Conjugate Heat Transfer Analysis

Conjugate heat transfer or simply CHT is used to describe the combination of heat transfer between solids and fluids. The exchange of thermal energy between solids and fluids are utilized in countless applications that involve heat-exchangers and hence making CHT analysis an important form of analyzing the efficiency of these applications.

For example; while designing a car radiator, we need to determine the heat transfer co-efficient of the model to check its efficiency or in the case of gas turbines, the highest and lowest temperatures has to be known or even when designing a space craft, the temperature distribution on its walls has to be known. For determining these aspects, although there are analytical methods of solution, it is not feasible for much complex situations and computational methods have proven to be much more efficient.

To understand the complex interactions of heat transfer mechanisms like in the case of cooling for gas turbine components, CHT analysis is used and can be performed without hassle. CHT analysis is widely used to understand the temperature and velocity distribution which helps to design efficient commercial vehicles, space-crafts and even agricultural equipments.

Conjugate Heat Transfer Analysis on an Exhaust Manifold Model:

An Exhaust port is an engine component that directs the exhaust gases from the engine cylinders to the exhaust pipe without much leakage of heat or gases and hence prevents over-heating. By conducting a CHT analysis on the exhaust port, we can understand how the temperature and velocity varies while gas flows through the manifold.

Ehaust Manifold Geometry:

The above image is that of a simple exhaust port with 4 inlets and an outlet. The body material was defined as Aluminium in Fluent and the gas flowing through it as air.

In SpaceClaim, the fluid volume was extracted and both the solid and fluid volumes were defined.

Meshing:

In the meshing stage, the faces of the geometry were named. The meshing was initially done by default values of Fluent, to get a baseline mesh and test thesimul

ation. The base line mesh is as shown below,

The default mesh generated by fluent had over 1.37 lakh elements.

Later, moved on to the setup.

Setup:

The simulation was run with an absolute pressure based, steady state solver. The turbulence model chosen for the simulation was K-Epsilon model.

Boundary conditions:

Inlet Fluid Velocity = 5 m/s

Inlet Fluid Temperature = 700 K0

Outlet Pressure = 0 Pa

Hest transfer coeffucient of the manifold walls= 20 w/m2-k

The extensions at the ends of the manifold was considered to be adaiabatic.

Solution:

The simulation was hybrid initialized and was run till certain parameters indicated convergence was achieved.

• Residuals:

While examining the residuals plot, it was observed that, the plots went sideways after about 250 iterations, indicating no change in the solution with further iterations.

• Fluid Outlet Temperature:

The fluid temperature had achieved a constant value of 681K at the outlet after passing through the manifold.

Results:

The results obtained from the simulation on the exhaust manifold with a baseline mesh are shown below;

• Temperature distribution across the solid surface:

The highest temperature was observed at the area near the outlet. The temerature was observed to begin increasing from the junction were all inlets meet.

• Velocity of fluid flow:

Although the velocities at each inlets were the same and uniform, at the junction were the gases from each inlet meets, the velocity increases significantly. To observe this increase, a closer look at velocity in that area is shown below,

Although the flow is coarse, the highest velocity was noted at the bend in the manifold as it approaches the outlet.

• Heat transfer coefficient at the inner wall of the manifold:

The heat transfer coefficient was observed to be the highest at the bend in the oulet region. This area also showed the highest velocity.

The below plane shows the heat transfer coefficient at the oullet region. As a baseline mesh, the results can be seen as coarse.

Now that the results obtained by the baseline mesh has been evaluated, lets refine the mesh and take a look at the changes that can be observed.

Refining the mesh:

For refining the mesh, particulary the meshing on manifold walls, body sizing was inserted with a maximum element size of 7.5mm on the manifold walls. The default value beiing 150mm, the mesh cell count observed a significant increase.

Also, an inflation layer of maximum thickness, 5 mm was inserted on the interface between fluid and manifold inner wall as shown below.

Now, the total element count is at 4.91lakhs which is significanlty higher than the baseline mesh.

Solution:

The setup and boundary conditions being the same, after hybrid initializing, the simulation was again run till convergence in fluent.

• Residuals:

The residuals going sideways indicates minimal change in solution with each iteration.

• Outlet temperature:

The fluid outlet temperature obtained by refined mesh was 676K, lower than that obtained by baseline mesh.

Resullts:

• Temperature distribution across the solid surface:

Although the temperature distributon is similar to the baseline mesh, the temperature is distributed much more evenly at the inlets and at the extensions of inlets and outlets.

• Velocity of fluid flow:

The velocity stream lines here shows the velocity changes with more clarity.

The plane shows velocity changes with very fine details unlike baseline mesh. The high velocity can be seen concentrated on the bend of the manifold.

• Heat transfer coefficient at the inner wall of the manifold:

The heat transfer coefficient accross the interface between fluid and solid is much more uniform than baseline mesh results.

Here we see that the heat transfer coefficient is highly concentrated at the bend in the exhaust manifold near outlet.

Unlike baseline mesh, where heat transfer coefficint was observed in a coarse area, here, it is limited to the inflation layter that has been an addition in the refined mesh. The highest value is observed at the bending on the manifold outlet region.

Conclusion:

• When the results of baseline mesh and refined mesh were compared, refined mesh had the upper hand at every step. The coarse, non-uniform results os the baseline mesh are much unreliable while the refined mesh gives a smooth, refined and accurate results.
• The rise invelocity at the junction where all inlets meet is due to the conservation of mass. Especially at the bend, the velocity is the highest.
• Due to the increased velocity, there is a higher bulk motion of fluid in the region. Hence, covective heat transfer rises in this region and therefore, the region has a higher heat transfer coefficient.
• The temperature is therefore, the highest near these regions on the exhaust manifold.

To validate and check the accuracy of the CHT results obtained, we have to check both theoretical principles and experimental test results. In case of theoretical principles, the CHT simulation results follows some of the theories of fluid motion and convection relating to it.

1. Law of conservation of mass: The fluid has an increase in velocity when it has to pass through the constricting area of the outlet to maintain the mass flow rate.
2. As velocity is directional, magnitude of velocity is affected by change in its direction. Hence, when a bend forces it to change its direction in the manifold, the velocity increases in magnitude.
3. Convective heat transfer equation, Q = h.A. ΔT suggests increase in the heat transfer rate at higher heat transfer coefficient values. As convective heat transfer depends on bullk motion, when there is an increased velocity in the exhaust manifold, a higher heat transfer rate is experienced.

The following reference papers were also used to validate the results obtained by comparing with the experimental results in these papers.

1)Analysis of Exhaust Manifold using Computational Fluid Dynamics-Marupilla Akhil Teja

https://www.hilarispublisher.com/open-access/analysis-of-exhaust-manifold-using-computational-fluid-dynamics-fmoa-1000129.pdf

2) CFD Analysis of Exhaust Manifold for Different Designs- Ömer Cihan , Mehmet Bulut

http://static.dergipark.org.tr/article-download/cbcf/ed95/9f5d/5dea5b38b0eb6.pdf?