Flat plate turbulent boundary layer flow

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 ... 

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 ... 

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. ... 

FIGURE 1.6 Laminar, transition, and turbulent boundary layer flow regimes in flow over a flat plate. 

As discussed in the previous chapter, most early efforts at trying to theoretically predict heat transfer rates in turbulent flow concentrated on trying to relate the wall heat transfer rate to the wall shear stress [1],[2],[3],[41. The reason for this is that a considerable body of experimental and semi-theoretical knowledge concerning the shear stress in various flow situations is available and that the mechanism of heat transfer in turbulent flow is obviously similar to the mechanism of momentum transfer. In the present section an attempt will be made to outline some of the simpler such analogy solutions for boundary layer flows, attention mainly being restricted to flow over a flat plate. 

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. 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

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) ... 

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. 

Perceptive readers will recognize this as being the lower limit of the transition from laminar to turbulent boundary layers on a flat plate and will conclude that this must be the iresult of the transition of the boundary layer on the sphere from laminar to jturbulent flow. This has been verified experimentally. The function of the dimples on the golf ball is to make this transition occur at a lower Reynolds number. 

Assuming that the transition from a laminar to a turbulent boundary layer takes place at a Reynolds number of 10 what is the maximum thickness for the laminar boundary layer on a flat plate for ( ) air flowing at 10 ft/s, (b) water flowing at jlOft/s, and (c) glycerin flowing at 10 ft/s = 8.07 x 10 ft /s) ... 

In order to derive the basic equation for a laminar or turbulent boundary layer, a small control volume in the boundary layer on a flat plate is used as shown in Fig. 3.10-5. The depth in the z direction is b. Flow is only through the surfacesand dj and also from the top curved surface at 8. An overall integral momentum balance using Eq. (2.8-8) and overall integral mass balance using Eq. (2.6-6) are applied to the control volume inside the boundary layer at steady state and the final integral expression by von Karman is (B2, S3)... 

Integral momentum analysis for turbulent boundary layer. The procedures used for the integral momentum analysis for laminar boundary layer can be applied to the turbulent boundary layer on a flat plate. A simple empirical velocity distribution for pipe flow which is valid up to a Reynolds number of 10 can be adapted for the boundary... 

Figure 5.7-1. Laminar flow offluid past a flat plate and thermal boundary layer. Sec. 5.7 Boundary-Layer Flow and Turbulence in Heat Transfer...

A suitable treatment for turbulent boundary layers on the surface of the rotor has not yet been given. In flat plate flow the onset position of a turbulent boundary layer is usually assumed to occur when Re(x) = 10, where Re(x) contains the distance from the upstream pad. In high speed bearings or those with a large gap between pads, the boundary layer may become turbulent before reaching the leading edge of a pad. 

Pamies et al. [19] expanded the method of Jarrin et al. [10] by dividing the inflow plane of an incompressible flat plate boundary layer into several zones depending on the wall distance. At each zone turbulent eddy shapes are prescribed in the sense of Marusic [17], i.e., these shapes are representative for t3q> ical coherent structures of the turbulent boundary layer. This resulted in a good approximation for the low-order statistics of wall-bounded flows and reduced the... 

Continuous Flat Surface Boundaiy layers on continuous surfaces drawn through a stagnant fluid are shown in Fig. 6-48. Figure 6-48 7 shows the continuous flat surface (Saldadis, AIChE J., 7, 26—28, 221-225, 467-472 [1961]). The critical Reynolds number for transition to turbulent flow may be greater than the 500,000 value for the finite flat-plate case discussed previously (Tsou, Sparrow, and Kurtz, J. FluidMech., 26,145—161 [1966]). For a laminar boundary layer, the thickness is given by... 

Flat Plate, Zero Angle of Incidence For flow over a wide, thin flat plate at zero angle of incidence with a uniform free-stream velocity, as shown in Fig. 6-47, the critical Reynolds number at which the boundary layer becomes turbulent is normally taken to be... 

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