Second - Order Closure. Material Derivative Gradient terms.

Slides:

Advertisements

Similar presentations

Subgrid-Scale Models – an Overview

Advertisements

Canopy Spectra and Dissipation John Finnigan CSIRO Atmospheric Research Canberra, Australia.

Giorgio Crasto University of Cagliari - ITALY Forest Modelling A canopy model for WindSim 4.5.

Lecture 15: Capillary motion

Jonathan Morrison Beverley McKeon Dept. Aeronautics, Imperial College

Louisiana Tech University Ruston, LA Slide 1 Time Averaging Steven A. Jones BIEN 501 Monday, April 14, 2008.

Turbulent Models.  DNS – Direct Numerical Simulation ◦ Solve the equations exactly ◦ Possible with today’s supercomputers ◦ Upside – very accurate if.

Lecture 10 - Turbulence Models Applied Computational Fluid Dynamics

..perhaps the hardest place to use Bernoulli’s equation (so don’t)

1 LES of Turbulent Flows: Lecture 9 (ME EN ) Prof. Rob Stoll Department of Mechanical Engineering University of Utah Fall 2014.

LES of Turbulent Flows: Lecture 10 (ME EN )

Anisotropic Pressure and Acceleration Spectra in Shear Flow Yoshiyuki Tsuji Nagoya University Japan Acknowledgement : Useful discussions and advices were.

Flow over an Obstruction MECH 523 Applied Computational Fluid Dynamics Presented by Srinivasan C Rasipuram.

Fluid Mechanics 3rd Year Mechanical Engineering Prof Brian Launder

Eddy Viscosity Model Jordanian-German Winter Academy February 5 th -11 th 2006 Participant Name : Eng. Tareq Salameh Mechanical Engineering Department.

1 B. Frohnapfel, Jordanian German Winter Academy 2006 Turbulence modeling II: Anisotropy Considerations Bettina Frohnapfel LSTM - Chair of Fluid Dynamics.

Models of Turbulent Angular Momentum Transport Beyond the  Parameterization Martin Pessah Institute for Advanced Study Workshop on Saturation and Transport.

CHE/ME 109 Heat Transfer in Electronics

California State University, Chico

Introduction to Convection: Flow and Thermal Considerations

Estimation of Prandtls Mixing Length

Transport Equations for Turbulent Quantities

Chapter 4 Fluid Flow, Heat Transfer, and Mass Transfer:

Reynolds Method to Diagnosize Symptoms of Infected Flows.... P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Reynolds Averaged.

Lecture of : the Reynolds equations of turbulent motions JORDANIAN GERMAN WINTER ACCADMEY Prepared by: Eng. Mohammad Hamasha Jordan University of Science.

Pipe Flow Considerations Flow conditions:  Laminar or turbulent: transition Reynolds number Re =  VD/  2,300. That is: Re 4,000 turbulent; 2,300

Conservation Laws for Continua

Introduction to Convection: Flow and Thermal Considerations

This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under.

CFD Modeling of Turbulent Flows

0 Local and nonlocal conditional strain rates along gradient trajectories from various scalar fields in turbulence Lipo Wang Institut für Technische Verbrennung.

1 LES of Turbulent Flows: Lecture 11 (ME EN ) Prof. Rob Stoll Department of Mechanical Engineering University of Utah Fall 2014.

Chapter Six Non-Newtonian Liquid.

Reynolds-Averaged Navier-Stokes Equations -- RANS

Mass Transfer Coefficient

Chapter 6 Introduction to Forced Convection:

Physics of turbulence at small scales Turbulence is a property of the flow not the fluid. 1. Can only be described statistically. 2. Dissipates energy.

On Describing Mean Flow Dynamics in Wall Turbulence J. Klewicki Department of Mechanical Engineering University of New Hampshire Durham, NH

Analogies among Mass, Heat, and Momentum Transfer

Convection in Flat Plate Boundary Layers P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A Universal Similarity Law ……

Quantification of the Infection & its Effect on Mean Fow.... P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Modeling of Turbulent.

MECH 221 FLUID MECHANICS (Fall 06/07) Chapter 8: BOUNDARY LAYER FLOWS

INTRODUCTION TO CONVECTION

Analysis of Turbulent (Infected by Disturbance) Flows

Basic dynamics ●The equations of motion and continuity Scaling Hydrostatic relation Boussinesq approximation ●Geostrophic balance in ocean’s interior.

Basic dynamics The equation of motion Scale Analysis

Turbulence Modeling In FLOTRAN Chapter 5 Training Manual May 15, 2001 Inventory # Questions about Turbulence What is turbulence and what are.

Scales of Motion, Reynolds averaging September 22.

Friction Losses Flow through Conduits Incompressible Flow.

1 CONSTITUTIVE RELATION FOR NEWTONIAN FLUID The Cauchy equation for momentum balance of a continuous, deformable medium combined with the condition of.

BOUNDARY LAYERS Zone of flow immediately in vicinity of boundary Motion of fluid is retarded by frictional resistance Boundary layer extends away from.

Pipe flow analysis.

Viscosità Equazioni di Navier Stokes. Viscous stresses are surface forces per unit area. (Similar to pressure) (Viscous stresses)

Direct numerical simulation has to solve all the turbulence scales from the large eddies down to the smallest Kolmogorov scales. They are based on a three-dimensional.

Modeling of Turbulence. Traditional one point closures are based on an implicit hypothesis of single scale description. This hypothesis can be incorrect.

Avaraging Procedure. For an arbitrary quantity  the decomposition into a mean and fluctuating part can be written as.

Turbulent Fluid Flow daVinci [1510].

1 LES of Turbulent Flows: Lecture 13 (ME EN ) Prof. Rob Stoll Department of Mechanical Engineering University of Utah Spring 2011.

Chapter 12-2 The Effect of Turbulence on Momentum Transfer

The Standard, RNG, and Realizable k- Models. The major differences in the models are as follows: the method of calculating turbulent viscosity the turbulent.

Introduction to the Turbulence Models

K-ε model, ASM model.

Reynolds-Averaged Navier-Stokes Equations -- RANS

Introduction to Symmetry Analysis

C. F. Panagiotou and Y. Hasegawa

The k-ε model The k-ε model focuses on the mechanisms that affect the turbulent kinetic energy (per unit mass) k. The instantaneous kinetic energy k(t)

Characteristics of Turbulence:

Turbulent Kinetic Energy (TKE)

Part VI:Viscous flows, Re<<1

Presentation transcript:

Second - Order Closure

Material Derivative

Gradient terms

Source and sink terms

Material derivative

Gradient terms

Source and sink terms

the second term is negligible at high turbulence Reynolds numbers, and in this case only the first term in fact represents the true dissipation rate.

In the Reynolds stress transport equations, closure hypotheses are necessary forthe following terms: viscous dissipation (f), redistribution of energy by pressure strain correlations (c), turbulent diffusion (d) + (e). In the present chapter, we shall consider only fully developed turbulence at high Reynolds numbers Re t.

The source and sink terms can be modeled with reference to homogenous turbulence. The other terms appear only in non- homogenous flows and in particular in wall flows. They are mainly turbulent diffusion terms and a part of the pressurestrain correlations and they will be considered separately.

Modelling viscous dissipation Viscous dissipation occurs at the level of small eddies, in the spectral zone of large wavenumbers in which turbulence is classically assumed to approach isotropy. If the Reynolds number is sufficiently high for the dissipation zone to be clearly separated from the production zone, the viscous dissipation process can be assumed to be isotropic. This is modeled using a second order isotropic tensor through the hypothesis:

Anisotropy tensor

Modelling turbulent diffusion terms Triple velocity correlations

(that being obtained by analogy with the approximation of the energy redistribution terms through pressure-strain correlations in the R ij transport equation

If the term (a) is neglected, then we recover approximation [6.6]. Coefficient c s in [6.6] is determined by referring to experimental data relative to various turbulent flows, the value c s = 0.11 is obtained in Launder B.E., Reece G.J., Rodi W.

Other proposals Donaldson: Where L is a macroscale. Mellor and Herring:

Other Proposals Daly Harlow:

Very little is known about diffusion due to pressure fluctuations. These correlations are not directly attainable by measurements using present time experimental means.

Other suggestions

Modelling pressure-strain PS=PHI(1)+PHI(2)+PHI(S) Purely turbulent İnteractions between turbulence and mean flow Wall effect

Launder B.E., Reece G.J. and Rodi W., suggest

Determination of model constants a) Constants c 1 and c 2 Constants c1 and c2 are determined by reference to the homogenous turbulent flow with uniform mean velocity gradient.

Constants c’1 and c’2