Concepts for radically increasing the numerical convergence rate of the Euler equations

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow

Vortex Instability of Free Convection Flow Over Horizontal and Inclined Surfaces

The vortex instability characteristics of laminar free convection flow over horizontal and inclined isothermal surfaces are studied analytically by linear theory. As a prelude to the analysis, the effects of the angle of inclination on the main flow and thermal fields are re-examined by a new approach. Numerical results are presented for wall shear stress, surface heat transfer, neutral stability curve, and critical Grashof number for Prandtl numbers of 0.7 and 7 over a wide range of angles of inclination, φ, from the horizontal. It is found that as the angle of inclination increases the rate of surface heat transfer increases, whereas the susceptibility of the flow to the vortex mode of instability decreases. The present study provides new vortex instability results for small angles of inclination (φ ≤ 30 deg) and more accurate results for large angles of inclination (φ ≥ 30 deg) than previous studies. The present results are also compared with available wave instability results

Wave Instability of Natural Convection Flow on Inclined Surfaces

Neutral stability results for Prandtl numbers of 6.7 and 0.733 were obtained by solving disturbance equations that take account of the nonparallelism of the basic flow. Compared with the results for the conventional parallel-flow model, the neutral curves are shifted to higher Grashof numbers and higher wave numbers but maintain their characteristic shapes. The effect of varying the plate inclination from downward-facing to upward facing is to increase the susceptibility of the flow to instability. The critical Grashof numbers are substantially lower than the Grashof numbers of experiments where instability was due to natural disturbances

Vortex Instability of Horizontal and Inclined Natural Convection Flows from Simultaneous Thermal and Mass Diffusion

An analysis is performed to study the heat/mass transfer and vortex instability characteristics of buoyancy induced flows that result from simultaneous diffusion of heat and mass in laminar boundary layers adjacent to horizontal and inclined surfaces. Numerical results are obtained for a Prandtl number of 0.7 over a range of Schmidt numbers and various angles of inclination from the horizontal,φ. For a given φ, it is found that when the two buoyancy forces from thermal and mass diffusion act in the same direction, both the surface heat and mass transfer rates increase, causing the flow to become more susceptible to the vortex mode of instability. These trends are reversed when the two buoyancy forces act in the opposite directions. On the other hand, as φ is increased, the heat and mass transfer rates are enhanced, but the instability of the flow to the vortex mode of disturbances decreases and eventually vanishes at φ = 90 deg

Wave Instability of Natural Convection Flow on Inclined Surfaces

Wave instability of natural convection boundary layer flow adjacent to inclined surfaces is analyzed by a linear theory. The effects of the nonparallelism of the main flow and thermal fields are taken into account in the analysis. Neutral stability results for Prandtl numbers of 0. 7 and 7. 0 are presented for upward-facing heated surfaces, for angles of inclination ranging from 0 to 90 degree . These results are compared with available analytical wave instability results for small angles of inclination. They are also compared with analytical vortex instability results and with available experimental data