Week 12 - Symmetry vs Wedge vs HP equation
Using the values from previous challege, leght of pipe is 5mm and average velocity is 0.1602m/s. This matlab program will provide the geometry file for any wedge angle. thus it needs the angle as input.
Matlab Program for different wedge angle:
clear all
close all
clc
wedge_angle = input('enter the wedge angle')
theta = wedge_angle/2;
x = 5*sin(theta*pi/180);
y = 5*cos(theta*pi/180);
f1 = fopen('blockMeshDict.txt','w')
L1 = ('/*--------------------------------*- C++ -*----------------------------------*\')
L2 = (' ========= |')
L3 = (' \\ / F ield | OpenFOAM: The Open Source CFD Toolbox')
L4 = (' \\ / O peration | Website: https://openfoam.org')
L5 = (' \\ / A nd | Version: 7')
L6 = (' \\/ M anipulation |')
L7 = ('\*---------------------------------------------------------------------------*/')
L8 = ('FoamFile')
L9 = ('{')
L10 = (' version 2.0;')
L11 = (' format ascii;')
L12 = (' class dictionary;')
L13 = (' object blockMeshDict;')
L14 = ('}')
L15 = ('// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //')
L16 = ('convertToMeters 0.001;')
L17 = ('vertices')
L18 = ('(')
L19 = (' (0 0 0) //0')
L20 = (' (')
L201 = (' 0) //1')
L21 = (' (')
L211 = (' 0) //2')
L22 = (' (0 0 1400) //3 ')
L23 = (' (')
L231 = (' 1400) //4')
L24 = (' (')
L241 = (' 1400) //5')
L25 = (');')
L26 = ('blocks')
L27 = ('(')
L28 = (' hex (0 1 2 0 3 4 5 3) (25 1 500) simpleGrading (0.1 1 0.1)')
L29 = (');')
L30 = ('edges')
L31 = ('(')
L32 = (' arc 2 1 (0 5 0)')
L33 = (' arc 5 4 (0 5 1400)')
L34 = (');')
L35 = ('boundary')
L36 = ('(')
L37 = (' inlet')
L38 = (' {')
L39 = (' type patch;')
L40 = (' faces')
L41 = (' (')
L42 = (' (0 1 2 0)')
L43 = (' );')
L44 = (' }')
L45 = (' outlet')
L46 = (' {')
L47 = (' type patch;')
L48 = (' faces')
L49 = (' (')
L50 = (' (3 5 4 3)')
L51 = (' );')
L52 = (' }')
L53 = (' pipeWall')
L54 = (' {')
L55 = (' type wall;')
L56 = (' faces')
L57 = (' (')
L58 = (' (2 1 4 5)')
L59 = (' );')
L60 = (' }')
L61 = (' leftsides')
L62 = (' {')
L63 = (' type wedge;')
L64 = (' faces')
L65 = (' (')
L66 = (' (3 0 2 5)')
L67 = (' );')
L68 = (' }')
L69 = (' rightsides')
L70 = (' {')
L71 = (' type wedge;')
L72 = (' faces')
L73 = (' (')
L74 = (' (0 3 4 1)')
L75 = (' );')
L76 = (' }')
L77 = (' axis')
L78 = (' {')
L79 = (' type empty;')
L80 = (' faces')
L81 = (' (')
L82 = (' (0 3 3 0)')
L83 = (' );')
L84 = (' }')
L85 = (');')
L86 = ('mergePatchPairs')
L87 = ('(')
L88 = (');')
L89 = ('// ************************************************************************* //')
fprintf(f1, '%s',L1)
fprintf(f1,'\n')
fprintf(f1, '%s',L2)
fprintf(f1,'\n')
fprintf(f1, '%s',L3)
fprintf(f1,'\n')
fprintf(f1, '%s',L4)
fprintf(f1,'\n')
fprintf(f1, '%s',L5)
fprintf(f1,'\n')
fprintf(f1, '%s',L6)
fprintf(f1,'\n')
fprintf(f1, '%s',L7)
fprintf(f1,'\n')
fprintf(f1, '%s',L8)
fprintf(f1,'\n')
fprintf(f1, '%s',L9)
fprintf(f1,'\n')
fprintf(f1, '%s',L10)
fprintf(f1,'\n')
fprintf(f1, '%s',L11)
fprintf(f1,'\n')
fprintf(f1, '%s',L12)
fprintf(f1,'\n')
fprintf(f1, '%s',L13)
fprintf(f1,'\n')
fprintf(f1, '%s',L14)
fprintf(f1,'\n')
fprintf(f1, '%s',L15)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L16)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L17)
fprintf(f1,'\n')
fprintf(f1, '%s',L18)
fprintf(f1,'\n')
fprintf(f1, '%s',L19)
fprintf(f1,'\n')
fprintf(f1, '%s',L20)
fprintf(f1, '%f %f',x, y)
fprintf(f1, '%s',L201)
fprintf(f1,'\n')
fprintf(f1, '%s',L21)
fprintf(f1, '%f %f',-x, y)
fprintf(f1, '%s',L211)
fprintf(f1,'\n')
fprintf(f1, '%s',L22)
fprintf(f1,'\n')
fprintf(f1, '%s',L23)
fprintf(f1, '%f %f',x, y)
fprintf(f1, '%s',L231)
fprintf(f1,'\n')
fprintf(f1, '%s',L24)
fprintf(f1, '%f %f',-x, y)
fprintf(f1, '%s',L241)
fprintf(f1,'\n')
fprintf(f1, '%s',L25)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L26)
fprintf(f1,'\n')
fprintf(f1, '%s',L27)
fprintf(f1,'\n')
fprintf(f1, '%s',L28)
fprintf(f1,'\n')
fprintf(f1, '%s',L29)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L30)
fprintf(f1,'\n')
fprintf(f1, '%s',L31)
fprintf(f1,'\n')
fprintf(f1, '%s',L32)
fprintf(f1,'\n')
fprintf(f1, '%s',L33)
fprintf(f1,'\n')
fprintf(f1, '%s',L34)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L35)
fprintf(f1,'\n')
fprintf(f1, '%s',L36)
fprintf(f1,'\n')
fprintf(f1, '%s',L37)
fprintf(f1,'\n')
fprintf(f1, '%s',L38)
fprintf(f1,'\n')
fprintf(f1, '%s',L39)
fprintf(f1,'\n')
fprintf(f1, '%s',L40)
fprintf(f1,'\n')
fprintf(f1, '%s',L41)
fprintf(f1,'\n')
fprintf(f1, '%s',L42)
fprintf(f1,'\n')
fprintf(f1, '%s',L43)
fprintf(f1,'\n')
fprintf(f1, '%s',L44)
fprintf(f1,'\n')
fprintf(f1, '%s',L45)
fprintf(f1,'\n')
fprintf(f1, '%s',L46)
fprintf(f1,'\n')
fprintf(f1, '%s',L47)
fprintf(f1,'\n')
fprintf(f1, '%s',L48)
fprintf(f1,'\n')
fprintf(f1, '%s',L49)
fprintf(f1,'\n')
fprintf(f1, '%s',L50)
fprintf(f1,'\n')
fprintf(f1, '%s',L51)
fprintf(f1,'\n')
fprintf(f1, '%s',L52)
fprintf(f1,'\n')
fprintf(f1, '%s',L53)
fprintf(f1,'\n')
fprintf(f1, '%s',L54)
fprintf(f1,'\n')
fprintf(f1, '%s',L55)
fprintf(f1,'\n')
fprintf(f1, '%s',L56)
fprintf(f1,'\n')
fprintf(f1, '%s',L57)
fprintf(f1,'\n')
fprintf(f1, '%s',L58)
fprintf(f1,'\n')
fprintf(f1, '%s',L59)
fprintf(f1,'\n')
fprintf(f1, '%s',L60)
fprintf(f1,'\n')
fprintf(f1, '%s',L61)
fprintf(f1,'\n')
fprintf(f1, '%s',L62)
fprintf(f1,'\n')
fprintf(f1, '%s',L63)
fprintf(f1,'\n')
fprintf(f1, '%s',L64)
fprintf(f1,'\n')
fprintf(f1, '%s',L65)
fprintf(f1,'\n')
fprintf(f1, '%s',L66)
fprintf(f1,'\n')
fprintf(f1, '%s',L67)
fprintf(f1,'\n')
fprintf(f1, '%s',L68)
fprintf(f1,'\n')
fprintf(f1, '%s',L69)
fprintf(f1,'\n')
fprintf(f1, '%s',L70)
fprintf(f1,'\n')
fprintf(f1, '%s',L71)
fprintf(f1,'\n')
fprintf(f1, '%s',L72)
fprintf(f1,'\n')
fprintf(f1, '%s',L73)
fprintf(f1,'\n')
fprintf(f1, '%s',L74)
fprintf(f1,'\n')
fprintf(f1, '%s',L75)
fprintf(f1,'\n')
fprintf(f1, '%s',L76)
fprintf(f1,'\n')
fprintf(f1, '%s',L77)
fprintf(f1,'\n')
fprintf(f1, '%s',L78)
fprintf(f1,'\n')
fprintf(f1, '%s',L79)
fprintf(f1,'\n')
fprintf(f1, '%s',L80)
fprintf(f1,'\n')
fprintf(f1, '%s',L81)
fprintf(f1,'\n')
fprintf(f1, '%s',L82)
fprintf(f1,'\n')
fprintf(f1, '%s',L83)
fprintf(f1,'\n')
fprintf(f1, '%s',L84)
fprintf(f1,'\n')
fprintf(f1, '%s',L85)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L86)
fprintf(f1,'\n')
fprintf(f1, '%s',L87)
fprintf(f1,'\n')
fprintf(f1, '%s',L88)
fprintf(f1,'\n \n')
fprintf(f1, '%s',L89)
fclose(f1)controlDict file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application icoFoam;
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 8;
deltaT 0.001;
writeControl timeStep;
writeInterval 20;
purgeWrite 0;
writeFormat ascii;
writePrecision 6;
writeCompression off;
timeFormat general;
timePrecision 6;
runTimeModifiable true;
// ************************************************************************* //
velocity file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
version 2.0;
format ascii;
class volVectorField;
object U;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 1 -1 0 0 0 0];
internalField uniform (0 0 0);
boundaryField
{
inlet
{
type fixedValue;
value uniform (0 0 0.1602);
}
outlet
{
type zeroGradient;
}
pipeWall
{
type noSlip;
}
leftsides
{
type wedge;
}
rightsides
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //
pressure file:
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 7
\\/ 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 0;
}
pipeWall
{
type zeroGradient;
}
leftsides
{
type wedge;
}
rightsides
{
type wedge;
}
axis
{
type empty;
}
}
// ************************************************************************* //
result:
for 4 deg:
image:
graph:
for 10 deg:
image:
for 25 deg:
image:
for 45 deg:
image:
Maximum velocity:
Vmax: 0.3204 (calculated value)
4deg: 0.3169
10deg: 0.3170
25deg: 0.3172
45deg: 0.3178
These results shows the exact physics in the flow of water through the pipe. The velocity is maximum at the centre of the pipe and zero at the wall of the pipe. the velocity is reduced due the viscosity of the fluid which has friction in between the layers of the fluid. the greater the wedge angle made the more the accuracy of flow is found caparing it with the analytical value.