikely to be isotropic, particularly at low wavenumbers. Maciejewski and Moffat (989) used a free jet to generate very high turbulence levels over a flat plate. They found that for turbulence intensities of between 2 and 6% the heat transfer coefficient was a function of the velocity fluctuations alone, i.e. h = camstant (3) p Cp u' In general, however, turbulence levels in high pressure turbines are less than 2% and this "non-boundary layer" regime will not apply. Ames and Moffat (99) built a simulated annular combustor sector to generate representative turbulence over a flat plate, and measured all three turbulence components using a triple hot-wire anemometer. The turbulence intensity and integral scale were in good agreement (if allowance is made for the changes in passage height and contraction ratio) with the values measured at exit from a genuine combustion chamber by Moss and Oldfield (99) using a pressure transducer. Heat transfer to the plate was measured by an electrical heating technique and they found that the increase in Stanton number could be correlated against a parameter XB similar to Hancock's parameter but using a boundary layer thickness defined in terms of temperature rather than velocity. The present work seeks to obtain predictive correlations which will enable the turbine designer to calculate the heat transfer enhancement due to typical levels of combustor exit turbulence. It follows that the correlation should be based on parameters that are themselves predictable (or easily measurable) if it is to be of use for design purposes. This paper describes a study of turbulence length scale effects using a transient technique on a pre-heated flat plate (Moss, 992). High frequency response thin-film heat flux gauges were used to measure heat transfer rates from a heated flat plate in controlled turbulent flows. The present paper deals mainly with enhancement of mean heat transfer rates. The high frequency measurements will be used to investigate enhancement mechanisms in a future paper. APPARATS. The experimental apparatus was based on an existing high speed (up to M =.5) wind tunnel in the Oxford niversity Turbomachinery Laboratories. A new working section (Figure ) was designed and built to allow transient heat transfer measurements. The flat plate was constructed from a sheet of machineable glass ceramic (MACOR) which has excellent mechanical, thermal and electrical properties for the use of thin-film gauges, (Oldfield et al, 978). An 8: involute profile that blended smoothly onto the flat surface was chosen for the leading edge after a series of tests on elliptical, involute and Rankine oval profiles to assess their freedom from separation at incidence. This was necessary to reduce the risk of high turbulence levels causing transient separation and so

3 producing heat transfer effects that would not be expected in the accelerating flow around the leading edge of an aerofoil. Shear sensitive liquid crystals (Bonnet et al, 989) were used to detect separation. These are easier to use than older flow visualisation techniques (eg. titanium dioxide and oil). The crystals gradually flow over the surface and accumulate at separation points in a manner that makes interpretation of the flow very easy. The involute profile chosen could withstand 4.5 incidence in a low turbulence flow before separation started. The transient technique of using thin-film resistance gauges to measure heat transfer requires a temperature difference between the plate surface and the free-stream. The tunnel flow should also start quickly. A spring operated flap valve (Figure ) allowed the tunnel fans to reach a stable speed with no flow through the working section. When the valve was released the flow settled in less than 2 ms. Measurements were then taken for a further 3 ms. The plate was heated prior to the run by passing hot air along both sides of it, and a sliding door in front of the plate prevented this air from heating the grids and ducting further upstream. A constant sensing current was passed through the thin film gauges and the change in voltage across the gauges during the run was converted to a heat flux signal using heat transfer analogues as described by Oldfield et al (982). This was then anti-alias filtered, sampled at 2 khz by a 2-bit transient recorder (Datalab DL2), and downloaded to an Opus PC V 8386 based computer for analysis. A movable probe holder allowed a single hot wire probe measuring + ' to be positioned anywhere along the plate. The wire could be positioned in the centre of the passage to measure turbulence in the freestream, or in the boundary layer to determine the velocity profile and turbulence parameters there. Hot wires were calibrated in situ in the tunnel, with the grids removed, by running the tunnel up to its maximum velocity and then recording the wire voltage and velocity as they fell slowly over the next 73 seconds after turning the fans off. The flow velocity was measured by a pitot probe and sidewall static tapping, connected to calibrated Sensym LX6D pressure transducers. The short time response of the measuring system (< ms) enabled accurate tracking of the decay of flow velocity. A Dantec 55M hot wire anemometer was used to control the hot wire probe. A set of interchangeable grid boxes and spacers allowed turbulence generating grids of various sizes to be placed at any position from 9 mm to mm upstream of the plate leading edge. TEST CONDITIONS. The maximum velocity possible with a 4% solidity grid was about 8 m/s; all tests were done at a similar velocity to achieve a suitably high Reynolds number near the front of the plate. Parallel bar grids were used as this allowed larger bar diameters (giving longer length scales) than square mesh grids for a given solidity. Table 2 shows the geometry of the five parallel bar grids used as turbulence generators. The grids were used with the bars perpendicular to the plate surface to minimise the risk of large transient incidence changes associated with the wake vortices causing separation. Grid A was chosen as having the smallest bars that would generate a useful turbulence level (of order 4%) over the plate. Bars smaller than this would have had to be placed very close to the leading edge, and the subsequent variation in turbulence levels along the plate could have led to difficulties in interpreting the results. b Wavenumber k (m -') Figure 2. Freestream turbulence wavenumber spectra at 8 mm from plate leading edge, produced by grids A to E. See Table 2 for intensities and length scales. Grid D was chosen as the largest single bar that could be placed in the 5 x 5 mm square inlet duct without causing excessive flow non-uniformity, and was placed close (x/d 6) to the leading edge to generate the highest possible turbulence intensity and length scale, albeit with a considerable degree of anisotropy. It had originally been hoped that variations in length scale would be possible at a constant turbulence intensity; this was not practical, so grids B, C and E were instead chosen to produce turbulence spectra differing from each other at either the large or small wavelength ends, but to be as close as possible to another spectrum at the other end of the wavenumber scale. It was felt that this would give the best indication of whether large or small wavelengths were responsible for any heat flux enhancement. Figure 2 compares the freestream wavenumber spectra from these grids at the x = 8 mm position. The data is plotted as a Power spectral density, defined as: a u,a, 4 (4) PSD = d metres. Wavenumber spectra are preferred to frequency spectra as they are insensitive to velocity changes and are relevant to length scales. It is desirable to be able to characterise the turbulence spectra in Figure 2 by a turbulence level:,z Tu(%) = u x = f o PSD dk (5) and a length scale, representing the "average" size of the eddies, which can then be compared to the boundary layer thickness when analysing heat transfer enhancement. LENGTH SCALES. A number of turbulent length scales are in use: (a) Integral length scale (Hinze, 975). This is a measure of the width of the central peak of the autocorrelation of the streamwise velocity fluctuation:

4 c.8 E.6 Grid D, x = mm. 25 y=3.54x A.4 V.2 5 Q 5 y=4.583x-2.5 B f +{ Dt *., C -.2' Lag distance (mm) igure 3. Typical autocorrelation of freestream u'(t) plotted against lag distance z. Integral length scale Ax = 4.6 mm (x + xg)/d Figure 4. Turbulence decay rate from single (B, D) and multiple (A, C, E) bar grids for calculating L. R(T) = u'(t).u'(t + i) (6) A mean of several point correlations, with 5 us time steps, was taken for each grid configuration. The autocorrelation of a typical turbulence velocity signal is shown in Figure 3. The integral length scale is traditionally defined as.2 ' = au2 = R (T) dt (7) r ax ) ` J` J = o.s(al( () by differentiating the fitted curve. As will be shown, this definition was more useful. Evaluating this may cause difficulties, as noted by Hinze (975), due to the negative part of the correlation being sufficient to make the length-scale tend to zero at large time lags; this can be shown to he inevitable for any finite, zero mean signal that effectively repeats every N points. To avoid this the correlation was integrated as far as the first zero point (i.e. while R(z) > ): = ')_ f ) ds (b) Dissipation length scale L. Two methods can be used to calculate the dissipation length scale. The first method (Hinze, 975) assumes R(-r) is parabolic near t = and takes L" as the point where a fitted parabola intersects the R(i) = line. In the present work, R(i) is characteristically sharply peaked near i = (Figure 3) and fitted parabolas underestimate L", with Le -.25 x A. The second method is to obtain L" from the streamwise decay of turbulence level by fitting the line (Castro, 984) l OO) Il2J d as shown in Figure 4. Castro used mesh pitch rather than bar diameter when fitting this line, but in this case (i.e. with a single bar in some cases) the diameter d is a more appropriate parameter; this has no effect on the resulting length scale value. The dissipation length scale is then obtained using (8) RESLTS. The measurements described here were taken at three positions along the plate (Table ). The boundary layer thickness has been calculated using a =.37xe =.36x () Redos (Schlichting, 979), and these values have been used for prediction purposes even though in practice freestream turbulence may modify the boundary layer thickness. Table. Measurement stations. x (m) Rex (m) Typical turbulence intensities, integral and dissipation scales and heat transfer enhancement factors are tabulated in Table 2. The L", and Ax values are similar for grids A, C and E, but vastly different for the single bar grids B and D. Nu and Nu, are measured at the same Rex 4

5 Table 2. Grid geometry and results. 3 GRID: A B C D E 25 E Bar diameter (mm) i Bar pitch (mm) 5 single 5 single 37.5 E 5 C BA Distance to LE xg (mm) c Tu (%) at x = mm mm mm Ax (mm) at x = mm mm mm L", (mm) at x = mm mm mm Nu/Nuo at x = mm mm mm HEAT TRANSFER ENHANCEMENT. Figure 5 shows the tripped and untripped Nusselt numbers from six gauges along the plate. The measured values are 25% to 3% lower than would be predicted by standard turbulent heat transfer correlations for a flat plate (e.g. Schlichting, 979). This may be due to the boundary layer thickening as the flow decelerates at the blend point between the involute and the flat surface; it is irrelevant to the conclusions presented here which are based on the ratio of results from tests with different turbulence levels, rather than on the absolute values. It can be seen that the trip strip produces Nusselt numbers slightly lower than those following natural transition. This is because the long laminar region prior to natural transition leads to a thinner turbulent boundary layer after transition than at this position in the tripped case. Figure 6 compares the Nusselt numbers with each grid against the datum tripped, low turbulence case, as an enhancement factor Nu/Nuo. The data points are at x = 6,, 4, 8, 24 and 3 mm; typically = 8.4 m/s, v =.55 x -5 m 2/s. Of these, the values at x =, 8 and 3 mm are shown in Figure 7 expressed as enhancement coefficients plotted against Tu. These enhancement factors are also tabulated in Table 2. It can be seen that no accurate correlation of enhancement factor is possible against turbulence intensity alone. If a least-squares straight line was fitted through these points, the standard deviation from the line would be 6.8% of Nuo for this data. It is to be expected that the enhancement factor will be a function of a length scale: boundary layer thickness ratio. The data is plotted 5 z 5 Figure 5. I- E N c N r y 2.5 L No grid, hipped No grid, untripped ti Reynolds number Rexx6 Heat transfer rate (Nusselt numbers) along plate for grids A to E Reynolds number Rexx5 Figure 6. Nusselt number enhancement (Nu/Nuo) on flat plate for grids A to E. against Hancock's parameter (called Xd here, Equation ) in Figure 8. There is considerable scatter of the points from the single bar grids. It seems probable that this is due to these grids being very close to the plate, and the width of the working section being insufficient to allow vortices of a similar size to the bar to develop properly. It seems for these grids that the decay rate (and the dissipation scale L", deduced from it) do not give a turbulence length scale that is useful for correlating the Nusselt number enhancement. Blair (98) used a similar parameter: xar Th R4 (b,.- 2) ( + 3e ) (2) 99s which allows for effects at low Reynolds numbers; this would make a % difference to the results from the x = mm position here. He noted that the dissipation scale could be well described as

6 .4J.4 o 6mmbar. «5 mm bars mm bars C.2 N y.s + o Turbulence intensity (%) Figure 7. Nusselt number enhancement factors (Nu/Nuo) calculated at x =, 8 and 3 mm. The enhancement factor cannot accurately be correlated against turbulence intensity alone..4j.4 6 mm bar.. 5 mm bars mm bars. c.3 Q) E.25 CO.2 C z Figure 8. Nusselt number enhancement plotted against X, as defined by Hancock (98). Xd [ Z..5 o 6 mm bar. 5 mm bars. + 6 mm bars o X Figure 9. Nusselt number enhancement factor (Nu/Nuo) plotted against integral length scale parameter X,i. I ti Z..5 6 mm bar. o 5 mm bars. + 6 nun bars. + o y =.85(Xir)^ Figure. Nusselt number enhancement factor (Nu/Nu ) plotted against integral length scale parameter with Reynolds number correction X,. X,., L, a.5 A, (3) In Table this relation does not seem to hold, as L" - A x for multi-bar turbulence grids, and L", - 2 to 3 x A x for single bar grids. The authors feel that the integral scale is a better correlating parameter for these grids. To allow comparison with the published correlations, however, the factor of.5 is retained. Figure 9 shows the present data plotted against a modified form of Hancock's parameter based on the integral length scale: X =7k i.5t! + 2) (4) a,s The data points now collapse satisfactorily onto a curve. nfortunately the functional form of Hancock's correlation was not published. Measurements from Figure 2(a) in Hancock and Bradshaw (983) suggest that the power law curve ^Cf = AXdx C>o (5) fits well for A =.39, n =.36. If a similar power law curve is fitted to the present data as plotted in Figure 9 the standard error of the data points from the line would be 2.4% in terms of enhancement factor. Figure shows the data from Figure 9 plotted against a new combined parameter 6

7 E Ce Ce r-. y z.4:.'.3:...2:.:.e.. + Present data + Blairs data o Hancocks data *.3 O.5 Q Hancocks correlation * o y =.85(xir)^.222 f*+ a Z * X,. Figure. Comparison of present data from Figure with data from Blair (983) and adjusted data from Hancock and Bradshaw (983) cc.6.5 z Grid D No grid Time (seconds) Figure 2. Comparison of heat flux signals from no-grid and grid D tests. x = 5 mm, bandwidth - 53 khz, = 74 m/s, Tu = 5.4%, AA = 5 mm. Xi* _ a 7; ( 5Ax + 2)( + 3e ) 995 (6) in the high turbulence case varies between a "low" level, which is typical of that in a turbulent boundary layer with no freestream turbulence, and a "high" level which may be up to % higher. The interpretation of these results will be the subject of a future paper. which applies Blair's correction to the parameter from equation 4. An empirical power law curve Nu =.85(XX,)- (7) Nu has been fitted and gives a standard error of 2.%. This curve is, of course, not valid for X, <.46, for which Nu/Nu =. Figure shows the same data compared with the results from Blair and his (Reynolds' analogy corrected) version of Hancock's line. Hancock's data points, similarly converted from skin friction to Nusselt number, are also included for completeness. Within the scatter, the similarity of these sets of results is gratifying, and supports the use of the correlating parameter X,, based on Ax rather than L in the present work which includes highly anisotropic turbulence. Ames and Moffat (99) used a tunnel with a significant length of unheated wall in front of the instrumented (heated) plate. This resulted in a ratio of velocity to thermal boundary layer thickness that was much larger over the front of the plate than would be expected over a uniformly-heated, free-standing plate. In Figure of their paper they plot enhancement factors against a parameter HB which is similar to Xd but is based on the thermal boundary layer thickness, and achieve a reasonable fit to Hancock and Bradshaw's (983) correlation. This suggests that the present work could be extended to cover configurations with an unheated starting length by correlating against a parameter X;,, using the predicted thermal instead of velocity boundary layer thickness. The heat flux signals from grid-out and grid D tests are compared in Figure 2. The signals have been scaled to Nu/Re ' 8 to avoid effects due to small differences in freestream velocity. The heat flux CONCLSIONS.. Accurate prediction of heat transfer enhancement due to freestream turbulence is not possible using the turbulence level alone. 2. Reasonable predictions can be made using the turbulence level and integral length scale, even for highly anisotropic turbulence at high intensities. 3. The correlation in Equation 7 (Figure ) is suggested as a suitable design tool for predicting high pressure nozzle guide vane heat transfer enhancement from the local freestream turbulence intensity and length scale. 4. Future work will use the wide-bandwidth time-dependent traces to investigate heat transfer enhancement mechanisms. ACKNOWLEDGEMENTS. The authors wish to thank Rolls-Royce plc and the Defence Research Agency Royal Aerospace Establishment (Pyestock) for funding and supporting this work. We are also very grateful to Mr J. Gills and Mr T. Norman for building the working section, and Mr J. Allen for instrumenting the flat plate. 7

8 REFERENCES. Ames, F.E., and Moffat, R.J., 99, "Effects of simulated combustor turbulence on boundary layer heat transfer", ASME HTD 38. Blair, M.F., 98, "Influence of Free-Stream Turbulence on Turbulent Boundary Layer Heat Transfer and Mean Profile Development", Part 2. Trans. ASME Journal of Heat Transfer, vol 5. Bonnet, P., Jones, T.V., and McDonnell, D.G., 989, "Shear Stress Measurements in Aerodynamic Testing using Cholesteric Liquid Crystals". Liquid Crystals, Vol 6, No. 3. Castro, I., 984, "Effects of Free-Stream Turbulence on Low Reynolds Number Boundary Layers". Trans ASME J. Fluids Engineering Vol 6, p Hancock, P.E., 98, "The Effect of Free-Stream Turbulence on Turbulent Boundary Layers", PhD Thesis, Imperial College, niversity of London. Hancock, P.E., and Bradshaw, P., 983, "The Effect of Free- Stream Turbulence on Turbulent Boundary Layers". Trans ASME J. Fluids Engineering, 5, p Hinze, J.O., 975, Turbulence, McGraw-Hill Book Company. pp Maciejewski, P.K., and Moffat, R.J., 989, "Effects of very high turbulence on heat transfer", Seventh Symposium on Turbulent Shear Flows, Stanford niversity, 989. Moss, R.W., 992, "The Effects of Turbulence Length Scale on Heat Transfer", D.Phil Thesis, Department of Engineering Science, niversity of Oxford. Moss, R.W., and Oldfield, M.L.G., 99, "Measurements of Hot Combustor Turbulence Spectra", ASME 9-GT-35. Oldfield, M.L.G., Bird, H.J., and Doe, N.G., 982, "Design of Wide-Bandwidth Analogue Circuits for Heat Transfer Instrumentation in Transient Tunnels", 6`h Symposium of the International Centre for Heat and Mass Transfer, Dubrovnik, Sept. 982, (papers edited by Metzger, D.E., and Afghan, N.H.). Oldfield, M.L.G., Jones, T.V., and Schultz, D.L., 978, "On-Line Computer for Transient Turbine Cascade Instrumentation", IEEE Transactions on Aerospace and Electronic Systems, vol AES-4, No.5. Schlichting, H., 979, Boundary-Layer Theory, McGraw-Hill Book Company.