Conjugate heat transfer analysis on an exhaust port

Aim:

To perform a conjugate heat transfer analysis on an exhaust port and draw suitable conclusions from the results obtained.

Theory:

Conjugate heat transfer analysis is generally used when there is a temperature variation during heating and cooling in the material due to the interaction between the solid and fluid domains in engineering problems. This analysis allows the simulation of the heat transfer between Solid and Fluid domains by exchanging thermal energy at the interfaces between them. In solids, the heat transfer is dominated by conduction, and in fluids, it is dominated by convection. Conjugate Heat transfer analysis is beneficial in accurately predicting the surface temperatures and heat exchanging capabilities of engineering devices. Through this analysis, engineers can optimize the thermal characteristics of product design.

The conjugate heat transfer analysis is performed in any engineering applications where the heat transfer takes place due to the interaction of the solid and fluid domains. Turbocharger, heat exchanger, air conditioning, automobile exhaust port, heat pipe, engine turbines are a few applications where CHT analysis must be performed in the design stage.

Exhaust port analysis using the baseline mesh:

To perform conjugate heat transfer analysis, the problem was first solved using the baseline mesh, without the use of any inflation layers near the boundary of the solid and fluid domains. This is done to compare the solutions obtained using the baseline mesh to that of the solution obtained using the refined mesh with inflation layers. The exhaust port geometry is imported into Spaceclaim, and the fluid domain extracted. The 'share topology' option must be enabled.

Once the geometry is created meshing is done. The baseline mesh was generated, and regular tetrahedral mesh elements are used. Once the mesh was generated, the total number of nodes was 33576, and the number of mesh elements was 137587. 

Since the 'share topology' option was enabled, the interconnections between the mesh elements in solid and fluid domains are consistent. The mesh quality of the generated mesh was checked, and since most of the mesh elements have the majority of mesh elements above 50%, the meshing is said to be suitable for performing the conjugate heat transfer analysis.

The problem was solved using the pressure-based solver, using the steady-state equation. The K-omega SST is chosen as the turbulence model to solve the problem. 

The solution was run for 150 iterations, and from the trend of the residuals plot, the solution is converged after around 135 iterations.

The temperature of the air at the outlet of the exhaust port was found to be 680.17K.

The above figure represents the temperature contours on the outer walls of the exhaust port. From this, we can say that the temperature of the exhaust port is highest near the outlet even though the temperature of the air near the inlet is 700K. 

In post-processing, a plane is placed in the XY plane at the origin and that plane is colored with temperature. The temperature of the fluid is higher than that of the solid component.

The above figure represents the velocity contours of the fluid(air) inside the exhaust port. The inlet velocity is 5m/s. As the flow moves towards the outlet of the exhaust port, the velocity increases gradually.

In post-processing, a plane is placed in the XY plane at the origin and that plane is colored with velocity magnitude. As the fluid enters the exhaust nozzle, there is a gradual increase in velocity. The local velocity is the highest near the turn, which is highlighted in red in the above contour diagram. This is simply because of the physics of the fluid flow.

In post-processing, a plane is placed in the XY plane at the origin and that plane is colored with pressure. The pressure of the fluid is higher near the entry of the outlet nozzle then that at the outlet. This makes the fluid flow from the inlet to the outlet, which is expected. There is a region of low pressure near the turn which is highlighted in blue in the above diagram. This is simply because of the physics of the fluid flow.

The above figure represents the velocity streamlines of the fluid(air) inside the exhaust port. The streamlines plot is used to simulate the path of the fluid inside the exhaust port from inlet to the outlet.

The contact region is colored with the heat transfer coefficient as shown below, and from observation, we can see that the heat transfer coefficient(HTC) is the highest where the velocity magnitude is high. The HTC is lesser near the inlets even though the temperature of the incoming fluid is 700K just because the flow velocity is around 5m/s, which is lesser than that near the outlet. There are regions with higher HTC where the local velocities are higher due to the physics of the flow.

A plane is placed in the XY plane at the origin and that plane is colored with the wall heat transfer coefficient. The first cell near the wall of the exhaust port is highlighted with the corresponding HTC. The highest HTC occurs where the velocity magnitude of the fluid is the highest, ie, near the turn. The contours are uneven because any inflation layers are not introduced in the mesh.

Now that we have performed the simulation using the baseline mesh, and the results obtained are within our expectations, the analysis can be performed using a refined mesh with inflation layers. This will help us in better visualization of results and improves the accuracy of the solution.

Exhaust port analysis using refined mesh:

To make the mesh more refined, the mesh element size for the solid domain was given as 0.016m and for the fluid domain is 0.05m. The solid domain was given a smaller mesh size so as to exactly calculate the temperature distribution on it due to the heat transfer between the solid and fluid domain. The fluid domain is provided with inflation layers. A total of 10 inflation layers were introduced in the fluid domain with a maximum thickness of  0.01m and with the cell growth rate of 1.2. Once this mesh was generated, a total of 173616 nodes and 457683 mesh elements are generated for the given geometry, which can be solved using the student license.

Once the mesh was generated, its quality is checked. The majority of Wed6 mesh elements have low-quality mesh. This can be improved by decreasing the size of the inflation layers, but this is not possible with the student license of Ansys, because decreasing the inflation layer size drastically increases the number of mesh elements, which exceeds the limit of 0.5 million mesh elements. The majority of tet4 mesh elements have a mesh quality greater than 50%. 

The problem was solved using the pressure-based solver, using the steady-state equation. The K-omega SST is chosen as the turbulence model to solve the problem. The solution was run for 200 iterations, and from the trend of the residuals plot, we can say that the solution is converged after 100 iterations. 

The temperature of the air at the outlet of the exhaust port was found to be 683.555K. This is different from the average temperature obtained using the baseline mesh. With the use of smaller mesh elements and the presence of inflation layers, the prediction of temperature is going to be more accurate. Hence, there is a variation in average temperature value at the outlet. 

The above figure represents the temperature contours on the outer walls of the exhaust port. From this, we can say that the temperature of the exhaust port is highest near the outlet even though the temperature of the air near the inlet is 700K.

In post-processing, a plane is placed in the XY plane at the origin and that plane is colored with temperature. The temperature of the fluid is higher than that of the solid component. In the temperature contours obtained, the boundary layers can be visualized more clearly if the refined mesh is used than the baseline mesh for solving the problem.

The above figure represents the velocity contours of the fluid(air) inside the exhaust port. The inlet velocity is 5m/s. As the flow moves towards the outlet of the exhaust port, the velocity increases gradually. Also, the maximum velocity magnitude obtained is 42.028m/s, which is higher than that obtained in the previous case. This is because the refined mesh gives more accurate results.

In post-processing, a plane is placed in the XY plane at the origin and that plane is colored with velocity magnitude. As the fluid enters the exhaust nozzle, there is a gradual increase in velocity. The local velocity is the highest near the turn, which is highlighted in red in the above contour diagram. This is simply because of the physics of the fluid flow. The boundary layers can be easily visualized in this case compared to the previous case.

In post-processing, a plane is placed in the XY plane at the origin and that plane is colored with pressure. The pressure of the fluid is higher near the entry of the outlet nozzle then that at the outlet. This makes the fluid flow from the inlet to the outlet, which is expected. There is a region of low pressure near the turn which is highlighted in blue in the above diagram. This is simply because of the physics of the fluid flow. There is a difference in results obtained in this case and the previous case, this is because of mesh refinement, which increases its accuracy.

The above figure represents the velocity streamlines of the fluid(air) inside the exhaust port. The streamlines plot is used to simulate the path of the fluid inside the exhaust port from inlet to the outlet.

The contact region is colored with the heat transfer coefficient as shown below, and from observation, we can see that the heat transfer coefficient(HTC) is the highest where the velocity magnitude is high. The HTC is lesser near the inlets even though the temperature of the incoming fluid is 700K just because the flow velocity is around 5m/s, which is lesser than that near the outlet. There are regions with higher HTC where the local velocities are higher due to the physics of the flow.

A plane is placed in the XY plane at the origin and that plane is colored with the wall heat transfer coefficient. The first cell near the wall of the exhaust port is highlighted with the corresponding HTC. The highest HTC occurs where the velocity magnitude of the fluid is the highest, ie, near the turn. The results obtained using the refined mesh is different from that obtained using the baseline mesh. This is because the refined mesh s more accurate then the baseline mesh and the main objective of the baseline mesh is to check whether or not desired results are obtained. 

Observations:

There is a difference in results obtained when the same problem is solved using the baseline mesh and refined mesh. This is because the main objective of the baseline mesh is to perform the analysis and check whether or not expected results can be obtained by solving the problem. If not the method of solving the problem is changed. The baseline mesh is not used to check the accuracy of the solution but to check whether or not the methods used to solve the problem give expected results. This is done because the baseline mesh contains less number of mesh elements and the solution can be found quicker. 

Verification of the results:

The results obtained in this simulation can be verified by performing a grid dependency test, wherein the mesh elements are further refined, and the problem is solved again. By increasing the number of mesh elements, the accuracy of the solution increases, but solving more number of mesh elements takes a lot of time. Hence, if the solution obtained in the refined mesh setup is within a certain tolerance value, the mesh is said to be grid-independent, and the results obtained in the previous case is said to be correct. The results can also be verified by comparing the results obtained in the simulation to any standard literature or experimental data.

Nusslets number = `0.023*Re^0.8*Pr^0.4 ---(1)`

Where Re= Reynolds number

Pr= Prandtl number

Also,  Nu = Convective heat transfer / Conductive heat transfer = h/k/L

`Nu=(h*L)/k ---(2)`

By equating the equations (1) and (2), the solution can be verified

Conclusions:

1. The baseline mesh is only used to check whether or not the expected results are obtained with the set boundary conditions or not. It is not used to check for the accuracy of the solution.
2. The accuracy of the solution increases with the increase in the number of mesh elements and the introduction of inflation layers in the mesh.
3. The accuracy of the solution also depends on the size and number of inflation layers, proper viscous model selection. The finer mesh gives more accurate results and the boundary layers can be visualized more clearly.
4. The heat transfer coefficient is high where the local velocity magnitude is high. One such position is the turn near the exhaust nozzle of the exhaust port.