Computational Fluid Dynamics 2


 Marjory Williams
 2 years ago
 Views:
Transcription
1 Seite 1 Introduction Computational Fluid Dynamics Computational Fluid Dynamics 2 Turbulence effects and Particle transport Martin Pietsch Computational Biomechanics Summer Term 2016
2 Seite 2 Review Computational Fluid Dynamics System equations: 1 mass conservation ρ t 2 momentum conservation 3 energy conservation + (ρ u ) = 0 ρ u t + (ρ u ) u = ρ f + σ ρ e t = ρ Q + (κ T ) + (σ u ) ( σ ) u 4 equation of state (e.g. ideal gas equation)
3 Seite 3 Review Computational Fluid Dynamics Incompressible fluid / flow assumption: Incompressible flow: 0 = dρ (x, t) dt = ρ(x, t) + ρ(x, t) u t Incompressible fluid: ρ (x, t) = ρ(x, t) = 0 t Continuity equation: 0,flow ass. {}}{ ρ ρ + (ρ u ) = + ρ u +ρ u = ρ u = 0 t }{{} t }{{} 0,fluid ass. 0,fluid ass. t It follows: u = 0 3 t 2 (divergency free velocity field) t 1
4 Seite 4 Review Computational Fluid Dynamics Incompressible flow/fluid + isothermal assumption: From T = const. with d dt ρ = 0 follows: 1 Pressure is given with p ρ (equation of state) 2 Energy is a function of ρ and u the energy conservation contains no extra information For a newtonian fluid we get the NavierStokes equations as NavierStokes equations u = 0 (1) u t + ( u ) u = f 1 p + ν τ (2) ρ Note: often, the kinematic viscosity ν := µ ρ is used
5 Seite 5 Dimensionless description Computational Fluid Dynamics Dimensionless NavierStokes: NavierStokes momentum equation u t + ( u ) u = f 1 ρ p + µ ρ τ Define characteristic time T, length L and velocity U with L = U T : τ = t T v = u U ξ = x L Dimensionless representation of the momentum equation: v τ + ( v ) v = L U 2 f 1 ρu 2 p + µ ρul τ dimensionless forcedensity κ := L f (look for Froude number) U 2 pressure rescaling p := (NOTE: only for inc. fluid) p ρu 2
6 Seite 6 Dimensionless description Computational Fluid Dynamics Diffusion term & Reynolds number: v µ + ( v ) v = κ p + τ ρul τ Definition of the Reynolds number: Re := inertia forces viscous forces = ρul µ inertia force: F in = ρl3 U T (momentum transfer) viscous force: F vis = µl 2 U L ( velocity diffusion ) Dimensionless NavierStokes equations v τ v = 0 (3) 1 + ( v ) v = κ p + τ (4) Re
7 Seite 7 Pressure equation Computational Fluid Dynamics Pressure equation: v τ + ( v ) v = κ p + 1 Re τ Divergency free velocity field implies ( ) ( v + ( v ) v = κ p + 1 ) τ Re τ with τ v = 0, we get the PoissinPressure equation: ( p = κ ( v ) v + 1 ) Re τ
8 Seite 8 Turbulent flow Computational Fluid Dynamics Turbulent flow: If Re << 1, the diffusion time scale is much smaller as the time scale for momentum transportation velocity field perturbations smooth out quickly velocity field tends to be laminar If Re >> 1, momentum transportation is the main effect for the fluid flow description velocity field perturbations increase quickly velocity field tends to be turbulent Example: (flow in pipe) Reynolds number: Re = ρ d vz µ Observation: Julius Rotta (at 1950) Re krit r v, µ, ρ z d
9 Seite 9 Turbulent flow Computational Fluid Dynamics Energy cascade: 1 energy injection range (small viscous effects) 2 inertial subrange 3 dissipation range (large viscous effects) log(e) log(k) visualization after the model of Lewis Fry Richardson e := energy, k := wave number
10 Seite 10 Turbulent flow Computational Fluid Dynamics Kolmogorov scales: The smallest scales that influences the turbulent flow by dissipation effects. Note: To retain energy conservation at the numerical domain, one have to resolve also the dissipative scales in the NavierStokes equation! The scales are given as: (ɛ is the average dissipation rate) ( ) 1 ( ) 1 µ 3 4 µ length : η = ɛ ρ 3 vel : u η = ρ ɛ 4 time : τ η = ( µ ρ ɛ ) 1 2 with Re η = η u η µ ρ = 1
11 Seite 11 Turbulence models Computational Fluid Dynamics Resolution problem: Approximation of the dissipation rate (from large scales): ɛ kinetic energy time U2 T = U3 L Therefore we get the relation: ( ) L µ 3 1 η = L ɛ ρ 3 4 L ( U 3 ρ 3 L µ 3 ) 1 4 = Re 3 4 Example: (L 10 3 m, v 1 m s Re , ρ 1.3 kg m 3, µ 17.1 µpa s) η m
12 Seite 12 Turbulence models Computational Fluid Dynamics Resolution problem: Approximation of the dissipation rate (from large scales): ɛ kinetic energy time U2 T = U3 L Therefore we get the relation: ( ) L µ 3 1 η = L ɛ ρ 3 4 L ( U 3 ρ 3 L µ 3 ) 1 4 = Re 3 4 Example: (L 10 3 m, v 0.1 m s Re 35 η m, ρ 1060 kg m 3, µ 3 mpa s)
13 Seite 13 Turbulence models Computational Fluid Dynamics Simulation approaches: Direct numerical simulation (DNS): Assumption that the flow inside of a volume element is purely laminar and no dissipation effect occurs. (Note: If this is not true, the energy conservation results in a different flow field.) Eddy dissipation modelling on small scales: ReynoldsAveraged Navier Stokes (RANS) LargeEddy Simulation... v = v + v and p = p + p with the mean value of and the fluctuating part.
14 Seite 14 Turbulence models Computational Fluid Dynamics RANS: Special cases: temporal or spatial averaging N In general: f ( x, t) = lim f ( x, t) N n Fluctuating part: f = 0 Reynolds equations: v t v = 0 + ( v ) v = f p + 1 Re τ ( v ) v }{{} correlation property v v v xv x v x v y v xv = v y v x v y v y v y v z v zv x v z v y v zv z
15 Seite 15 Turbulence models Computational Fluid Dynamics RANS models: Zero equation models ν T = ξ 2 v (mixing length ξ) One equation models (example: Spalart and Allmaras) ( ) ν T νt + v ν T = ν T + S ν t σ T Two equation models (k ɛ, k ω, SST) k = 1 2 tr v v (mean of the fluctuating kinetic energy) dissipation rate ɛ eddy frequency ω 1 k ɛ: good on free flow fields with no walls 2 k ω: near wall approximation is good 3 SST brings the advantage of booth together
16 Seite 16 Turbulence models Computational Fluid Dynamics LargeEddy simulations (LES): spatial averaging method v( x, t) := v( x, t) G( x, x, ) dv with 1 stepfunction { 1, if x x < /2 G := 3 0, else V 2 gaussfilter { β x x } G := A( ) exp
17 Seite 17 Turbulence models Computational Fluid Dynamics LargeEddy simulations (LES): LES equation: v t v = 0 + ( v ) v = f p + 1 Re τ τ S with τ S := v v v v. Detailed look: τ S = v v v v + v v v v + v v }{{}}{{}}{{} L C τ SR Leonardstrain: creation of small eddys through large eddys Crossstress: interaction of the different scales Subgridscale Reynolds stress tensor
Modeling of turbulence in stirred vessels using large eddy simulation
Modeling of turbulence in stirred vessels using large eddy simulation André Bakker (presenter), Kumar Dhanasekharan, Ahmad Haidari, and SungEun Kim Fluent Inc. Presented at CHISA 2002 August 2529, Prague,
More informationAER1310: TURBULENCE MODELLING 1. Introduction to Turbulent Flows C. P. T. Groth c Oxford Dictionary: disturbance, commotion, varying irregularly
1. Introduction to Turbulent Flows Coverage of this section: Definition of Turbulence Features of Turbulent Flows Numerical Modelling Challenges History of Turbulence Modelling 1 1.1 Definition of Turbulence
More informationMath 575Lecture Viscous Newtonian fluid and the NavierStokes equations
Math 575Lecture 13 In 1845, tokes extended Newton s original idea to find a constitutive law which relates the Cauchy stress tensor to the velocity gradient, and then derived a system of equations. The
More informationTurbulence and its modelling. Outline. Department of Fluid Mechanics, Budapest University of Technology and Economics.
Outline Department of Fluid Mechanics, Budapest University of Technology and Economics October 2009 Outline Outline Definition and Properties of Properties High Re number Disordered, chaotic 3D phenomena
More informationMass Transfer in Turbulent Flow
Mass Transfer in Turbulent Flow ChEn 6603 References: S.. Pope. Turbulent Flows. Cambridge University Press, New York, 2000. D. C. Wilcox. Turbulence Modeling for CFD. DCW Industries, La Caada CA, 2000.
More informationEddy viscosity. AdOc 4060/5060 Spring 2013 Chris Jenkins. Turbulence (video 1hr):
AdOc 4060/5060 Spring 2013 Chris Jenkins Eddy viscosity Turbulence (video 1hr): http://cosee.umaine.edu/programs/webinars/turbulence/?cfid=8452711&cftoken=36780601 Part B Surface wind stress Wind stress
More informationAnswers to Homework #9
Answers to Homework #9 Problem 1: 1. We want to express the kinetic energy per unit wavelength E(k), of dimensions L 3 T 2, as a function of the local rate of energy dissipation ɛ, of dimensions L 2 T
More information2. Conservation Equations for Turbulent Flows
2. Conservation Equations for Turbulent Flows Coverage of this section: Review of Tensor Notation Review of NavierStokes Equations for Incompressible and Compressible Flows Reynolds & Favre Averaging
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 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 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 informationTurbulence Modeling. Cuong Nguyen November 05, The incompressible NavierStokes equations in conservation form are u i x i
Turbulence Modeling Cuong Nguyen November 05, 2005 1 Incompressible Case 1.1 Reynoldsaveraged NavierStokes equations The incompressible NavierStokes equations in conservation form are u i x i = 0 (1)
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 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 informationTurbulence modelling. Sørensen, Niels N. Publication date: Link back to DTU Orbit
Downloaded from orbit.dtu.dk on: Dec 19, 2017 Turbulence modelling Sørensen, Niels N. Publication date: 2010 Link back to DTU Orbit Citation (APA): Sørensen, N. N. (2010). Turbulence modelling. Paper presented
More informationIntroduction to Turbulence and Turbulence Modeling
Introduction to Turbulence and Turbulence Modeling Part I Venkat Raman The University of Texas at Austin Lecture notes based on the book Turbulent Flows by S. B. Pope Turbulent Flows Turbulent flows Commonly
More informationAn Introduction to Theories of Turbulence. James Glimm Stony Brook University
An Introduction to Theories of Turbulence James Glimm Stony Brook University Topics not included (recent papers/theses, open for discussion during this visit) 1. Turbulent combustion 2. Turbulent mixing
More informationBefore we consider two canonical turbulent flows we need a general description of turbulence.
Chapter 2 Canonical Turbulent Flows Before we consider two canonical turbulent flows we need a general description of turbulence. 2.1 A Brief Introduction to Turbulence One way of looking at turbulent
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 informationmeters, we can rearrange this expression to give
Turbulence When the Reynolds number becomes sufficiently large, the nonlinear term (u ) u in the momentum equation inevitably becomes comparable to other important terms and the flow becomes more complicated.
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 informationSimulations for Enhancing Aerodynamic Designs
Simulations for Enhancing Aerodynamic Designs 2. Governing Equations and Turbulence Models by Dr. KANNAN B T, M.E (Aero), M.B.A (Airline & Airport), PhD (Aerospace Engg), Grad.Ae.S.I, M.I.E, M.I.A.Eng,
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 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 informationEuler equation and NavierStokes equation
Euler equation and NavierStokes equation WeiHan Hsiao a a Department of Physics, The University of Chicago Email: weihanhsiao@uchicago.edu ABSTRACT: This is the note prepared for the Kadanoff center
More informationTurbulence  Theory and Modelling GROUPSTUDIES:
Lund Institute of Technology Department of Energy Sciences Division of Fluid Mechanics Robert Szasz, tel 0460480 Johan Revstedt, tel 04643 0 Turbulence  Theory and Modelling GROUPSTUDIES: Turbulence
More informationLecture 14. Turbulent Combustion. We know what a turbulent flow is, when we see it! it is characterized by disorder, vorticity and mixing.
Lecture 14 Turbulent Combustion 1 We know what a turbulent flow is, when we see it! it is characterized by disorder, vorticity and mixing. In a fluid flow, turbulence is characterized by fluctuations of
More informationIntroduction to Turbulence Modeling
Introduction to Turbulence Modeling UPV/EHU  Universidad del País Vasco Escuela Técnica Superior de Ingeniería de Bilbao March 26, 2014 G. Stipcich BCAM Basque Center for Applied Mathematics, Bilbao,
More informationOE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004
OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie
More informationEngineering. Spring Department of Fluid Mechanics, Budapest University of Technology and Economics. LargeEddy Simulation in Mechanical
Outline Geurts Book Department of Fluid Mechanics, Budapest University of Technology and Economics Spring 2013 Outline Outline Geurts Book 1 Geurts Book Origin This lecture is strongly based on the book:
More informationChapter 2. General concepts. 2.1 The NavierStokes equations
Chapter 2 General concepts 2.1 The NavierStokes equations The NavierStokes equations model the fluid mechanics. This set of differential equations describes the motion of a fluid. In the present work
More informationTurbulence: Basic Physics and Engineering Modeling
DEPARTMENT OF ENERGETICS Turbulence: Basic Physics and Engineering Modeling Numerical Heat Transfer Pietro Asinari, PhD Spring 2007, TOP UIC Program: The Master of Science Degree of the University of Illinois
More informationOpenFOAM selected solver
OpenFOAM selected solver Roberto Pieri  SCS Italy 1618 June 2014 Introduction to NavierStokes equations and RANS Turbulence modelling Numeric discretization NavierStokes equations Convective term {}}{
More information1 Introduction to Governing Equations 2 1a Methodology... 2
Contents 1 Introduction to Governing Equations 2 1a Methodology............................ 2 2 Equation of State 2 2a Mean and Turbulent Parts...................... 3 2b Reynolds Averaging.........................
More informationAA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS
AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS Hierarchy of Mathematical Models 1 / 29 AA214B: NUMERICAL METHODS FOR COMPRESSIBLE FLOWS 2 / 29
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.unierlangen.de
More informationChapter 7 The TimeDependent NavierStokes Equations Turbulent Flows
Chapter 7 The TimeDependent NavierStokes Equations Turbulent Flows Remark 7.1. Turbulent flows. The usually used model for turbulent incompressible flows are the incompressible Navier Stokes equations
More informationExercises in Combustion Technology
Exercises in Combustion Technology Exercise 4: Turbulent Premixed Flames Turbulent Flow: Task 1: Estimation of Turbulence Quantities BorghiPeters diagram for premixed combustion Task 2: Derivation of
More informationTutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace
Tutorial School on Fluid Dynamics: Aspects of Turbulence Session I: Refresher Material Instructor: James Wallace Adapted from Publisher: John S. Wiley & Sons 2002 Center for Scientific Computation and
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 informationBOUNDARY LAYER ANALYSIS WITH NAVIERSTOKES EQUATION IN 2D CHANNEL FLOW
Proceedings of,, BOUNDARY LAYER ANALYSIS WITH NAVIERSTOKES EQUATION IN 2D CHANNEL FLOW Yunho Jang Department of Mechanical and Industrial Engineering University of Massachusetts Amherst, MA 01002 Email:
More informationBAE 820 Physical Principles of Environmental Systems
BAE 820 Physical Principles of Environmental Systems Stokes' law and Reynold number Dr. Zifei Liu The motion of a particle in a fluid environment, such as air or water m dv =F(t)  F dt d  1 4 2 3 πr3
More informationThe Johns Hopkins Turbulence Databases (JHTDB)
The Johns Hopkins Turbulence Databases (JHTDB) HOMOGENEOUS BUOYANCY DRIVEN TURBULENCE DATA SET Data provenance: D. Livescu 1 Database Ingest and Web Services: C. Canada 1, K. Kalin 2, R. Burns 2 & IDIES
More informationA combined application of the integral wall model and the rough wall rescalingrecycling method
AIAA 25299 A combined application of the integral wall model and the rough wall rescalingrecycling method X.I.A. Yang J. Sadique R. Mittal C. Meneveau Johns Hopkins University, Baltimore, MD, 228, USA
More informationA Computational Investigation of a Turbulent Flow Over a Backward Facing Step with OpenFOAM
206 9th International Conference on Developments in esystems Engineering A Computational Investigation of a Turbulent Flow Over a Backward Facing Step with OpenFOAM Hayder AlJelawy, Stefan Kaczmarczyk
More informationCharacteristics of LinearlyForced Scalar Mixing in Homogeneous, Isotropic Turbulence
Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, July 913, 2012 ICCFD71103 Characteristics of LinearlyForced Scalar Mixing in Homogeneous, Isotropic Turbulence
More informationPhysical Properties of Fluids
Physical Properties of Fluids Viscosity: Resistance to relative motion between adjacent layers of fluid. Dynamic Viscosity:generally represented as µ. A flat plate moved slowly with a velocity V parallel
More informationIntroduction to Fluid Mechanics
Introduction to Fluid Mechanics TienTsan Shieh April 16, 2009 What is a Fluid? The key distinction between a fluid and a solid lies in the mode of resistance to change of shape. The fluid, unlike the
More informationChapter 7. Basic Turbulence
Chapter 7 Basic Turbulence The universe is a highly turbulent place, and we must understand turbulence if we want to understand a lot of what s going on. Interstellar turbulence causes the twinkling of
More informationTurbulence (January 7, 2005)
http://www.tfd.chalmers.se/grkurs/mtf071 70 Turbulence (January 7, 2005) The literature for this lecture (denoted by LD) and the following on turbulence models is: L. Davidson. An Introduction to Turbulence
More informationMultiscale Computation of Isotropic Homogeneous Turbulent Flow
Multiscale Computation of Isotropic Homogeneous Turbulent Flow Tom Hou, Danping Yang, and Hongyu Ran Abstract. In this article we perform a systematic multiscale analysis and computation for incompressible
More informationCOMMUTATION ERRORS IN PITM SIMULATION
COMMUTATION ERRORS IN PITM SIMULATION B. Chaouat ONERA, 93 Châtillon, France Bruno.Chaouat@onera.fr Introduction Large eddy simulation is a promising route. This approach has been largely developed in
More informationCHAPTER 11: REYNOLDSSTRESS 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 loglaw 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 Reynoldsstress anisotropy
More informationChapter 2: Fluid Dynamics Review
7 Chapter 2: Fluid Dynamics Review This chapter serves as a short review of basic fluid mechanics. We derive the relevant transport equations (or conservation equations), state Newton s viscosity law leading
More informationNumerical simulation of wave breaking in turbulent twophase Couette flow
Center for Turbulence Research Annual Research Briefs 2012 171 Numerical simulation of wave breaking in turbulent twophase Couette flow By D. Kim, A. Mani AND P. Moin 1. Motivation and objectives When
More informationB.1 NAVIER STOKES EQUATION AND REYNOLDS NUMBER. = UL ν. Re = U ρ f L μ
APPENDIX B FLUID DYNAMICS This section is a brief introduction to fluid dynamics. Historically, a simplified concept of the boundary layer, the unstirred water layer, has been operationally used in the
More informationIMPLEMENTATION AND VALIDATION OF THE HYBRID TURBULENCE MODELS IN AN UNSTRUCTURED GRID CODE
University of Kentucky UKnowledge University of Kentucky Master's Theses Graduate School 007 IMPLEMENTATION AND VALIDATION OF THE HYBRID TURBULENCE MODELS IN AN UNSTRUCTURED GRID CODE Sri S. Panguluri
More information7 The NavierStokes Equations
18.354/12.27 Spring 214 7 The NavierStokes Equations In the previous section, we have seen how one can deduce the general structure of hydrodynamic equations from purely macroscopic considerations and
More informationSimulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions
Simulating Drag Crisis for a Sphere Using Skin Friction Boundary Conditions Johan Hoffman May 14, 2006 Abstract In this paper we use a General Galerkin (G2) method to simulate drag crisis for a sphere,
More informationLES of Turbulent Flows: Lecture 3
LES of Turbulent Flows: Lecture 3 Dr. Jeremy A. Gibbs Department of Mechanical Engineering University of Utah Fall 2016 1 / 53 Overview 1 Website for those auditing 2 Turbulence Scales 3 Fourier transforms
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 NavierStokes equations Consider the RANS equations with
More informationDirect Numerical Simulations of convergingdiverging channel flow
Intro Numerical code Results Conclusion Direct Numerical Simulations of convergingdiverging channel flow J.P. Laval (1), M. Marquillie (1) JeanPhilippe.Laval@univlille1.fr (1) Laboratoire de Me canique
More informationESCI 485 Air/sea Interaction Lesson 2 Turbulence Dr. DeCaria
ESCI 485 Air/sea Interaction Lesson Turbulence Dr. DeCaria References: Airsea Interaction: Laws and Mechanisms, Csanady An Introduction to Dynamic Meteorology ( rd edition), J.R. Holton An Introduction
More informationManhar Dhanak Florida Atlantic University Graduate Student: Zaqie Reza
REPRESENTING PRESENCE OF SUBSURFACE CURRENT TURBINES IN OCEAN MODELS Manhar Dhanak Florida Atlantic University Graduate Student: Zaqie Reza 1 Momentum Equations 2 Effect of inclusion of Coriolis force
More informationA simple subgridscale model for astrophysical turbulence
CfCA User Meeting NAOJ, 2930 November 2016 A simple subgridscale model for astrophysical turbulence Nobumitsu Yokoi Institute of Industrial Science (IIS), Univ. of Tokyo Collaborators Axel Brandenburg
More informationEngineering. Spring Department of Fluid Mechanics, Budapest University of Technology and Economics. LargeEddy Simulation in Mechanical
Outline Department of Fluid Mechanics, Budapest University of Technology and Economics Spring 2011 Outline Outline Part I First Lecture Connection between time and ensemble average Ergodicity1 Ergodicity
More informationSOME DYNAMICAL FEATURES OF THE TURBULENT FLOW OF A VISCOELASTIC FLUID FOR REDUCED DRAG
SOME DYNAMICAL FEATURES OF THE TURBULENT FLOW OF A VISCOELASTIC FLUID FOR REDUCED DRAG L. Thais Université de Lille Nord de France, USTL F9 Lille, France Laboratoire de Mécanique de Lille CNRS, UMR 817
More informationO. A Survey of Critical Experiments
O. A Survey of Critical Experiments 1 (A) Visualizations of Turbulent Flow Figure 1: Van Dyke, Album of Fluid Motion #152. Generation of turbulence by a grid. Smoke wires show a uniform laminar stream
More informationLecture 4: The NavierStokes Equations: Turbulence
Lecture 4: The NavierStokes Equations: Turbulence September 23, 2015 1 Goal In this Lecture, we shall present the main ideas behind the simulation of fluid turbulence. We firts discuss the case of the
More informationENGINEERING MECHANICS 2012 pp Svratka, Czech Republic, May 14 17, 2012 Paper #195
. 18 m 2012 th International Conference ENGINEERING MECHANICS 2012 pp. 309 315 Svratka, Czech Republic, May 14 17, 2012 Paper #195 NUMERICAL SIMULATION OF TRANSITIONAL FLOWS WITH LAMINAR KINETIC ENERGY
More informationGetting started: CFD notation
PDE of pth order Getting started: CFD notation f ( u,x, t, u x 1,..., u x n, u, 2 u x 1 x 2,..., p u p ) = 0 scalar unknowns u = u(x, t), x R n, t R, n = 1,2,3 vector unknowns v = v(x, t), v R m, m =
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 informationChapter 1: Basic Concepts
What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms
More informationNonequilibrium Dynamics in Astrophysics and Material Science YITP, Kyoto
Nonequilibrium Dynamics in Astrophysics and Material Science 20111102 @ YITP, Kyoto Multiscale coherent structures and their role in the Richardson cascade of turbulence Susumu Goto (Okayama Univ.)
More informationMathematical Theory of NonNewtonian Fluid
Mathematical Theory of NonNewtonian Fluid 1. Derivation of the Incompressible Fluid Dynamics 2. Existence of NonNewtonian Flow and its Dynamics 3. Existence in the Domain with Boundary Hyeong Ohk Bae
More informationConservation of Mass. Computational Fluid Dynamics. The Equations Governing Fluid Motion
http://www.nd.edu/~gtryggva/cfdcourse/ http://www.nd.edu/~gtryggva/cfdcourse/ Computational Fluid Dynamics Lecture 4 January 30, 2017 The Equations Governing Fluid Motion Grétar Tryggvason Outline Derivation
More informationDifferential relations for fluid flow
Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow
More information10. Buoyancydriven flow
10. Buoyancydriven flow For such flows to occur, need: Gravity field Variation of density (note: not the same as variable density!) Simplest case: Viscous flow, incompressible fluid, densityvariation
More information7.6 Example von Kármán s Laminar Boundary Layer Problem
CEE 3310 External Flows (Boundary Layers & Drag, Nov. 11, 2016 157 7.5 Review NonCircular Pipes Laminar: f = 64/Re DH ± 40% Turbulent: f(re DH, ɛ/d H ) Moody chart for f ± 15% BernoulliBased Flow Metering
More informationMostafa Momen. Project Report Numerical Investigation of Turbulence Models. 2.29: Numerical Fluid Mechanics
2.29: Numerical Fluid Mechanics Project Report Numerical Investigation of Turbulence Models Mostafa Momen May 2015 Massachusetts Institute of Technology 1 Numerical Investigation of Turbulence Models Term
More informationFLUID MECHANICS. Atmosphere, Ocean. Aerodynamics. Energy conversion. Transport of heat/other. Numerous industrial processes
SG2214 Anders Dahlkild Luca Brandt FLUID MECHANICS : SG2214 Course requirements (7.5 cr.) INL 1 (3 cr.) 3 sets of home work problems (for 10 p. on written exam) 1 laboration TEN1 (4.5 cr.) 1 written exam
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 informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
More informationCandidates must show on each answer book the type of calculator used. Log Tables, Statistical Tables and Graph Paper are available on request.
UNIVERSITY OF EAST ANGLIA School of Mathematics Spring Semester Examination 2004 FLUID DYNAMICS Time allowed: 3 hours Attempt Question 1 and FOUR other questions. Candidates must show on each answer book
More informationThe mean shear stress has both viscous and turbulent parts. In simple shear (i.e. U / y the only nonzero mean gradient):
8. TURBULENCE MODELLING 1 SPRING 2019 8.1 Eddyviscosity models 8.2 Advanced turbulence models 8.3 Wall boundary conditions Summary References Appendix: Derivation of the turbulent kinetic energy equation
More informationProject Topic. Simulation of turbulent flow laden with finitesize particles using LBM. Leila Jahanshaloo
Project Topic Simulation of turbulent flow laden with finitesize particles using LBM Leila Jahanshaloo Project Details Turbulent flow modeling Lattice Boltzmann Method All I know about my project Solidliquid
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 informationCorso di Laurea in Ingegneria Aerospaziale. Performance of CFD packages for flow simulations in aerospace applications
Universitá degli Studi di Padova Dipartimento di Ingegneria Industriale DII Department of Industrial Engineering Corso di Laurea in Ingegneria Aerospaziale Performance of CFD packages for flow simulations
More informationApplied Computational Fluid Dynamics
Lecture 9  Kolmogorov s Theory Applied Computational Fluid Dynamics Instructor: André Bakker André Bakker (20022005) Fluent Inc. (2002) 1 Eddy size Kolmogorov s theory describes how energy is transferred
More informationfluctuations based on the resolved mean flow
Temperature Fluctuation Scaling in Reacting Boundary Layers M. Pino Martín CTR/NASA Ames, Moffett Field, CA 94035 Graham V. Candler Aerospace Engineering and Mechanics University of Minnesota, Minneapolis,
More informationDNS Study on Small Length Scale in Turbulent Flow
DNS Study on Small ength Scale in Turbulent Flow Yonghua Yan Jie Tang Chaoqun iu Technical Report 201411 http://www.uta.edu/math/preprint/ DNS Study on Small ength Scale in Turbulent Flow Yonghua Yan,
More information15. Physics of Sediment Transport William Wilcock
15. Physics of Sediment Transport William Wilcock (based in part on lectures by Jeff Parsons) OCEAN/ESS 410 Lecture/Lab Learning Goals Know how sediments are characteried (sie and shape) Know the definitions
More informationThe Kolmogorov Law of turbulence
What can rigorously be proved? IRMAR, UMR CNRS 6625. Labex CHL. University of RENNES 1, FRANCE Introduction Aim: Mathematical framework for the Kolomogorov laws. Table of contents 1 Incompressible NavierStokes
More informationThe Turbulent Rotational Phase Separator
The Turbulent Rotational Phase Separator J.G.M. Kuerten and B.P.M. van Esch Dept. of Mechanical Engineering, Technische Universiteit Eindhoven, The Netherlands j.g.m.kuerten@tue.nl Summary. The Rotational
More informationBasic concepts in viscous flow
Élisabeth Guazzelli and Jeffrey F. Morris with illustrations by Sylvie Pic Adapted from Chapter 1 of Cambridge Texts in Applied Mathematics 1 The fluid dynamic equations NavierStokes equations Dimensionless
More informationThe lattice Boltzmann equation (LBE) has become an alternative method for solving various fluid dynamic
36th AIAA Fluid Dynamics Conference and Exhibit 58 June 2006, San Francisco, California AIAA 20063904 Direct and LargeEddy Simulation of Decaying and Forced Isotropic Turbulence Using Lattice Boltzmann
More informationTurbulence. 2. Reynolds number is an indicator for turbulence in a fluid stream
Turbulence injection of a water jet into a water tank Reynolds number EF$ 1. There is no clear definition and range of turbulence (multiscale phenomena) 2. Reynolds number is an indicator for turbulence
More informationIncompressible MHD simulations
Incompressible MHD simulations Felix Spanier 1 Lehrstuhl für Astronomie Universität Würzburg Simulation methods in astrophysics Felix Spanier (Uni Würzburg) Simulation methods in astrophysics 1 / 20 Outline
More informationLecture 7. Turbulence
Lecture 7 Content Basic features of turbulence Energy cascade theory scales mixing Basic features of turbulence What is turbulence? spiral galaxies NGC 2207 and IC 2163 Turbulent jet flow Volcano jet flow
More informationTurbulent drag reduction by streamwise traveling waves
51st IEEE Conference on Decision and Control December 1013, 2012. Maui, Hawaii, USA Turbulent drag reduction by streamwise traveling waves Armin Zare, Binh K. Lieu, and Mihailo R. Jovanović Abstract For
More information