Numerical and asymptotic flow stability analysis of vortex structures

Vadim Akhmetov,P Akimov,A Tusnin,A Doroshenko,N Vatin

doi:10.1051/e3sconf/202126303003

Abstract

Stability problem of an axisymmetric swirling flow of a viscous incompressible fluid with respect to nonaxisymmetric perturbations is considered. The system of ordinary differential equations for the amplitude functions is solved numerically by the Runge-Kutta method and orthogonalization procedure. Solutions of equations for perturbations at the neighborhood of singular points are obtained by the Frobenius method. The maximum of amplification coefficients and phase velocities of five unstable modes are calculated.

Highlights

Vortex flows are often observed in hydraulic engineering problems
The properties of the swirling flow are used in the suction tubes of hydraulic turbines, vortex spillways, countervortex energy absorbers, counter-vortex aerators, heat exchangers, purification structures, temperature and fractional separation devices [1-7]
An effective tool for studying the hydrodynamic stability of a viscous incompressible swirling flows is a model based on the Navier-Stokes equations

Summary

Introduction

Vortex flows are often observed in hydraulic engineering problems. The properties of the swirling flow are used in the suction tubes of hydraulic turbines, vortex spillways, countervortex energy absorbers, counter-vortex aerators, heat exchangers, purification structures, temperature and fractional separation devices [1-7]. Flow stability analysis for the considered constructions is very important and actual problem. An effective tool for studying the hydrodynamic stability of a viscous incompressible swirling flows is a model based on the Navier-Stokes equations. The hydrodynamic stability problem of swirling flows for various configurations was studied numerically in [8-15]. The results of experiments on the stability of swirling flows are presented in [16-18]. An effective method for calculating the stability of a swirling flow with an arbitrary initial velocity profile is presented

Problem formulation

Numerical method

Calculation results and discussion

Сonсlusions