Conjugate heat transfer (CHT) analysis on a model of exhaust manifold of four cylinder internal combustion engine using ANSYS FLUENT

Objective

• To give a brief description of Conjugate Heat Transfer (CHT) and its applications.
• Perform CHT analysis on the model of an exhaust manifold. And compare the solutions for two different sizes of mesh. The first one with the baseline mesh and the second one with finer mesh on the solid zone and also with inflation layers.
• To Show the velocity, temperature, and heat transfer coefficient plots and explain if refining the mesh produced any changes to the results.
• Verify the HTC predictions from the simulation and discuss the factors on which the accuracy of the prediction depends.

Conjugate Heat Transfer

Conjugate heat transfer (CHT) is a process that involves the variation of temperature within solid and fluid due to thermal interaction between them. CHT analysis allows the simulation of the heat transfer between solid and fluid domains by exchanging thermal energy at the interfaces between them.

CHT analysis is advantageous in accurately simulating the surface temperature and heat exchanging capabilities of various devices and engineering machines. With the help of CHT analysis, we can optimize the thermal properties during the product design phase and save millions of dollars before actually producing the prototype or the final machine.

Applications:

CHT analysis helps to understand the effectiveness of various thermal systems involving solid and fluid medium. It helps us to simulate and understand thermal systems like heat sinks, coolers, heat exchangers, exhaust ports of vehicles, Internal combustion engines, boilers, HVAC, etc.

                                                           CASE 1: Baseline Mesh

1. Geometry

• This is an exhaust manifold, it has four inlets and one outlet.
• before meshing we have to extract the volume from the geometry. And then combine the extracted volume and the solid geometry to create a shared topology.
• Shared topology is necessary for generating a seamless and connected mesh during th meshing process.

• Here we can see the extracted volume for the fluid flow. The pink-colored circles at the inlet and outlet indicate that the topology between fluid volume and the solid geometry has been shared.

2. Meshing

• First, we have to name all the boundaries. After naming all the boundaries we can generate the mesh. The following named selections were defined:
• Inlets, outlet, and outer wall convection.
• In case 1, we have to generate a baseline mesh. In the image below we can see the mesh details.

• Element size: 150 mm.
• Total nodes: 27460.
• Total No. of elements: 137,746.

Generated mesh

• In the image, we can see the generated mesh, the generated mesh in the fluid volume and the solid volume is perfectly connected and aligned. this is happening because of shared topology is turned on.

3. Setup

• Steady-state analysis.
• Solver: pressure based.
• Velocity formulation: absolute.
• Solution method used: SIMPLE.
• Viscous model: k-epsilon.
• Solid material: Aluminium, Fluid: air
• Now we have to define the boundary condition.
• Inlet velocity: 5 m/s. Temperature: 700 k.
• Outlet gauge pressure: 0 pascals.
• Outer wall thermal condition: convection, heat transfer coefficient: 20 W m^-2 K^-1.
• After initializing the solution, in the postprocessing menu, we will create a contour plot to monitor the temperature on the outer wall of the exhaust manifold.
• Run the calculation for 200 iterations.

4. Solution

Residuals

• The above graph is of residuals, we can see in the above image that the solution is converged after 40 iterations.

Temperature contour on the outer wall of the exhaust manifold.

• Here we can see that the outer wall is hottest near the outlet region.

Temperature contour on a cutplane for fluid volume.

• In the above two images, we can see the temperature at the four inlets and the outlet.
• The temperature of the flowing fluid is highest at the outlet pipe of the exhaust manifold.

Velocity streamlines and velocity contours

• In the above image, we can see that the highest velocity of the fluid flow is at the curved surface of the outlet pipe.

Heat transfer coefficient

• The above contour is of heat transfer coefficient between the fluid and the solid outer surface. We can see that the maximum heat transfer coefficient is 99.27 W m^-2 K^-1.

                                                          CASE 2: Mesh refinement

1. Geometry

The geometry and the extracted fluid volume will remain the same as case 1. In case 2 we will refine the mesh and insert some inflation layers to see any changes in the CHT analysis.

2. Meshing

• First, we have to name all the boundaries. After naming all the boundaries we can generate the mesh. The following named selections were defined:
• Inlets, outlet, and outer wall convection.
• In case 2, we have to generate a more refined mesh. In the image below we can see the mesh details.

• Here we can see the mesh details, as compared to case 1 we have created much finner mesh with inflation layers.
• Element size: 10 mm.
• The total thickness for the inflation layer: 5 mm.
• Total no. of inflation layers: 5
• Total nodes: 254358.
• Total no of elements: 1,196,317.

Generated mesh

• In the image, we can see the generated mesh, the generated mesh is much finer in this case.

Inflation layers

3. Setup

• Steady-state analysis.
• Solver: pressure based.
• Velocity formulation: absolute.
• Solution method used: SIMPLE.
• Viscous model: k-epsilon.
• Solid material: Aluminium, Fluid: air
• Now we have to define the boundary condition.
• Inlet velocity: 5 m/s. Temperature: 700 k.
• Outlet gauge pressure: 0 pascals.
• Outer wall thermal condition: convection, heat transfer coefficient: 20 W m^-2 K^-1.
• After initializing the solution, in the postprocessing menu, we will create a contour plot to monitor the temperature on the outer wall of the exhaust manifold.
• Run the calculation for 200 iterations.

4. Solution

Residuals

• The above graph is of residuals, we can see in the above image that the solution is converged after 30 iterations.

Temperature contour on the outer wall of the exhaust manifold.

• In case 2 we can see that the lowest temperature is 504.56 K, in case 1 the lowest temperature is 463.96 K.
• We can clearly see that the mesh refinement has led to a change in the temperature contour of the outer wall of the exhaust manifold.
• the highest temperature is at the outlet region of the exhaust manifold.

Temperature contour on a cutplane for fluid volume.

• In the above two images, we can see the temperature at the four inlets and the outlet.
• The temperature of the flowing fluid is highest at the outlet pipe of the exhaust manifold.
• Here we can see that the temperature contour is much more detailed. The contour is much more defined properly near the inner surface of the exhaust manifold.

Velocity streamlines and velocity contours

• In case 2 we can see that the maximum velocity is 40.09 m/s while in case 1 the maximum velocity was 37.51 m/s. The velocity is more accurately simulated after mesh refinement in case 2. 
• The velocity contour is much more detailed in case 2 because of mesh refinement.

Heat transfer coefficient

• The heat transfer coefficient is higher in case 2 as compared to case 1. The mesh refinement and inflation layers led to better simulation in case 2.
• The maximum heat transfer coefficient is 211.05 W m^-2 K^-1 in case 2. 

Conclusion

• Performed CHT analysis on the exhaust manifold for two cases.
• The results are different in case 2 which has finner mesh with inflation layers.
• The second case has a higher value of HTC and fluid velocity.
• The contour plots are much more detailed in case 2 because of the mesh refinement and inflation layers.

Comparison

Verification of the Heat Transfer Coefficient (HTC) results

Verification of the simulation results can be done by performing a grid dependence test. We can run the simulation for different grid sizes until the results are independent of the grid size.

We can also verify the HTC results by calculating the theoretical value of the Nusselt number (Nu) and then equating it with the numerical results.

Theoretical Nusselt number

`Nu = 0.023*Re^(4/5)*Pr^(0.4)`

Re - Reynolds number.

Pr - Prandtl number.

Numerical value

`Nu = (h*l)/k`

h - convective heat transfer coefficient of the flow.

l - characteristic length.

k - thermal conductivity of the fluid.

Factors affecting the accuracy of the prediction

• The total number of elements in the mesh.
• The type of elements in the generated mesh.
• The perfect connection between the mesh of fluid volume and the solid volume.
• Use of inflation layers.
• Mesh quality criteria.
• Appropriate selection of the turbulence model.