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A computer code for solving the two-dimensional compressible Navier-Stokes equations governing the supersonic/hypersonic flow over a compression ramp as developed by MacCormack was extended to apply to axisymmetric flows over cylinder-flare shapes. Two new operators were developed for this extension, one of which was found to produce an upper stability bound on the step size. This bound is proportional to the Prandtl number and inversely proportional to the ratio of thermal capacities of the fluid times the maximum value over all grid points of the kinematic viscosity scaled by the radial coordinate value. Additionally, the computer code was modified to allow for the option of wall mass transfer. This required reformulation of the hyperbolic fine mesh operator because of an assumption in the development of the original operator that the wall-normal velocity in the fine mesh is much less than the sound speed. Numerical results are presented for a particular hollow cylinder-flare configuration, and comparisons are made with the experimental data of Roshko and Thomke and with the results of a boundary-layer code attributable to Patankar and Spalding. (Author).
A computer code for solving the two-dimensional compressible Navier-Stokes equations governing the supersonic/hypersonic flow over a compression ramp as developed by MacCormack was extended to apply to axisymmetric flows over cylinder-flare shapes. Two new operators were developed for this extension, one of which was found to produce an upper stability bound on the step size. This bound is proportional to the Prandtl number and inversely proportional to the ratio of thermal capacities of the fluid times the maximum value over all grid points of the kinematic viscosity scaled by the radial coordinate value. Additionally, the computer code was modified to allow for the option of wall mass transfer. This required reformulation of the hyperbolic fine mesh operator because of an assumption in the development of the original operator that the wall-normal velocity in the fine mesh is much less than the sound speed. Numerical results are presented for a particular hollow cylinder-flare configuration, and comparisons are made with the experimental data of Roshko and Thomke and with the results of a boundary-layer code attributable to Patankar and Spalding. (Author).
A computer code for solving the two-dimensional compressible Navier-Stokes equations governing the supersonic/hypersonic flow over a compression ramp as developed by MacCormack was extended to apply to axisymmetric flows over cylinder-flare shapes. Two new operators were developed for this extension, one of which was found to produce an upper stability bound on the step size. This bound is proportional to the Prandtl number and inversely proportional to the ratio of thermal capacities of the fluid times the maximum value over all grid points of the kinematic viscosity scaled by the radial coordinate value. Additionally, the computer code was modified to allow for the option of wall mass transfer. This required reformulation of the hyperbolic fine mesh operator because of an assumption in the development of the original operator that the wall-normal velocity in the fine mesh is much less than the sound speed. Numerical results are presented for a particular hollow cylinder-flare configuration, and comparisons are made with the experimental data of Roshko and Thomke and with the results of a boundary-layer code attributable to Patankar and Spalding. (Author).
MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.
Equilibrium convective heat transfer in several real gases was investigated. The gases considered were air, nitrogen, hydrogen, carbon dioxide, and argon. Solutions to the similar form of the boundary-layer equations were obtained for flight velocities to 30,000 ft/sec for a range of parameters sufficient to define the effects of pressure level, pressure gradient, boundary-layer-edge velocity, and wall temperature. Results are presented for stagnation-point heating and for the heating-rate distribution. For the range of parameters investigated the wall heat transfer depended on the transport properties near the wall and precise evaluation of properties in the high-energy portions of the boundary layer was not needed. A correlation of the solutions to the boundary-layer equations was obtained which depended only on the low temperature properties of the gases. This result can be used to evaluate the heat transfer in gases other than those considered. The largest stagnation-point heat transfer at a constant flight velocity was obtained for argon followed successively by carbon dioxide, air, nitrogen, and hydrogen. The blunt-body heating-rate distribution was found to depend mainly on the inviscid flow field. For each gas, correlation equations of boundary-layer thermodynamic and transport properties as a function of enthalpy are given for a wide range of pressures to a maximum enthalpy of 18,000 Btu/lb.
Written for those who want to calculate compressible and viscous flow past aerodynamic bodies, this book allows you to get started in programming for solving initial value problems and to understand numerical accuracy and stability, matrix algebra, finite volume formulations, and the use of flux split algorithms for solving the Euler equations.