CHT Analysis on an Exhaust Manifold

INTRODUCTION

Conjugate Heat Transfer(CHT) is the combination of heat transfer in solids (where conduction is dominant) and heat transfer in fluids (where convection is dominant). CHT analysis is done whenever there is heat transfer between a solid body and fluid flow. A simple CHT analysis is a hot body immersed in a fluid flow which is the case in heat treatment of materials where appropriate cooling rate is required to attain the desired properties for the material. Here CHT analysis is required to control the cooling rate by predicting the heat transfer coefficient and to show the temperature variation of solid. CHT is also used in analyzing the heat transfer in a heat exchanger. A heat exchanger is a system where heat is transferred between two fluids (may be of different phases) without mixing of these two fluids. A Shell and tube heat exchanger is a perfect example of CHT, here one fluid flows through tubes and other fluid flows in the shell over the tubes. The heat is transferred from one fluid to the walls of the tube and then from the tube wall to other fluid. Here CHT analysis is useful for predicting the heat transfer coefficient and to improve the effective heat transfer rate. CHT is also used in analyzing the cooling of electronic devices.

In this report, CHT analysis of an Exhaust port manifold is performed. In the exhaust port, the high-temperature gas exhaust components coming from the IC engine cylinders flows out. Here using CHT analysis the temperature variation in the solid walls and the fluid are shown. Heat transfer coefficient is also predicted using CHT analysis.

NUMERICAL MODEL

(i)Geometry:

The geometry of the exhaust port is shown in the below figure. The geometry is prepared by extracting the required volume in space-claim. As it is CHT analysis the solid is also considered for simulations. In a multibody part, a mesh that nodes on both sides of interface matches is defined as conformal mesh. A conformal mesh reduces the computational cost and ensures high accuracy in solutions. Here between the solid and fluid interface, a conformal mesh should be used. For this, the bodies should be overlapped and the share option should be enabled in space-claim. For confirming the bodies are shared, the geometry\'s shared topology shows share option.

(ii) Mesh:

The below images show the non-conformal mesh where we can see the nodes on either side of the interface doesn\'t match.

The below image shows the conformal mesh where nodes on either side of interface matches.

A conformal mesh is used for our simulations as it is the best mesh for this problem.

(a) Baseline mesh:

The below figure shows the baseline mesh and all the elements are of element type tetrahedral.

The zoom view near one of the inlets of the exhaust manifold is shown below. This shows how the inlet cross-section has meshed. As it is a CHT analysis both fluid and solid parts have meshed.

The below image shows the mesh quality. This is a baseline mesh, we can make the mesh more fine to get accurate results. The quality is good and we can proceed for performing simulations. The mesh parameters are shown in below table:

Element Type	Tetrahedral
Element size	0.15 m
Cell Count	137926

(b)Fine Mesh:

The below figure shows the fine mesh, as we can see the number of elements in the solid zone as increased.

The below figure shows the mesh at one of the inlet cross-section, as we can see inflation layers are added near the solid and fluid interface for accurately capturing the gradients near the wall.

The below image shows the mesh quality metrics. As we see that around 80000 elements have the quality of approximately 7% (shown by green color), this due to the formation of 6 node wedge near the interface due to inflation layers. The mesh quality can be increased by doing face meshing at the interface. As we are restricted to 515k element count in the academic license, so this quality can be considered for simulations. Remaining all elements are tetrahedral elements with quality more than 25%. Overall quality is good and can be used for performing numerical analysis. The mesh parameters are shown in the table below:

Element Type	Tetrahedral and Wedge Inflation layer at fluid and solid interface.
Element size	Fluid: 0.15 m Solid: 0.01 m Inflation at fluid and solid interface: Total thickness - 0.005 mm Number of layers - 5 Growth rate - 1.2
Cell Count	475388

(iii) Setup:

Air is used as the fluid and Aluminium is used as solid for these simulations and properties of air used for simulations are shown in below table:

Density	Aluminium: 2719 kg/m3 Air: 1.225 kg/m3
Specific heat capacity, Cp	Aluminium: 871 J/kg-K Air: 1006.43 J/kg-K
Thermal Conductivity	Aluminium: 202.4 W/m-K Air: 0.0242 W/m-K
Viscosity	Air: 1.7894e-05 kg/m-s

The equations solved are the RANS (continuity and momentum) equations and the Energy Equation. The turbulence model used in the simulations is standard two equation k − ε turbulence model which is widely used for industrial applications because of its robustness. The computations are performed using ANSYS FLUENT with steady, double precision and a pressure based solver is used. The SIMPLE algorithm is selected for the velocity-pressure coupling. The second-order upwind scheme is used for the space discretization for higher accuracy. The boundary conditions for the model are shown in below table:

Boundary	Condition
Inlet	Velocity = 5 m/s, Normal to boundary Turbulent Intensity = 5% Turbulent Viscosity ratio = 10 Temperature = 700 K
Outer Wall of solid	Convection: Heat transfer coefficient = 20 W/m2K Free stream temperature = 300 K At all walls no-slip condition
Outlet	Gage pressure = 0 Turbulent Intensity = 5% Turbulent Viscosity ratio = 10

The operating pressure used for the simulations is 1 atm or 101325 Pa.

RESULTS AND DISCUSSIONS

(a) Baseline Mesh:

The below figure shows the residuals of the simulation. The residuals look good as they are under limits.

The below figure shows the variation of outlet temperature with the number of iterations. It can be observed that the solution is converged after around 200 iterations. The outlet area averaged temperature for the baseline mesh is 681 K.

The below figure shows the temperature variation of the outer surface of solid.

The below figure shows the temperature variation at a midplane which is located on the origin and its perpendicular is in the z-direction.

The below figure shows the velocity variation on the midplane. The velocity in the outlet tube is high because the mass flow rate in the outlet tube is four times the mass flow rate in a single inlet tube. The higher velocity is found at the bend region in the outlet tube.

The below figure shows the wall heat transfer coefficient at the solid-fluid interface. It is observed that the heat transfer coefficient is high at the bend region as the velocity is high in that region. This implies a higher heat transfer rate at the bend region. So the temperature of solid is high in the outlet tube than in the inlet tubes as observed from the outer wall temperature variation figure.

The below figure shows the streamlines from the inlets to the outlet.

(b) Fine Mesh:

The below figure shows the residuals of the simulation. The residuals look good as they are under limits.

The below figure shows the variation of outlet temperature with the number of iterations. It can be observed that the solution is converged after around 200 iterations. The outlet area averaged temperature for the baseline mesh is 677 K.

The below figure shows the temperature variation of the outer surface of solid. When compared with the baseline simulation, the fine simulation outer wall temperature is higher.

The below figure shows the temperature variation at a midplane which is located on the origin and its perpendicular is in the z-direction.

The below figure shows the velocity variation on the midplane. The velocity in the outlet tube is high because the mass flow rate in the outlet tube is four times the mass flow rate in a single inlet tube. The higher velocity is found at the bend region in the outlet tube. When compared with the baseline mesh the velocity at the bend for fine mesh is higher.

The below figure shows the wall heat transfer coefficient at the solid-fluid interface. It is observed that the heat transfer coefficient is high at the bend region as the velocity is high in that region. This implies a higher heat transfer rate at the bend region. So the temperature of solid is high in the outlet tube than in the inlet tubes as observed from the outer wall temperature variation figure. When compared with the baseline mesh the highest heat transfer coefficient for fine mesh is higher.

The below figure shows the streamlines from the inlets to the outlet.

The below table shows the comparison between the baseline and fine mesh.

	Baseline Mesh	Fine Mesh
Outlet Average Temperature (K)	681	677
Highest HTC (W/m2K)	105.77	215.278
Outlet Average Velocity	25.24	25.36

As the solid part is made finer in fine mesh case the outer solid wall temperature is higher than that of the baseline mesh case. As the inflation layers are added in the fine mesh case, there is a variation in the highest wall HTC between the baseline and fine case.

To verify whether the HTC predictions from these simulations are right, the numerical model must be validated with the experimental data. Once the numerical model is validated with the experimental data, all the predictions made by that numerical model regarding this system can be right.

The accuracy of the prediction depends on the mesh size and the second order approximation in space discretization. On doing the mesh independent analysis i.e., the results from the simulation are not changing with the change in mesh and using higher order schemes makes the predictions more accurate i.e., the numerical error associated with the numerical model reduces.

CONCLUSIONS

The CHT analysis is performed on an exhaust manifold. The variation of temperature, velocity, and heat transfer coefficient for two different meshes is reported. Further for the right predictions from the numerical model, the numerical model should be validated with the experimental data.