Conjugate Heat Transfer (CHT) Analysis on an Exhaust Manifold using Ansys Fluent

Objective: Perform Conjugate Heat Transfer (CHT) Analysis on an Exhaust Manifold using Ansys Fluent and write a detailed report explaining the results obtained.

Question:

1. Give a brief description of why and where a CHT analysis is used.
2. Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas.
3. Maintain the y+ value according to the turbulence model and justify the results.
4. How would you verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend on?

• Give a brief description of why and where a CHT analysis is used.

Conjugate Heat Transfer:

The term conjugate heat transfer (CHT) is used to describe processes that involve variations of temperature within solids and fluids, due to thermal interaction. The CHT analysis allows us to simulate the heat transfer between solid and fluid volumes by interchanging the thermal energy at interfaces. In solids, conduction often dominates whereas in fluids, convection usually dominates. The rate of transferred heat is directly proportional to the temperature difference between the bodies.

CHT analysis has an advantage over the FE thermal analysis in calculating the wall heat transfer coffecient. CHT analysis is used to correctly predict the surface temperature and heat exchanging capabilities of engineering devices.

Applications:

• Interactions between solid and fluid bodies.
• Heat exchangers
• electronic equipments like graphic cards,motherboards,etc
• General heating and cooling systems.
• Turbochargers
• HVAC
• Radiators
• IC Engines
• Boilers
• Exhaust port manifolds, etc.

• Calculate the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate areas.

Case Setup and Execution:

Geometry: Geometry is imported to Ansys Space Claim.

Volume is extracted using prepare option for fluid. And shared topology is used for contact between solid and fluid volumes.

CASE-1:

Mesh: Mesh generated using default element size (150mm)

Named Selections: Named selections has been created for boundaries as shown below.

Geometry:

1. Solver - Pressure-Based
2. Time - Steady

Models:

1. Energy - On
2. Viscous - K-Epsilon (standard)

Materials:

1. Fluid - Air
2. Solid - Aluminum

Boundary Conditions:

1. Inlets - Velocity Inlet (5m/s), Thermal (700 k)
2. Outer-wall-convection - COnvection, Heat Transfer Coefficient (20 w/m2-k)
3. Outlet - Pressure (Guage pressure - 0 pa)

Solution is run for 500 iterations.

Results:

Residuals: Number of iterations to converge - 157.

Temparature Contour on outer wall convection:

Temparature Contour on cut plane:

Temparature Contour on cut plane near outlet:

Velocity Contour on cut plane:

Velocity Contour on cut plane near outlet:

Wall Heat Transfer Coefficient Contour on cut plane:

Wall Heat Transfer Coefficient Contour on cut plane near outlet: Wall Heat Transfer Coefficient obtained at the neck region - 100.5 Wm^-2 K^-1.

CASE-2: Refined Mesh

Named Selections: One more Named selection (inflation layer) has been created for refining mesh as shown below.

Mesh: Mesh generated using default element size (150mm)

Body Sizing: Element Size 10mm for Solid Volume.

Inflation option is used for refining mesh as shown below.

Geometry:

1. Solver - Pressure-Based
2. Time - Steady

Models:

1. Energy - On
2. Viscous - K-Epsilon (standard)

Materials:

1. Fluid - Air
2. Solid - Aluminum

Boundary Conditions:

1. Inlets - Velocity Inlet (5m/s), Thermal (700 k)
2. Outer-wall-convection - COnvection, Heat Transfer Coefficient (20 w/m2-k)
3. Outlet - Pressure (Guage pressure - 0 pa)

Solution is run for 1250 iterations.

Results:

Residuals: Number of iterations to converge - 1042.

Temparature Contour on outer wall convection:

Temparature Contour on cut plane:

Temparature Contour on cut plane near outlet:

Velocity Contour on cut plane:

Velocity Contour on cut plane near outlet:

Wall Heat Transfer Coefficient Contour on cut plane:

Wall Heat Transfer Coefficient Contour on cut plane near outlet: Wall Heat Transfer Coefficient obtained at the neck region - 217.3 Wm^-2 K^-1.

• Maintain the y+ value according to the turbulence model and justify the results.

The y+ value is a non-dimensional term that can be used to understand how coarse or fine our grid is. This can then be used to determine if wall functions need to be used or not. If your flow is somewhat complex you will have a large range of y+ on your walls. Technically, the first nodal point should be inside the turbulent layer, i.e. y+ > 30.

Case-1: Y+ value ranges from 2.99 to 419

Case-2: After refining the mesh Y+ value ranges from 1.7 to 30.09 or 35 by which we can state the value is in the range for K-epsilon Turbulent model.

The first nodal point's Y+ value is 30.09 or 35 which can be observed from the above image.

• How would you verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend on?

Result can be verified by calculating Nusselts number and heat transfer coefficient and compare with simulated plots.

`Nu = 0.023*Reunderset(D)^(4/5). Pr^n` and equating it to `Nu = (hl)/k`

This equation is called The Dittus-Boelter equation (for turbulent flow) is an explicit function for calculating the Nusselt number.

Where D = Inside diameter of the body

Pr = Prandtl number

Re = reynolds number

k = thermal diffusivity.

n = 0.4 for hot fluid, 0.3 for cold fluid

l = characteristic length

h = heat transfer coefficient

By this method,One can verify the Heat transfer coefficient from the simulation result

Factors affecting the prediction are as follows:-

• Inflation layers need to be used to capture the interface physics of the solid and the fluid domain where the heat transfer actually occurs.
• Selecting an appropriate number of layers in the inflation. Too many layers will lead to a false solution.
• A proper Viscous model should be selected to refer to the problem.

Conclusion

• Wall Heat transfer coefficient is captured very well in case 2 than case 1, as the element size is smaller.
• By comparing the results, it observed that the Heat transfer coefficient, temperature, and velocity values are higher in the refined mesh case.
• It can be observed that by refining the mesh and adding the inflation layers we get smooth plot at the inner boundary.
• Inflation layers are must at the interface of solid and fluid volumes to calculate the parameters accurately.
• The heat transfer coefficient is only available in the first cell that is attached to the wall.
• The Y+ value is higher in the first cell that is attached to the wall and just 1.7 afterwards.

Reference:

For Y+:

• An Introduction to Computational Fluid Dynamics" by H K Versteeg and W Malalasekera
• https://skill-lync.freshdesk.com/support/solutions/articles/43000561288-what-is-yplus

For Heat Transfer Coefficient:

• https://www.simscale.com/docs/content/simulation/analysis_types/OF_conjugateHeatTransfer.html
• https://trivista.co.uk/design-and-analysis/cfd-overview/heat-transfer/