Conjugate heat transfer analysis of exhaust manifold

Conjugate heat transfer analysis of exhaust manifold

The term \"conjugate heat transfer\" refers to scenarios wherein there is a combination of and coupling between heat transfer in solids and fluids. In solids heat transfer occurs mainly by conduction whereas in fluids convection is the dominant mode of heat transfer.

Shell and tube type heat exchanger is one such application where conjugate heat transfer occurs. The fluid flowing inside the tube carries thermal energy along the flow by convection whereas the tube carries the thermal energy by conduction. However these two heat transfer processes are not independent of each other and are coupled by heat transfer between fluid and tube, along the flow. Hence if the temperature field within the tube is to be determined (say), then a CHT analysis needs to be performed such that energy equation is solved in both the fluid and the tube.

In the current project, CHT analysis is performed on a model of exhaust manifold using ANSYS Fluent. Two different meshes are used for the analysis:

(i) Baseline mesh with 138326 cells.

(ii) Refined mesh with 375275 cells.

Finally the results obtained from the analysis are used to understand the effect (if any) of mesh modeling strategies adopted in Refined mesh.

I. Geometry

The given model of exhaust manifold is utilized for both the simulations. The image attached below shows the geometry.

II. Mesh

1. Baseline mesh: It consists of tetrahedral type elements with a default element size of 150mm. The total count of computational cells is 138326. The image attached below shows the baseline mesh.

2. Refined mesh: The following effects are added to the baseline mesh in order to get the refined mesh:

(i) Inflation layer: Five inflation layers, of \"total thickness\" type and maximum thickness 5mm, are added to the outer faces of the fluid volume. This is done to achieve body-fitted mesh at the fluid-solid interface.

(ii) Body sizing: This characteristic is added to the solid volume in order to achieve mesh refinement in the same. An element size of 10mm is adopted.

With the above features, the resultant cell count for refined mesh is 375275. The image attached below shows the refined mesh.

III. Solver

For both baseline mesh and refined mesh, the three dimensional Navier-Stokes equations are solved using a steady state pressure-based solver with absolute formulation of velocity. For modeling turbulence the standard `K-epsilon` model is employed.

IV. Initial and boundary conditions

The solution is initialized using a hybrid initialization scheme and the following boundary conditions are implemented for both simulations:

(i) Inlet: The following images show the boundary conditions applied at the four inlet ports.

(ii) Outlet: The following images show the boundary conditions applied at the outlet port:

(iii) Outer wall: The following image shows the thermal boundary condition applied at the outer wall.

No-slip type momentum boundary condition is applied.

(iv) Wall: The solid features attached to the manifold, near the inlet and outlet ports, are termed together as wall. The following thermal boundary condition is applied at the wall.

No-slip type momentum boundary condition is applied.

V. Results

This section deals with the results obtained from the two simulations.

1. Residuals

The residuals for the following equations are plotted over iterations:

(a) Continuity equation

(b) X momentum equation

(c) Y momentum equation

(d) Z momentum equation

(e) Turbulent kinetic energy equation

(f) Rate of dissipation of turbulent kinetic energy equation

(g) Energy equation

(i) Baseline mesh

(ii) Refined mesh

2. Temperature contours

The temperature contours are plotted over the outer wall.

(i) Baseline mesh

(ii) Refined mesh

Discussion:

(i) Both the contours show that the exhaust manifold is hottest near the outlet and relatively cooler near the inlet.

(ii) The baseline mesh is able to predict the temperature distribution quite well, qualitatively.

3. Streamlines

Three-dimensional streamlines are plotted inside the exhaust manifold.

(i) Baseline mesh

(ii) Refined mesh

Discussion:

(i) Both plots show a high velocity region near the outlet, which is in accordance with the continuity equation since the flow streams entering from all four inlet ports (each with almost the same cross-section area as the outlet port) exit through the same outlet port.

4. Heat transfer coefficient contours

Heat transfer coefficient contours are plotted at the solid-fluid interface.

(i) Baseline mesh

(ii) Refined mesh

Discussion:

(i) For both the plots, the heat transfer coefficient is highest at the bend near the outlet.

(ii) The heat transfer coefficient is comparatively high near the outlet.

(iii) The baseline mesh is able to predict the qualitative distribution of heat transfer coefficient quite well.

(iv) The area averaged heat transfer coefficient predicted by baseline mesh simulation is `28.12 W//m^2K`.

(v) The area averaged heat transfer coefficient predicted by refined mesh simulation is `82.53 W//m^2K`.

(vi) Although the baseline mesh does capture the overall trend of heat transfer coefficient qualitatively, it lacks in the quantitative prediction of the same.

5. Contours near the outlet

In this section, for both simulations, the following contours are plotted on the cross-section plane near the outlet port:

(a) Temperature contours

(b) Velocity contours

(c) Heat transfer coefficient contours

(i) Baseline mesh

(a) Temperature contours

(b) Velocity contours

(c) Heat transfer coefficient contours

(ii) Refined mesh

(a) Temperature contours

(b) Velocity contours

(c) Heat transfer coefficient contours

Discussion:

(i) Refined mesh generates smooth contour plots near the wall due to the presence of inflation layers.

(ii) The baseline mesh predicts the qualitative distribution of parameters well enough. However, the contours are jagged near the wall due to the distribution of cell centers in the absence of body-fitted mesh.

(iii) Near the bend, the flow features are better resolved in case of refined mesh.

Accuracy of numerical simulations

In order to establish the credibility and accuracy of numerical simulations in predicting the real world physics, they need to be validated. Validation implies comparing the results from simulation with either experimental or analytical results. Such results or studies may already be present in the literature.

For example: in order to validate the CHT simulation of exhaust manifold, one can perform the analysis using same conditions that were used in an experimental study (published in literature). Based on the experimental results, simulation results such as temperature distribution on the manifold, average temperature of exit stream etc. can be used for validation.

The accuracy of numerical simulations depend on the following factors:

(a) Physical model: Appropriate physical models should be employed to capture the real world physics. For instance, in certain cases the `K-epsilon` model performs better than the `K-omega`model.

(b) Mesh: Proper mesh should be chosen for simulation such that it is able to capture the essential features of the phenomenon, such as flow separation, accurately. Also the results need to be independent of the mesh size. This is achieved by performing grid independence study on the chosen mesh.

(c) Time step: If a transient simulation is desired then appropriate time step should be chosen to capture the effects such as shocks, flow instabilities etc.

(d) Initial and boundary conditions: The initial and boundary conditions implemented in the numerical model should correspond to the real world phenomenon being simulated.

(e) Solver: Certain solvers are better equipped to model a particular physical phenomenon. For instance, in ANSYS Fluent the density-based solver is more suited to model hypersonic flows than the pressure-based solver.