An Introduction to Turbulence Models - Chalmers（介绍湍流模型-查尔默斯）.pdf

Publication 97/2 An Introduction to Turbulence Models Lars Davidson, http://www.tfd.chalmers.se/ ˜lada Department of Thermo and Fluid Dynamics CHALMERS UNIVERSITY OF TECHNOLOGY G¨oteborg, Sweden, September 6, 2016 CONTENTS 2 Contents Nomenclature 3 1 Turbulence 5 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Turbulent Scales . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Vorticity/Velocity Gradient Interaction . . . . . . . . . . . . . 7 1.4 Energy spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Turbulence Models 12 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Boussinesq Assumption . . . . . . . . . . . . . . . . . . . . . 15 2.3 Algebraic Models . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4 Equations for Kinetic Energy . . . . . . . . . . . . . . . . . . 16 2.4.1 The Exact k Equation . . . . . . . . . . . . . . . . . . . 16 ¯ ¯ 2.4.2 The Equation for 1/2(U U ) . . . . . . . . . . . . . . . 18 i i 2.5 The Modelled k Equation . . . . . . . . . . . . .