Computational fluid dynamics (CFD) 9 th SIMLAB Course

Similar documents

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics

TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW

Boundary Conditions in lattice Boltzmann method

Introduction to COMSOL. The Navier-Stokes Equations

MEL 807 Computational Heat Transfer (2-0-4) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

ME6130 An introduction to CFD 1-1

Experiences Extending the CFD Solver of the PDE Framework Peano

Practice Problems on the Navier-Stokes Equations

Iterative Solvers for Linear Systems

Simulation of magneto-hydrodynamic (MHD) flows: electric potential formulation

Dynamic Process Modeling. Process Dynamics and Control

Express Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology

Steady Flow: Laminar and Turbulent in an S-Bend

OpenFOAM Opensource and CFD

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Use of OpenFoam in a CFD analysis of a finger type slug catcher. Dynaflow Conference 2011 January , Rotterdam, the Netherlands

Heat Transfer by Free Convection

OpenFOAM Optimization Tools

STCE. Outline. Introduction. Applications. Ongoing work. Summary. STCE RWTH-Aachen, Industrial Applications of discrete adjoint OpenFOAM, EuroAD 2014

Part II: Finite Difference/Volume Discretisation for CFD

Fluid Dynamics and the Navier-Stokes Equation

Paper Pulp Dewatering

A CODE VERIFICATION EXERCISE FOR THE UNSTRUCTURED FINITE-VOLUME CFD SOLVER ISIS-CFD

Benchmark Computations of 3D Laminar Flow Around a Cylinder with CFX, OpenFOAM and FeatFlow

COMPONENTS OF VECTORS

Module 5: Solution of Navier-Stokes Equations for Incompressible Flow Using SIMPLE and MAC Algorithms Lecture 27:

Computational Fluid Dynamics Research Projects at Cenaero (2011)

COMPARISON OF SOLUTION ALGORITHM FOR FLOW AROUND A SQUARE CYLINDER

Aerodynamic Department Institute of Aviation. Adam Dziubiński CFD group FLUENT

Abaqus/CFD Sample Problems. Abaqus 6.10

Laminar-Turbulent Transition: Calculation of Minimum Critical Reynolds Number in Channel Flow

Design and Optimization of OpenFOAM-based CFD Applications for Hybrid and Heterogeneous HPC Platforms

Module 6 Case Studies

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

OPTIMISE TANK DESIGN USING CFD. Lisa Brown. Parsons Brinckerhoff

Numerical Simulation of the External Flow Field. Around a Bluff Car*

Navier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering Computing, Wiley (2006).

Development and Application of a Finite Volume Method for the Computation of Flows Around Moving Bodies on Unstructured, Overlapping Grids

Introduction to CFD Basics

Customer Training Material. Lecture 2. Introduction to. Methodology ANSYS FLUENT. ANSYS, Inc. Proprietary 2010 ANSYS, Inc. All rights reserved.

How To Write A Program For The Pd Framework

THE CFD SIMULATION OF THE FLOW AROUND THE AIRCRAFT USING OPENFOAM AND ANSA

Laminar Flow in a Baffled Stirred Mixer

Adaptation of General Purpose CFD Code for Fusion MHD Applications*

CFD Based Air Flow and Contamination Modeling of Subway Stations

HPC enabling of OpenFOAM R for CFD applications

Section 7.2 Linear Programming: The Graphical Method

Interactive simulation of an ash cloud of the volcano Grímsvötn

Keywords: Heat transfer enhancement; staggered arrangement; Triangular Prism, Reynolds Number. 1. Introduction

sin(θ) = opp hyp cos(θ) = adj hyp tan(θ) = opp adj

CFD modelling of floating body response to regular waves

. Address the following issues in your solution:

Aeroacoustic Analogy for the Computation of Aeroacoustic Fields in Partially Closed Domains

CFD Application on Food Industry; Energy Saving on the Bread Oven

x y The matrix form, the vector form, and the augmented matrix form, respectively, for the system of equations are

Hardware-Aware Analysis and. Presentation Date: Sep 15 th 2009 Chrissie C. Cui

Self Financed One Week Training

Lecture 4 Classification of Flows. Applied Computational Fluid Dynamics

Addition and Subtraction of Vectors

Multiphase Flow - Appendices

Christof Hinterberger, Mark Olesen

Math, Trigonometry and Vectors. Geometry. Trig Definitions. sin(θ) = opp hyp. cos(θ) = adj hyp. tan(θ) = opp adj. Here's a familiar image.

CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER

Course Outline for the Masters Programme in Computational Engineering

Jim Lambers MAT 169 Fall Semester Lecture 25 Notes

Overset Grids Technology in STAR-CCM+: Methodology and Applications

Introduction to CFD Analysis

Design and Analysis of Engine Cooling Fan

CFD Application on Food Industry; Energy Saving on the Bread Oven

Problem Statement In order to satisfy production and storage requirements, small and medium-scale industrial

Pushing the limits. Turbine simulation for next-generation turbochargers

Differential Balance Equations (DBE)

Physics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal

CHAPTER 4 CFD ANALYSIS OF THE MIXER

Introduction to CFD Analysis

Linear Inequality in Two Variables

Slope-Intercept Form and Point-Slope Form

Contents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1

AB3080 L. Learning Objectives: About the Speaker:

Mathematical Model of Blood Flow in Carotid Bifurcation. Phd student: Eng. Emanuel Muraca. 16/10/09 Milan

The Navier Stokes Equations

HPC realization of a controlled turbulent round jet using OpenFOAM a)

- momentum conservation equation ρ = ρf. These are equivalent to four scalar equations with four unknowns: - pressure p - velocity components

3 The boundary layer equations

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET)

CFD Grows Up! Martin W. Liddament Ventilation, Energy and Environmental Technology (VEETECH Ltd) What is Computational Fluid Dynamics?

Mixed Precision Iterative Refinement Methods Energy Efficiency on Hybrid Hardware Platforms

Which strategy to move the mesh in the Computational Fluid Dynamic code OpenFOAM

Lecture 11 Boundary Layers and Separation. Applied Computational Fluid Dynamics

Model of a flow in intersecting microchannels. Denis Semyonov

APPENDIX 3 CFD CODE - PHOENICS

NUMERICAL SIMULATION OF REGULAR WAVES RUN-UP OVER SLOPPING BEACH BY OPEN FOAM

A Memory-Efficient Data Handling for Octree-Like Grids

Vista: A Multi-field Object Oriented CFD-package

O.F.Wind Wind Site Assessment Simulation in complex terrain based on OpenFOAM. Darmstadt,

Transcription:

Computational fluid dnamics (CFD) 9 th SIMLAB Course Janos Benk October 3-9, Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Overview Introduction Potential flow Stokes equation and discretization Boundar Conditions Navier-Stokes equation and its dicretization (Parallelization) Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Introduction What defines a flow? What are the quantities in such a incompressible flow field? Velocit vector pressure scalar Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Introduction We are looking for a relation between the velocit vector and the pressure We note vel (u,v) the velocit vector in D The pressure is noted b p For the case of simplicit we consider onl stationar scenarios though the whole tutorial We use a regular structured grid (as the simplest grid) The cells form a mesh One cell Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Introduction Grid based method Finite difference (reuse some knowledge from the previous lecture) Other discretization techniques are more favorable in practice, due to the limitations of the finite difference method. Finite volume Finite element Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Potential flow v The first tr is the Potential flow, the simples flow equation The velocit is directl derived from the pressure (potential) flow u p u First we specif that per cell no matter can be gained or disappear. ( vel (u,v) ) v vel u v Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Potential flow Replace the? with values X? vel - p -X? u v 3 Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Potential flow Replace the? with values 4 vel 3 p -3? u v - Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Potential flow The potential is a Poisson equation, with zero right hand side. The velocit is directl derived from the pressure (potential) flow The different boundar conditions can be implemented through the potential To be the solution uniquel determined, we use a Dirichlet boundar condition for n p p n p p p out Walls Outlet Inlet Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Potential flow Is the velocit still divergence free? Is the following equation still satisfied? vel(u,v) With the following equations: vel p vel p vel p Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Potential flow How does the potential field looks for a channel flow? And the velocit field (u,v) Walls ( u, v) p p p Inlet p- Outlet p u Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation There is a complete new second equation: vel vel t p Re vel f et Since we consider onl stationar problems: vel t p vel Re f et Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation What does the second equation mean? p vel Re f et This is the so called impulse equation, at each point the sum of the acting forces must equal zero vel Grad(p) Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation Reformulate the equation in terms of u,v and p instead of vel,p Vel(u,v) The equations are p vel p vel Re u v Re u u f et, f et p Re v v f et, Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, Stokes equation Calculate the parabolic profile of a channel flow: ) ( H u Re c u p 3 Re ) ( c c c u f et u u p, Re f et v v p, Re ) ( c c p ) u( p c

Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, Stokes equation Finite difference discretization: Cell wise view of the cont. eq. f et u u p, Re f et v v p, Re v u The operators in the velocit points, since the impulse is point wise satisfied ( and ).

Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, Stokes equation f et u u p, Re f et v v p, Re v u

Stokes equation Boundar conditions: No-Slip: ( u, v) (,) Free-Slip: Inflow: ( u, v) ( u,) ( u, v) (, v) ( u, v) ( u, v) v a i Outflow: ( u, v) / n v r v Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation Driven cavit Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation Which are the unknowns? Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation What to do at the boundar? Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation What to do at the boundar? p u p v p u v p3 Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation -u p u p -v v v -v p u p3 -u Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation -u Continuit equation: u v -v p v u p v -v p u p3 -u v u u v -v - u -v u Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation -u p p Re Re u u v v -v p v u p v -v p u p3 -u (/Re)(5v v)p-p (/Re)(5u-u)-pp (/Re) (/Re)(-v 5v)p-p3 (/Re)(-u 5u)-pp3 Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, Stokes equation v u u v -v - u -v u (/Re)(5v v)p-p (/Re)(5u-u)-pp (/Re) (/Re)(-v 5v)p-p3 (/Re)(-u 5u)-pp3 3 5 5 5 5 p p p p u v u v Write the sstem of equation with Re With unknown vector [v,u,v,u,p,p,p,p3], first cont. eq. then momentum equation

Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, Stokes equation Due to the singularit we set p and delete the fourth line from the sstem 3 5 5 5 5 p p p u v u v We calculate the solution with Octave

Stokes equation The solution vector is: [.83333.83333 -.83333 -.83333.5.5.] Visualize these data on the grid.83.5.83 -.83.5 -.83. Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Stokes equation 3D Eample: Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Navier-Stokes equation Is the velocit still divergence free? vel t vel ( vel ) vel p vel fet Re Since we consider onl stationar problems: vel t Re ( vel ) vel p vel fet Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, Navier-Stokes equation The new term in the equation is the so called convective or transport term ( )vel vel v v v u u v u u v u v u Which in more detailed form is (see the non-linearit) The velocit field transports the velocit. The diffusion spreads the velocit in each direction equall This transports in the flow direction velocit Grad(p) vel

Navier-Stokes equation Which model to use when? Would ou use Navier-Stokes for slow, viscous flow (diffusion term is dominant)? Would ou use Navier-Stokes for non viscous flow? (Péclet number, is a good indicator for this) Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Navier-Stokes equation We reformulate the equation in terms of u,v and p instead of vel,p Vel(u,v) p vel Re vel ( vel ) vel fet The equations are (the convection term is transformed slightl) p p Re Re u v u u v v uv ( u ) ( uv) f et, Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7, ( ) ( v ) f et,

Navier-Stokes equation Convection term, component Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Navier-Stokes equation Convection term, component Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Navier-Stokes equation Outline of the solving method: Coupled approach: u A ( u, v) v p Using non-linear solvers (fi point or Newton method) b Partitioned approach onl for time dependent problem ( u p, v t t )...... Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Navier-Stokes equation D Eample: Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Parallelization Shared memor sstems The basics of parallelization on the matri level on distributed memor sstem Distribute the unknown vector to processes A b Distribute the corresponding lines of the matri and the right hand side p p p p p p p p p Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Parallelization Let s think in terms of iterative processes How to divide among processors? Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Parallelization We need additional cells in the same wa as we need boundar cells Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Parallelization (Ghost cells) Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Parallelization Communication needed (?) Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,

Thank ou for our attention! Janos Benk: Computational fluid dnamics (CFD) www5.in.tum.de/wiki/inde.php/lab_course_computational_fluid_dnamics_-_summer_ 9 th SIMLAB Course, Belgrade, October 7,