Turbulence Model for Boundary Layers near Walls

A turbulence model is proposed for the prediction of boundary‐layer flows near walls. Two differential equations are solved: one for the kinetic energy of turbulence, and one for its length scale. The local effective viscosity in the flow is taken as proportional to the product of the length and the square root of the energy. The constants appearing in the equations are determined by reference to experimental data. Four cases of self‐similar flow are predicted with the model and found to compare favorably with the relevant experimental data. Satisfactory predictions for more general flows are also reported.

[1]  R. H. Eustis,et al.  Plane Turbulent Wall Jet Flow Development and Friction Factor , 1963 .

[2]  Coleman duP. Donaldson,et al.  A computer study of an analytical model of boundary-layer transition. , 1968 .

[3]  Francis H. Harlow,et al.  Transport Equations in Turbulence , 1970 .

[4]  Francis H. Harlow,et al.  Turbulence Transport Equations , 1967 .

[5]  P. Bradshaw.  Calculation of boundary-layer development using the turbulent energy equation , 1967, Journal of Fluid Mechanics.

[6]  L. Prandtl.  7. Bericht über Untersuchungen zur ausgebildeten Turbulenz , 1925 .

[7]  M. Wolfshtein.  The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient , 1969 .

[8]  J. Rotta,et al.  Statistische Theorie nichthomogener Turbulenz , 1951 .

[9]  A. Townsend,et al.  Decay of isotropic turbulence in the initial period , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[10]  D. Spalding,et al.  Heat and Mass Transfer in Boundary Layers. 2nd edition. By S. V. PATANKAR and D. B. SPALDING. Intertext Books, 1970. 255 pp. £6. , 1971, Journal of Fluid Mechanics.

[11]  W. G. Rose.  Results of an attempt to generate a homogeneous turbulent shear flow , 1966, Journal of Fluid Mechanics.

[12]  Ulrich Grigull,et al.  Progress in heat and mass transfer , 1969 .

[13]  Leslie S. G. Kovasznay,et al.  Simple Phenomenological Theory of Turbulent Shear Flows , 1969 .

[14]  D. B. Spalding,et al.  A two-parameter model of turbulence, and its application to free jets , 1970 .

[15]  Dudley Brian Spalding,et al.  Heat transfer from turbulent separated flows , 1967, Journal of Fluid Mechanics.

[16]  P. Chou.  On velocity correlations and the solutions of the equations of turbulent fluctuation , 1945 .