Conjugate Heat Transfer CHT analysis on an Exhaust Manifold

Conjugate Heat Transfer (CHT) analysis on an exhaust manifold:

Objective: To discuss why and where a Conjugate Heat Transfer analysis is used and its importance in several areas. Here to perform a total of two simulations by comparing the mesh size. One simulation should be the baseline mesh and the second one should have a finer mesh on the solid zone and also with inflation layers. Come to results, going to compare the temperature, velocity, and heat transfer coefficient on the walls of the manifold and explain if refining the mesh produced any changes to the results. To give validation of the results, How to verify if the HTC predictions from the simulations are right? On what factors does the accuracy of the prediction depend on?

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 between the solids and fluids. The CHT analysis allows here us to simulate the heat transfer between solid and fluid volumes by interchanging the thermal energy at interfaces.
• The rate of transferred heat is directly proportional to the temperature difference between the bodies.
• In solids, conduction often dominates whereas, in fluids, convection usually dominates.
• Surface temperature and heat exchanging capabilities of various electric devices and mechanical machinery are accurately simulated which is difficult to calculate empirically. And this one of the Main advantage of CHT
• While we designing a component, we need to invest millions of dollars in developing the actual prototype. Once we understand the CHT concept there and perform the simulation, we can optimize the prototype in the thermal properties domain and can save the money.

Applications:

• After knowing why we need to develop or simulate the CHT concept, now we need to know where to use it.
• Using the CHT analysis, we come to know the effectiveness of various thermal systems involving solid and fluid medium.
• CHT analysis can perform on thermal systems that we come to see in our day to day life are:

1. Coolers
2. Radiators
3. IC Engines
4. Heat exchangers
5. HVAC (Heating, Ventilation, and Air-Condition Unit)
6. Boilers
7. Exhaust port manifolds, etc.

Case1: Baseline Mesh

Geometry:

• The given Exhaust manifold, and contains four inlets and one outlet.

• To perform the CHT simulation we need to extract the fluid volume from the geometry.
• After extracting the fluid domain we need to mesh the model.
• In meshing, we come to know there are mismatches of vortex lines of mesh.
• To overcome that, we need to obtain a conformal mesh between the solid volume and fluid volume.
• In Spaceclaim, go to workbench --> Shareprep --> let it load (take some time).
• Without doing this step and we directly generate the mesh, mesh gets failed definitely.
• Actually, this creates a single interface between solid and fluid volume where the heat transfer is happening actually.
• We can confirm that it is done, by observing the pink circles at inlets and outlet where we are given as shown above pictures.
• After that we have to do other activities, share topology --> Share. It means the topology between solid volume and fluid volume is shared.

Meshing:

1. Element Size - 150 mm
2. No. of Nodes - 27616
3. No. of Elements - 138552
4. Mesh type - Tetrahedral
5. Inflation - No

• The baseline mesh has been generated.
• Both the fluid volume and solid volume are perfectly connected. This action won\'t be seen if didn\'t share the topology.

Setup:

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)

Methods:

1. Scheme - Coupled
2. Initialization - Hybrid
3. Run calculation - 500 Iterations

Results:

1. Graphs - temperature-contour (outer-wall-convection)
2. Animation - temperature-animation

Solution:

Residual:

• The solution gets converged after iteration number 200.
• It takes less computational time because of the baseline mesh is applied.

Temperature contour:

• By observing the above contour figure, we can say that at four inlets the temperature inlet is 700k which is the given temperature.
• At the bend near the outlet of the manifold, the temperature gets raised on the wall. This is because the entire flow from the four inlets is getting jammed at that bend.
• When it gets jammed, the heat transfer coefficient between the solid and fluid domain is increased and it is exactly what we need to study.
• If we observe closely at inlets and outlet, the flow doesn\'t attach to the wall of solid volume perfectly. This is because of the lack of mesh quality.

Temperature contour inside the Manifold (cut plane):

• An above contour is a plane in yz-direction.
• Here we can observe the difference between the heat transfer rate at inlets and at the outlet by observing temperatures at the edges of the manifold.
• This can give the justification for the point discussed in the temperature contour.

• The maximum temperature is obtained at the outlet of the manifold, this can be understood by observing the above two figures.
• As we know that the outlet velocity is more. More the velocity Higher the Reynolds number, Higher the Re, Higher the heat transfer coefficient.

Velocity inside the Manifold:

• An above contour is a plane in yz-direction.
• The given velocity is 5 m/s and it is maintained till some distance inside the manifold. After some distance, the velocity is increasing gradually because the total mass of the particles is increasing at the outlet.
• As the dimension of the inlets is the same, velocity is also approximately the same. Due to the conservation of mass, the velocity becomes increasing at the only output.

• At the corner of the Exhaust manifold, the velocity is shown as high. This is because of the law of conservation of energy.
• The air has 5 m/s initially at the inlets. But the at the outlet maximum is showing as nearly 37 m/s.

Streamlines of Velocity:

• This contour shows us both temperature and velocity development in a single contour.
• The temperature and the velocity are increasing at the corner location of the manifold Which is acceptable.

Heat-Transfer Coefficient:

• In this contour, it is showing the heat transfer coefficient between the solid and fluid domains.
• As we know that at outlet corner the velocity is high. Where velocity is higher, the heat transfer coefficient is also high.
• It shows that heat transfer is looking quite the same at the inlet corners. But maximum can occur at the outlet curve. We can validate it by using the probe option (To know the obtained values at a particular location).

• Maximum heat transfer coefficient recorded is 104.2 W/m2 k

Case1: Finer Mesh

Geometry:

• There is no change in Geometry.

Meshing:

1. Element Size - 150 mm
2. Body Sizing - Fluid Domain (10 mm)
3. No. of Nodes - 114013
4. No. of Elements - 377599
5. Mesh type - Tetrahedral
6. Inflation - 5 Layers (Max. Thickness - 5 mm)
7. Growth Rate - 1.2

• The fine mesh has been generated.
• The elements and the nodes get increased as we decrease the element size of the fluid domain and given the inflation, it can be visualized.
• Inflation is given to get accurate physics at the interface of the Solid and Fluid volumes Which is previously not get simulated well.

Setup:

• Everything is the same as given in the baseline mesh case.

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)

Methods:

1. Scheme - Coupled
2. Initialization - Hybrid
3. Run calculation - 500 Iterations

Results:

1. Graphs - temperature-contour (outer-wall-convection)
2. Animation - temperature-animation

Solution:

Residual:

• By looking at the above residual, the solution gets converged after iteration number 200.
• After 200, the solution becomes similar.
• It takes more computational time as we were given the element size as 10 mm.
• Except for the energy equation, all are fluctuating at the residuals of 0.001.

Temperature contour:

• This time it is too clear that how the temperature is behaving inside the manifold compared to baseline mesh case. Much more detailed and defined properly at the inner side and at the walls of the body.
• The temperature on the walls at the inlets is decreasing firstly when the flow has no obstruction.
• Wall temperature gets increased as all the flows get mixed.
• We can also see how the flow become when it reaches to a curve in the body.

• The maximum temperature is obtained at the outlet of the manifold, this can be understood by observing the above two figures.
• As we know that the outlet velocity is more. More the velocity Higher the Reynolds number, Higher the Re, Higher the heat transfer coefficient.

Velocity inside the Manifold:

• An above contour is a plane in yz-direction.
• The given velocity is 5 m/s and it is maintained till some distance inside the manifold. After some distance, the velocity is increasing gradually because the total mass of the particles is increasing at the outlet.
• As the dimension of the inlets is the same, velocity is also approximately the same. Due to the conservation of mass, the velocity becomes increasing at the only output.
• Through this plot, we cant see the maximum velocity developed.

• At the corner of the Exhaust manifold, the velocity is shown as high. This is because of the law of conservation of energy.
• The air has 5 m/s initially at the inlets. But the at the outlet maximum is showing as nearly 40.31 m/s but in the previous case, it is 37 m/s.
• It gives smooth contour and easy to understand.

Streamlines of Velocity:

• Streamline is one of the options in fluent to check the velocity.

Heat-Transfer Coefficient:

• The heat transfer coefficient is higher in the fine mesh case as compared to the baseline mesh case.
• So, definitely refinement of mesh will help to get close to the desired values.
• Here the maximum geat transfer coefficient value is 214.2 W/m2 k.

Comparison of Results:

Verification Heat Transfer Coefficient results:

• Come to the verification of the Heat transfer coefficient of the simulation, we can be done by the grid dependency method.
• We need to lower the element size from 10 mm to 8, 5, 2 mm, etc and can compare the results.
• The other way to verify the heat transfer coefficient is by calculating the Nusselt number theoretically and compare it with the simulation results.

Nusselt number:

• In fluid dynamics, the Nusselt number (Nu) is the ratio of convective to conductive heat transfer at a boundary in a fluid.
• A larger Nusselt number corresponds to more active convection, with turbulent flow typically in the 100–1000 range.

Nu (L) = Convective heat transfer / Conductive heat transfer = `(hL)/(K)`

• Where h = convective heat transfer coefficient

K = thermal conductivity

L = characteristic length

• Nusselt number for the forced convection in turbulent pipe flow which is relative to our problem is

`Nu_D = 0.023Re_D^(4/5)Pr^n`

• 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

n = 0.4 for hot fluid, 0.3 for cold fluid

Prandtl number, Reynolds number, and characteristic length depend upon the fluid taken and the geometry.

On what factors does the accuracy of the prediction depend on?

• Without doing the Sharing topology of the solid and fluid volume interface, the solution definitely gets odd results as mesh doesn\'t consider.
• Grid dependency, size of the element of the mesh will definitely a factor to obtain the accuracy in solution.
• The type of Mesh can also show the effect on the accuracy of the results.
• 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 (K-Epsilon) should be selected to refer to the problem.
• Boundary conditions should be taken carefully, especially while giving the input of the heat transfer coefficient. it has to be meaningful and taken from the experimental data.

Conclusion:

The Conjugate Heat Transfer analysis is performed on the Exhaust Manifold for the two different Mesh cases. By comparing the results, it observed that the Heat transfer coefficient, temperature, and velocity values are higher in the fine mesh case. It gives us the confidence that refining the mesh can give us accurate results. Comparing the contour plots, Each and every plot is very clear in fine mesh cases compare to the baseline mesh case. Inflation layers are must at the interface of solid and fluid volumes to calculate the parameters accurately.