Simulation of Flow through pipe in OpenFoam using Matlab software

AIM:- IN THIS PROJECT SIMULATION IS DONE ON THE FLUID FLOW THROUGH PIPE USING OPENFOAM SOFTWARE AND MATLAB . THE TOPIC GIVEN BELOW IS COVERED IN THIS PROJECT.

  • TO MAKE A PROGRAM IN MATLAB THAT CAN GENERATE MESH AUTOMATICALLY FOR ANY WEDGE ANGLE AND GRADING SCHEME.
  • TO SHOW ENTRY LENGTH IS SUFFICIENT TO PRODUCE VELOCITY PROFILE.
  • TO CALCULATE  THE LENGTH OF PIPE USING MATLAB PROGRAM.
  • TO GENERATE FULLY DEVELOP VELOCITY PROFILE AND MATCH WITH HAIGEN-POISEUILLE EQUATION.
  • TO POST PROCESS VELOCITY AND SHEAR STRESS AND AND  MAKE COMPARISON WITH HAIGEN-POISEUILLE EQUATION.

 

ASSUMPTIONS:-

  • WEDGE ANGLE FOR PIPE IS TAKEN BELOW 5 DEGREE.
  • NUMBER OF CELLS ALONG "AXI SYMMETRIC".
  • CALCULATION OF LENGTH OF PIPE THROUGH  ENTRY LENGTH FORMULA.
  • TEMPERATURE CONSIDERED 4 degree.
  • ICOFOAM SOLVER FOR POST PROCESSING.
  • TIME FOR SIMULATION IS TAKEN 15 SECONDS.

DATA ASSUMPTION FOR SIMULATION:-

  • KINEMATIC VISCOSITY=1.3E-6`m^2s^-1`.
  • DYNAMIC VISCOSITY=0.0013 Pa.s
  • REYNOLDS NUMBER=2100.

 

IN THIS PROJECT, I HAVE MADE SIMULATION ON FLOW(MOTION) OF FLUID THROUGH AN OPEN PIPE USING OPENFOAM SOFTWARE .

IN THIS, I HAVE CONSIDERED AN OPEN PIPE IN WHICH THERE IS INLET FOR FLUID FROM ONE END AND OUTLET FROM OTHER END. WE HAVE ALSO CONSIDERED THE CIRCULAR EDGE OF PIPE AS NOSLIP WALL WHICH MAKES VELOCITY AT THERE ZERO SUCH THAT THE VELOCITY PROFILE OBTAINED FROM SIMULATION CAN BE SAME AS OBTAINED FROM HAIGEN-POISEUILLE EQUATION.

HERE THE REYNOLDS NUMBER FOR VELOCITY IS TAKEN AS 2100 WHICH MAKES IT LAMINAR FLOW AND PROVIDES ADVANTAGE OF FINDING OUT THE ENTRY LENGTH FOR PIPE.

ENTRY LENGTH OF PIPE=0.06*`R_e` , WHERE ENTRY LENGTH IS DEFINED AS TOTAL LENGTH TRAVELLED BY THE FLUID BEFORE BECOMING FULLY DEVELOPED(VELOCITY PROFILE) IN THE PIPE.

 

 

 

                                                               

 

THE ENTRY LENGTH HELPS IN FINDIND OUT THE MAXIMUM VELOCITY OF FLUID FLOWING THROUGH PIPE AT PARTICULAR LOCATION DUE TO WHICH WE ARE ALSO ABLE PREDICT THE AVERAGE VELOCITY OF FLUID. 

THE VELOCITY PROFILE HELPS IN FINDING OUT THE NATURE OF FLUID THROUGH FLOWING THROUGH PIPE. SO IN ORDER TO FIND THE NATURE OF FLUID AND SHEAR STRESS DUE TO MOTION OF FLUID, I HAVE DONE SIMULATION HERE.

FORMULA FOR VELOCITY PROFILE IS DEFINED AS :-

`v=-1/(4mu)(delp)/(delx)(R^2-r^2).`

IT FORMULA PROVES THAT VELOCITY IS MAXIMUM AT CENTRE OF PIPE AND MINIMUM AT EDGE OF PIPE. 

FORMULA FOR PRESSURE GRADIENT :-

 

 `(delp)/(delx)=-(8*mu*u)/R^2`

THIS FORMULA IS ALSO KNOWN AS "HAIGEN-POISEUILLE'S LAW".

 

 MATLAB PRGRAM:-

PROGRAM SCRIPTED IN MATLAB SO THAT IT CAN AUTOMATICALLY GENERATE MESH FOR ANY WEDGE ANGLE AND GRADING SCHEME FOR ANY GEOMETRY IN OPENFOAM.

clear all
close all
clc

% data for analysis of flow:-

rey_no=2100;  %% reynolds number describing the type of flow

rho=input("give density of water\t")

mu=input("give dynamic viscosity of water\t")

d=input("give diameter of the pipe (in meter)\t")

theta=input("give wedge angle for pipe\t")

%% ENTRY LENGTH OF PIPE:-

l_e=d*(0.06*rey_no);

%% Actual length of pipe:-
l=0.5+l_e;

% BOUNDARY CONDITION:-

v_avg=(rey_no*mu)/(rho*l);

v_max=2*v_avg;

dp=(32*v_avg*mu*l)/(d)^2;

nu=mu/rho;

% vertices of the wedge geometry:-

v_0=[0 0 0];
v_1=[0 d/2*cosd(theta/2) -d/2*sind(theta/2)];
v_2=[0 d/2*cosd(theta/2) d/2*sind(theta/2)];
v_3=[l 0 0];
v_4=[l d/2*cosd(theta/2) -d/2*sind(theta/2)];
v_5=[l d/2*cosd(theta/2) d/2*sind(theta/2)];

arc_1=[0.0 d/2 0.0];

arc_2=[l d/2 0.0];

x=input("give number of grid points along x-axis\t")

y=input("give number of grid points along y-axis\t")

z=input("give number of grid points along z-axis\t")

xx=input("give grading number along x-axis\t")

yy=input("give grading number along y-axis\t")

zz=input("give grading number along z-axis\t")

n=input("give conversion unit value\t")


line1='|/*-------------------------------------c++ -------------------------------------------*\|';
line2='|     ========                                                                           |';
line3='|    \        /      F ield              | OpenFOAM: The Open Source CFD Toolbox         |';
line4='|     \      /       O peration          | Website: https://openfoam.org                 |';
line5='|      \    /        A nd                | Version:  6                                   |';
line6='|       \  /         M anipulation       |                                               |';
line7='|\*------------------------------------------------------------------------------------*/|';
line8='FoamFile ';
line9=' { ';

%% "CREATING BLOCKMESH DICTIONERY FILE BELOW USING FILE PARSING"%%

f1=fopen('blockMeshDict.txt','w')
fprintf(f1,'%s\n',line1);
fprintf(f1,'%s\n',line2);
fprintf(f1,'%s\n',line3);
fprintf(f1,'%s\n',line4);
fprintf(f1,'%s\n',line5);
fprintf(f1,'%s\n',line6);
fprintf(f1,'%s\n',line7);
fprintf(f1,'\n');
fprintf(f1,'%s\n',line8);
fprintf(f1,'%s\n\n',line9);

fprintf(f1,'%16s %10s \n','version','  2.0;           ');
fprintf(f1,'%16s %10s \n','format' ,'  ascii;         ');
fprintf(f1,'%16s %10s \n','class'  ,'  dictionary;    ');
fprintf(f1,'%16s %10s \n','object' ,'  blockMeshDict; ');
fprintf(f1,'\n } \n \n');
fprintf(f1,'// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\n ');
fprintf(f1,' convertToMeters %d;\n \n',n);

% DEFINING VERTICES OF GEOMETRY :-

fprintf(f1,'\t\tvertices \n');
fprintf(f1,'\t\t(\n');
fprintf(f1,'\t\t\t(%f %f %f)\n',v_0);
fprintf(f1,'\t\t\t(%f %f %f)\n',v_1);
fprintf(f1,'\t\t\t(%f %f %f)\n',v_2);
fprintf(f1,'\t\t\t(%f %f %f)\n',v_3);
fprintf(f1,'\t\t\t(%f %f %f)\n',v_4);
fprintf(f1,'\t\t\t(%f %f %f)\n',v_5);
fprintf(f1,'\t\t);\n\n');
fprintf(f1,'\t\tblocks \n');
fprintf(f1,'\t\t( \n');
fprintf(f1,'\t\t\t hex (0 1 2 0 3 4 5 3)  (%d %d %d)  simpleGrading (%d %d %d)\n\t\t); \n \n',x,y,z,xx,yy,zz);

%% DEFININIG SIDES OF GEOMETRY:-

%EDGE OF PIPE:- 
fprintf(f1,'\t\tedges \n');
fprintf(f1,'\t\t(\n ');
fprintf(f1,'\t\t\tarc 1 2 (%f %f %f) \n',arc_1);
fprintf(f1,'\t\t\tarc 4 5 (%f %f %f) \n',arc_2);
fprintf(f1,' \t\t); \n \n');

% DEFINING BOUNDARY OF PIPE:- 
fprintf(f1,' \t\tboundary\n\t\t(\n');

%INLET SECTION:-
fprintf(f1,'%16s\n','inlet');
fprintf(f1,'%10s\n','{');
fprintf(f1,'%25s\n','type patch;');
fprintf(f1,'%19s\n','faces');
fprintf(f1,'%15s\n','(');
fprintf(f1,'%28s\n','(0 1 2 0)');
fprintf(f1,'%16s\n',');');
fprintf(f1,'%10s\n','}');
fprintf(f1,'\n');

%OUTLET SECTION:-
fprintf(f1,'%15s\n','outlet');
fprintf(f1,'%10s\n','{');
fprintf(f1,'%25s\n','type patch;');
fprintf(f1,'%19s\n','faces');
fprintf(f1,'%15s\n','(');
fprintf(f1,'%28s\n','(3 4 5 3)');
fprintf(f1,'%16s\n',');');
fprintf(f1,'%10s\n','}');
fprintf(f1,'\n');

%FRONT SIDE OF PIPE:-
fprintf(f1,'%13s\n','Front');
fprintf(f1,'%10s\n','{');
fprintf(f1,'%25s\n','type wedge;');
fprintf(f1,'%19s\n','faces');
fprintf(f1,'%15s\n','(');
fprintf(f1,'%28s\n','(0 2 5 3)');
fprintf(f1,'%16s\n',');');
fprintf(f1,'%10s\n','}');
fprintf(f1,'\n');

%BACK SIDE OF PIPE:-
fprintf(f1,'%13s\n','Back');
fprintf(f1,'%10s\n','{');
fprintf(f1,'%25s\n','type wedge;');
fprintf(f1,'%19s\n','faces');
fprintf(f1,'%15s\n','(');
fprintf(f1,'%28s\n','(0 3 4 1)');
fprintf(f1,'%16s\n',');');
fprintf(f1,'%10s\n','}');
fprintf(f1,'\n');

% TOP SIDE OF PIPE
fprintf(f1,'%12s\n','TOP');
fprintf(f1,'%10s\n','{');
fprintf(f1,'%24s\n','type patch;');
fprintf(f1,'%19s\n','faces');
fprintf(f1,'%15s\n','(');
fprintf(f1,'%28s\n','(1 2 5 4)');
fprintf(f1,'%16s\n',');');
fprintf(f1,'%10s\n','}');
fprintf(f1,'\n');

% AXIS OF PIPE
fprintf(f1,'%13s\n','axis');
fprintf(f1,'%10s\n','{');
fprintf(f1,'%25s\n','type empty;');
fprintf(f1,'%19s\n','faces');
fprintf(f1,'%15s\n','(');
fprintf(f1,'%28s\n','(0 3 3 0)');
fprintf(f1,'%16s\n',');');
fprintf(f1,'%10s\n','}');
fprintf(f1,'%5s\n',');');
fprintf(f1,'\n');


fprintf(f1,'%20s\n','mergePatchPairs');
fprintf(f1,'%6s\n','(');
fprintf(f1,'%7s\n',');');
fclose(f1)
 
%%%%%%%%%%FILES PARSING PROCESS COMPLETED HERE AND TEXT FILE IS GENERATE%%%%%%%%%%%%%%%








 

  PREPROCESSING STEPS :-

  1. FILE PARSING TECHNIQUE IS USED FOR GENERATION OF BLOCKMESH DICTIONARY IN TEXT FILE MODE THAT DEFINES THE GEOMETRY OF OBJECT.
  2. IN OPENFOAM, CASE FILE OF CAVITY FROM COMPRESSIBLE SETUP IS COPIED AND THEN PASTE IT IN THE RUN FILE USING RUN COMMAND TERMINAL.
  3. THE FILE THERE RENAMED AS "CAVITY_2" .
  4. AFTER GENERATION OF BLOCKMESH FILE IN MATLAB, THE TEXT FILE IS FED IN CASE FILE OF CAVITY KNOWN AS "SYSTEM". 
  5. AFTER IT, TIME STEP VALUE IS GIVEN IN CONTROLDICT FILE TO DEFINE SIMULATION TIME.
  6. AFTER THAT USERDEFINED VALUE FOR VELOCITY AND PRESSURE IS PROVIDED IN PRESSURE FILE AND VELOCITY FILE.
  7. AFTER PROVIDING THE ABOVE DETAILS, VISCOSITY IS PROVIDED IN TRANSPORT PROPERTIES TO GIVE VALUE FOR KINEMATIC VISCOSITY.
  8. AFTER COMPLETING ALL DETAILS,THE " BLOCKMESH " COMMAND IS RUN IN RUN TERMINAL TO EXECUTE PROGRAM. THEN " CHECKMESH " IS EXECUTED TO CHECK MESH OF GEOMETRY IS CORRECT OR NOT.
  9. AFTER THAT "ICOFOAM" SOLVER IS EXECUTED IN THE RUN TERMINAL WHICH CAUSES THE SIMULATION OF FLOW TO THE DESIRED SIMULATION TIME VALUE.
  10. HENCE, IN THIS WAY THE PROCESS FOR PREPROCESSING IS COMPLETED. AND AFTER IT, STEPS FOR POST PROCESSING IS TAKEN .

 

BLOCKMESHDICT :-

THIS IS THE FILE WHERE THE GEOMETRY IS DEFINED AND ALSO MESHING AND GRADING IS DEFINED.

/*---------------------------*-c++ ---------------------------*
  =======                  
  \           /     F ield                 | OpenFOAM: The Open Source CFD Toolbox 
    \        /      O peration          | Website: https://openfoam.org
     \     /        A nd                  | Version:  6
       \ /          Manipulation        |
\*---------------------------------------------------------------*/  
FoamFile 
 { 
     version      2.0; 
     format       ascii;
     class         dictionary;
     object       blockMeshDict; 
 } 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 convertToMeters 1;
 
 vertices 
 ( 
    (0 0 0)
    (0 0.00999391 -0.000348995)
    (0 0.00999391 0.000348995)
    (3.02 0 0)
    (3.02 0.00999391 -0.000348995)
    (3.02 0.00999391 0.000348995) 
 );
 
 blocks 
 ( 
        hex (0 1 2 0 3 4 5 3)  (100 1 200)  simpleGrading (1 1 1) 
 );
 
 edges 
 ( arc 1 2 (0.000000 0.010000 0.000000)
   arc 4 5 (3.020000 0.010000 0.000000) 
 ); 
 
 boundary 
       ( 
    inlet 
     { 
          type patch; 
          faces    
          ( 
            (0 1 2 0) 
         ); 
     } 
 
     outlet 
    { 
        type patch; 
        faces 
        ( 
           (3 4 5 3) 
        ); 
     }
 
 Front 
 { 
     type wedge;
     faces 
    ( 
      (0 2 5 3) 
    ); 
 } 
 Back 
 { 
     type wedge; 
     faces 
 ( 
     (0 3 4 1) 
 ); 
 }
    TOP 
   { 
      type wall; 
      faces 
     ( 
        (1 2 5 4) 
     ); 
   }

    axis 
   { 
     type empty; 
     faces 
     (  
      (0 3 3 0) 
     ); 
   }
     );
 
 mergePatchPairs 
 ( 
 ) ;

 

CONTROLDICT:-

IN THIS FILE, THE TIME STEP VALUE IS DEFINED WHICH WILL HELP IN ACCOUNTING THE FLOW OF FLUID OVER THE TIME STEP.

 

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  6
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         0.8;

deltaT          1e-4;

writeControl    timeStep;

writeInterval   10;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;

 functions
 {
   #includeFunc streamlines
 }


// ************************************************************************* //

 

PRESSURE FILE:-

IN THIS FILE, TYPE OF PRESSURE IS DEFINED AT INLET AND OUTLET SECTION AND ALSO AT INTERNAL FIELD.

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  6
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volScalarField;
    object      p;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 2 -2 0 0 0 0];

internalField   uniform 0;

boundaryField
{
    inlet
    {
        type           zeroGradient;
    }

    outlet
    {
        type           fixedValue;
        value          uniform 5.377;
    }

    Front
    {
        type            wedge;
    }

    Back
    {
        type            wedge;
    }

    TOP
    {
        type            zeroGradient;

    }
}

// ************************************************************************* //

 

VELOCITY FILE:-

IN THIS FILE, TYPE OF VELOCITY IS DEFINED AT INLET AND OUTLET SECTION AND ALSO AT INTERNAL FIELDS.

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  6
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    version     2.0;
    format      ascii;
    class       volVectorField;
    object      U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

dimensions      [0 1 -1 0 0 0 0];

internalField   uniform (0.05292 0 0);

boundaryField
{
  inlet
    {
        type           fixedValue;
        value          uniform (0.05292 0 0);
    }

    outlet
    {
        type           zeroGradient;
    }

    Front
    {
        type            wedge;
    }

    Back
    {
        type            wedge;
    }

    TOP
    {
        type          noSlip;
    }
}


// ************************************************************************* //

 

POSTPROCESSING STEPS:-

  1. AFTER EXECUTING THE "ICOFOAM"SOLVER ,THE SIMULATION COMPLETES FOR REQUIRED TIME AND NOW WE ARE ABLE TO EXTRACT DATA FROM SIMULATION.
  2. IN ORDER TO DO THAT, OPEN THE PARAVIEW USING PARAFOAM COMMAND IN RUN TERMINAL. 
  3. AFTER OPENING PARAVIEW, CLICK  APPLY ON PROPERTIES MENU. IT WILL GENERATE THE GEOMETRY(MODEL).
  4. AFTER THAT CLICK ON 'PROBE OVER LINE' TAB IN STATUS BAR. IT WILL OPEN THAT, THERE PROVIDE THE COORIDINATES FOR LINE FROM STARTING TO ENDING POINT OF LINE.
  5. JUST MAKE SURE FOR WHICH PHYSICAL PARAMETER(LIKE PRESSURE,VELOCITY) ARE YOU SEARCHING THE PROBE. HERE IT IS VELOCITY PROFILE. THEN CLICK APPLY.
  6. NOW, VELOCITY PROFILE IS GENERATED
  7. CLICK ON FILE OPTION ON TOP LEFT OF THE WINDOW  AND CLICK ON SAVE DATA. IT WILL STORE ALL THE VALUES AT GRID POINTS FOR ALL THE PARAMETER.
  8. NOW SAVE THE DATA AS  FILENAME AS ".CSV" EXTENSION.
  9. NOW, IMPORT THE SAVE DATA IN MATLAB SOFTWARE AND WITH THE HELP OF CODING , PLOT THE DATA FOR SHEAR STRESS.
  10. SIMILARLY, VALUES AT EACH POINT FOR VELOCITY IS GENERATED AND WE CAN FIND OUT THE MAXIMUM AND MINIMUM VELOCITY ACROSS RADIUS OF PIPE.
  11. IN THIS WAY, THE POST PROCESSING IS COMPLETED AND SHEAR STRESS IS DEVELOPED ALONG WITH MAXIMUM AND MINIMUM VELOCITY OF FLUID.

 

 

GEOMETRY AND  MESH GENERATED IN PARAFOAM:-

 

 

 

SIMULATION OF FLUID FLOW AFTER 15 SECONDS IN THE PIPE FOR WEDGE ANGLE OF 4:-

 

 

NUMERICAL RESULT FOR VELOCITY PROFILE:-

VELOCITY PROFILE OF FLUID IN THE PIPE AT 0.5m LENGTH FROM THE INLET SECTION:-

                     

 

 

  VELOCITY PROFILE OF FLUID IN THE PIPE AT 1.0m LENGTH FROM THE INLET SECTION:-

                     

 

 

 

VELOCITY PROFILE OF FLUID IN THE PIPE AT 1.5m LENGTH FROM THE INLET SECTION:-

                   

 

VELOCITY PROFILE OF FLUID IN THE PIPE AT 2.5 m LENGTH FROM THE INLET SECTION:-

                       

 

ANALYTICAL RESULT FOR VELOCITY PROFILE:-

                               

      NUMERICAL RESULT FOR PRESSURE GRADIENT:-             

 

 

ANALYTCAL RESULT FOR PRESSURE GRADIENT:-

                                   

NUMERICAL RESULT OF SHEAR STRESS  :-

                                                              

 

 

ANAYTICAL RESULT OF SHEAR STRESS  :-

                                           


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