The Effect of Boundary Conditions on Three-Dimensional Turbulent Flow

The effect of boundary conditions on 3D turbulent flow is studied by the Direct Numerical Simulation of an initially homogeneous and isotropic velocity field under forced and freely decaying conditions. Simulations are performed for both Channel (Plane) and Box flows and code validation is conducted by simulations of decaying box turbulence confirming a power-law decay of energy and Reynolds number with time. he change in energy decay rate for plane flow is explained in terms of the transfer of energy between stream-/span-wise directions and a potential equilibrium state. No-slip boundary conditions not only increase the viscous shear forces within the system, but also inhibit the cascade of energy through the inertial sub-range range. The presence of Kolmogorov spectra in Plane flow is observed at lower Reynolds number than possible for Box flow. Very low Reynolds number simulations of forced turbulence, show that eventually both plane and box turbulence flows give similar spectra, owing to the increased effectiveness of viscous forces in removing energy from low wave-numbers.t is concluded that boundary conditions give rise to additional stresses within the system that dampen normal-wise components of velocity, transfer energy out into the main flow and inhibit the cascade process resulting in the presence of Kolmogorov spectra where, under similar conditions, Box turbulence shows no such phenomena.ACKNOWLEDGEMENTS 2BSTRACT 3ABLE OF CONTENTS 4IST OF FIGURES 7IST OF TABLES 13OMENCLATURE 14HAPTER 1: INTRODUCTION 16.1 Introduction 16.2 Previous Research 18.3 Problem Description 22HAPTER 2: BACKGROUND THEORY 24.1 The Navier-Stokes Equations 24.2 The Scales of Turbulence 25.2.1 Length Scales 25.2.2 Reynolds numbers at different scales 27.3 Reynolds Stress 29HAPTER 3: NUMERICAL METHODS 31.1 The Fourier Transform 31.2 The Chebyshev Transform 35.3 NS Equations and the Fourier-Chebyshev Method 37.4 Discretization 42.5 Initial Conditions 44.6 Application of Forcing 46.7 Chebyshev and Fourier Node Interpolation 49.8 Solution Description 51.8.1 Freely Decaying Turbulence 51.8.2 Forced Stationary Turbulence 54HAPTER 4: RESULTS & DISCUSSION 55.1 Freely - Decaying Turbulence 55.2 Forced Turbulence 75HAPTER 5: CONCLUSION 98.1 Conclusion 98EFERENCES 100PPENDIX A: ADDITIONAL RESULTS 104.1 Freely Decaying Box turbulence 104.2 Freely Decaying Plane turbulence 107.3 Forced Turbulence 11