Flat plate turbulent boundary layer

DeGraaff, D. B. and J. K. Eaton. Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Lluid Mech. 422, 319-346 (2000). 

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)... 

Laminar and turbulent boundary layers over a flat plate... 

The transition to a turbulent boundary layer for a flat plate has been experimentally determined to occur at an Rcx value of between 3 x 10 and 6 x 10. For this example, the transition would occur between 15 and 30 cm after the start of the plate. Thus, the computations for a laminar boundary layer at 0.6 and 1 m are not realistic. However, the Blasius solution helps in the analysis of experimental data for a turbulent boundary layer, because it can tell us which parameters are likely to be important for this analysis, although the equations may take a different form. 

The conditions under which transition occurs depend on the geometrical situation being considered, on the Reynolds number, and on the level of unsteadiness in the flow well away from the surface over which the flow is occurring [2], [30]. For example, in the case of flow over a flat plate as shown in Figure 5.6, if the level of unsteadiness in the freestream flow ahead of the plate is very low, transition from laminar to turbulent boundary layer flow occurs approximately when ... 

The mean velocity distribution in the outer portion of the turbulent boundary layer on a flat plate is approximately given by ... 

Transition in a turbulent boundary layer on a flat plate. 

Turbulent boundary layer flow over a flat plate with an unheated leading edge section. 

EFFECTS OF DISSIPATION ON TURBULENT BOUNDARY LAYER FLOW OVER A FLAT PLATE... 

The effects of fluid property variations on heat transfer in turbulent boundary layer flow over a flat plate have also been numerically evaluated. This evaluation indicates that if the properties are as with If minar boundary layers evaluated at ... 

Numerically determine the local Nusselt number variation with two-dimensional turbulent boundary layer air flow over an isothermal flat plate for a maximum Reynolds number of 107. Assume that transition occurs at a Reynolds number of 5 X 105. Compare the numerical results with those given by the Reynolds analogy. 

At an altitude of 30,000 m the atmospheric pressure is approximately 1200 Pa and the temperature is approximately -4S°C. Assuming a turbulent boundary layer flow over an adiabatic flat plate, plot the variation of the adiabatic wall temperature with Mach number for Mach numbers between 0 and 5. 

The Grashof number may be interpreted physically as a dimensionless group representing the ratio of the buoyancy forces to the viscous forces in the free-convection flow system. It has a role similar to that played by the Reynolds number in forced-convection systems and is the primary variable used as a criterion for transition from laminar to turbulent boundary-layer flow. For air in free convection on a vertical flat plate, the critical Grashof number has been observed by Eckert and Soehngen [1] to be approximately 4 x 10". Values ranging between 10" and 109 may be observed for different fluids and environment turbulence levels. ... 

We utilize the physics of rolling particles on a surface as developed by Bhattacharya and Mittal. Our treatment differs from that of Bhattacharya and Mittal in that we provide a more detailed description of the turbulent boundary layer which is formed in the steady state when a fluid flows over a flat plate.The drag force we use is consistent with the treatment of Gim et al. ... 

Turbulent flow over a flat plate is characterized by three re-gions f l (a) a viscous sublayer often called the laminar sublayer, which exists right next to the plate, (b) an adjacent turbulent boundary layer, and (c) the turbulent core. Viscous forces dominate inertial forces in the viscous sublayer, which is relatively quiescent compared to the other regions and is therefore also called the laminar sublayer. This is a bit of a misnomer, since it is not really laminar. It is in this viscous sublayer that the velocity changes are the greatest, so that the shear is largest. Viscous forces become less dominant in the turbulent boundary layer. These forces are not controlling factors in the turbulent core. 

Structure of the flow. Velocity profile. The flow in the boundary layer on a flat plate is laminar until Rex = U[X/v 3 x 105. On a longer plate, the boundary layer becomes turbulent, that is, its thickness increases sharply and the longitudinal velocity profile alters. 

Experiments show [56, 212, 289, 427] that the turbulent boundary layer on a flat plate includes two qualitatively different regions, namely, the wall region (adjacent to the plate surface) and the outer region (bordering the unperturbed stream). By analogy with the flow through a circular tube, it is common to subdivide the thin wall region into three subdomains (von Karman s scheme) ... 

Falkner, V. M., The resistance of a smooth flat plate with turbulent boundary layer, Aircraft Eng., Vol. 15, pp. 65-69, 1943. 

The parameter k is called the von Karman constant, and the value that fits most of the data is 0.41. The corresponding value of B is 5.0. Intermediate between these layers is the buffer layer, where both shear mechanisms are important. The essential feature of this data correlation is that the wall shear completely controls the turbulent boundary layer velocity distribution in the vicinity of the wall. So dominant is the effect of the wall shear that even when pressure gradients along the surface are present, the velocity distributions near the surface are essentially coincident with the data obtained on plates with uniform surface pressure [82]. Within this region for a flat plate, the local shear stress remains within about 10 percent of the surface shear stress. It is noted that this shear variation is often ignored in turbulent boundary layer theory. 

FIGURE 6.42 Local skin friction coefficient for a compressible turbulent boundary layer on a flat plate, r(0) = 0.9, T, = 400 R (222 K). 

Similar behavior is observed in a turbulent boundary layer over a rough flat plate, where Prandtl and Schlichting [128] showed that the important parameter is kslx. The local skin friction coefficient is shown in Fig. 6.45 as a function of Re with x/ks as a parameter. 

The contents of this section are an extension of the work of Ref. 147 to include the effects of variable fluid properties. The ideas employed are based on the observations of Ref. 148 that on a flat plate the distribution of (3, the fraction of time a surface point is covered by a fully turbulent boundary layer, is closely approximated by a Gaussian integral curve throughout the transition zone, i.e.,... 

M. W. Rubesin, A Modified Reynolds Analogy for the Compressible Turbulent Boundary Layer on a Flat Plate, NACA Tech. Note 2917, 1953. 

D. B. Spalding and S. W. Chi, The Drag of a Compressible Turbulent Boundary Layer on a Smooth Flat Plate With and Without Heat Transfer, J. Fluid Mech. (18) 117-143,1964. 

M. W. Rubesin and C. C. Pappas, An Analysis of the Turbulent Boundary Layer Characteristics on a Flat Plate With Distributed Light Gas Injection, NACA Tech. Note 4149, 1958. 

Most of the results available for turjbulent boundary layers have been found by measuring time-average velocities at various points in flow in pipes or over flat plates and by attempting to generalize the velocity profiles. For various experimental reasons it is easier to make such measurements in pipes, so most of the results are pipe results. Now we consider the turbulent flow in pipes for one section, and then we return to the turbulent boundary layer. 

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