Quality Criteria for Large Eddy Simulation - Turbulence Mechanics ...

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Chapter 2 Literature Review 2.1 Numerical Analysis of Turbulence In the past half century, the numerical analysis of turbulence has seen a phenomenal amount of research and development. This field of study has been applied in a range of areas; various branches of engineering, pure and applied sciences and medicine. An important factor in the growth and suc- cess of numerical analysis is attributable to the rapid growth and increased accessibility of computational power. In the area of fluid dynamics, the various numerical and computataional methods of analysis developed over the years are collectively termed as methods in Computational Fluid Dynamics (CFD). The most common modern CFD methods for turbulent flows are broadly classified as Direct Numeri- cal Simulation (DNS), Large Eddy Simulation (LES) and Reynolds Averaged Navier Stokes (RANS) methods. 6
CHAPTER 2. LITERATURE REVIEW 7 2.1.1 The Navier-Stokes Equations The general equations for fluid flow are known as the Navier-Stokes equations, which comprise the conservation of mass (continuity) equation and the conservation of momentum equations. For an incompressible Newtonian fluid, these can be written as ∂U ∂t ∇ · U = 0 + (U∇) · U = −1 ρ ∇p + ν∇2 U (2.1) where U is the fluid velocity at a point in the flow domain, p is the pressure of the fluid, ρ is the fluid density and ν is the kinematic viscosity, related to the dynamic viscosity µ by the relation ν = µ ρ . According to whether the viscous (ν∇ 2 U) or inertial ((U∇) · U) forces are predominant, the fluid flow is said to be either laminar or turbulent re- spectively. In 1883, Osborne Reynolds discovered a non-dimensional number, known today as the Reynolds number, which can be used to quantitatively define the point at which the flow ‘transitions’ from laminar to turbulent conditions, or vice versa. It is defined as: Re = Ul ν (2.2) where U is the fluid velocity, l is the characteristic length of the flow domain and ν is the kinematic viscosity. This number limits the transition between the laminar and turbulent flow regimes and its actual numerical value differs according to flow configuration. At Re lower than the transition limit, the viscous stresses damp out small perturbations, if indeed there are any, thereby restraining the flow from be- coming turbulent. However, once the transition Re is crossed, the viscous stresses become insufficient relative to the inertial perturbations in the flow, which then amplify; at this point the flow is said to become fully turbulent.
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CHAPTER 4. TURBULENT CHANNEL FLOW 5
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CHAPTER 6. FUTURE WORK 69 Figure 6.
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CHAPTER 6. FUTURE WORK 71 Table 6.1
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Bibliography S. A. Ahmed and A. S.
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BIBLIOGRAPHY 85 M. Freitag and M. K
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BIBLIOGRAPHY 87 J. L. Lumley. Inter
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