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Week 12 - Validation studies of Symmetry BC vs Wedge BC in OpenFOAM vs Analytical H.P equation

RRajat Thakur11 Aug 2022
CFDMATLABOPENFOAM

AIM:- Simulate the axis symetric and wedge boundary condition in open foam for different angles 10,25,45.

SOLUTIONS

Hagen poiseuille's law

In non-ideal fluid dynamics the hagen poiseuille equation is aphysical law that gives the pressure drop in an incompressible and newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross-section. The pressure drop is given by:

`DeltaP=(32muLV)/D^2`

where

`triangle P` is pressure drop

`mu`is dynamic viscosity

L is length of pipe

V is velocity

At enterance the flow is said to be in hydrodynamic enterance region where the velocity profil gradually takes the shape of parabola from a straight line. As soon as the parabolic velocity profile becomes steady the flow is said to be in its fully developed state . Normally hagen Poiseuilles equation is applicable for a fully developed flow which helps us to calculate pressure loss.

Equations used

Average velocity

`V_(avg)=(R_emu)/(rhoD)`

Maximum velocity

`V_max=2*V_(avg)`

Pressure drop

`DeltaP=(32muLV)/D^2`

Kinematic pressure drop

`(DeltaP)/rho`

STEPS & PROCEDURE

(1) Will start copying the cavity file to FOAM_RUN folder.

(2) Then we uses the blockmeshdict files ,pressure files, velocity ,controldict & transportfiles which we created using file parsing in matlab

(3) Then we run the blockMesh to create mesh structure.

(4) After we run for icoFoam and then paraFoam to get results for various cases for wedges at different angles.

(5) Compute data for analytical and Cfd to compare results.

CODES

MATLAB CODE FOR SYMMETRICAL

close all
clear all
clc


  %% Input data
% Reynolds number
Re = 2100;
% density of water in kg/m^3
rho=1000;
% Dia of pipe in metres
D= .004;
% Entrance Length of pipe
L= 0.06*Re*D;
% Fully developed length
L_d = 0.4;
% Total length of pipe
L_p= L+L_d;
% Radius of pipe
r=D/2;
% Angle of wedge(in degrees)
theta= 25;
% Dynamic viscosity
mu= 0.89e-3;
% Kinematic viscosity
nu= mu/rho;

%Hagen poisuille flow equations
v_avg= Re*nu/D;
v_max= 2*v_avg;
del_p= (8*mu*L_d*v_avg)/(r^2);
kinematic_p= del_p/rho;

%calculating shear stress
R= linspace(0,(D/2),1000);

for i= 1:length(R)
    tau(i)= 2*mu*v_max*(abs(R(i)))/(r^2);
    vel(i)= v_max*(1-(R(i)/r)^2);
end

figure(1)
plot(R,tau)
xlabel('Radius')
ylabel('Shear stress')
grid on
legend ('Shear stress')


figure(2)
plot(R,vel)
xlabel('Radius')
ylabel('Shear stress')
grid on
legend ('Velocity Profile')



%% Creating files for blockmeshdict
%Header files
h1='/*----------------------------------*- C++ -*------------------------------------*\\\'
h2='  =========                 |                                                         \' 
h3='   \\\\      /  F ield               | OpenFOAM: The Open Source CFD Toolbox          \'
h4='    \\\\    /   O peration           | Website:  https://openfoam.org                 \'
h5='     \\\\  /    A nd                 | Version:  7                                    \'
h6='      \\\\/     M anipulation   |                                                     \'
h7='\\*----------------------------------------------------------------------------------*/\'
h8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\'
h9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\'
%vertices
v0=[0 0 0] %for point 0
v1=[0 r*cosd(theta/2) r*sind(theta/2)] %point 1
v2=[0 r*cosd(theta/2) -r*sind(theta/2)]
v3=[L_p 0 0]
v4=[L_p r*cosd(theta/2) r*sind(theta/2)]
v5=[L_p r*cosd(theta/2) -r*sind(theta/2)]

% Creating text 
f1 = fopen( ' blockMeshDict_symmetry_angle_25', 'w');
fprintf(f1, ' %s \n ', h1 ) 
fprintf(f1, ' %s \n ', h2 )
fprintf(f1, ' %s \n ', h3 )
fprintf(f1, ' %s \n ', h4 )
fprintf(f1, ' %s \n ', h5 )
fprintf(f1, ' %s \n ', h6 )
fprintf(f1, ' %s \n \n ', h7 )

fprintf(f1, 'FoamFile \n{ \n \n ')
fprintf(f1, '%12s \t \t 2.0; \n ','version ')
fprintf(f1, '%12s \t \t ascii; \n','format ')
fprintf(f1, '%12s \t \t dictionary; \n','class ')
fprintf(f1, '%12s \t \t blockMeshDict; \n','object ')
fprintf(f1, '} \n \n')
fprintf(f1, '%s \n \n', h8)

fprintf(f1, 'convertToMeters  1; \n \n')

fprintf(f1, 'vertices \n ( \n ')
fprintf(f1, '\t (%d %d %d) \n',v0)
fprintf(f1, '\t (%d %d %d) \n',v1)
fprintf(f1, '\t (%d %d %d) \n',v2)
fprintf(f1, '\t (%d %d %d) \n',v3)
fprintf(f1, '\t (%d %d %d) \n',v4)
fprintf(f1, '\t (%d %d %d) \n',v5)
fprintf(f1, '); \n \n')

fprintf(f1, 'blocks \n ( \n ')
fprintf(f1, '\t hex (0 3 5 2 0 3 4 1) (%d %d %d) ', 300,30,1)
fprintf(f1, ' SimpleGrading (1 0.1 1) \n \n ); \n \n')

fprintf(f1, 'edges \n ( \n')
fprintf(f1, '\t arc %d %d (%d %d %d) \n', 1,2,0,r,0)
fprintf(f1, '\t arc %d %d (%d %d %d) \n', 4,5,L_p,r,0)
fprintf(f1, '); \n \n')

fprintf(f1, 'boundary \n ( \n ')
fprintf(f1, '\t inlet \n \t { \n')
fprintf(f1, '\t \t type patch; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 1 2 0)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t outlet \n \t { \n')
fprintf(f1, '\t \t type patch; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (3 5 4 3)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t top \n \t { \n')
fprintf(f1, '\t \t type wall; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (1 4 5 2)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t front \n \t { \n')
fprintf(f1, '\t \t type symmetry; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 3 4 1)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t back \n \t { \n')
fprintf(f1, '\t \t type symmetry; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 2 5 3)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t axis \n \t { \n')
fprintf(f1, '\t \t type empty; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 3 3 0)\n')
fprintf(f1, '\t \t ); \n \t } \n ); \n \n')

fprintf(f1, 'mergePatchPairs \n')
fprintf(f1, '( \n\')
fprintf(f1, '); \n\')
fprintf(f1, '%s \n\',h9)

f1(close)

MATLAB FOR WEDGES

close all
clear all
clc


  %% Input data
% Reynolds number
Re = 2100;
% density of water in kg/m^3
rho=1000;
% Dia of pipe in metres
D= .004;
% Entrance Length of pipe
L= 0.06*Re*D;
% Fully developed length
L_d = 0.4;
% Total length of pipe
L_p= L+L_d;
% Radius of pipe
r=D/2;
% Angle of wedge(in degrees)
theta= 10;
% Dynamic viscosity
mu= 0.89e-3;
% Kinematic viscosity
nu= mu/rho;

%Hagen poisuille flow equations
v_avg= Re*nu/D;
v_max= 2*v_avg;
del_p= (8*mu*L_d*v_avg)/(r^2);
kinematic_p= del_p/rho;

%calculating shear stress
R= linspace(0,(D/2),1000);

for i= 1:length(R)
    tau(i)= 2*mu*v_max*(abs(R(i)))/(r^2);
    vel(i)= v_max*(1-(R(i)/r)^2);
end

figure(1)
plot(R,tau)
xlabel('Radius')
ylabel('Shear stress')
grid on
legend ('Shear stress')


figure(2)
plot(R,vel)
xlabel('Radius')
ylabel('Shear stress')
grid on
legend ('Velocity Profile')



%% Creating files for blockmeshdict
%Header files
h1='/*----------------------------------*- C++ -*------------------------------------*\\\'
h2='  =========                 |                                                         \' 
h3='   \\\\      /  F ield               | OpenFOAM: The Open Source CFD Toolbox          \'
h4='    \\\\    /   O peration           | Website:  https://openfoam.org                 \'
h5='     \\\\  /    A nd                 | Version:  7                                    \'
h6='      \\\\/     M anipulation   |                                                     \'
h7='\\*----------------------------------------------------------------------------------*/\'
h8='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\'
h9='// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\'
%vertices
v0=[0 0 0] %for point 0
v1=[0 r*cosd(theta/2) r*sind(theta/2)] %point 1
v2=[0 r*cosd(theta/2) -r*sind(theta/2)]
v3=[L_p 0 0]
v4=[L_p r*cosd(theta/2) r*sind(theta/2)]
v5=[L_p r*cosd(theta/2) -r*sind(theta/2)]

% Creating text 
f1 = fopen( ' blockMeshDict_wedge_angle10', 'w');
fprintf(f1, ' %s \n ', h1 ) 
fprintf(f1, ' %s \n ', h2 )
fprintf(f1, ' %s \n ', h3 )
fprintf(f1, ' %s \n ', h4 )
fprintf(f1, ' %s \n ', h5 )
fprintf(f1, ' %s \n ', h6 )
fprintf(f1, ' %s \n \n ', h7 )

fprintf(f1, 'FoamFile \n{ \n \n ')
fprintf(f1, '%12s \t \t 2.0; \n ','version ')
fprintf(f1, '%12s \t \t ascii; \n','format ')
fprintf(f1, '%12s \t \t dictionary; \n','class ')
fprintf(f1, '%12s \t \t blockMeshDict; \n','object ')
fprintf(f1, '} \n \n')
fprintf(f1, '%s \n \n', h8)

fprintf(f1, 'convertToMeters  1; \n \n')

fprintf(f1, 'vertices \n ( \n ')
fprintf(f1, '\t (%d %d %d) \n',v0)
fprintf(f1, '\t (%d %d %d) \n',v1)
fprintf(f1, '\t (%d %d %d) \n',v2)
fprintf(f1, '\t (%d %d %d) \n',v3)
fprintf(f1, '\t (%d %d %d) \n',v4)
fprintf(f1, '\t (%d %d %d) \n',v5)
fprintf(f1, '); \n \n')

fprintf(f1, 'blocks \n ( \n ')
fprintf(f1, '\t hex (0 3 5 2 0 3 4 1) (%d %d %d) ', 300,30,1)
fprintf(f1, ' SimpleGrading (1 0.1 1) \n \n ); \n \n')

fprintf(f1, 'edges \n ( \n')
fprintf(f1, '\t arc %d %d (%d %d %d) \n', 1,2,0,r,0)
fprintf(f1, '\t arc %d %d (%d %d %d) \n', 4,5,L_p,r,0)
fprintf(f1, '); \n \n')

fprintf(f1, 'boundary \n ( \n ')
fprintf(f1, '\t inlet \n \t { \n')
fprintf(f1, '\t \t type patch; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 1 2 0)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t outlet \n \t { \n')
fprintf(f1, '\t \t type patch; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (3 5 4 3)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t top \n \t { \n')
fprintf(f1, '\t \t type wall; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (1 4 5 2)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t front \n \t { \n')
fprintf(f1, '\t \t type wedge; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 3 4 1)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t back \n \t { \n')
fprintf(f1, '\t \t type wedge; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 2 5 3)\n')
fprintf(f1, '\t \t ); \n \t }\n')

fprintf(f1, '\t axis \n \t { \n')
fprintf(f1, '\t \t type empty; \n')
fprintf(f1, '\t \t faces \n \t \t ( \n')
fprintf(f1, '\t \t \t (0 3 3 0)\n')
fprintf(f1, '\t \t ); \n \t } \n ); \n \n')

fprintf(f1, 'mergePatchPairs \n')
fprintf(f1, '( \n\')
fprintf(f1, '); \n\')
fprintf(f1, '%s \n\',h9)

BLOCKMESHDICT FOR SYMMETRY ANGLE DEGREE- 10

 /*----------------------------------*- 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; 
     object  	 	 blockMeshDict; 
} 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\ 
 
convertToMeters  1; 
 
vertices 
 ( 
 	 (0 0 0) 
	 (0 1.992389e-03 1.743115e-04) 
	 (0 1.992389e-03 -1.743115e-04) 
	 (9.040000e-01 0 0) 
	 (9.040000e-01 1.992389e-03 1.743115e-04) 
	 (9.040000e-01 1.992389e-03 -1.743115e-04) 
); 
 
blocks 
 ( 
 	 hex (0 3 5 2 0 3 4 1) (300 30 1)  SimpleGrading (1 0.1 1) 
 
 ); 
 
edges 
 ( 
	 arc 1 2 (0 2.000000e-03 0) 
	 arc 4 5 (9.040000e-01 2.000000e-03 0) 
); 
 
boundary 
 ( 
 	 inlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (0 1 2 0)
	 	 ); 
 	 }
	 outlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (3 5 4 3)
	 	 ); 
 	 }
	 top 
 	 { 
	 	 type wall; 
	 	 faces 
 	 	 ( 
	 	 	 (1 4 5 2)
	 	 ); 
 	 }
	 front 
 	 { 
	 	 type symmetry; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 4 1)
	 	 ); 
 	 }
	 back 
 	 { 
	 	 type symmetry; 
	 	 faces 
 	 	 ( 
	 	 	 (0 2 5 3)
	 	 ); 
 	 }
	 axis 
 	 { 
	 	 type empty; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 3 0)
	 	 ); 
 	 } 
 ); 
 
mergePatchPairs 
( 
); 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\

BLOCKMESHDICT FOR WEDGES ANGLE DEGREE-10

 /*----------------------------------*- 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; 
     object  	 	 blockMeshDict; 
} 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\ 
 
convertToMeters  1; 
 
vertices 
 ( 
 	 (0 0 0) 
	 (0 1.992389e-03 1.743115e-04) 
	 (0 1.992389e-03 -1.743115e-04) 
	 (9.040000e-01 0 0) 
	 (9.040000e-01 1.992389e-03 1.743115e-04) 
	 (9.040000e-01 1.992389e-03 -1.743115e-04) 
); 
 
blocks 
 ( 
 	 hex (0 3 5 2 0 3 4 1) (300 30 1)  SimpleGrading (1 0.1 1) 
 
 ); 
 
edges 
 ( 
	 arc 1 2 (0 2.000000e-03 0) 
	 arc 4 5 (9.040000e-01 2.000000e-03 0) 
); 
 
boundary 
 ( 
 	 inlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (0 1 2 0)
	 	 ); 
 	 }
	 outlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (3 5 4 3)
	 	 ); 
 	 }
	 top 
 	 { 
	 	 type wall; 
	 	 faces 
 	 	 ( 
	 	 	 (1 4 5 2)
	 	 ); 
 	 }
	 front 
 	 { 
	 	 type wedge; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 4 1)
	 	 ); 
 	 }
	 back 
 	 { 
	 	 type wedge; 
	 	 faces 
 	 	 ( 
	 	 	 (0 2 5 3)
	 	 ); 
 	 }
	 axis 
 	 { 
	 	 type empty; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 3 0)
	 	 ); 
 	 } 
 ); 
 
mergePatchPairs 
( 
); 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\

BLOCKMESHDICT FOR SYMMETRY ANGLE DEGREE - 25

 /*----------------------------------*- 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; 
     object  	 	 blockMeshDict; 
} 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\ 
 
convertToMeters  1; 
 
vertices 
 ( 
 	 (0 0 0) 
	 (0 1.952592e-03 4.328792e-04) 
	 (0 1.952592e-03 -4.328792e-04) 
	 (9.040000e-01 0 0) 
	 (9.040000e-01 1.952592e-03 4.328792e-04) 
	 (9.040000e-01 1.952592e-03 -4.328792e-04) 
); 
 
blocks 
 ( 
 	 hex (0 3 5 2 0 3 4 1) (300 30 1)  SimpleGrading (1 0.1 1) 
 
 ); 
 
edges 
 ( 
	 arc 1 2 (0 2.000000e-03 0) 
	 arc 4 5 (9.040000e-01 2.000000e-03 0) 
); 
 
boundary 
 ( 
 	 inlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (0 1 2 0)
	 	 ); 
 	 }
	 outlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (3 5 4 3)
	 	 ); 
 	 }
	 top 
 	 { 
	 	 type wall; 
	 	 faces 
 	 	 ( 
	 	 	 (1 4 5 2)
	 	 ); 
 	 }
	 front 
 	 { 
	 	 type symmetry; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 4 1)
	 	 ); 
 	 }
	 back 
 	 { 
	 	 type symmetry; 
	 	 faces 
 	 	 ( 
	 	 	 (0 2 5 3)
	 	 ); 
 	 }
	 axis 
 	 { 
	 	 type empty; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 3 0)
	 	 ); 
 	 } 
 ); 
 
mergePatchPairs 
( 
); 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\

BLOCKMESHDICT FOR WEDGES ANGLE DEGREE-25

 /*----------------------------------*- 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; 
     object  	 	 blockMeshDict; 
} 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\ 
 
convertToMeters  1; 
 
vertices 
 ( 
 	 (0 0 0) 
	 (0 1.952592e-03 4.328792e-04) 
	 (0 1.952592e-03 -4.328792e-04) 
	 (9.040000e-01 0 0) 
	 (9.040000e-01 1.952592e-03 4.328792e-04) 
	 (9.040000e-01 1.952592e-03 -4.328792e-04) 
); 
 
blocks 
 ( 
 	 hex (0 3 5 2 0 3 4 1) (300 30 1)  SimpleGrading (1 0.1 1) 
 
 ); 
 
edges 
 ( 
	 arc 1 2 (0 2.000000e-03 0) 
	 arc 4 5 (9.040000e-01 2.000000e-03 0) 
); 
 
boundary 
 ( 
 	 inlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (0 1 2 0)
	 	 ); 
 	 }
	 outlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (3 5 4 3)
	 	 ); 
 	 }
	 top 
 	 { 
	 	 type wall; 
	 	 faces 
 	 	 ( 
	 	 	 (1 4 5 2)
	 	 ); 
 	 }
	 front 
 	 { 
	 	 type wedge; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 4 1)
	 	 ); 
 	 }
	 back 
 	 { 
	 	 type wedge; 
	 	 faces 
 	 	 ( 
	 	 	 (0 2 5 3)
	 	 ); 
 	 }
	 axis 
 	 { 
	 	 type empty; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 3 0)
	 	 ); 
 	 } 
 ); 
 
mergePatchPairs 
( 
); 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\

BLOCKMESHDICT SYMMETRY ANGLE DEGREE-45

 /*----------------------------------*- 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; 
     object  	 	 blockMeshDict; 
} 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\ 
 
convertToMeters  1; 
 
vertices 
 ( 
 	 (0 0 0) 
	 (0 1.847759e-03 7.653669e-04) 
	 (0 1.847759e-03 -7.653669e-04) 
	 (9.040000e-01 0 0) 
	 (9.040000e-01 1.847759e-03 7.653669e-04) 
	 (9.040000e-01 1.847759e-03 -7.653669e-04) 
); 
 
blocks 
 ( 
 	 hex (0 3 5 2 0 3 4 1) (300 30 1)  SimpleGrading (1 0.1 1) 
 
 ); 
 
edges 
 ( 
	 arc 1 2 (0 2.000000e-03 0) 
	 arc 4 5 (9.040000e-01 2.000000e-03 0) 
); 
 
boundary 
 ( 
 	 inlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (0 1 2 0)
	 	 ); 
 	 }
	 outlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (3 5 4 3)
	 	 ); 
 	 }
	 top 
 	 { 
	 	 type wall; 
	 	 faces 
 	 	 ( 
	 	 	 (1 4 5 2)
	 	 ); 
 	 }
	 front 
 	 { 
	 	 type symmetry; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 4 1)
	 	 ); 
 	 }
	 back 
 	 { 
	 	 type symmetry; 
	 	 faces 
 	 	 ( 
	 	 	 (0 2 5 3)
	 	 ); 
 	 }
	 axis 
 	 { 
	 	 type empty; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 3 0)
	 	 ); 
 	 } 
 ); 
 
mergePatchPairs 
( 
); 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\

BLOCKMESHDICT 45 WEDGES ANGLE AT 45

 /*----------------------------------*- 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; 
     object  	 	 blockMeshDict; 
} 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\ 
 
convertToMeters  1; 
 
vertices 
 ( 
 	 (0 0 0) 
	 (0 1.847759e-03 7.653669e-04) 
	 (0 1.847759e-03 -7.653669e-04) 
	 (9.040000e-01 0 0) 
	 (9.040000e-01 1.847759e-03 7.653669e-04) 
	 (9.040000e-01 1.847759e-03 -7.653669e-04) 
); 
 
blocks 
 ( 
 	 hex (0 3 5 2 0 3 4 1) (300 30 1)  SimpleGrading (1 0.1 1) 
 
 ); 
 
edges 
 ( 
	 arc 1 2 (0 2.000000e-03 0) 
	 arc 4 5 (9.040000e-01 2.000000e-03 0) 
); 
 
boundary 
 ( 
 	 inlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (0 1 2 0)
	 	 ); 
 	 }
	 outlet 
 	 { 
	 	 type patch; 
	 	 faces 
 	 	 ( 
	 	 	 (3 5 4 3)
	 	 ); 
 	 }
	 top 
 	 { 
	 	 type wall; 
	 	 faces 
 	 	 ( 
	 	 	 (1 4 5 2)
	 	 ); 
 	 }
	 front 
 	 { 
	 	 type wedge; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 4 1)
	 	 ); 
 	 }
	 back 
 	 { 
	 	 type wedge; 
	 	 faces 
 	 	 ( 
	 	 	 (0 2 5 3)
	 	 ); 
 	 }
	 axis 
 	 { 
	 	 type empty; 
	 	 faces 
 	 	 ( 
	 	 	 (0 3 3 0)
	 	 ); 
 	 } 
 ); 
 
mergePatchPairs 
( 
); 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //\

PRESSURE SYMMETRY

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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  1.0073;
    }
 
    top
    {
        type            zeroGradient;       
    }
    
    front    
    {
        type            symmetry;
    }
    
    back
    {
        type            symmetry;
    }    
    axis
    {
        type            empty;
    }        
        
}

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

VELOCITY SYMMETRY

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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 (1 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    
    top
    {
        type            noSlip;      
    }
    
    front    
    {
        type            symmetry;
    }
    
    back
    {
        type            symmetry;
    }    
    axis
    {
        type            empty;
    }        
        
}

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

PRESSURE AT WEDGE

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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  1.0073;
    }
 
    top
    {
        type            zeroGradient;       
    }
    
    front    
    {
        type            wedge;
    }
    
    back
    {
        type            wedge;
    }    
    axis
    {
        type            empty;
    }        
        
}

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

VELOCITY AT WEDGE

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    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 (1 0 0);
    }

    outlet
    {
        type            zeroGradient;
    }
    
    top
    {
        type            noSlip;      
    }
    
    front    
    {
        type            wedge;
    }
    
    back
    {
        type            wedge;
    }    
    axis
    {
        type            empty;
    }        
        
}

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

CONTROLDICT

/*--------------------------------*- C++ -*----------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     | Website:  https://openfoam.org
    \\  /    A nd           | Version:  10
     \\/     M anipulation  |
\*---------------------------------------------------------------------------*/
FoamFile
{
    format      ascii;
    class       dictionary;
    location    "system";
    object      controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

application     icoFoam;

startFrom       startTime;

startTime       0;

stopAt          endTime;

endTime         1;

deltaT          1e-3;

writeControl    timeStep;

writeInterval   5;

purgeWrite      0;

writeFormat     ascii;

writePrecision  6;

writeCompression off;

timeFormat      general;

timePrecision   6;

runTimeModifiable true;


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

RESULTS

SYMMETRY AT ANGLE 10

VELOCITY COMPARISION

MATLAB

OPENFOAM

SHEAR STRESS

MATLAB

OPENFOAM

SYMMETRY RESULTS AT 25 DEGREE

VELOCITY

MATLAB

OPENFOAM

SHEAR STRESS

MATLAB

OPENFOAM

SYMMETRY AT 45 DEGREE

VELOCITY

MATLAB

OPENFOAM

SHEAR STRESS

MATLAB

OPENFOAM

WEDGE AT ANGLE 10 DEGREE

VELOCITY

MATLAB

OPENFOAM

SHEAR STRESS

MATLAB

OPENFOAM

WEDGE AT 25 DEGREES

VELOCITY

MATLAB

OPENFOAM

SHEAR STRESS

MATLAB

OPENFOAM

WEDGES AT 45 DEGREE

VELOCITY

MATLAB

OPENFOAM

SHEAR STRESS

MATLAB

OPENFOAM

HP postulate

CONCLUSION

We perfored the simulation for two boundary conditions those are symmetry and wedges boundary conditions.

During wedge boundary conditions simulation across the arc of the wedge is not done.But whereas in symmetrical the simulaation across the arc is done.So, The simulation time is higher in that case.The courant number is increasing slightly in case of wedge condition hence the symmetry boundary condition will be more accurate.Symmetry condition consider mesh as 3d and the calculations are done among all axis.

The result did'nt change due to boundary conditions because the physical properties were same difference was just in accuracy .

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