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Solutions of the Navier-Stokes Equations for Flows over Configurations at High Angles of Attack

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High Angle of Attack Aerodynamics

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Abstract

The Navier-Stokes equations represent the conservation of mass, momentum and energy in a flow of a compressible, viscous and heat conducting fluid. They are known to simulate correctly the compressibility and viscous stresses effects. As the Mach number increases from subsonic to transonic, supersonic and hypersonic speeds, the Navier-Stokes equations are able to capture the shock waves in their proper positions and strengths as given by the Rankin-Hugoniot relations. The Navier-Stokes equations are capable as well to calculate the effects of viscosity on the flow fields, including the effects of three-dimensional separations. It is expected that the Navier-Stokes formulation is capable of capturing the vortical structures, such as the rolled-up vortices and the three-dimensional separating vortex sheets, generated in the flow over configurations at high angles of attack. It was shown in Chapter 8 that the Euler equations solutions are able to capture vortical structures due to the effects of “numerical viscosity” which is introduced by the numerical differencing schemes, the grid schemes and the artificial viscosity. However, since the “numerical viscosity” in the Euler solution is different from the physical viscosity of the flow, the Euler solutions must be used for the calculation of vortical flows with serious reservations. It is hoped that introducing the correct physical viscous laws into the Navier-Stokes equations may enable correct simulation of the viscous effects. This is the case for laminar flows.

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  1. Department of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Josef Rom

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Rom, J. (1992). Solutions of the Navier-Stokes Equations for Flows over Configurations at High Angles of Attack. In: High Angle of Attack Aerodynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2824-0_9

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  • DOI: https://doi.org/10.1007/978-1-4612-2824-0_9

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