Week 10 - Simulation of Flow through a pipe in OpenFoam

Numerical Simulation Setup (OpenFOAM)

• Define a wedge-shaped domain using blockMeshDict (automated using MATLAB).
• Specify boundary conditions:
  • Inlet: Parabolic velocity profile (or uniform if developing flow is studied).
  • Wall: No-slip condition.
  • Outlet: Zero pressure gradient.
  • Wedge: Symmetry condition.
• Run steady or transient flow simulation using simpleFoam or pimpleFoam.
• Extract results for velocity, pressure, and shear stress.

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2. Validation Criteria

• Hydrodynamic Entrance Length:
  • $L_h \approx 0.05 \times \text{Re} \times D$Lh​≈0.05×Re×D
• Velocity Profile (Hagen-Poiseuille Law):
  • $u(r) = U_{\max} \left( 1 - \frac{r^2}{R^2} \right)$u(r)=Umax​(1−R2r2​)
  • $U_{\max} = \frac{2U_{\text{avg}}}{3}$Umax​=32Uavg​​
• Pressure Drop:
  • $\frac{\Delta P}{L} = \frac{32 \mu U_{\text{avg}}}{D^2}$LΔP​=D232μUavg​​
• Wall Shear Stress:
  • $\tau_w = \frac{\mu du}{dr} \bigg|_{r=R}$τw​=drμdu​​r=R
  • ​
  • function generateBlockMeshDict(pipe_length, diameter, wedge_angle, num_cells_axial, num_cells_radial)
  • % Define file path
  • fileID = fopen('blockMeshDict', 'w');
  • % Compute key dimensions
  • R = diameter / 2;
  • theta = wedge_angle * (pi / 180); % Convert to radians
  • % Write blockMeshDict header
  • fprintf(fileID, 'FoamFile\n{\n version 2.0;\n format ascii;\n class dictionary;\n object blockMeshDict;\n}\n\n');
  • 
    
  • % Define vertices
  • fprintf(fileID, 'vertices\n(\n');
  • fprintf(fileID, ' (0 0 0)\n'); % Vertex 0
  • fprintf(fileID, ' (%f 0 0)\n', R); % Vertex 1
  • fprintf(fileID, ' (%f %f 0)\n', R*cos(theta), R*sin(theta)); % Vertex 2
  • fprintf(fileID, ' (0 %f 0)\n', R*sin(theta)); % Vertex 3
  • fprintf(fileID, ' (0 0 %f)\n', pipe_length); % Vertex 4
  • fprintf(fileID, ' (%f 0 %f)\n', R, pipe_length); % Vertex 5
  • fprintf(fileID, ' (%f %f %f)\n', R*cos(theta), R*sin(theta), pipe_length); % Vertex 6
  • fprintf(fileID, ' (0 %f %f)\n', R*sin(theta), pipe_length); % Vertex 7
  • fprintf(fileID, ');\n\n');
  • 
    
  • % Define blocks
  • fprintf(fileID, 'blocks\n(\n');
  • fprintf(fileID, ' hex (0 1 2 3 4 5 6 7) (%d %d 1) simpleGrading (1 1 1)\n', num_cells_axial, num_cells_radial);
  • fprintf(fileID, ');\n\n');
  • 
    
  • % Define boundary conditions
  • fprintf(fileID, 'boundary\n(\n');
  • fprintf(fileID, ' inlet\n {\n type patch;\n faces ((0 3 7 4));\n }\n');
  • fprintf(fileID, ' outlet\n {\n type patch;\n faces ((1 5 6 2));\n }\n');
  • fprintf(fileID, ' wall\n {\n type wall;\n faces ((3 2 6 7));\n }\n');
  • fprintf(fileID, ' wedge1\n {\n type wedge;\n faces ((0 1 5 4));\n }\n');
  • fprintf(fileID, ' wedge2\n {\n type wedge;\n faces ((2 3 7 6));\n }\n');
  • fprintf(fileID, ');\n');
  • 
    
  • % Close file
  • fclose(fileID);
  • fprintf('blockMeshDict file generated successfully!\n');
  • end
  • Running the OpenFOAM Simulation

1.Generate Mesh

blockMesh

2.Run the Simulation

simpleFoam

3.Post-process Results

paraFoam

5. Expected Results

• Hydrodynamic length should match $L_h = 0.05 \times \text{Re} \times D$Lh​=0.05×Re×D.
• Velocity profile should be parabolic and match Hagen-Poiseuille.
• Pressure drop along the pipe should match theoretical values.
• Shear stress at the wall should match analytical values.