Exhaust Port Challenge

Introduction:

Conjugate Heat Transfer (CHT) is the process of thermal energy exchange when solid and fluid domain interacts with each other. i.e. conjugate heat transfer corresponds with the combination of heat transfer in solids and fluids. 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 coolers, heaters, or heat exchangers, condensers, fins, etc. basically where there is the interaction of high-temperature applications such as engines, pumps, compressors.

Forced convection is the most common way to achieve a high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapor phase change)

Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls and because solids are usually immersed in a fluid.

Aim:

To analyze conjugate heat transfer on exhaust manifold geometry where exhaust gases are coming with 5m/s velocity and at 700K. Aluminum material is considered as exhaust port material for now (usually it is cast iron).

Geometry:

Following geometry is used. The first step was to extract the fluid volume from where the air is expected to be flown. This fluid volume and the remaining solid volume are selected and together moved to a new component, and the empty components were deleted after this step. For meshing to be proper between these volumes, they should share information within one another, i.e topology should be shared. For this, the ‘share prep’ option in the ‘workbench’ tab was selected. Geometry process is completed.

Mesh Setup:

Base Mesh

For base mesh, the default value of mesh size was selected (435mm).

This gave No. of Nodes: 25677

                  No. of elements: 127369

Improved Mesh

For base mesh, the default value of mesh size was selected (25mm). Fluid volume was treated for the inflation layer so that the heat transfer coefficient should be captured precisely.

This gave No. of Nodes: 88511

                  No. of elements: 245383

We were about to use k-ꞷ SST turbulence model, so Y plus values must be maintained between 0-5. First layer thickness 0.5mm with 10 layers and increment of 1.2 per layer.

Physics Setup:

Turbulence Model: k-ꞷ SST, with a coupled method for the solver. With Pressure under relaxation factor as 0.1 and momentum  factor as 0.3

The solution ran for 150 iterations, till the residuals drop below 1e-3 and showing a stable trend.

Solution and Post Processing:

1. HTC captured

Base Mesh

                          Fig. Convective heat transfer coefficient base mesh

Improved Mesh

                                   Fig. Convective heat transfer coefficient improved mesh

2. Velocity trend

Base Mesh

                   Fig. Velocity distribution base mesh case

Improved Mesh

                    Fig. Velocity distribution improved mesh case

3. Temperature distribution

Base Mesh

             Fig. Temperature distribution for base mesh case

Improved Mesh

                  Fig. Temperature distribution for improved mesh case

Prediction of HTC analytically:

Mathematical calculation of HTC:                                                                  

One can determine the heat transfer coefficient by using the Dittus-Boelter correlation. This can be helpful for the purpose of designing heat exchangers, which are devices that are designed to transfer heat from one medium to another for commercial purposes. Although the Dittus-Boelter correlation is not perfectly accurate, it is useful for some applications and is estimated to be, accurate to within 15 percent. Using the Dittus-Boelter correlation the heat transfer coefficient can be calculated in the following way using two further dimensionless groups, the Reynolds number, and the Prandtl number:

h = (K_w/D_H)*Nu

where k_w is the thermal conductivity of the liquid, D_H is the Hydraulic diameter, and Nu is the Nusselt Number which is determined by the following equation:

Nu = 0.023Re^0.8Prⁿ

In this equation, Re is the Reynolds number which equates to:

Re = (m .D_H)/(μ.A)

And Pr is the Prandtl number, equating to:

Pr = (C_p* μ)/k_w

For the Reynolds number, m is equal to the mass flow rate, and A is a cross-sectional area of flow taken from the tube. For the Prandtl number, C_p is equal to heat capacity (assuming a constant pressure), and in both equations, μ is the viscosity of the fluid in consideration. The Reynolds number is a measure of the relative importance of viscous and inertial forces (which will bring about turbulence).

The temperature will be maximum on the solid part, where the heat transfer from the fluid would be maximum. This would be at a point where Reynold’s number and incidentally happen where the velocity is maximum considering the constant diameter of the pipe.

Conclusion:

CHT analysis is performed on the exhaust manifold. Variation of temperature, heat transfer coefficient, and the velocity compared for different mesh patterns. The accuracy of the values coming from the simulation should be compared with either mathematical data, experimental data, or any research paper data. To improve accuracy, meshing and turbulence under relaxation factors should be modified further.

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