Approximate Calculation of Turbulent Boundary-layer Development in Compressible Flow


Book Description

Numerical solutions of quantities appearing in the Karman momentum equation for the development of a turbulent boundary layer in plane and in radial compressible flows along thermally insulated surfaces are presented in tabular form for a range of Mach numbers from 0.100 to 10. Through the use of these tables, approximate calculation of boundary-layer growth is reduced to routine arithmetric computation. The variation of local skin-friction coefficient with Mach number is obtained through the assumption that the Falkner relation for low-speed flat-plate friction coefficents is dependent only on Reynolds number provided that the fluid properties are evaluated at the arithmetic mean of the wall temperature and the stream temperature.




A Method of Calculating Turbulent-boundary-layer Growth at Hypersonic Mach Numbers


Book Description

A method is developed for calculating the growth of a turbulent boundary layer at hypersonic Mach numbers. Excellent agreement with experimental results from axisymmetric nozzles has been obtained by the application of this method. The method utilizes a modification of Stewartson's transformation to simplify the integration of the momentum equation. Heat transfer is taken into account by evaluating the gas properties at Eckert's reference temperature and by using a modification of Crocco's quadratic for the temperature distribution in the boundary layer. A new empirical relation is used for the incompressible friction coefficient which agrees with experimental data over a Reynold's number range from 10(superscript 5) to 10(superscript 9).




Approximate Calculation of the Compressible Turbulent Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient


Book Description

The method, as applied to insulated surfaces, is quite well founded but, for noninsulated isothermal surfaces, depends on a number of speculative assumptions. These assumptions are qualitatively proper, and it is hoped that they will yield reasonable quantitative results. The detailed application of the method for practical calculations is described.




Nondimensional Calculation of Turbulent Boundary-layer Development in Two-dimensional Nozzles of Supersonic Wind Tunnels


Book Description

The method developed by Maurice Tucker (Approximate Calculation of Turbulent Boundary Layer Development in Compressible Flow, NACA TN 2337, 1951) for calculating the growth of turbulent boundary layers in two-dimensional compressible flow has been adapted to the computation of a dimensionless boundary-layer parameter. Equations and calculational procedures are presented for correcting two-dimensional supersonic nozzles for boundary-layer growth using only one or two tables, depending on the geometry. The tables are supplied for the Mach number range fro 1.5 to 8.0. Agreement of calculated data with measured data and effect of Mach number distribution are shown.










Calculation of Turbulent Boundary Layers with Heat Transfer and Pressure Gradient Utilizing a Compressibility Transformation


Book Description

An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.