An Account of Free-Stream-Turbulence Length Scale on Laminar Heat Transfer

Abstract

The effect of length scale in free-stream turbulence is considered for heat transfer in laminar boundary layers. A model is proposed which accounts for an “effective” intensity of turbulence based on a dominant frequency for a laminar boundary layer. Assuming a standard turbulence spectral distribution, a new turbulence parameter which accounts for both turbulence level and length scale is obtained and used to correlate heat transfer data for laminar stagnation flows. The result indicates that the heat transfer for these flows is linearly dependent on the “effective” free-stream turbulence intensity.

Effects of High Intensity, Large-Scale Freestream Combustor Turbulence on Heat Transfer in Transonic Turbine Blades

“…The results are presented below in The correlation was applied to the current data and the results are plotted in From the figure, it is demonstrated that the correlation matches the measured data well for the pressure surface locations, but the suction surface data St' results are much higher than the correlation predicts. This is similar to the result observed for the Dullenkopf and Mayle (1995) correlation.…”

“…In general, results of their tests agreed with those from turbine vane testing in terms of locations of highest heat and mass transfer and early boundary layer transition on the suction surface. Leading edge results agreed well with published correlations from Kestin and Wood (1971) and Dullenkopf and Mayle (1995). Holmberg (1996) studied the effects of small-scale, relatively low intensity turbulence on heat transfer in high-turning turbine blades in transonic flow and measured time-resolved heat flux and velocity.…”

“…The analysis of the model data in this form is similar to the analysis performed in Dullenkopf and Mayle (1995). In that work, it was stated: "The effective turbulence level, Tu eff , is obtained by integrating the spectral energy density over a band width of frequencies centered about the dominant frequency."…”

“…The model would then break down above these frequencies. Mayle, et al (1998) In work by Dullenkopf and Mayle (1995) and Mayle, et al (1998), the idea of an Figure 3.28b, which presents the same data as Figure 3.28a plotted on a linear scale. The application of the coherence function has effectively attenuated the large predicted increases in heat transfer at higher frequencies, which is expected from the coherence and measured heat flux spectra.…”

“…Since combustor turbulence, as will be discussed later, has been shown to be of fairly large scale, the lower bound of the correlation presented by Van Fossen may not be of particular interest in direct application to turbine design. Dullenkopf and Mayle (1995) presented a new correlation that introduced the idea of an "effective" turbulence level. The correlation was developed based on stability theory for a laminar boundary layer.…”