EXHAUST PORT MANIFOLD SIMULATION

WHAT IS CHT?

The term conjugate heat transfer (CHT) is used to describe processes that involve a variation in temperature within solids and fluids because of thermal interaction between solids and fluids. It corresponds to the combination of heat transfer in solids and heat transfer in fluids.

Conduction: Heat transfer takes place between solid to solid.

Convection: Heat transfer takes place between liquid to solid.

In solids, conduction often dominates, whereas in fluids, convection usually dominates. Efficiently combining heat transfer in fluids and solids is the key to designing effective machines involving heat transfer.

ADVANTAGES OF CHT

1. The Conjugate Heat Transfer setup replaces the empirical relation of proportionality of heat flux to the temperature difference WITH the heat transfer coefficient. The wall heat transfer coefficients & their local variations are directly computed within the model without complex mathematics of the empirical relations. Thus, the simulations are carried out much faster.

2. Solutions have higher-order accuracy provided boundary conditions are correctly set.

3. There is no limitation to the number of surfaces. Therefore, a complex geometry may be simulated with ease.

4. CHT models can be applied for all combinations of interactions (i.e. Solid - Fluid interaction, Solid - Solid interaction and Fluid - Fluid interaction).

AREAS OF APPLICATION OF CHT

• Investigation of natural phenomenons such as thermal interactions in the atmosphere.
• Simulating flow during the design of various vehicles and machines.
• Can be performed to improve the cooling performance of the water jacket and improve engine life.
• Results of CHT simulations become inputs to structural simulations as thermal loads.

OBJECTIVES OF THE CURRENT SIMULATION

• Simulate & analyse the fluid flow through an exhaust manifold using Conjugate Heat Transfer (CHT) modelling.
• Plot the velocity, temperature, and heat transfer coefficient contours at the outlet region.

STEP 1: GEOMETRY

STEP 2: MESHING

We simulated the problem with two different meshes. Summary of the two mesh settings is given below:-

Parameter	Sub Parameter	BASELINE CASE	REFINED CASE
Element Order		Linear	Linear
Element Size	150 mm	150 mm
Body Sizing (On outer Pipe)	Element Size	-	15.5 mm
Inflation Layer (On inner pipe)	No. Of Layers	-	5
Growth Rate	1.2
Total Thickness	5 mm
ELEMENT COUNT	BASELINE CASE	REFINED CASE
No. of Nodes	27371	179282
No. of Elements	137172	508386

BASELINE MESH

BASELINE MESH METRICS

The lowest quality of mesh is above 10% and hence can be accepted for simulation.

REFINED MESH

REFINED MESH METRICS

Some areas of the mesh have very low quality. This is due to the inflation layers added to capture the wall heat transfer coefficient at the boundary. A mesh check needs to be performed in Fluent before proceeding with the simulation.

SETP 3 AND STEP 4: SIMULATION SETUP AND SOLVING

The setup for both baseline and the refined case is the same. We have used the double precision option with 4 parallel processors. The following table summarizes the simulation setup settings.

Parameter	Sub Parameter	PROPERTY DETAILS	VALUE
Solver	-	Steady State
Type	Pressure Based
Turbulence Model	k-epsilon (Standard)
Boundaries	Inlet (4 inlets)	Type	Velocity Inlet
Velocity	5 m/s
Temperature	700 K
Outlet (1 outlet)	Type	Pressure Outlet
Pressure	0 Pa (Gauge)
Temperature	300 K
Outer Wall Convection	Type	Wall
Thermal Conditions	Convection
Heat Transfer Coefficient	20 W/m2-K
Free Stream Temperature	300 K
Initialization Method	-	Hybrid
No. Of Iterations	300

STEP 5 AND STEP 6: SOLUTION RESULTS AND POST PROCESSING

RESIDUALS

BASELINE CASE

REFINED CASE

In both cases, the residuals repeat themselves periodically after a number of iterations. This can be observed more predominantly in the refined case as compared to the baseline case. Though in the refined case, after 200 iterations the residuals are almost the same. Hence, the solution can be assumed to have converged in both cases.

TEMPERATURE CONTOURS

1. SOLID TEMPERATURE CONTOUR

BASELINE CASE

REFINED CASE

In both cases, we can see that the temperature of across the body of the inlets is low as compared to the outlet where the temperature increases because of the combination of the hot fluids.

2. VOLUME TEMPERATURE CONTOUR

BASELINE CASE

REFINED CASE

VELOCITY CONTOURS ALONG THE OUTLET

BASELINE CASE

REFINED CASE

VELOCITY STREAMLINES

BASELINE CASE

REFINED CASE

WALL HEAT TRANSFER COEFFICIENT CONTOUR AT BEND NEAR THE OUTLET

1. WITHOUT MESH LINES

BASELINE CASE

REFINED CASE

2. WITH MESH LINES

BASELINE CASE

REFINED CASE

From the above figures, we can observe that the addition of a body-fitted mesh gives us a much smoother and accurate representation of the wall heat transfer coefficient. The wall heat transfer coefficient is still maximum at the inner bend of the pipe, which remains consistent with the baseline simulation result.

TEMPERATURE CONTOUR ALONG THE OUTLET

BASELINE CASE

REFINED CASE

As observed in the temperature contours for both baseline and refined simulations, more heat is transferred between the solid and the fluid in the outlet of the pipe due to the increase in heat transfer coefficient.

RESULTS

1. Refining the mesh by decreasing the mesh size increases the accuracy of the solution.

2. Generating a body-fitted mesh helps to capture the boundary functions such as the wall heat transfer coefficient accurately.

3. The velocity increases from the region of the junction of the four inlets until the outlet to ensure mass conservation.

4. The wall heat transfer coefficient is higher at the pipe bend near the outlet because of the increase in Reynold\'s number.

5. There is more heat transfer at the bend near the outlet because of the increase in the wall heat transfer coefficient.

6. The quality of the refined mesh is low because of the addition of a body-fitted mesh. Hence, the accuracy of the solution near the boundaries cannot be determined.

VERIFICATION OF HEAT TRANSFER COEFFICIENT VALUE

We require the Nusselt number to find \'h\' which is convective heat transfer coefficient. The physical interpretation of the Nusselt number is the enhancement of heat transfer because of convection over conduction alone. If Nu=1, all heat transfer is by conduction.

The following equations can be used to calculate the Nusselt number and hence the convective heat transfer coefficient.

`R_e=(ρ*v*l)/μ` (Reynold\'s Number)

`Pr=(mu*Cp)/K` (Prandtl\'s Number)

`Nu = 0.023 ⋅ (Re) ^n ⋅ (Pr) ^n` (Nusselt Number)

`Nu=(h*l)/k`

Factors which the accuracy of the prediction depend on as already discussed in the Results Section:

1. Mesh element size and smoothness.

2. Shape or curvature of the body.

CONCLUSION

The flow simulation through the exhaust manifold is carried out using Conjugate Heat Transfer methods. The solution is obtained very quickly & the physics expected from the flow is accurately displayed in the solution contours.