Solution of the General Boundary-layer Equations for Compressible Laminar Flow, Including Equilibrium Dissociation
Solution of the General Boundary-layer Equations for Compressible Laminar Flow, Including Equilibrium Dissociation

Author: Darwin W. Clutter

Publisher:

Published: 1963

Total Pages: 37

ISBN-13:

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An accurate and rapid method is presented for solution of the complete equations of compressible, steady, laminar-boundary-layer flow. The method allows arbitrary conditions for all of the following: pressure gradient, surface temperature and its gradient, heat transfer, mass transfer, and fluid properties. It can handle flows in which equilibrium dissociation occurs. Also, the second-order effect of transverse curvature is retained. The only restrictions are geometric. The method of solution consists of replacing the partial derivatives with respect to the flow direction by finite differences, while retaining the derivatives in a direction normal to the boundary. Arbitrary fluid properties may be used in the method of solution, if they are inputs in the computer program in the form of formulas or tables. The method has been programmed on an IBM 7094 computer, and solutions for a variety of flows are presented. Comparisons are made with other exact and approximate methods and with experiment. Calculations and comparisons establish that the method is rapid, highly accurate, and powerful. (Author).

Solutions of the Second-order Boundary-layer Equations for Laminar Incompressible Flow
Solutions of the Second-order Boundary-layer Equations for Laminar Incompressible Flow

Author: Michael J Werle

Publisher:

Published: 1968

Total Pages: 224

ISBN-13:

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Use is made of self similarity approach and integral momentum technique to obtain solutions of Van Dyke's second-order boundary-layer equations for laminar incompressible flow. Accurate numerical solutions of the most general self similar equations are tabulated for the four second-order contributions due to vorticity interaction, displacement speed, longitudinal curvature, and transverse curvature. A limited number of closed form solutions are obtained which appear to have special significance at the point of first-order boundary-layer separation. In particular it is found that the displacement speed problem can proceed up to separation for only two values of the second-order pressure gradient. All other cases display an infinite discontinuity at this point. Numerical solutions of a large number of cases for the longitudinal and transverse curvature effects well support an identical conclusion. The integral momentum technique applied (a straight forward extension of the Karmen-Pohlhausen solutions) is found to be oversensitive to approximations and in the final analysis is rejected in favor of locally similar solutions. (Author).

Numerical Solution of the Equations for Compressible Laminar, Transitional, and Turbulent Boundary Layers and Comparisons with Experimental Data
Numerical Solution of the Equations for Compressible Laminar, Transitional, and Turbulent Boundary Layers and Comparisons with Experimental Data

Author: Julius E. Harris

Publisher:

Published: 1971

Total Pages: 92

ISBN-13:

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A numerical method for solving the equations for laminar, transitional, and turbulent compressible boundary layers for either planar or axisymmetric flows is presented. The fully developed turbulent region is treated by replacing the Reynolds stress terms with an eddy viscosity model. The mean properties of the transitional boundary layer are calculated by multiplying the eddy viscosity by an intermittency function based on the statistical production and growth of the turbulent spots. A specifiable turbulent Prandtl number relates the turbulent flux of heat to the eddy viscosity. A three-point implicit finite-difference scheme is used to solve the system of equations. The momentum and energy equations are solved simultaneously without iteration. Numerous test cases are compared with experimental data for supersonic and hypersonic flows; these cases include flows with both favorable and mildly unfavorable pressure gradient histories, mass flux at the wall, and traverse curvature.

Numerical Solution of the Equations for Compressible Laminar, Transitional, and Turbulent Boundary Layers and Comparisons with Experimental Data
Numerical Solution of the Equations for Compressible Laminar, Transitional, and Turbulent Boundary Layers and Comparisons with Experimental Data

Author: Julius E. Harris

Publisher:

Published: 1971

Total Pages: 92

ISBN-13:

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A numerical method for solving the equations for laminar, transitional, and turbulent compressible boundary layers for either planar or axisymmetric flows is presented. The fully developed turbulent region is treated by replacing the Reynolds stress terms with an eddy viscosity model. The mean properties of the transitional boundary layer are calculated by multiplying the eddy viscosity by an intermittency function based on the statistical production and growth of the turbulent spots. A specifiable turbulent Prandtl number relates the turbulent flux of heat to the eddy viscosity. A three-point implicit finite-difference scheme is used to solve the system of equations. The momentum and energy equations are solved simultaneously without iteration. Numerous test cases are compared with experimental data for supersonic and hypersonic flows; these cases include flows with both favorable and mildly unfavorable pressure gradient histories, mass flux at the wall, and traverse curvature.

The Solution of the Laminar-boundary-layer Equation for the Flat Plate for Velocity and Temperature Fields for Variable Physical Properties and for the Diffusion Field at High Concentration
The Solution of the Laminar-boundary-layer Equation for the Flat Plate for Velocity and Temperature Fields for Variable Physical Properties and for the Diffusion Field at High Concentration

Author: H. Shuh

Publisher:

Published: 1950

Total Pages: 28

ISBN-13:

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In connection with Pohlhausen's solution for the temperature field on the flat plate, a series of formulas were indicated by means of which the velocity and temperature field for variable physical characteristics can be computed by an integral equation and an iteration method based on it. With it, the following cases were solved: On the assumption that the viscosity simply varies with the temperature while the other fluid properties remain constant, the velocity and temperature field on the heated and cooled plate, respectively, was computed at the Prandtl numbers 12.5 and 100 (viscous fluids). A closer study of these two cases resulted in general relations: The calculations for a gas of Pr number 0.7 (air) were conducted on the assumption that all fluid properties vary with the temperature, and the velocities are low enough for the heat of friction to be discounted. The result was a thickening of the boundary layers, but no appreciable modification in shearing stress or heat-transfer coefficient.