Abstract
In this study, analysis of flow properties around a sphere and its aerodynamic coefficients in the high-Mach-and-low-Reynolds-numbers conditions is carried out by direct numerical simulations solving the three-dimensional compressible Navier–Stokes equations. The calculation is performed on a boundary-fitted coordinate system with a high-order scheme of sufficient accuracy. The analysis is conducted by assuming a rigid sphere with a Reynolds number of between 50 and 300, based on the diameter of the sphere and the freestream velocity and a freestream Mach number of between 0.3 and 2.0, together with the adiabatic wall boundary condition. The calculation shows the following yields: (1) unsteady fluctuation of hydrodynamic forces become smaller as the Mach number increases under the same Reynolds number condition, (2) the drag coefficient increases with the Mach number due to an increase in the pressure drag by the shock wave, and (3) an accurate prediction of the drag coefficient in the supersonic regime using traditional models might be difficult.
Highlights
Certain acoustic phenomena are caused by fluid behavior
The calculation shows the following yields: (1) unsteady fluctuation of hydrodynamic forces become smaller as the Mach number increases under the same Reynolds number condition, (2) the drag coefficient increases with the Mach number due to an increase in the pressure drag by the shock wave, and (3) an accurate prediction of the drag coefficient in the supersonic regime using traditional models might be difficult
The method proposed in NASA SP-8072 is based on a large amount of flight data and the result of static firing tests that were conducted by the organization in the United States; it does not consider the effects of the launch pad and the facility because the model proposed in NASA SP-8072 assumes that sound sources are distributed along a jet path
Summary
Certain acoustic phenomena are caused by fluid behavior. In particular, the exhaust gas from a rocket engine generates strong acoustic waves. A drag model under high-Mach-and-low-Reynolds-numbers conditions is necessary to perform an analysis that considers the influence of the particle on the jet flow because the previous gas-particle multiphase flow model includes the drag model to consider the interaction of the fluid and particles. The model appears to include rarefaction, inertial, and compressibility effects Another drag model for calculations of gas-particle flow in rocket nozzles was suggested by Crowe.[11] This model is based on the empirical expression at rarefied flows and the experimental data. This model includes effects of the temperature ratio between the gas and the particle Those drag models are not based on direct experimental data because the accurate measurement of the aerodynamic force is difficult under the high-Mach-and-low-Reynolds-numbers conditions.
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