# Turbulent flow ppt

###### turbulence modeling lecture ppt and turbulence lecture notes ppt
Dr.TomHunt,United States,Teacher
Published Date:23-07-2017
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Turbulence CEFRC Combustion Summer School 2014 Prof. Dr.-Ing. Heinz Pitsch Copyright ©2014 by Heinz Pitsch. This material is not to be sold, reproduced or distributed without prior written permission of the owner, Heinz Pitsch. Turbulent Mixing • Combustion requires mixing at the molecular level • Turbulence: convective transport ↑  molecular mixing ↑ Surface Area ↑ diffusion fuel oxidizer = + diffusion 2 Course Overview Part II: Turbulent Combustion • Characteristics of Turbulent Flows • Statistical Description of Turbulent Flows • Reynolds decomposition • Turbulence • Favre decomposition • Types of turbulence • Turbulent Premixed Combustion • Mean-flow Equations • Turbulent Non-Premixed • Reynolds Stress Equations Combustion • k-Equation • Modelling Turbulent Combustion • Turbulence Models • Applications • Scales of Turbulent Flows/Energy Cascade • Kolmogorov Hypotheses • Scalar Transport Equations • Large Eddy Simulation 3 Characteristics of Turbulent Flows Transition to turbulence • From observations: laminar flow becomes turbulent  Characteristic length d↑  Flow velocity u↑  Viscosity ν↓  Dimensionless number: Reynolds number Re 4 Characteristics of Turbulent Flows Characteristics of turbulent flows: • Random • 3D • Has Vorticity • Large Re 5 Course Overview Part II: Turbulent Combustion • Characteristics of Turbulent Flows • Statistical Description of Turbulent Flows • Reynolds decomposition • Turbulence • Favre decomposition • Types of turbulence • Turbulent Premixed Combustion • Mean-flow Equations • Turbulent Non-Premixed • Reynolds Stress Equations Combustion • k-Equation • Modelling Turbulent Combustion • Turbulence Models • Applications • Scales of Turbulent Flows/Energy Cascade • Kolmogorov Hypotheses • Scalar Transport Equations • Large Eddy Simulation 6 Statistical Description of Turbulent Flows Conventional Averaging/Reynolds Decomposition • Averaging  Ensemble average N and Δt  Time average sufficiently large • For constant density flows:  Reynolds decomposition: mean and fluctuation, e.g. for the flow velocity u i 7 Reynolds-Zerlegung • Mean of the fluctuation is zero (applies for all quantities) • Mean of squared fluctuation differs from zero: • These averages are named RMS-values (root mean square) 8 Favre averaging (density weighted averaging) Combustion: change in density  correlation of density and other quantities • Reynolds decomposition (for ρ ≠ const.) • Favre averaging → By definition: mean of density weighted fluctuation  0 → Density weighted mean velocity 9 Favre average ↔ conventional average • Favre average as a function of conventional mean and fluctuation • and for the fluctuating quantity → For non-constant density: Favre average leads to much simpler expression 10 Course Overview Part II: Turbulent Combustion • Characteristics of Turbulent Flows • Statistical Description of Turbulent Flows • Reynolds decomposition • Turbulence • Favre decomposition • Types of turbulence • Turbulent Premixed Combustion • Mean-flow Equations • Turbulent Non-Premixed • Reynolds Stress Equations Combustion • k-Equation • Modelling Turbulent Combustion • Turbulence Models • Applications • Scales of Turbulent Flows/Energy Cascade • Kolmogorov Hypotheses • Scalar Transport Equations • Large Eddy Simulation 11 Types of Turbulence Statistically Homogeneous Turbulence • All statistics of fluctuating quantities are invariant under translation of the coordinate system → for averaged fluctuating quantities (more generally ) applies • Constant gradients of the mean velocity are permitted: Scalar dissipation rate in statistically homogeneous turbulent flow 12 Statistically Isotropic Turbulence • All statistics are invariant under translation, rotation and reflection of the coordinate system • Mean velocities = 0 • Isotropy requires homogeneity • Relevance of this flow case:  Simplifications allow theoretical conclusions DNS of statistically homogeneous and isotropic about turbulence turbulence: x -component of the velocity 1  Turbulent motions on small scales are typically assumed to be isotropic (Kolmogorov hypotheses) 13 Turbulent Shear Flow • Relevant flow cases in technical systems  Round jet  Flow around airfoil  Flows in combustion chamber • Due to the complexity of these turbulent flows they cannot be described theoretically Quelle: www-ah.wbmt.tudelft.nl „Temporally evolving shear layer“: Scalar dissipation rate χ (left), mixture fraction Z (rechts) Turbulent jet: magnitude of vorticity 14 Example: DNS of Homogeneous Shear Turbulence Scalar dissipation rate in homogeneous shear turbulence Close-up/detail 2048x2048x2048 collocation points 15 Example: DNS of a Shear Flow inhomogeneous Scalar dissipation rate statistically homogeneous Statistically homogeneous 16 Course Overview Part II: Turbulent Combustion • Characteristics of Turbulent Flows • Statistical Description of Turbulent Flows • Reynolds decomposition • Turbulence • Favre decomposition • Types of turbulence • Turbulent Premixed Combustion • Mean-flow Equations • Turbulent Non-Premixed • Reynolds Stress Equations Combustion • k-Equation • Modelling Turbulent Combustion • Turbulence Models • Applications • Scales of Turbulent Flows/Energy Cascade • Kolmogorov Hypotheses • Scalar Transport Equations • Large Eddy Simulation 17 Mean-flow Equations • Starting from the Navier-Stokes-equations for incompressible fluids (continuity) (momentum) → Four unknowns within four equations: u , u , u , p 1 2 3 • Reynolds decomposition 18 Averaged Continuity Equation 1. From continuity equation it follows and → Linearity of the continuity equation: no correlations of fluctuating quantities 19 Averaged Momentum Equation 2. This does not apply for the momentum equation  Convective term Contin.  Time-averaging yields Contin. → This term includes product of components of fluctuating velocities: this is due to the non-linearity of the convective term 20
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