Week 11 - Simulation of Flow through a pipe in OpenFoam
imulation of Flow through a pipe in OpenFoam.
In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, is a physical 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.
EQUATION:
In standard fluid-kinetics notation.
where:
- Δp is the pressure difference between the two ends,
- L is the length of pipe,
- μ is the dynamic viscosity,
- Q is the volumetric flow rate,
- R is the pipe radius,
- A is the cross section of pipe.
The equation does not hold close to the pipe entrance.
Given parameters.
- Wedge angle less than 5 degrees,
- Flow is axi symetrical.
- Fluid is incompressible and the flow is laminar.
Expected Velocity Profile.
Assuming the following:
- The distance the fluid has to travel to become fully developed is given by the Entry Length formula.
- Given Reynolds number is 2100. This implies flow is laminar.
- Hence Entry length formula for Laminar is given by:
L d = 0.06 . R e - where L is effective length; d is dia of pipe and Re is reyonolds number.
- Assuming the dia of pipe as 10mm; substituting the values, we get L = 1.2m;
Steps to follow
- First, the geometry is created in the blockmesh Dict file, this is done by creating the file through the matlab code.
- The mesh is generated according to requirement.
- The velocity and preassure bc are applied
- The controlDict file is edited for Simulation run time and timestep;
- After the geometry is input, the simulation can be started by calling 'icoFoam' command in the terminal.
- 'paraFoam' command helps to open paraView
- The shear stress diagram is obtained by post-processing the velocity results obtained from Openfoam.
- Matlab Code :
-
clc clear all close all % variable values D = 0.01; r = D/2; L = 1.2; theta = input(' input the value of wedge angle='); % String for header, h1 =' /*---------------------------------*- C++ -*-------------------------------------------------*\ '; h2 =' | ========== | |'; h3 =' | \\ / F ield | OpenFOAM: The Open Source CFD Toolbox |'; h4 =' | \\ / O peration | Version: 7 |'; h5 =' | \\ / A nd | Web: www.OpenFOAM.org |'; h6 =' | \\ / M anipulation | |'; h7 =' \*------------------------------------------------------------------------------------------*/ '; h8 =' FoamFile'; h9 ='{'; h10 =' version 2.0;'; h11 =' format ascii;'; h12 =' class dictionary;'; h13 =' object blockMeshDict;'; h14 ='}'; h15 =' // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * \\'; conv ='convertToMeters 1;'; sp1 = blanks(5); %sp = space sp2 = blanks(10); sp3 = blanks(15); v_0 = [0 0 0]; v_1 = [r*sind(theta/2) r*cosd(theta/2) 0]; v_2 = [-r*sind(theta/2) r*cosd(theta/2) 0]; v_3 = [0 0 L]; v_4 = [r*sind(theta/2) r*cosd(theta/2) L]; v_5 = [-r*sind(theta/2) r*cosd(theta/2) L]; block ='hex (0 0 1 2 3 3 4 5) (1 50 200) simpleGrading (1 0.5 1)'; edge1 ='arc 1 2'; edge2 ='arc 4 5'; e1 = [0 r 0]; e2 = [0 r L]; inlet = '(0 0 2 1)'; outlet = '(3 4 5 3)'; wedge1 = '(0 1 4 3)'; wedge2 = '(3 5 2 0)'; wall =' (4 1 2 5)'; axis =' (0 3 3 0)'; final = '// ************************************************************************************************************************************************** //'; f1 = fopen('blockMeshDict','wt'); 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',h7); fprintf(f1,'%s\n',h8); fprintf(f1,'%s\n',h9); fprintf(f1,'%s\n',h10); fprintf(f1,'%s\n',h11); fprintf(f1,'%s\n',h12); fprintf(f1,'%s\n',h13); fprintf(f1,'%s\n',h14); fprintf(f1,'%s\n',h15); fprintf(f1,'\n'); fprintf(f1,'%s\n',conv); fprintf(f1,'\n'); fprintf(f1,'%s\n','vertices'); fprintf(f1,'%s\n','('); fprintf(f1,'%s (%f %f %f) \n',sp1,v_0(1),v_0(2),v_0(3)); fprintf(f1,'%s (%f %f %f) \n',sp1,v_1(1),v_1(2),v_1(3)); fprintf(f1,'%s (%f %f %f) \n',sp1,v_2(1),v_2(2),v_2(3)); fprintf(f1,'%s (%f %f %f) \n',sp1,v_3(1),v_3(2),v_3(3)); fprintf(f1,'%s (%f %f %f) \n',sp1,v_4(1),v_4(2),v_4(3)); fprintf(f1,'%s (%f %f %f) \n',sp1,v_5(1),v_5(2),v_5(3)); fprintf(f1,'%s \n',');'); fprintf(f1,'\n'); fprintf(f1,'%s\n','blocks'); fprintf(f1,'%s\n','('); fprintf(f1,'%s %s \n',sp1,block); fprintf(f1,'%s \n',');'); fprintf(f1,'\n'); fprintf(f1,'%s \n','edges'); fprintf(f1,'%s \n','('); fprintf(f1,'%s %s (%f %f %f) \n',sp1,edge1,e1(1),e1(2),e1(3)); fprintf(f1,'%s %s (%f %f %f) \n',sp1,edge2,e2(1),e2(2),e2(3)); fprintf(f1,'%s \n',');'); fprintf(f1,'\n'); fprintf(f1,'%s \n','boundary'); fprintf(f1,'%s \n','('); fprintf(f1,'%s %s \n',sp1,'inflow'); fprintf(f1,'%s %s \n',sp1,'{'); fprintf(f1,'%s %s \n',sp2,'type patch;'); fprintf(f1,'%s %s \n',sp2,'faces'); fprintf(f1,'%s %s \n',sp2,'('); fprintf(f1,'%s %s \n',sp3,inlet); fprintf(f1,'%s %s \n',sp2,');'); fprintf(f1,'%s %s \n',sp1,'}'); fprintf(f1,'%s %s \n',sp1,'outflow'); fprintf(f1,'%s %s \n',sp1,'{'); fprintf(f1,'%s %s \n',sp2,'type patch;'); fprintf(f1,'%s %s \n',sp2,'faces'); fprintf(f1,'%s %s \n',sp2,'('); fprintf(f1,'%s %s \n',sp3,outlet); fprintf(f1,'%s %s \n',sp2,');'); fprintf(f1,'%s %s \n',sp1,'}'); fprintf(f1,'%s %s \n',sp1,'front'); fprintf(f1,'%s %s \n',sp1,'{'); fprintf(f1,'%s %s \n',sp2,'type wedge;'); fprintf(f1,'%s %s \n',sp2,'faces'); fprintf(f1,'%s %s \n',sp2,'('); fprintf(f1,'%s %s \n',sp3,wedge1); fprintf(f1,'%s %s \n',sp2,');'); fprintf(f1,'%s %s \n',sp1,'}'); fprintf(f1,'%s %s \n',sp1,'back'); fprintf(f1,'%s %s \n',sp1,'{'); fprintf(f1,'%s %s \n',sp2,'type wedge;'); fprintf(f1,'%s %s \n',sp2,'faces'); fprintf(f1,'%s %s \n',sp2,'('); fprintf(f1,'%s %s \n',sp3,wedge2); fprintf(f1,'%s %s \n',sp2,');'); fprintf(f1,'%s %s \n',sp1,'}'); fprintf(f1,'%s %s \n',sp1,'wall'); fprintf(f1,'%s %s \n',sp1,'{'); fprintf(f1,'%s %s \n',sp2,'type wall;'); fprintf(f1,'%s %s \n',sp2,'faces'); fprintf(f1,'%s %s \n',sp2,'('); fprintf(f1,'%s %s \n',sp3,wall); fprintf(f1,'%s %s \n',sp2,');'); fprintf(f1,'%s %s \n',sp1,'}'); fprintf(f1,'%s %s \n',sp1,'axis'); fprintf(f1,'%s %s \n',sp1,'{'); fprintf(f1,'%s %s \n',sp2,'type empty;'); fprintf(f1,'%s %s \n',sp2,'faces'); fprintf(f1,'%s %s \n',sp2,'('); fprintf(f1,'%s %s \n',sp3,axis); fprintf(f1,'%s %s \n',sp2,');'); fprintf(f1,'%s %s \n',sp1,'}'); fprintf(f1,'%s \n',');'); fprintf(f1,'\n'); fprintf(f1,'%s \n','mergePatchPairs'); fprintf(f1,'%s \n','('); fprintf(f1,'%s \n',');'); fprintf(f1,'\n'); fprintf(f1,'%s \n',final); fclose(f1); VELOCITY BOUNDARY CONDITIONS. /*--------------------------------*- 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 { inflow { type fixedValue; value uniform (0 0 0.1869); } outflow { type zeroGradient; } wall { type noSlip; } front { type wedge; } back { type wedge; } axis { type empty; } } // ************************************************************************* - VELOCITY BOUNDARY CONDITIONS.
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/*--------------------------------*- 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 { inflow { type zeroGradient; } outflow { type fixedValue; value uniform 0.0638749; } wall { type zeroGradient; } front { type wedge; } back { type wedge; } axis { type empty; } } // ************************************************************************* // - PRESSURE BOUNDARY CONDITIONS.
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------------------------------*- 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 { inflow { type zeroGradient; } outflow { type fixedValue; value uniform 0.0638749; } wall { type zeroGradient; } front { type wedge; } back { type wedge; } axis { type empty; } -
Velocity profiles:
Shear Stress :-
shear stress = (dynamic Viscosity)*(du/dy)