Computational fluid dynamics (CFD) 9 th SIMLAB Course
|
|
- Sibyl Thompson
- 8 years ago
- Views:
Transcription
1 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,
2 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,
3 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,
4 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,
5 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,
6 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,
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,
8 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,
9 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,
10 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,
11 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,
12 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,
13 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,
14 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,
15 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
16 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 ).
17 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
18 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,
19 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,
20 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,
21 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,
22 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,
23 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,
24 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,
25 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,
26 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)-pp 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
27 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 p p p u v u v We calculate the solution with Octave
28 Stokes equation The solution vector is: [ ] Visualize these data on the grid 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,
29 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,
30 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,
31 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
32 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,
33 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,
34 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,
35 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,
36 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,
37 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,
38 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,
39 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,
40 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,
41 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,
42 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,
43 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,
Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics
Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.
More informationTWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW
TWO-DIMENSIONAL FINITE ELEMENT ANALYSIS OF FORCED CONVECTION FLOW AND HEAT TRANSFER IN A LAMINAR CHANNEL FLOW Rajesh Khatri 1, 1 M.Tech Scholar, Department of Mechanical Engineering, S.A.T.I., vidisha
More informationBoundary Conditions in lattice Boltzmann method
Boundar Conditions in lattice Boltzmann method Goncalo Silva Department of Mechanical Engineering Instituto Superior Técnico (IST) Lisbon, Portugal Outline Introduction 1 Introduction Boundar Value Problems
More informationIntroduction to COMSOL. The Navier-Stokes Equations
Flow Between Parallel Plates Modified from the COMSOL ChE Library module rev 10/13/08 Modified by Robert P. Hesketh, Chemical Engineering, Rowan University Fall 2008 Introduction to COMSOL The following
More informationMEL 807 Computational Heat Transfer (2-0-4) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi
MEL 807 Computational Heat Transfer (2-0-4) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi Time and Venue Course Coordinator: Dr. Prabal Talukdar Room No: III, 357
More informationME6130 An introduction to CFD 1-1
ME6130 An introduction to CFD 1-1 What is CFD? Computational fluid dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically
More informationHow To Write A Pde Framework For A Jubilian (Jubilians)
FEM Simulations of Incompressible Flow using AD in the PDE Framework Peano Hans-Joachim Bungartz,, Fakultät für Informatik TU München Germany Outline The PDE Framework Peano Different Approaches for Jacobians
More informationExperiences Extending the CFD Solver of the PDE Framework Peano
Experiences Extending the CFD Solver of the PDE Framework Peano T. Neckel, M. Lieb, R. Sangl TUM, Department of Informatics, Chair of Scientific Computing in Computer Science P. Schoeffel, F. Weyermann
More informationPractice Problems on the Navier-Stokes Equations
ns_0 A viscous, incompressible, Newtonian liquid flows in stead, laminar, planar flow down a vertical wall. The thickness,, of the liquid film remains constant. Since the liquid free surface is eposed
More informationIterative Solvers for Linear Systems
9th SimLab Course on Parallel Numerical Simulation, 4.10 8.10.2010 Iterative Solvers for Linear Systems Bernhard Gatzhammer Chair of Scientific Computing in Computer Science Technische Universität München
More informationSimulation of magneto-hydrodynamic (MHD) flows: electric potential formulation
Simulation of magneto-hdrodnamic (MHD) flows: electric potential formulation, Ola Widlund 5th OpenFOAM workshop Göteborg, June 22-24, 2010 Outline Motivations for studing MHD flows Wh a formulation with
More informationDynamic Process Modeling. Process Dynamics and Control
Dynamic Process Modeling Process Dynamics and Control 1 Description of process dynamics Classes of models What do we need for control? Modeling for control Mechanical Systems Modeling Electrical circuits
More informationExpress Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology
Express Introductory Training in ANSYS Fluent Lecture 1 Introduction to the CFD Methodology Dimitrios Sofialidis Technical Manager, SimTec Ltd. Mechanical Engineer, PhD PRACE Autumn School 2013 - Industry
More informationSteady Flow: Laminar and Turbulent in an S-Bend
STAR-CCM+ User Guide 6663 Steady Flow: Laminar and Turbulent in an S-Bend This tutorial demonstrates the flow of an incompressible gas through an s-bend of constant diameter (2 cm), for both laminar and
More informationOpenFOAM Opensource and CFD
OpenFOAM Opensource and CFD Andrew King Department of Mechanical Engineering Curtin University Outline What is Opensource Software OpenFOAM Overview Utilities, Libraries and Solvers Data Formats The CFD
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More informationUse of OpenFoam in a CFD analysis of a finger type slug catcher. Dynaflow Conference 2011 January 13 2011, Rotterdam, the Netherlands
Use of OpenFoam in a CFD analysis of a finger type slug catcher Dynaflow Conference 2011 January 13 2011, Rotterdam, the Netherlands Agenda Project background Analytical analysis of two-phase flow regimes
More informationHeat Transfer by Free Convection
Heat Transfer by Free Convection Introduction This example describes a fluid flow problem with heat transfer in the fluid. An array of heating tubes is submerged in a vessel with fluid flow entering at
More informationOpenFOAM Optimization Tools
OpenFOAM Optimization Tools Henrik Rusche and Aleks Jemcov h.rusche@wikki-gmbh.de and a.jemcov@wikki.co.uk Wikki, Germany and United Kingdom OpenFOAM Optimization Tools p. 1 Agenda Objective Review optimisation
More informationSTCE. Outline. Introduction. Applications. Ongoing work. Summary. STCE RWTH-Aachen, Industrial Applications of discrete adjoint OpenFOAM, EuroAD 2014
Industrial Applications of discrete adjoint OpenFOAM Arindam Sen Software and Tools for Computational Engineering Science RWTH Aachen University EuroAD 2014, Nice, 16-17. June 2014 Outline Introduction
More informationPart II: Finite Difference/Volume Discretisation for CFD
Part II: Finite Difference/Volume Discretisation for CFD Finite Volume Metod of te Advection-Diffusion Equation A Finite Difference/Volume Metod for te Incompressible Navier-Stokes Equations Marker-and-Cell
More informationFluid Dynamics and the Navier-Stokes Equation
Fluid Dynamics and the Navier-Stokes Equation CMSC498A: Spring 12 Semester By: Steven Dobek 5/17/2012 Introduction I began this project through a desire to simulate smoke and fire through the use of programming
More informationPaper Pulp Dewatering
Paper Pulp Dewatering Dr. Stefan Rief stefan.rief@itwm.fraunhofer.de Flow and Transport in Industrial Porous Media November 12-16, 2007 Utrecht University Overview Introduction and Motivation Derivation
More informationA CODE VERIFICATION EXERCISE FOR THE UNSTRUCTURED FINITE-VOLUME CFD SOLVER ISIS-CFD
European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006 P. Wesseling, E. Oñate and J. Périaux (Eds) c TU Delft, The Netherlands, 2006 A CODE VERIFICATION EXERCISE FOR THE UNSTRUCTURED FINITE-VOLUME
More informationBenchmark Computations of 3D Laminar Flow Around a Cylinder with CFX, OpenFOAM and FeatFlow
Benchmark Computations of 3D Laminar Flow Around a Cylinder with CFX, OpenFOAM and FeatFlow E. Bayraktar, O. Mierka and S. Turek Institute of Applied Mathematics (LS III), TU Dortmund Vogelpothsweg 87,
More informationCOMPONENTS OF VECTORS
COMPONENTS OF VECTORS To describe motion in two dimensions we need a coordinate sstem with two perpendicular aes, and. In such a coordinate sstem, an vector A can be uniquel decomposed into a sum of two
More informationModule 5: Solution of Navier-Stokes Equations for Incompressible Flow Using SIMPLE and MAC Algorithms Lecture 27:
The Lecture deals with: Introduction Staggered Grid Semi Implicit Method for Pressure Linked Equations (SIMPLE) x - momentum equation file:///d /chitra/nptel_phase2/mechanical/cfd/lecture%2027/27_1.htm[6/20/2012
More informationComputational Fluid Dynamics Research Projects at Cenaero (2011)
Computational Fluid Dynamics Research Projects at Cenaero (2011) Cenaero (www.cenaero.be) is an applied research center focused on the development of advanced simulation technologies for aeronautics. Located
More informationCOMPARISON OF SOLUTION ALGORITHM FOR FLOW AROUND A SQUARE CYLINDER
Ninth International Conference on CFD in the Minerals and Process Industries CSIRO, Melbourne, Australia - December COMPARISON OF SOLUTION ALGORITHM FOR FLOW AROUND A SQUARE CYLINDER Y. Saito *, T. Soma,
More informationAerodynamic Department Institute of Aviation. Adam Dziubiński CFD group FLUENT
Adam Dziubiński CFD group IoA FLUENT Content Fluent CFD software 1. Short description of main features of Fluent 2. Examples of usage in CESAR Analysis of flow around an airfoil with a flap: VZLU + ILL4xx
More informationAbaqus/CFD Sample Problems. Abaqus 6.10
Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel
More informationLaminar-Turbulent Transition: Calculation of Minimum Critical Reynolds Number in Channel Flow
Laminar-Turbulent Transition: Calculation of Minimum Critical Renolds Number in Channel Flow Hidesada Kanda Universit of Aizu, Aizu-Wakamatsu, Fukushima 965-8580, Japan kanda@u-aizu.ac.jp Abstract A conceptual
More informationDesign and Optimization of OpenFOAM-based CFD Applications for Hybrid and Heterogeneous HPC Platforms
Design and Optimization of OpenFOAM-based CFD Applications for Hybrid and Heterogeneous HPC Platforms Amani AlOnazi, David E. Keyes, Alexey Lastovetsky, Vladimir Rychkov Extreme Computing Research Center,
More informationModule 6 Case Studies
Module 6 Case Studies 1 Lecture 6.1 A CFD Code for Turbomachinery Flows 2 Development of a CFD Code The lecture material in the previous Modules help the student to understand the domain knowledge required
More informationNUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES
Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics
More informationOPTIMISE TANK DESIGN USING CFD. Lisa Brown. Parsons Brinckerhoff
OPTIMISE TANK DESIGN USING CFD Paper Presented by: Lisa Brown Authors: Lisa Brown, General Manager, Franz Jacobsen, Senior Water Engineer, Parsons Brinckerhoff 72 nd Annual Water Industry Engineers and
More informationNumerical Simulation of the External Flow Field. Around a Bluff Car*
Numerical Simulation of the External Flow Field Around a Bluff Car* Sun Yongling, Wu Guangqiang, Xieshuo Automotive Engineering Department Shanghai Tongji University Shanghai, China E-mail: wuqjuhyk@online.sh.cn
More informationNavier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering Computing, Wiley (2006).
Introduction to Chemical Engineering Computing Copyright, Bruce A. Finlayson, 2004 1 Navier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering
More informationDevelopment and Application of a Finite Volume Method for the Computation of Flows Around Moving Bodies on Unstructured, Overlapping Grids
Development and Application of a Finite Volume Method for the Computation of Flows Around Moving Bodies on Unstructured, Overlapping Grids Vom Promotionsausschuss der Technischen Universität Hamburg-Harburg
More informationIntroduction to CFD Basics
Introduction to CFD Basics Rajesh Bhaskaran Lance Collins This is a quick-and-dirty introduction to the basic concepts underlying CFD. The concepts are illustrated by applying them to simple 1D model problems.
More informationCustomer Training Material. Lecture 2. Introduction to. Methodology ANSYS FLUENT. ANSYS, Inc. Proprietary 2010 ANSYS, Inc. All rights reserved.
Lecture 2 Introduction to CFD Methodology Introduction to ANSYS FLUENT L2-1 What is CFD? Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions,
More informationHow To Write A Program For The Pd Framework
Enhanced divergence-free elements for efficient incompressible flow simulations in the PDE framework Peano, Miriam Mehl, Christoph Zenger, Fakultät für Informatik TU München Germany Outline Derivation
More informationTHE CFD SIMULATION OF THE FLOW AROUND THE AIRCRAFT USING OPENFOAM AND ANSA
THE CFD SIMULATION OF THE FLOW AROUND THE AIRCRAFT USING OPENFOAM AND ANSA Adam Kosík Evektor s.r.o., Czech Republic KEYWORDS CFD simulation, mesh generation, OpenFOAM, ANSA ABSTRACT In this paper we describe
More informationLaminar Flow in a Baffled Stirred Mixer
Laminar Flow in a Baffled Stirred Mixer Introduction This exercise exemplifies the use of the rotating machinery feature in the CFD Module. The Rotating Machinery interface allows you to model moving rotating
More informationAdaptation of General Purpose CFD Code for Fusion MHD Applications*
Adaptation of General Purpose CFD Code for Fusion MHD Applications* Andrei Khodak Princeton Plasma Physics Laboratory P.O. Box 451 Princeton, NJ, 08540 USA akhodak@pppl.gov Abstract Analysis of many fusion
More informationCFD Based Air Flow and Contamination Modeling of Subway Stations
CFD Based Air Flow and Contamination Modeling of Subway Stations Greg Byrne Center for Nonlinear Science, Georgia Institute of Technology Fernando Camelli Center for Computational Fluid Dynamics, George
More informationHPC enabling of OpenFOAM R for CFD applications
HPC enabling of OpenFOAM R for CFD applications Towards the exascale: OpenFOAM perspective Ivan Spisso 25-27 March 2015, Casalecchio di Reno, BOLOGNA. SuperComputing Applications and Innovation Department,
More informationSection 7.2 Linear Programming: The Graphical Method
Section 7.2 Linear Programming: The Graphical Method Man problems in business, science, and economics involve finding the optimal value of a function (for instance, the maimum value of the profit function
More informationInteractive simulation of an ash cloud of the volcano Grímsvötn
Interactive simulation of an ash cloud of the volcano Grímsvötn 1 MATHEMATICAL BACKGROUND Simulating flows in the atmosphere, being part of CFD, is on of the research areas considered in the working group
More informationKeywords: Heat transfer enhancement; staggered arrangement; Triangular Prism, Reynolds Number. 1. Introduction
Heat transfer augmentation in rectangular channel using four triangular prisms arrange in staggered manner Manoj Kumar 1, Sunil Dhingra 2, Gurjeet Singh 3 1 Student, 2,3 Assistant Professor 1.2 Department
More informationsin(θ) = opp hyp cos(θ) = adj hyp tan(θ) = opp adj
Math, Trigonometr and Vectors Geometr 33º What is the angle equal to? a) α = 7 b) α = 57 c) α = 33 d) α = 90 e) α cannot be determined α Trig Definitions Here's a familiar image. To make predictive models
More informationCFD modelling of floating body response to regular waves
CFD modelling of floating body response to regular waves Dr Yann Delauré School of Mechanical and Manufacturing Engineering Dublin City University Ocean Energy Workshop NUI Maynooth, October 21, 2010 Table
More information. Address the following issues in your solution:
CM 3110 COMSOL INSTRUCTIONS Faith Morrison and Maria Tafur Department of Chemical Engineering Michigan Technological University, Houghton, MI USA 22 November 2012 Zhichao Wang edits 21 November 2013 revised
More informationAeroacoustic Analogy for the Computation of Aeroacoustic Fields in Partially Closed Domains
INSTITUT FÜR MECHANIK UND MECHATRONIK Messtechnik und Aktorik Aeroacoustic Analogy for the Computation of Aeroacoustic Fields in Partially Closed Domains A. Hüppe 1, M. Kaltenbacher 1, A. Reppenhagen 2,
More informationCFD Application on Food Industry; Energy Saving on the Bread Oven
Middle-East Journal of Scientific Research 13 (8): 1095-1100, 2013 ISSN 1990-9233 IDOSI Publications, 2013 DOI: 10.5829/idosi.mejsr.2013.13.8.548 CFD Application on Food Industry; Energy Saving on the
More informationx y The matrix form, the vector form, and the augmented matrix form, respectively, for the system of equations are
Solving Sstems of Linear Equations in Matri Form with rref Learning Goals Determine the solution of a sstem of equations from the augmented matri Determine the reduced row echelon form of the augmented
More informationHardware-Aware Analysis and. Presentation Date: Sep 15 th 2009 Chrissie C. Cui
Hardware-Aware Analysis and Optimization of Stable Fluids Presentation Date: Sep 15 th 2009 Chrissie C. Cui Outline Introduction Highlights Flop and Bandwidth Analysis Mehrstellen Schemes Advection Caching
More informationSelf Financed One Week Training
Self Financed One Week Training On Computational Fluid Dynamics (CFD) with OpenFOAM December 14 20, 2015 (Basic Training: 3days, Advanced Training: 5days and Programmer Training: 7days) Organized by Department
More informationLecture 4 Classification of Flows. Applied Computational Fluid Dynamics
Lecture 4 Classification of Flows Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (00-006) Fluent Inc. (00) 1 Classification: fluid flow vs. granular flow
More informationAddition and Subtraction of Vectors
ddition and Subtraction of Vectors 1 ppendi ddition and Subtraction of Vectors In this appendi the basic elements of vector algebra are eplored. Vectors are treated as geometric entities represented b
More informationMultiphase Flow - Appendices
Discovery Laboratory Multiphase Flow - Appendices 1. Creating a Mesh 1.1. What is a geometry? The geometry used in a CFD simulation defines the problem domain and boundaries; it is the area (2D) or volume
More informationChristof Hinterberger, Mark Olesen
Application of of a Continuous Adjoint Flow Solver for for Geometry Optimisation of of Automotive Exhaust Systems Christof Hinterberger, Mark Olesen FLOWHEAD Workshop, Varna Sept. 2010 Workshop on industrial
More informationMath, Trigonometry and Vectors. Geometry. Trig Definitions. sin(θ) = opp hyp. cos(θ) = adj hyp. tan(θ) = opp adj. Here's a familiar image.
Math, Trigonometr and Vectors Geometr Trig Definitions Here's a familiar image. To make predictive models of the phsical world, we'll need to make visualizations, which we can then turn into analtical
More informationCFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER
International Journal of Advancements in Research & Technology, Volume 1, Issue2, July-2012 1 CFD SIMULATION OF SDHW STORAGE TANK WITH AND WITHOUT HEATER ABSTRACT (1) Mr. Mainak Bhaumik M.E. (Thermal Engg.)
More informationCourse Outline for the Masters Programme in Computational Engineering
Course Outline for the Masters Programme in Computational Engineering Compulsory Courses CP-501 Mathematical Methods for Computational 3 Engineering-I CP-502 Mathematical Methods for Computational 3 Engineering-II
More informationJim Lambers MAT 169 Fall Semester 2009-10 Lecture 25 Notes
Jim Lambers MAT 169 Fall Semester 009-10 Lecture 5 Notes These notes correspond to Section 10.5 in the text. Equations of Lines A line can be viewed, conceptually, as the set of all points in space that
More informationOverset Grids Technology in STAR-CCM+: Methodology and Applications
Overset Grids Technology in STAR-CCM+: Methodology and Applications Eberhard Schreck, Milovan Perić and Deryl Snyder eberhard.schreck@cd-adapco.com milovan.peric@cd-adapco.com deryl.snyder@cd-adapco.com
More informationIntroduction to CFD Analysis
Introduction to CFD Analysis Introductory FLUENT Training 2006 ANSYS, Inc. All rights reserved. 2006 ANSYS, Inc. All rights reserved. 2-2 What is CFD? Computational fluid dynamics (CFD) is the science
More informationDesign and Analysis of Engine Cooling Fan
International Journal of Current Engineering and Technology ISSN 2277-4106 2014 INPRESSCO. All Rights Reserved. Available at http://inpressco.com/category/ijcet Research Article Design and Analysis of
More informationCFD Application on Food Industry; Energy Saving on the Bread Oven
Iranica Journal of Energy & Environment 3 (3): 241-245, 2012 ISSN 2079-2115 IJEE an Official Peer Reviewed Journal of Babol Noshirvani University of Technology DOI: 10.5829/idosi.ijee.2012.03.03.0548 CFD
More informationProblem Statement In order to satisfy production and storage requirements, small and medium-scale industrial
Problem Statement In order to satisfy production and storage requirements, small and medium-scale industrial facilities commonly occupy spaces with ceilings ranging between twenty and thirty feet in height.
More informationPushing the limits. Turbine simulation for next-generation turbochargers
Pushing the limits Turbine simulation for next-generation turbochargers KWOK-KAI SO, BENT PHILLIPSEN, MAGNUS FISCHER Computational fluid dynamics (CFD) has matured and is now an indispensable tool for
More informationTHE EFFECTS OF UNIFORM TRANSVERSE MAGNETIC FIELD ON LOCAL FLOW AND VELOCITY PROFILE
International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 2, March-April 2016, pp. 140 151, Article ID: IJCIET_07_02_011 Available online at http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=7&itype=2
More informationDifferential Balance Equations (DBE)
Differential Balance Equations (DBE) Differential Balance Equations Differential balances, although more complex to solve, can yield a tremendous wealth of information about ChE processes. General balance
More informationPhysics 53. Kinematics 2. Our nature consists in movement; absolute rest is death. Pascal
Phsics 53 Kinematics 2 Our nature consists in movement; absolute rest is death. Pascal Velocit and Acceleration in 3-D We have defined the velocit and acceleration of a particle as the first and second
More informationCHAPTER 4 CFD ANALYSIS OF THE MIXER
98 CHAPTER 4 CFD ANALYSIS OF THE MIXER This section presents CFD results for the venturi-jet mixer and compares the predicted mixing pattern with the present experimental results and correlation results
More informationIntroduction to CFD Analysis
Introduction to CFD Analysis 2-1 What is CFD? Computational Fluid Dynamics (CFD) is the science of predicting fluid flow, heat and mass transfer, chemical reactions, and related phenomena by solving numerically
More informationLinear Inequality in Two Variables
90 (7-) Chapter 7 Sstems of Linear Equations and Inequalities In this section 7.4 GRAPHING LINEAR INEQUALITIES IN TWO VARIABLES You studied linear equations and inequalities in one variable in Chapter.
More informationSlope-Intercept Form and Point-Slope Form
Slope-Intercept Form and Point-Slope Form In this section we will be discussing Slope-Intercept Form and the Point-Slope Form of a line. We will also discuss how to graph using the Slope-Intercept Form.
More informationContents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationAB3080 L. Learning Objectives: About the Speaker:
AB3080 L While architects have tested their designs in wind tunnels for many years, the process is typically outsourced to engineering firms and not easily accessible to architects during the conceptual
More informationMathematical Model of Blood Flow in Carotid Bifurcation. Phd student: Eng. Emanuel Muraca. 16/10/09 Milan
Presented at the COMSOL Conference 2009 Milan Mathematical Model of Blood Flow in Carotid Bifurcation Phd student: Eng. Emanuel Muraca 16/10/09 Milan 1 Research s s goal The goal of this research is to
More informationThe Navier Stokes Equations
1 The Navier Stokes Equations Remark 1.1. Basic principles and variables. The basic equations of fluid dynamics are called Navier Stokes equations. In the case of an isothermal flow, a flow at constant
More informationHPC realization of a controlled turbulent round jet using OpenFOAM a)
Open Source CFD 2013 HPC realization of a controlled turbulent round jet using OpenFOAM a) Asim Onder 1, b) and Johan Meyers 1 Department of Mechanical Engineering, Katholieke Universiteit Leuven The present
More information- momentum conservation equation ρ = ρf. These are equivalent to four scalar equations with four unknowns: - pressure p - velocity components
J. Szantyr Lecture No. 14 The closed system of equations of the fluid mechanics The above presented equations form the closed system of the fluid mechanics equations, which may be employed for description
More information3 The boundary layer equations
3 The boundar laer equations Having introduced the concept of the boundar laer (BL), we now turn to the task of deriving the equations that govern the flow inside it. We focus throughout on the case of
More informationINTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET)
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) Proceedings of the 2 nd International Conference on Current Trends in Engineering and Management ICCTEM -2014 ISSN 0976 6340 (Print)
More informationDr. Fritz Wilhelm, DVC,8/30/2004;4:25 PM E:\Excel files\ch 03 Vector calculations.doc Last printed 8/30/2004 4:25:00 PM
E:\Ecel files\ch 03 Vector calculations.doc Last printed 8/30/2004 4:25:00 PM Vector calculations 1 of 6 Vectors are ordered sequences of numbers. In three dimensions we write vectors in an of the following
More informationEFFECT ON HEAT TRANSFER AND THERMAL DEVELOPMENT OF A RADIATIVELY PARTICIPATING FLUID IN A CHANNEL FLOW
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 6340 (Print) ISSN 0976 6359
More informationCFD Grows Up! Martin W. Liddament Ventilation, Energy and Environmental Technology (VEETECH Ltd) What is Computational Fluid Dynamics?
CIBSE/ASHRAE Meeting CFD Grows Up! Martin W. Liddament Ventilation, Energy and Environmental Technology (VEETECH Ltd) 10 th December 2003 What is Computational Fluid Dynamics? CFD is a numerical means
More informationMixed Precision Iterative Refinement Methods Energy Efficiency on Hybrid Hardware Platforms
Mixed Precision Iterative Refinement Methods Energy Efficiency on Hybrid Hardware Platforms Björn Rocker Hamburg, June 17th 2010 Engineering Mathematics and Computing Lab (EMCL) KIT University of the State
More informationWhich strategy to move the mesh in the Computational Fluid Dynamic code OpenFOAM
Which strategy to move the mesh in the Computational Fluid Dynamic code OpenFOAM Christophe Kassiotis April 12, 2008 École Normale Supérieure de Cachan, Laboratoire de Mécanique et Technologies (LMT) Secteur
More informationLecture 11 Boundary Layers and Separation. Applied Computational Fluid Dynamics
Lecture 11 Boundary Layers and Separation Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Overview Drag. The boundary-layer
More informationModel of a flow in intersecting microchannels. Denis Semyonov
Model of a flow in intersecting microchannels Denis Semyonov LUT 2012 Content Objectives Motivation Model implementation Simulation Results Conclusion Objectives A flow and a reaction model is required
More informationAPPENDIX 3 CFD CODE - PHOENICS
166 APPENDIX 3 CFD CODE - PHOENICS 3.1 INTRODUCTION PHOENICS is a general-purpose software code which predicts quantitatively the flow of fluids in and around engines, process equipment, buildings, human
More informationNUMERICAL SIMULATION OF REGULAR WAVES RUN-UP OVER SLOPPING BEACH BY OPEN FOAM
NUMERICAL SIMULATION OF REGULAR WAVES RUN-UP OVER SLOPPING BEACH BY OPEN FOAM Parviz Ghadimi 1*, Mohammad Ghandali 2, Mohammad Reza Ahmadi Balootaki 3 1*, 2, 3 Department of Marine Technology, Amirkabir
More informationA Memory-Efficient Data Handling for Octree-Like Grids
A Memory-Efficient Data Handling for Octree-Like Grids, Tobias Weinzierl, Tobias Neckel June 2010 Outline grid adaptivity for fluid-structure interactions our grid and data concept application examples
More informationVista: A Multi-field Object Oriented CFD-package
Vista: A Multi-field Object Oriented CFD-package T. Kvamsdal 1, R. Holdahl 1 and P. Böhm 2 1 SINTEF ICT, Applied Mathematics, Norway 2 inutech GmbH, Germany Outline inutech & SINTEF VISTA a CFD Solver
More informationO.F.Wind Wind Site Assessment Simulation in complex terrain based on OpenFOAM. Darmstadt, 27.06.2012
O.F.Wind Wind Site Assessment Simulation in complex terrain based on OpenFOAM Darmstadt, 27.06.2012 Michael Ehlen IB Fischer CFD+engineering GmbH Lipowskystr. 12 81373 München Tel. 089/74118743 Fax 089/74118749
More information