General principle of maximum pressure in stationary flows of inviscid gas

Abstract

Within the framework of the Euler equations, the possibility of achieving extreme pressure values at the inner point of a stationary flow of a nonviscous gas is considered. The flow can be non-barotropic. The well-known (G.B.Sizykh, 2018) subsonic principle of maximum pressure (SPMP) cannot be applied in transonic and supersonic flow regions. Under the conditions of the classical principle of maximum pressure by C.Truesdell (1953), there is no restriction on the values of local Mach numbers, but it has a number of features that do not allow it to be used to verify numerical calculations in the same way as it can be done when using SPMP in subsonic regions. A previously unknown principle of maximum pressure is discovered: a function of derivative flow parameters is found, which must have a certain sign (different for minimum and for maximum pressure) at the point where the pressure reaches a strict or nonstrict local extremum. This principle of maximum pressure is called general (GPMP) because its conditions do not include barotropicity, restrictions on the values of local Mach numbers, and the assumption that the gas obeys the MendeleevClapeyron equation. One of the consequences of GPMP is the conclusion that the requirement of barotropicity can be excluded from the conditions of Truesdell's principle of maximum pressure. It is proposed to use GPMP to verify numerical calculations of the ideal gas flow behind a detached shock wave formed in a supersonic flow around bodies and to verify numerical calculations of a viscous gas flow around bodies in regions remote from sources of vorticity, where the effect of viscosity can be neglected.

Keywords

• euler equations
• principle of maximum pressure
• inviscid gas
• perfect gas
• exact solutions
• q-parameter