Elliptic relaxation for near wall turbulence models
|
|
- Byron Chambers
- 6 years ago
- Views:
Transcription
1 Elliptic relaxation for near wall turbulence models J.C. Uribe University of Manchester School of Mechanical, Aerospace & Civil Engineering Elliptic relaxation for near wall turbulence models p. 1/22
2 Outline Introduction The elliptic relaxation approach The v 2 f model The ϕ f model Test cases and applications Conclusion Elliptic relaxation for near wall turbulence models p. 2/22
3 Introduction Why modelling the near-wall region? In the near-wall region, viscosity and nohomogeneties are dominant. High shear and large rates of turbulence production are present. Here is where the skin friction and heat transfer are controlled, therefore, of vital importance for engineering applications that require these quantities. The wall normal fluctuations are reduced therefore reducing mixing. Elliptic relaxation for near wall turbulence models p. 3/22
4 Introduction The wall effects: No-slip: The boundary condition on the mean velocities creates large gradients where the turbulent production originates. Elliptic relaxation for near wall turbulence models p. 4/22
5 Introduction The wall effects: No-slip: The boundary condition on the mean velocities creates large gradients where the turbulent production originates k -uv.2 P k y y+ Elliptic relaxation for near wall turbulence models p. 4/22
6 Introduction The wall effects: No-slip: The boundary condition on the mean velocities creates large gradients where the turbulent production originates k -uv.2 P k y y+ Low Reynolds number effects: Interaction between energetic and dissipative scales. Elliptic relaxation for near wall turbulence models p. 4/22
7 Introduction The wall effects: Blocking effect: The impermeability condition affects the flow by adjusting the pressure field to ensure the incompressibility condition. Wall echo: Image term in Green s function at the other side of the wall produces an increase in the pressure. Elliptic relaxation for near wall turbulence models p. 5/22
8 Introduction The wall effects: Blocking effect: The impermeability condition affects the flow by adjusting the pressure field to ensure the incompressibility condition. Wall echo: Image term in Green s function at the other side of the wall produces an increase in the pressure. x x x Elliptic relaxation for near wall turbulence models p. 5/22
9 Introduction The wall effects: Blocking effect: The impermeability condition affects the flow by adjusting the pressure field to ensure the incompressibility condition. Wall echo: Image term in Green s function at the other side of the wall produces an increase in the pressure. x x x p i (x, t) = 1 4π S(x, t) ( 1 r + 1 r ) dx Elliptic relaxation for near wall turbulence models p. 5/22
10 Elliptic relaxation approach Starting from the Reynolds-stress equation: Du i u i Dt + ε u iu j k = P ij + ij + x k ( ν Tkl u i u j x l ) + ν 2 u i u j x 2 k with ij = ( ε ) Π ij + ε ij u i u j k To solve ij a non-homogeneous elliptic equation is derived. By integrating the pressure equation and assuming that the two point correlation Ψ ij can be approximated as Ψ ij (x, x ) = Ψ ij (x, x ) exp( r/l) (Durbin,1993) Elliptic relaxation for near wall turbulence models p. 6/22
11 Elliptic relaxation approach The solution is the modified Helmotz-type equation: ij L 2 2 ij = h ij Where any quasi homogenous model can be used for h ij. In fact the model solves for f ij = ij /k in order to enforce correct behaviour at the wall. The length scale is prescribed as: L = C L max ( k 3/2 ε, C η ( ν 3 ) 1/4 ) ε Elliptic relaxation for near wall turbulence models p. 7/22
12 Elliptic relaxation approach The model accurately represents the asymptotic behaviour of the stresses even in the near wall layer. There is no need to prescribe the distance from the wall, so no ill defined in complex geometries. No use of empiricall damping functions. Good representation of the stresses in channel flows and boundary layers. Requires 13 transport equations ( 6 for u i u j, 6 for f ij and one for ε). Numerical difficulties with wall boundary conditions for f 22, f 12, f 23. Equations required to be solved coupled. Elliptic relaxation for near wall turbulence models p. 8/22
13 The v 2 f model In order the simplify the RSM, the elliptic relaxation is introduced to the eddy viscosity approximation (Durbin,1995). Use of correct velocity scale near the wall, ν t = C µ v 2 T 4 3 ν t 2 1 ν t = -uv/du/dy νt = C µ k 2 /ε νt = C µ k υ 2 /ε y+ Elliptic relaxation for near wall turbulence models p. 9/22
14 The v 2 f model Solve transport equations for k, ε and v 2, and elliptic equation for f 22 [ ( Dv 2 Dt = kf ε v2 k + ν + ν ) ] t v 2 x j σ k x j [ ] L 2 2 f x 2 f = 1 j T (C v 1 1) 2 k 2 P C k 2 3 k v 2 has no tensorial meaning, is now a scalar. So is f. Wall boundary condition f = 2νv2 εy 4 Elliptic relaxation for near wall turbulence models p. 1/22
15 The v 2 f model Advantages: Reproduces the correct behaviour of the turbulent viscosity near the wall No need to include the distance from the wall. Can be used in any geometry Improves predictions on separating flows, as well as heat transfer and skin friction. Drawbacks: One transport and one elliptic equations more than the standard k ε Stiffness of the boundary condition makes it necessary to solve v 2 f coupled. Elliptic relaxation for near wall turbulence models p. 11/22
16 The ϕ f model Instead of solving v 2, a transport equation is solved for the ratio ϕ = v 2 /k (Laurence et al., 24): D(υ 2 /k) Dt = f (υ2 /k) k P + x k [( ν + ν t σ (υ2 /k) Where X is the "cross diffusion" term from the transformation: ( ) X = 2 ν + ν t (υ 2 /k) k k x k x k σ (υ2 /k) ) (υ 2 /k) x k ] + X Elliptic relaxation for near wall turbulence models p. 12/22
17 The ϕ f model Advantages of the substitution are: The term εv 2 /k is not present, leaving stable viscous diffusion as a dominant mechanism near the wall. The wall boundary condition for f is reduced to: f w = lim y 2ν(υ 2 /k) y 2 (1) which is more convenient and easier to reproduce since it has y 2 instead of y 4 of the original model. The LDM modification (Lien and Durbin,1996) proposed as a method to uncouple the equations, does not ensure the correct behaviour in the region far from the wall. Elliptic relaxation for near wall turbulence models p. 13/22
18 The ϕ f model A changes of variable is applied to the original model: f = f + 2ν( ϕ k) k + ν 2 ϕ (2) Leading to: Dϕ Dt = f P ϕ k + 2 k L 2 2 f f = 1 T (C 1 1) ν t ϕ k σ k x j [ ϕ x j ] x j C 2 P k 2ν k [ νt σ k ϕ x j ] (3) ϕ k ν 2 ϕ x j x j Far from the wall the last two terms are negligible, ensuring the correct behaviour. (4) Elliptic relaxation for near wall turbulence models p. 14/22
19 The ϕ f model The boundary condition of f is zero at the wall, improving robustness. The equations can be solved totally uncouple. Useful for unstructured codes (Implemented in the industrial Code_Saturne of EDF) Modification ensures correct behaviour far from the wall (see Laurence et al., 24) ƒ ƒ hom L 2 ƒ term neglected in LDM term neglected in ϕ model y+ y+ a) b) Elliptic relaxation for near wall turbulence models p. 15/22
20 Test cases Flat plate: Channel Flow: (Exp: Weighardt and Tillman) (Kim et al., 1987).5.45 Exp LDM ϕ - f.4 Cf e+6 4e+6 6e+6 8e+6 Re x Elliptic relaxation for near wall turbulence models p. 16/22
21 Test cases Natural convection: Tall cavity (Exp: Betts and Bokhari, 1995). V(m/s) V (m/s) V(m/s) Exp y/h =.5 ϕ - f LDM k-ε L-S Exp y/h =.7 Exp y/h =.95 a) x (m) V (m/s) V (m/s) V (m/s) Exp y/h =.5 ϕ - f LDM k-ε L-S Exp y/h =.7 Exp y/h = x(m) a) Ra =.86x1 6 b) Ra = 1.43x1 6 b) Elliptic relaxation for near wall turbulence models p. 17/22
22 Test cases Separated flows: Asymmetric plane diffuser (Exp: Buice and Eaton, 1997) 4 Profiles at x/h = ϕ model k-ε k-ω y/h 2 y/h Cp.4.2 Exp k-ε k - ω ϕ model U/Ub uu/ub 4 3 y/h 2 y/h x/h vv/ub uv/ub Elliptic relaxation for near wall turbulence models p. 18/22
23 Test cases Flow over periodic hills (Fine LES, Temmerman and Leschziner, 21) LES ϕ model k - ε Y/h a) Y/h U+x/h b) Streamlines: LES, k ε, ϕ Elliptic relaxation for near wall turbulence models p. 19/22
24 Test cases Three dimensional symmetric bump: Work in progress. (Simpson, 22) Elliptic relaxation for near wall turbulence models p. 2/22
25 Test cases Multiple impinging jets. Work in progress. (Geers et. al, 23) Top: Exp, Middle: k ε, Bottom: ϕ f Elliptic relaxation for near wall turbulence models p. 21/22
26 Conclusions The elliptic relaxation approach reproduces the near-wall effects. No need for damping functions or distance from the wall. With full Reynolds stress model too expensive (13 equations) v 2 f with EVM, cheaper but stiff due to boundary conditions. ϕ f better. Same effects but allows for uncoupling of equations, can be used in industrial codes. Tested in separated, impinging and buoyant flows. It is still more expensive than two-equation models. Elliptic relaxation for near wall turbulence models p. 22/22
(υ 2 /k) f TURBULENCE MODEL AND ITS APPLICATION TO FORCED AND NATURAL CONVECTION
(υ /k) f TURBULENCE MODEL AND ITS APPLICATION TO FORCED AND NATURAL CONVECTION K. Hanjalić, D. R. Laurence,, M. Popovac and J.C. Uribe Delft University of Technology, Lorentzweg, 68 CJ Delft, Nl UMIST,
More informationA Robust Formulation of the v2-f Model
Flow, Turbulence and Combustion 73: 169 185, 2004. C 2004 Kluwer Academic Publishers. Printed in the Netherlands. 169 A Robust Formulation of the v2-f Model D.R. LAURENCE 1,2, J.C. URIBE 1 and S.V. UTYUZHNIKOV
More informationA SEAMLESS HYBRID RANS/LES MODEL WITH DYNAMIC REYNOLDS-STRESS CORRECTION FOR HIGH REYNOLDS
A SEAMS HYBRID RANS/ MODEL WITH DYNAMIC REYNOLDS-STRESS CORRECTION FOR HIGH REYNOLDS NUMBER FLOWS ON COARSE GRIDS P. Nguyen 1, J. Uribe 2, I. Afgan 1 and D. Laurence 1 1 School of Mechanical, Aerospace
More information6.2 Governing Equations for Natural Convection
6. Governing Equations for Natural Convection 6..1 Generalized Governing Equations The governing equations for natural convection are special cases of the generalized governing equations that were discussed
More informationTurbulence Modeling I!
Outline! Turbulence Modeling I! Grétar Tryggvason! Spring 2010! Why turbulence modeling! Reynolds Averaged Numerical Simulations! Zero and One equation models! Two equations models! Model predictions!
More informationTurbulence - Theory and Modelling GROUP-STUDIES:
Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 046-0480 Johan Revstedt, tel 046-43 0 Turbulence - Theory and Modelling GROUP-STUDIES: Turbulence
More informationProbability density function (PDF) methods 1,2 belong to the broader family of statistical approaches
Joint probability density function modeling of velocity and scalar in turbulence with unstructured grids arxiv:6.59v [physics.flu-dyn] Jun J. Bakosi, P. Franzese and Z. Boybeyi George Mason University,
More informationTurbulence Solutions
School of Mechanical, Aerospace & Civil Engineering 3rd Year/MSc Fluids Turbulence Solutions Question 1. Decomposing into mean and fluctuating parts, we write M = M + m and Ũ i = U i + u i a. The transport
More informationMODELLING TURBULENT HEAT FLUXES USING THE ELLIPTIC BLENDING APPROACH FOR NATURAL CONVECTION
MODELLING TURBULENT HEAT FLUXES USING THE ELLIPTIC BLENDING APPROACH FOR NATURAL CONVECTION F. Dehoux Fluid Mechanics, Power generation and Environment Department MFEE Dept.) EDF R&D Chatou, France frederic.dehoux@edf.fr
More informationSTRESS TRANSPORT MODELLING 2
STRESS TRANSPORT MODELLING 2 T.J. Craft Department of Mechanical, Aerospace & Manufacturing Engineering UMIST, Manchester, UK STRESS TRANSPORT MODELLING 2 p.1 Introduction In the previous lecture we introduced
More informationABSTRACT OF ONE-EQUATION NEAR-WALL TURBULENCE MODELS. Ricardo Heinrich Diaz, Doctor of Philosophy, 2003
ABSTRACT Title of dissertation: CRITICAL EVALUATION AND DEVELOPMENT OF ONE-EQUATION NEAR-WALL TURBULENCE MODELS Ricardo Heinrich Diaz, Doctor of Philosophy, 2003 Dissertation directed by: Professor Jewel
More informationRECONSTRUCTION OF TURBULENT FLUCTUATIONS FOR HYBRID RANS/LES SIMULATIONS USING A SYNTHETIC-EDDY METHOD
RECONSTRUCTION OF TURBULENT FLUCTUATIONS FOR HYBRID RANS/LES SIMULATIONS USING A SYNTHETIC-EDDY METHOD N. Jarrin 1, A. Revell 1, R. Prosser 1 and D. Laurence 1,2 1 School of MACE, the University of Manchester,
More informationBoundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity
Boundary layer flows The logarithmic law of the wall Mixing length model for turbulent viscosity Tobias Knopp D 23. November 28 Reynolds averaged Navier-Stokes equations Consider the RANS equations with
More informationFundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.
Fundamental Concepts of Convection : Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 6.1 Boundary Layers: Physical Features Velocity Boundary Layer
More information6. Laminar and turbulent boundary layers
6. Laminar and turbulent boundary layers John Richard Thome 8 avril 2008 John Richard Thome (LTCM - SGM - EPFL) Heat transfer - Convection 8 avril 2008 1 / 34 6.1 Some introductory ideas Figure 6.1 A boundary
More informationTurbulent boundary layer
Turbulent boundary layer 0. Are they so different from laminar flows? 1. Three main effects of a solid wall 2. Statistical description: equations & results 3. Mean velocity field: classical asymptotic
More informationNONLINEAR FEATURES IN EXPLICIT ALGEBRAIC MODELS FOR TURBULENT FLOWS WITH ACTIVE SCALARS
June - July, 5 Melbourne, Australia 9 7B- NONLINEAR FEATURES IN EXPLICIT ALGEBRAIC MODELS FOR TURBULENT FLOWS WITH ACTIVE SCALARS Werner M.J. Lazeroms () Linné FLOW Centre, Department of Mechanics SE-44
More informationMasters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,
Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =
More informationOptimizing calculation costs of tubulent flows with RANS/LES methods
Optimizing calculation costs of tubulent flows with RANS/LES methods Investigation in separated flows C. Friess, R. Manceau Dpt. Fluid Flow, Heat Transfer, Combustion Institute PPrime, CNRS University
More informationCalculations on a heated cylinder case
Calculations on a heated cylinder case J. C. Uribe and D. Laurence 1 Introduction In order to evaluate the wall functions in version 1.3 of Code Saturne, a heated cylinder case has been chosen. The case
More informationNumerical Methods in Aerodynamics. Turbulence Modeling. Lecture 5: Turbulence modeling
Turbulence Modeling Niels N. Sørensen Professor MSO, Ph.D. Department of Civil Engineering, Alborg University & Wind Energy Department, Risø National Laboratory Technical University of Denmark 1 Outline
More informationResolving the dependence on free-stream values for the k-omega turbulence model
Resolving the dependence on free-stream values for the k-omega turbulence model J.C. Kok Resolving the dependence on free-stream values for the k-omega turbulence model J.C. Kok This report is based on
More informationComputation of turbulent natural convection at vertical walls using new wall functions
Computation of turbulent natural convection at vertical alls using ne all functions M. Hölling, H. Herig Institute of Thermo-Fluid Dynamics Hamburg University of Technology Denickestraße 17, 2173 Hamburg,
More informationFLOW-NORDITA Spring School on Turbulent Boundary Layers1
Jonathan F. Morrison, Ati Sharma Department of Aeronautics Imperial College, London & Beverley J. McKeon Graduate Aeronautical Laboratories, California Institute Technology FLOW-NORDITA Spring School on
More informationRANS simulations of rotating flows
Center for Turbulence Research Annual Research Briefs 1999 257 RANS simulations of rotating flows By G. Iaccarino, A. Ooi, B. A. Pettersson Reif AND P. Durbin 1. Motivation and objectives Numerous experimental
More informationTurbulent Boundary Layers & Turbulence Models. Lecture 09
Turbulent Boundary Layers & Turbulence Models Lecture 09 The turbulent boundary layer In turbulent flow, the boundary layer is defined as the thin region on the surface of a body in which viscous effects
More informationA robust k ε v 2 /k elliptic blending turbulence model with improved predictions in near-wall, separated and buoyant flows 1
A robust ε v 2 / elliptic blending turbulence model with improved predictions in near-wall, separated and buoyant flows 1 F. Billard a,, D. Laurence a,b a School of Mechanical, Aerospace and Civil Engineering,
More information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
More informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
More informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 19 Turbulent Flows Fausto Arpino f.arpino@unicas.it Introduction All the flows encountered in the engineering practice become unstable
More informationProblem 4.3. Problem 4.4
Problem 4.3 Problem 4.4 Problem 4.5 Problem 4.6 Problem 4.7 This is forced convection flow over a streamlined body. Viscous (velocity) boundary layer approximations can be made if the Reynolds number Re
More informationTable of Contents. Foreword... xiii. Preface... xv
Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationDIVERGENCE FREE SYNTHETIC EDDY METHOD FOR EMBEDDED LES INFLOW BOUNDARY CONDITIONS
DIVERGECE FREE SYTHETIC EDDY METHOD FOR EMBEDDED LES IFLOW BOUDARY CODITIOS R. Poletto, A. Revell, T. Craft,. Jarrin 1 School of Mechanical Aerospace and Civil Engineering University of Manchester, Manchester,
More informationCHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION
CHAPTER 7 SEVERAL FORMS OF THE EQUATIONS OF MOTION 7.1 THE NAVIER-STOKES EQUATIONS Under the assumption of a Newtonian stress-rate-of-strain constitutive equation and a linear, thermally conductive medium,
More informationComparison of Turbulence Models in the Flow over a Backward-Facing Step Priscila Pires Araujo 1, André Luiz Tenório Rezende 2
Comparison of Turbulence Models in the Flow over a Backward-Facing Step Priscila Pires Araujo 1, André Luiz Tenório Rezende 2 Department of Mechanical and Materials Engineering, Military Engineering Institute,
More informationDAY 19: Boundary Layer
DAY 19: Boundary Layer flat plate : let us neglect the shape of the leading edge for now flat plate boundary layer: in blue we highlight the region of the flow where velocity is influenced by the presence
More informationModeling Separation and Reattachment Using the Turbulent Potential Model
Modeling Separation and Reattachment Using the urbulent Potential Model Blair Perot & Hudong Wang Department of Mechanical Engineering University of Massachusetts, Amherst, MA ABSRAC A new type of turbulence
More informationρ t + (ρu j ) = 0 (2.1) x j +U j = 0 (2.3) ρ +ρ U j ρ
Chapter 2 Mathematical Models The following sections present the equations which are used in the numerical simulations documented in this thesis. For clarity, equations have been presented in Cartesian
More informationIntroduction to Turbulence AEEM Why study turbulent flows?
Introduction to Turbulence AEEM 7063-003 Dr. Peter J. Disimile UC-FEST Department of Aerospace Engineering Peter.disimile@uc.edu Intro to Turbulence: C1A Why 1 Most flows encountered in engineering and
More informationCHAPTER 11: REYNOLDS-STRESS AND RELATED MODELS. Turbulent Flows. Stephen B. Pope Cambridge University Press, 2000 c Stephen B. Pope y + < 1.
1/3 η 1C 2C, axi 1/6 2C y + < 1 axi, ξ > 0 y + 7 axi, ξ < 0 log-law region iso ξ -1/6 0 1/6 1/3 Figure 11.1: The Lumley triangle on the plane of the invariants ξ and η of the Reynolds-stress anisotropy
More informationSECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES
SECONDARY MOTION IN TURBULENT FLOWS OVER SUPERHYDROPHOBIC SURFACES Yosuke Hasegawa Institute of Industrial Science The University of Tokyo Komaba 4-6-1, Meguro-ku, Tokyo 153-8505, Japan ysk@iis.u-tokyo.ac.jp
More informationNon-linear k;";v 2 modeling. with application to high-lift. By F. S. Lien 1 AND P. A. Durbin 2
Center for Turbulence Research Proceedings of the Summer Program 1996 5 Non-linear k;";v 2 modeling with application to high-lift By F. S. Lien 1 AND P. A. Durbin 2 The k;";v 2 model has been investigated
More informationProbability density function and Reynolds-stress modeling of near-wall turbulent flows
Probability density function and Reynolds-stress modeling of near-wall turbulent flows Thomas D. Dreeben and Stephen B. Pope Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca,
More informationHeat Transfer from An Impingement Jet onto A Heated Half-Prolate Spheroid Attached to A Heated Flat Plate
1 nd International Conference on Environment and Industrial Innovation IPCBEE vol.35 (1) (1) IACSIT Press, Singapore Heat Transfer from An Impingement Jet onto A Heated Half-Prolate Spheroid Attached to
More informationHEAT TRANSFER IN A RECIRCULATION ZONE AT STEADY-STATE AND OSCILLATING CONDITIONS - THE BACK FACING STEP TEST CASE
HEAT TRANSFER IN A RECIRCULATION ZONE AT STEADY-STATE AND OSCILLATING CONDITIONS - THE BACK FACING STEP TEST CASE A.K. Pozarlik 1, D. Panara, J.B.W. Kok 1, T.H. van der Meer 1 1 Laboratory of Thermal Engineering,
More informationFundamentals of Fluid Dynamics: Elementary Viscous Flow
Fundamentals of Fluid Dynamics: Elementary Viscous Flow Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research
More informationStability of Shear Flow
Stability of Shear Flow notes by Zhan Wang and Sam Potter Revised by FW WHOI GFD Lecture 3 June, 011 A look at energy stability, valid for all amplitudes, and linear stability for shear flows. 1 Nonlinear
More information4.2 Concepts of the Boundary Layer Theory
Advanced Heat by Amir Faghri, Yuwen Zhang, and John R. Howell 4.2 Concepts of the Boundary Layer Theory It is difficult to solve the complete viscous flow fluid around a body unless the geometry is very
More informationZonal hybrid RANS-LES modeling using a Low-Reynolds-Number k ω approach
Zonal hybrid RANS-LES modeling using a Low-Reynolds-Number k ω approach S. Arvidson 1,2, L. Davidson 1, S.-H. Peng 1,3 1 Chalmers University of Technology 2 SAAB AB, Aeronautics 3 FOI, Swedish Defence
More informationCOMPARISON OF DIFFERENT SUBGRID TURBULENCE MODELS AND BOUNDARY CONDITIONS FOR LARGE-EDDY-SIMULATIONS OF ROOM AIR FLOWS.
7 TH INTRNATINAL CNFRNC N AIR DISTRIBTIN IN RMS, RMVNT 2 pp. 31-36 CMPARISN F DIFFRNT SBGRID TRBLNC MDLS AND BNDARY CNDITINS FR LARG-DDY-SIMLATINS F RM AIR FLWS. D. Müller 1, L. Davidson 2 1 Lehrstuhl
More informationComputational Fluid Dynamics 2
Seite 1 Introduction Computational Fluid Dynamics 11.07.2016 Computational Fluid Dynamics 2 Turbulence effects and Particle transport Martin Pietsch Computational Biomechanics Summer Term 2016 Seite 2
More informationTurbulent Flows. g u
.4 g u.3.2.1 t. 6 4 2 2 4 6 Figure 12.1: Effect of diffusion on PDF shape: solution to Eq. (12.29) for Dt =,.2,.2, 1. The dashed line is the Gaussian with the same mean () and variance (3) as the PDF at
More informationA TURBULENT HEAT FLUX TWO EQUATION θ 2 ε θ CLOSURE BASED ON THE V 2F TURBULENCE MODEL
TASK QUARTERLY 7 No 3 (3), 375 387 A TURBULENT HEAT FLUX TWO EQUATION θ ε θ CLOSURE BASED ON THE V F TURBULENCE MODEL MICHAŁ KARCZ AND JANUSZ BADUR Institute of Fluid-Flow Machinery, Polish Academy of
More informationCHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW
CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW 4.1 Introduction Boundary layer concept (Prandtl 1904): Eliminate selected terms in the governing equations Two key questions (1) What are the
More informationThe mean shear stress has both viscous and turbulent parts. In simple shear (i.e. U / y the only non-zero mean gradient):
8. TURBULENCE MODELLING 1 SPRING 2019 8.1 Eddy-viscosity models 8.2 Advanced turbulence models 8.3 Wall boundary conditions Summary References Appendix: Derivation of the turbulent kinetic energy equation
More informationCONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 4 HEAT TRANSFER IN CHANNEL FLOW BASIC CONCEPTS BASIC CONCEPTS Laminar
More informationLaminar Flow. Chapter ZERO PRESSURE GRADIENT
Chapter 2 Laminar Flow 2.1 ZERO PRESSRE GRADIENT Problem 2.1.1 Consider a uniform flow of velocity over a flat plate of length L of a fluid of kinematic viscosity ν. Assume that the fluid is incompressible
More informationLarge eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions
June 30 - July 3, 2015 Melbourne, Australia 9 P-26 Large eddy simulation of turbulent flow over a backward-facing step: effect of inflow conditions Jungwoo Kim Department of Mechanical System Design Engineering
More informationBoundary-Layer Theory
Hermann Schlichting Klaus Gersten Boundary-Layer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22
More informationModel Studies on Slag-Metal Entrainment in Gas Stirred Ladles
Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Anand Senguttuvan Supervisor Gordon A Irons 1 Approach to Simulate Slag Metal Entrainment using Computational Fluid Dynamics Introduction &
More informationRobust turbulence modelling of complex wall-bounded flows with heat transfer
Robust turbulence modelling of complex wall-bounded flows with heat transfer M. POPOVAC and K. HANJALIĆ Department of Multi-scale Physics Faculty of Applied Sciences Delft University of Technology Lorentzweg,
More informationCFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University
CFD in Heat Transfer Equipment Professor Bengt Sunden Division of Heat Transfer Department of Energy Sciences Lund University email: bengt.sunden@energy.lth.se CFD? CFD = Computational Fluid Dynamics;
More informationIntroduction to ANSYS FLUENT
Lecture 6 Turbulence 14. 0 Release Introduction to ANSYS FLUENT 1 2011 ANSYS, Inc. January 19, 2012 Lecture Theme: Introduction The majority of engineering flows are turbulent. Successfully simulating
More informationGoverning Equations for Turbulent Flow
Governing Equations for Turbulent Flow (i) Boundary Layer on a Flat Plate ρu x Re x = = Reynolds Number µ Re Re x =5(10) 5 Re x =10 6 x =0 u/ U = 0.99 層流區域 過渡區域 紊流區域 Thickness of boundary layer The Origin
More informationHybrid LES RANS Method Based on an Explicit Algebraic Reynolds Stress Model
Hybrid RANS Method Based on an Explicit Algebraic Reynolds Stress Model Benoit Jaffrézic, Michael Breuer and Antonio Delgado Institute of Fluid Mechanics, LSTM University of Nürnberg bjaffrez/breuer@lstm.uni-erlangen.de
More informationUNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences. MEK4300/9300 Viscous flow og turbulence
UNIVERSITY OF OSLO Faculty of Mathematics and Natural Sciences Examination in: Day of examination: Friday 15. June 212 Examination hours: 9. 13. This problem set consists of 5 pages. Appendices: Permitted
More informationExplicit algebraic Reynolds stress models for boundary layer flows
1. Explicit algebraic models Two explicit algebraic models are here compared in order to assess their predictive capabilities in the simulation of boundary layer flow cases. The studied models are both
More informationHEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1
HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the
More informationAn evaluation of a conservative fourth order DNS code in turbulent channel flow
Center for Turbulence Research Annual Research Briefs 2 2 An evaluation of a conservative fourth order DNS code in turbulent channel flow By Jessica Gullbrand. Motivation and objectives Direct numerical
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In
More informationBOUNDARY LAYER FLOWS HINCHEY
BOUNDARY LAYER FLOWS HINCHEY BOUNDARY LAYER PHENOMENA When a body moves through a viscous fluid, the fluid at its surface moves with it. It does not slip over the surface. When a body moves at high speed,
More informationTurbulent eddies in the RANS/LES transition region
Turbulent eddies in the RANS/LES transition region Ugo Piomelli Senthil Radhakrishnan Giuseppe De Prisco University of Maryland College Park, MD, USA Research sponsored by the ONR and AFOSR Outline Motivation
More informationNumerical simulations of heat transfer in plane channel flow
Numerical simulations of heat transfer in plane channel flow Najla EL GHARBI 1, 3, a, Rafik ABSI 2, b and Ahmed BENZAOUI 3, c 1 Renewable Energy Development Center, BP 62 Bouzareah 163 Algiers, Algeria
More informationA dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries
Center for Turbulence Research Annual Research Briefs 2006 41 A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries By D. You AND P. Moin 1. Motivation
More information2.3 The Turbulent Flat Plate Boundary Layer
Canonical Turbulent Flows 19 2.3 The Turbulent Flat Plate Boundary Layer The turbulent flat plate boundary layer (BL) is a particular case of the general class of flows known as boundary layer flows. The
More informationFOUR-WAY COUPLED SIMULATIONS OF TURBULENT
FOUR-WAY COUPLED SIMULATIONS OF TURBULENT FLOWS WITH NON-SPHERICAL PARTICLES Berend van Wachem Thermofluids Division, Department of Mechanical Engineering Imperial College London Exhibition Road, London,
More informationChapter 6: Incompressible Inviscid Flow
Chapter 6: Incompressible Inviscid Flow 6-1 Introduction 6-2 Nondimensionalization of the NSE 6-3 Creeping Flow 6-4 Inviscid Regions of Flow 6-5 Irrotational Flow Approximation 6-6 Elementary Planar Irrotational
More informationTurbulence Laboratory
Objective: CE 319F Elementary Mechanics of Fluids Department of Civil, Architectural and Environmental Engineering The University of Texas at Austin Turbulence Laboratory The objective of this laboratory
More informationV (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
More informationChapter 7 The Time-Dependent Navier-Stokes Equations Turbulent Flows
Chapter 7 The Time-Dependent Navier-Stokes Equations Turbulent Flows Remark 7.1. Turbulent flows. The usually used model for turbulent incompressible flows are the incompressible Navier Stokes equations
More informationPeriodic planes v i+1 Top wall u i. Inlet. U m y. Jet hole. Figure 2. Schematic of computational domain.
Flow Characterization of Inclined Jet in Cross Flow for Thin Film Cooling via Large Eddy Simulation Naqavi, I.Z. 1, Savory, E. 2 and Martinuzzi, R. J. 3 1,2 The Univ. of Western Ontario, Dept. of Mech.
More informationChapter 9: Differential Analysis
9-1 Introduction 9-2 Conservation of Mass 9-3 The Stream Function 9-4 Conservation of Linear Momentum 9-5 Navier Stokes Equation 9-6 Differential Analysis Problems Recall 9-1 Introduction (1) Chap 5: Control
More informationExercise 5: Exact Solutions to the Navier-Stokes Equations I
Fluid Mechanics, SG4, HT009 September 5, 009 Exercise 5: Exact Solutions to the Navier-Stokes Equations I Example : Plane Couette Flow Consider the flow of a viscous Newtonian fluid between two parallel
More informationHomework 4 in 5C1212; Part A: Incompressible Navier- Stokes, Finite Volume Methods
Homework 4 in 5C11; Part A: Incompressible Navier- Stokes, Finite Volume Methods Consider the incompressible Navier Stokes in two dimensions u x + v y = 0 u t + (u ) x + (uv) y + p x = 1 Re u + f (1) v
More informationProbability density function modeling of scalar mixing from concentrated sources in turbulent channel flow
PHYSICS OF FLUIDS 19, 115106 2007 Probability density function modeling of scalar mixing from concentrated sources in turbulent channel flow J. Bakosi, a P. Franzese, and Z. Boybeyi College of Science,
More informationFluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
More informationConvection in Three-Dimensional Separated and Attached Flow
Convection in Three-Dimensional Separated and Attached Flow B. F. Armaly Convection Heat Transfer Laboratory Department of Mechanical and Aerospace Engineering, and Engineering Mechanics University of
More informationSome remarks on grad-div stabilization of incompressible flow simulations
Some remarks on grad-div stabilization of incompressible flow simulations Gert Lube Institute for Numerical and Applied Mathematics Georg-August-University Göttingen M. Stynes Workshop Numerical Analysis
More informationModifications of the V2 Model for Computing the Flow in a 3D Wall Jet Davidson, L.; Nielsen, Peter Vilhelm; Sveningsson, A.
Aalborg Universitet Modifications of the V2 Model for Computing the Flow in a D Wall Jet Davidson, L.; Nielsen, Peter Vilhelm; Sveningsson, A. Published in: Proceedings of the International Symposium on
More informationAPPLICATION OF THE DEFECT FORMULATION TO THE INCOMPRESSIBLE TURBULENT BOUNDARY LAYER
APPLICATION OF THE DEFECT FORMULATION TO THE INCOMPRESSIBLE TURBULENT BOUNDARY LAYER O. ROUZAUD ONERA OAt1 29 avenue de la Division Leclerc - B.P. 72 92322 CHATILLON Cedex - France AND B. AUPOIX AND J.-PH.
More information(1) Transition from one to another laminar flow. (a) Thermal instability: Bernard Problem
Professor Fred Stern Fall 2014 1 Chapter 6: Viscous Flow in Ducts 6.2 Stability and Transition Stability: can a physical state withstand a disturbance and still return to its original state. In fluid mechanics,
More informationTurbulence modelling for rotating flows
Turbulence modelling for rotating flows Presentation plan. Thesis context, goals and roadmap 2. Effects of rotation on a turbulent flow 3. RANS modelling of rotating flows 4. Conclusion and perspectives
More informationChapter 9: Differential Analysis of Fluid Flow
of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known
More informationRANS modeling for compressible and transitional flows
Center for Turbulence Research Proceedings of the Summer Program 1998 267 RANS modeling for compressible and transitional flows By F. S. Lien 1, G. Kalitzin AND P. A. Durbin Recent LES suggested that the
More informationDIVERGENCE FREE SYNTHETIC EDDY METHOD FOR EMBEDDED LES INFLOW BOUNDARY CONDITIONS
DIVERGECE FREE SYTHETIC EDDY METHOD FOR EMBEDDED LES IFLOW BOUDARY CODITIOS R. Poletto, A. Revell, T. Craft,. Jarrin School of Mechanical Aerospace and Civil Engineering University of Manchester, Manchester,
More informationJ. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and
J. Szantyr Lecture No. 4 Principles of the Turbulent Flow Theory The phenomenon of two markedly different types of flow, namely laminar and turbulent, was discovered by Osborne Reynolds (184 191) in 1883
More informationModelling of turbulent flows: RANS and LES
Modelling of turbulent flows: RANS and LES Turbulenzmodelle in der Strömungsmechanik: RANS und LES Markus Uhlmann Institut für Hydromechanik Karlsruher Institut für Technologie www.ifh.kit.edu SS 2012
More informationA Low Reynolds Number Variant of Partially-Averaged Navier-Stokes Model for Turbulence
Int. J. Heat Fluid Flow, Vol., pp. 65-669 (), doi:.6/j.ijheatfluidflow... A Low Reynolds Number Variant of Partially-Averaged Navier-Stokes Model for Turbulence J.M. Ma,, S.-H. Peng,, L. Davidson, and
More information7 The Navier-Stokes Equations
18.354/12.27 Spring 214 7 The Navier-Stokes Equations In the previous section, we have seen how one can deduce the general structure of hydrodynamic equations from purely macroscopic considerations and
More information