Free-stream turbulence

However, the transition Reynolds number depends on free-stream turbulence and may range from 3 X 10 to 3 X lO ". The laminar boundary layer thickness 8 is a function of distance from the leading edge ... 

This relation is valid for 10"1 < Re/ < 105 provided excessive free-stream turbulence is not encountered. 

Experiments on transition for 2D attached boundary layer have revealed that the onset process is dominated by TS wave creation and its evolution, when the free stream turbulence level is low. Generally speaking, the estimated quantities like frequency of most dominant disturbances, eigenvalues and eigenvectors matched quite well with experiments. It is also noted from experiments that the later stages of transition process is dominated by nonlinear events. However, this phase spans a very small streamwise stretch and therefore one can observe that the linear stability analysis more or less determines the extent of transitional flow. This is the reason for the success of all linear stability based transition prediction methods. However, it must be emphasized that nonlinear, nonparallel and multi-modal interaction processes are equally important in some cases. 

Figure 2.14 Effect of free stream turbulence on transition for flat plate boundary layers. (Taken from Schubauer Skramstad...

The problem of excitation of shear layer by disturbance sources convect-ing outside the shear layer has been experimentally investigated by Kendall (1987, 1990) and Dietz (1999). Kendall (1990) through his experiments on jet-induced free stream turbulence, has provided direct evidence of TS waves and wave packets forming in a nominally flat plate boundary layer. 

Kendall, J.M. (1990). Boundary layer receptivity to free stream turbulence. AIAA paper no. 90-1504. 

Klebanoff, P.S. (1971). Effect of free stream turbulence on the laminar boundary layer. Bull. Am. Phys. Soc. 10, 1323. 

Leib, S.J., Wundrow, D.W. and Goldstein, M.E. (1999). Generation and growth of boundary-layer disturbances due to free-stream turbulence. AIAA-99-0408. 

Fio. 22. Kearney s MTEN calculation of the effects of free-stream turbulence on an... 

The i ITE methods include a calculation of the turbulence energy, and hence one may study the effects of variable free stream turbulence. Kearney et al. (K3) have compared such predictions with their data, and Fig. 22 shows a typical result for strongly accelerated turbulent boundary layer. 

The relations for cylinders above are for single cylinders or cylinders oriented such that the flow over them is not affected by the presence of others. Also, they are applicable to smooth surfaces. Surface roughness and ti t free-stream turbulence may affect the drag and heat transfer coefficients significantly. Eq. 7 -37 provides a simpler alternative to Eq. 7-35 for flow over cylinders. However, Eq. 7-35 is more accurate, and thus should be preferred in calculations whenever possible. 

Stream is turbulent. Torobin and Guvin AlChE J., 7,615-619 [1961]) found that the drag crisis Reynolds nnmber decreases with increasing free-stream turbulence, reaching a valne of 400 when the relative turbulence intensity, dejlned as VuVC/jj is 0.4. Here Vu is the rms fluctuating velocity and C/r is the relative velocity between the particle and the fluid. 

To summarize, no firm conclusions regarding the impact of free stream turbulence on the drag and lift force coefficients can be drawn analyzing the available data. More detailed experiments are obviously needed to better understand the affect of turbulence on the drag and lift force coefficients. 

Corrections by Morgan [66] for the combined effects of free-stream turbulence and wind tunnel blockage on Nusselt numbers measured in air are shown in Fig. 6.27. Here, dldT is the ratio of the cylinder diameter to the wind tunnel height or diameter, 8 Nu<( is the increase in the Nusselt number over Hilpert s measurements (Fig. 6.26), and Tu is the intensity of the longitudinal turbulent fluctuations in the free stream. In addition to these corrections, Morgan also proposed the Nusselt number correlations shown in Table 6.7 that are applicable to an extremely wide range of Reynolds numbers in air. At the higher Reynolds numbers, these Nusselt numbers are quite consistent with those of Fig. 6.26. 

FIGURE 6.27 Correction factors to Nusselt numbers for combined effects of wind tunnel blockage and free-stream turbulence [66]. (Reprinted by permission of Academic Press.)... 

The local heat transfer distribution is extremely sensitive to the free-stream turbulence intensity according to the measurements of Kestin and Maeder [69] this is reflected in the correction terms shown in Fig. 6.27 for the average Nusselt number. 

Free-Stream Turbulence and Unsteadiness. It was shown in Fig. 6.27 that the free-stream turbulence level significantly affects local and overall heat transfer from single cylinders in cross flow. This is caused primarily by early transition of the laminar boundary layer on the forward portion of the cylinder and subsequently by delayed separation of the turbulent boundary layer from the surface of the cylinder. Free-stream turbulence and unsteadiness also affect, to varying degrees, the heat transfer behavior of a turbulent boundary layer in the absence of transition-point shift and separation. 

A summary of the available experimental data on the effects of free-stream turbulence on heat transfer was presented by Kestin [138]. The experiments of Refs. 139-141 showed that for free-stream turbulence intensities ranging from 0.75 percent to about 4 percent, the skin friction and heat transfer coefficients at a fixed Re remained practically unchanged. 

A later study by Hancock [142] revealed a significant dependence of the boundary layer momentum thickness on the free-stream turbulence level. Consequently, significant effects were observed when skin friction data were compared at the same momentum-thickness... 

Reynolds number Ree. The correlated data are shown in Fig. 6.50, where the increase in the skin friction is plotted versus a parameter that accounts for both the intensity and the scale of the free-stream turbulence. The effect of free-stream turbulence is primarily in the outer region of the boundary layer, where the law of the wake is modified, and, hence, the boundary layer integral thicknesses are modified. 

FIGURE 6 JO Effect of free-stream turbulence on skin friction for a flat-plate turbulent boundary layer [142], (All details about different data points are given in Ref 142.) (Reprinted by permission of the authors)... 

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