层流射流流动的简化Navier-Stokes方程(SNSE)解

本文利用十一种简化 Navier-Stokes 方程(SNSE) 求解已知Navier-Stokes(NS)方程准确解的层射流流动,表明:多数SNSE~([1-6])的解与NS方程的准确解不一致;少数SNSE~([7,8])的解与NS方程的准确解一致,文中在射流的喉部和拐点位置,给出几种SNSE解与准确解的相对偏差,并把粘性及惯性诸项加以定量比较,强调指出:按照边界层理论量级分析为Re~(1/2)和Re~1量级的惯性项以及Re~(-1/2)量级的粘性项具有重要影响;据此从力学角度论证了简化 NS 方程时,保留全部惯性项和合理取舍粘性项的必要性。

SOLUTIONS TO THE SIMLIFIED NAVIER-STOKES EQUATIONS (SNSE) FOR THE ROUND LAMINAR JET

This paper uses eleven kinds of the simplified Navier-Stokes equations (SNSE) to solve the round laminar jet for which the exact solution to the complete Navier-Stokes equations (CNSE) had been found. It shows that for the eight kinds of the SNSE, such as the Davis viscous-layer SNSE, the thin-layer-1-order SNSE, the parabolized Navier-Stokes equations (PNSE), the Baldwin-Lomax thin-layer approximation and the SNSE in which the streamwise viscous stress derivatives are neglected, their solutions are not consistent with the exact solution to CNSE. The solutions to the former four kinds of SNSE are actually the solution to the classical boundary-layer equations. The solutions of the other three kinds of SNSE, such as, the innerouter-layer-matched SNSE, are completely consistent with the exact solution to CNSE. The deviations of the boundary-layer solution from the exact one to CNSE. and the quantitative comparison between the inertia and viscous terms are given at the positions of both the turning-point where the derivative of the streamfunction with respect to 0 equals to zero and the throat where the stream-tubes have a minimum area. From here we see thai it is necessary for simplifying CNSE to retain all the inertial terms included CNSE and to accept-or-reject reasonably rhe viscous terms and that the inner-otiter-layer matched SNSE would be more reasonable in mechanics and in mathematics.