CRITICAL REYNOLDS NUMBERS FOR THE FLOWS AROUND GEOMETRICALLY SYMMETRIC BODIES ON THE BASIS OF THEORY OF STOCHASTIC EQUATIONS - AN OVERVIEW

The purpose of the article is to provide an overview of the results of analytical solutions for critical Reynolds numbers based on stochastic equations for geometrically symmetric bodies. A comparative analysis of the equations for the critical point and the critical Reynolds number, obtained on the basis of the theory of stochastic equations and the equivalence of measures between turbulent and laminar states for the flow around the cylinder and around the sphere, is carried out. It is shown that for geometrically symmetric bodies the equations for critical Reynolds numbers obtained on the basis of stochastic theory have similar expressions and differ by a constant. It is well known that the modern numerical methods (RANS, LES, DNS) need proof of validity for obtained solutions. In the scientific literature there is no information for equations for the critical Reynolds number with the parameters of the initial fluctuation for geometrically symmetric bodies. In this paper, an overview of the derivation of explicit formulas for the critical point and critical Reynolds number are presented for the flow around the sphere and the cylinder. Calculations of the critical Reynolds numbers based on the obtained analytical dependences show a satisfactory agreement with the experimental values. In addition, for geometrically symmetric bodies the new formulas of the friction coefficients as a function of the Reynolds number up to the critical number are also proposed in the article.