cfd - openfoam

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OverOverviewview Basics of CFD/FEA

Concepts of CFD

Software's for CFD

Preprocessing

Post Processing

Evaluation of Results

Solving

OpenFOAM




Basics ofBasics of C CFFD & FEAD & FEA

is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as of integral equations.

Finite Element Analysis/Method Finite Element Analysis/Method (FEA/FEM)(FEA/FEM)

numerical methods for approximating the solutions to differential equations using finite difference equations to approximate derivatives.

Finite Difference Method Finite Difference Method (FDM)(FDM)

numerical methods for representing and evaluating partial difference equations as a algebraic equations. similar to the FDM, the values are calculated at discrete places on a meshed geometry.

Finite Volume Method Finite Volume Method (FVM)(FVM)




Basics ofBasics of CFD & FEA CFD & FEA•The Finite Difference Method (FDM) is an approximation to the differential equation

•The Finite Element Method (FEM) is an approximation to its solution

•FEM is its ability to handle complex geometries (and boundaries) with relative ease

•FDM in its basic form is restricted to handle rectangular shapes and simple alterations

•FEM is the method of choice in all types of analysis in structural mechanics for ex. Structural Linear and Non - Linear Analysis, Thermal, Electromagnetic Applications

•Computational fluid dynamics (CFD) tends to use FDM or FVM



Computational Computational Fluid DynamicsFluid Dynamics

- is one which solves some distribution of physical variable in the certain domain with using mathematical approximation methods.

- Typically FVM is hired with iterative methods using basis of FDM

- that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows.

- The fundamental basis of any CFD problem, or the flow of any fluids may be analyzed mathematically by using two flow equations which was described in next steps,

It consists of a time-dependent continuity equation for conservation of mass three time-dependent conservation of momentum equations and a time-dependent conservation of energy equation.




Flow Flow EquationsEquationsContinuity Equation – (mass balance)

mass of fluid entering the volume = mass of fluid leaving the volume

The flow of most fluids (,, air, etc,) may be analyzed by the following equations

tWhere the symbol for example is a partial derivative with respect to time




Momentum Equation or Navier – Stokes Equation (Momentum Balance)

It was based on Newton’s Second law of motion, force equals mass time acceleration

F = m*aThe equations were derived independently by G.G. Stokes, in England, and M. Navier, in France, in the early 1800's.

The equations are extensions of the Euler Equations and include the effects of viscosity on the flow.

It was a the three-dimensional unsteady form describes how the velocity, pressure, temperature, and density of a moving fluid are related

Thus to solve a flow problem, you mainly have to solve all five equations simultaneously; that is why we call this a coupled system of equations.




X-Momentum

Y-Momentum

Z-Momentum

Conservation of Momentum



Navier -Stokes Navier -Stokes EquationsEquationsrate of change of momentumin the control volume

external forces acting on the control volume.

the net momentum flux into the control volume

= +


Conservation of Energy



Navier -Stokes Navier -Stokes EquationsEquations

If the flow is compressible ( is not constant), the energy equation may be used.

The change in energy of the fluid within the control volume

the net thermal energy transferred into the control volume

the rate of work done by external forces.

= +


Software’s for CFDIn general, there are many commercial software’s available for CFD like

Fluent V4 (Fluent Inc.)ANSYS - CFX, CFX (AEA Technology)FIDAP (Fluid Dynamics International Inc.)CFDesignSiemens – Femap Flow (an UGS product)COSMIC NASAICEM CFD (Icepak)FLOWTHERM (Flowmerics Inc.)

OpenFOAM is a free open source software. It is one of CFD codes using FVM with specific solvers, i.e., incompressible, compressible, laminar ,turbulent, steady state and transient




Open FOAM – an open source CFD technique

OpenFOAM is free open source software mainly meant for Computational Fluid Dynamics (CFD) supported by OpenCFD Ltd.

OpenCFD was established in 2004 to coincide with the release of its OpenFOAM software under general public license. The teams assembled at OpenCFD each have 10 – 20 years of experience in CFD and have supplied development and support services for OpenFOAM to various organizations including:

Engineering Companies Audi, Airbus, Bayer, DANONE, Daimler, Delphi, Honda, Mitsubishi, SKF, Shell

Academic Institutions: Chalmers University, University of Exeter, Imperial College of London, Hirosaki University, Tokyo Institute of Technology.



Open Open Foam – 1.5Foam – 1.5


OpenFOAM – A set of generic tools to simulate complex physics on real,3D cases

OpenFOAM is a programmable tool kit using C++ • supplied with source code and compilers, customized applications are created for specific problems• using functionality built into generic libraries

OpenFOAM runs on Linux Platform, where we have installed OpenSUSE, a free Linux environment.

The current version of OpenFOAM is 1.5 and for OpenSUSE its 11.0. We working in OpenFOAM 1.4.1 and OpenSUSE 10.3

Numerous applications are preconfigured for complex fluid flows, solid dynamics, pre/post processing, mesh generation, etc.,





Generally, there are three steps in performing an analysis,

Pre-processingIn Pre-processing, the entire inputs for performing an analysis will be given likePhysical Properties, Fluid Properties, Initial Conditions, Boundary Conditions

Solvers - pre-programmed solvers are used to do the mathematical calculations for the specified conditions of the flow medium along the generated mesh geometries

Ex: Incompressible, compressible, Laminar, turbulent, steady – state and transient

Post-processing-The calculated results are converted into the graphical outputs for user interface.

-The interpolation of the results for the various parameters can be done in post processing




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After the flow model is created by using solid edge, the flow model is converted into IGES format.

Adventure is a third party software which has capability of analyzing small linear analysis.

Adventure on windows operates with the help of another software's for visualization like BC Tool (inbuilt software), Meshman Viewer (to view the generated mesh)

The generated mesh will be in the *.cmsh format which enables to read in Open FOAM

The procedure to create a mesh is shown in forthcoming slides

The IGES is used as input to generate the mesh using this Adventure on WindowsSoftware.



Mesh Mesh GenerationGeneration




Adventure Adventure on Windowson Windows


After the mesh generation from Adventure software, the input of generated mesh for OpenFOAM would extract from *.msh format.

Open FOAM is a Linux based software, where we using OpenSUSE 10.3 Linux operating system. The current version is Open SUSE 11.0.

The both OpenFOAM and OpenSUSE software is a free open source software which we can download the entire software from their website

For OpenSUSE, the software can be download from http://software.opensuse.org/

For OpenFOAM, the software can be download from http://opencfd.co.uk

Basically, for the Linux environment the software is a CASE SENSITIVE software and its just as like working through our command prompt.



Open Open Foam – 1.4.1Foam – 1.4.1


OpenFOAM is first and foremost a C++ library, used primarily to create executables, known as “applications”. The applications fall into two categories: Solvers: that are each designed to solve a specific problem in continuum mechanics, Utilities: that are designed to perform tasks that involve data manipulation.





It contains the full description of the case mesh in a sub directory “polyMesh”

This polyMesh folder contains the files specifying the physical properties for the application concerned.

for setting the parameters associated with the solution procedure itself.controlDict - which run the control parameters for the time step and for data output.

fvSolution - where the equation solvers, tolerances and other algorithm controls are set for the run.

fvSchemes - where discretisation schemes used in the solution may be selected at run-time

Contains individual files of data for particular fieldThe data can be: either, initial values and boundary conditions that the user mustspecify to define the problem; or, results written to file by OpenFOAM



Open Open Foam – 1.4.1Foam – 1.4.1Constant Constant DirectoryDirectory

System System DirectoryDirectory

Time Time DirectoryDirectory


There was a dual boot system which created in my system can work in both Microsoft and Linux environment. We have installed the OpenSUSE 10.3 OS.

The files can be created and handled in two methods1.Command User Interface (CUI) – when need to operate through the commands2.Graphical User Interface (GUI) – it operates with the help of FoamX window

The forthcoming slides will show the procedure and the operations using this CUI/GUI for an analysis.

As like as FEA, here also three steps basically to do an analysis. They are1.Pre Processing2.Solving 3.Post Processing





Some of the important points to be considered,

Time and data input/output control :The OpenFOAM solvers begin all runs by setting up a database. Since the database controls I/O and output of data is usually requested at intervals of time, so it is an inextricable part of the database. The controlDict dictionary sets input parameters essential for the creation of the database.

fvSchemes dictionary : in the system directory sets the numerical schemes for terms, such as derivatives in equations, that appear in applications being run.There are many numerical schemes listed in this dictionaries as a sub dictionaries , They are Interpolation schemes, Surface normal gradient schemes, Gradient schemes, Laplacian schemes, Divergence Schemes, Time Schemes, Flux Calculation.

Surface normal gradient schemesThe snGradSchemes sub-dictionary contains surface normal gradient terms. A surface normal gradient is evaluated at a cell face; it is the component, normal to the face, of the gradient of values at the centre's of the 2 cells that the face connects





Some of the important points to be considered,

The corrected coefficient of 1 will be used in Gaussian integration to evaluate the Laplacian terms. By default snGradSchemes of limited 0.5 will be used in special cases.

Solution and algorithm controlThe equation solvers, tolerances and algorithms are controlled from the fvSolution dictionary in the system directory.

fvSolution - contains a set of sub-dictionaries that are specific to the solver being run. Some of the sub-dictionaries included are solvers, relaxation Factors, PISO and SIMPLE





It specifies each ” linear-solver” that is used for each discretised equation; it also refers to the method of number-crunching to solve the set of linear equations. The term ‘linear-solver’ is abbreviated to ‘solver’. There are different type of solvers and its mentioned below:

Preconditioned conjugate gradient solversThere are a range of options for preconditioning of matrices in the conjugate gradient solvers, represented by the “preconditioner” keyword in the solver dictionary

Smooth solversThe solvers that use a smoother require the smoother to be specified. Generally “GaussSeidel” is the most reliable option.

Geometric-algebraic multi-grid solversgenerating a quick solution on a mesh with a small number of cells; mapping this solution onto a finer mesh; using it as an initial guess to obtain an accurate solution on the fine mesh.

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Open Open Foam – 1.4.1Foam – 1.4.1SolSolversvers




Open Open Foam – 1.4.1Foam – 1.4.1SolSolversvers


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The Ultimate result to extract from the ParaView window after the calculation was theVelocity “U” magnitude. Actually, the obtained result will be in m3/s, i.e., Volume Flow rate.

ResResultsults

The Volume flow rate will be calculated by integrating the each individual cell values at the sectioned area by using the FILTER > INTEGRATE Command in ParaView.

As per the result, the x magnitude of the volume flow rate is -0.0077 m3/s, the rest of them are Y and Z magnitudes. The negative sign indicates the reverse flow direction

As per formula, Flow = Velocity * Area

The mean Velocity over the area will be arrived using this formula.




ResResultsults

psiGPpsiGP

PPPscfmQ

wherePPQCv

::

:,

)7.14(

2

1

21

2

The Cv will be calculated using “Mass Flow Rate”, “Upstream Pressure” and “Downstream Pressure”.

The units of dimensions are necessary to be converted from SI units adopted in CFD.




ResResultsults

3/8"-NC 1-2 3/8"-NC 2-3 3/4"-NC 1-2 3/4"-NC 1-2 2"- 2 to 3 2"- 1 to 2smart3_12 smart3_23 TEST04 TEST03 lox_23 lox_12

Diameter m 1.270E-02 1.270E-02 2.000E-02 1.600E-02 5.232E-02 5.232E-02Sectional Area sq-m 1.613E-04 1.613E-04 3.142E-04 2.011E-04 2.150E-03 2.150E-03Mean Velocity m/sec 4.053E+01 4.539E+01 3.760E+01 7.700E+01 3.808E+01 2.951E+01

Volume Flow Rate from CFD cu-m/sec 6.538E-03 7.322E-03 1.181E-02 1.548E-02 8.189E-02 6.345E-02Upstream Pressure psiG 1.000E+00 1.000E+00 1.000E+00 1.000E+00 1.000E+00 1.000E+00

Downstream Pressure psiG 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00Averaged Pressure psiA 3.834E+00 3.834E+00 3.834E+00 3.834E+00 3.834E+00 3.834E+00

Standard Volume Flow cu-m/sec 6.538E-03 7.322E-03 1.181E-02 1.548E-02 8.189E-02 6.345E-02Differencial Pressure psiA 1.000E+00 1.000E+00 1.000E+00 1.000E+00 1.000E+00 1.000E+00

Cv ------ 3.613E+00 4.046E+00 6.528E+00 8.556E+00 4.525E+01 3.507E+01

Item Unit

Cases of Calculated by OpenFOAM-1.5SmartValve size3 TEST 3/4" 2inches L-O-X




Special Special NotesNotesSome of the key factors to consider to get good convergence in the results are

The sparse matrix solvers are iterative, i.e. they are based on reducing the equation residual over a succession of solutions. The residual is ostensibly a measure of the error in the solution so that the smaller it is, the more accurate the solution.

The solver stops if either of the following conditions are reached:

• the ratio of current to initial residuals falls below the solver relative tolerance, relTol

• the residual falls below the solver tolerance, tolerance,




Special Special NotesNotesFluctuation of both K and epsilon

If Log file shows the negative value due to bounding K (kinematic energy) and epsilon (energy dissipation) in each iterations, you have to change the Laplacian scheme regarding pressure.

As “Gauss linear corrected” scheme is default, “Gauss linear limited 0.5” scheme provides better. Both K and epsilon cannot have negative values in the theory.

But non - orthoganality affects the bounding between positive and negative values of K and epsilon.




Evaluation Evaluation of Resultsof Results

The pressure distribution and its value is the key

If there are some areas where pressures are extremely lower and/or higher, the calculation may be wrong.

It is necessary to change the relaxation factors become smaller.

The pressure distribution is smoothly reduced from upstream to downstream as same as the pressure boundary conditions applied.

Also the residual of pressure might become 10-4 orders in log file.




Other Other ResultsResults




QueQueriesries……




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