The Verification of the Calculation of Stationary Subsonic Flows and the Presentation of Results

Abstract

The principle of pressure maximum is proved for a stationary three-dimensional vortex ideal gas flow (without the assumption of barotropicity). Based on the fact that in regions where the solution is modeled with a high degree of accuracy within the boundary value problem for the Euler equations, the consequences of the Euler equations must also hold, and the obtained subsonic principle is proposed to be used for verification of the numerical solutions of the boundary value problems for Euler equations for an ideal gas and for the Navier-Stokes equations for viscous gas. The conditions of the maximum principle include the value of the Q-parameter, whose surface level image is currently widely used to visualize the flow pattern. The proposed principle of the maximum pressure reveals the meaning of the surface Q = 0. It divides the flow region into the subdomain Q > 0 in which there can be no local pressure maximum and subdomain Q < 0 in which there can be no local pressure minimum. A similar meaning of parameter Q was known for incompressible fluid (H. Rowland, 1880; G. Hamel, 1936). The expression for the Q-parameter contains only the first derivatives of the velocity components, which allows determining the sign (+/–) of Q even for numerical solutions obtained by the low-order methods. An example of the numerical solution’s verification using the subsonic principle of the pressure maximum is presented. Analysis of the results of the numerical calculation of the flow around a moving aircraft carrier in the presence of atmospheric winds showed that if the calculation results are used for the simulation of complex flight modes and analyze the state of the atmosphere from the point of view of safe air traffic, visualizing the flow pattern by Q = const surfaces is not informative. In particular, these surfaces do not reflect the true picture of the wind shear perceived by the aircraft directly entering it. To verify the numerical method, it is sufficient to provide only a surface Q = 0 which has a clear physical meaning.