Exhaust Port Challenge

Conjugate Heat Transfer:

Conjugate heat transfer is the combined phenomena of heat transfer in both solids and fluids in contact. The dominating mode of heat transfer in solids is conduction whereas in fluids is convection. Conjugate heat transfer phenomena is observed many times inn day-to-day life.

Heat transfer in solids:

Heat transfer in solids is governed by Fourier’s law of conduction which is stated as the conductive heat flux is directly proportional to the temperature gradient.

`q=-k∆T`

For time-dependent problems the variation of temperature in solids is given by equation:

`ρC_p ∂T/∂t=∇.(k∇T)+Q`

Heat transfer in fluid:

The heat transfer in fluid is affected by several factors due to fluid motion:

1. The transport of fluid means transport of energy too, which appears in heat equation as convective contribution. This is mainly dependent on the fluid properties.
2. As we are dealing with the real fluids, it has some viscosity. Viscous effects of fluid flow produce the fluid heating. This term is of great significance in fast flow of viscous flows.
3. When the fluid density is temperature dependent, pressure work also contributes to the heat equation.

When above said contributions to heat equation from conductive and convective heat transfer are taken into account the heat equation looks as:

`ρC_p ∂T/∂t+ρC_p u∙∇T=α_p T((∂P_A)/∂t+u∙∇P_A )+∇.(k∇T)+Q`

Conjugate heat transfer solves the energy equation in solid phase simultaneously with the governing equations in fluid phase to evaluate the heat interactions in solid wall. This solution strategy makes the CHT modelling capable of predicting the time-accurate heat flux on the exhaust port wall, and a realistic and dynamic temperature distribution on the wall can be solved. Therefore, the CHT modelling allows a more accurate estimation of both the heat loss through exhaust port wall.

CHT modelling is used extensively in commercial CFD programs for flow and thermal analysis in various devices.

Typical design problems determines:

The highest temperature in a system, overall HTC, temperature distribution over body, estimation of heating or cooling rates etc.

CHT analysis can be performed to improve engine cooling performance and thereby improving its life. Critical cooling applications such as the electronics cooling or CHT study in microchannel are the challenging applications of CHT nowadays.

1. If we consider the case of heat exchanger, the combination of heat transfer in fluids and solids is the key to design the effective heat exchanger. The solids in heat exchanger are used to transfer the heat without mixing of two fluids.
2. In case of heat sinks which is made up of metal with high thermal conductivity and it exchanges heat with the surrounding fluid.
3. Cooling of electronic chips and PCB’s is also best example where we can employ CHT approach to solve the problem. PCB’s are generally cooled by air in direct contact with it.

Perform CHT analysis on Exhaust manifold model.

Geometry:

The received cad model was not fit for simulation deirectly, as it is having some exra-edges. Hence those extra edges must be removed before Fluid Volume extraction.

Fluid Volume Extraction:

The fluid volume is extracted as shown in figure.

In order to generate the conformal mesh, the share tab is enabled under the Share Topology option. Upon clicking the SharePrep tool, Geometry Modeling will search the assembly structure for shared topology and apply it to the model. A summary of the result will be displayed in the status bar. At this point, the other sharing tools in the ribbon group will be enabled.

Model after upgrading shared topology

Notice the coloured edges indicating that the shared topology has been upgraded.

Here we will perform simulation on both baseline mesh and refined mesh.

Baseline Mesh:

The default mesh is generated. As we can see from the figure the mesh is generated nicely. A conformal mesh is generated between the fluid volume and solid part of exhaust port.

Mesh Statistics:

Nodes: 27208

Elements: 136807

Element size: 150 mm

Mesh Quality:

In order to specify the inlet, outlet and convective boundary conditions proper named selections are given.

Solver Settings:

Type: steady state, pressure based

Models:

• Energy: On
• Viscous: k-e, standard wall function

Materials:

• Fluid: Air
• Solid: Aluminium

Boundary conditions:

• Velocity inlet: 5 m/s, temperature 700 k.
• Pressure outlet: 0 pa (gauge)
• Convective wall: 20 W/m²k

Case 1: Baseline simulation

Residuals:

velocity Streamlines:

velocity near outlet port:

Heat tranfer Coefficient on wall:

Temperature on outer wall:

temperature on Mid-plane:

heat transfer coefficient on wall:

Refined Case

Mesh Statistics:

Nodes: 128061

Elements: 464419

Body sizing (Solid): 10 mm

Inflation Layer: total thickness: 5 mm

Number of layers: 5

Growth Rate: 1.2

Case 2: Refined Mesh: Turbulence model - k-e model

Residuals:

velocity stramline:

wall heat transfer coefficient:

temperature on mid-plane:

velocity on mid-plane:

Heat transfer Coefficient on wall of exhaust port:

Wall Y+:

The average value of wall Y+ is less than 10.

The k-w SST model will predict the near wall effects better than k-e model.

Case 3: Turbulence Model: k-w SST model (Y+ 1)

residual:

velocity Streamline

velocity on mid-plane:

temperature on Mid-plane:

temperature on wall:

Wall heat transfer coefficient:

Y+ plot:

Verification of HTC prediction:

The local Nusselt number for fully developed turbulent internal flow is obtained from Dittus Boelter equation:

Correlation:

Where,

Dh- hydraulic diameter

Re- Reynolds Number

Pr- Prandtl Number

Nu- Nusselt Number

The above stated correlation is valid only for 0.6 < Pr < 160, Re>10000 and L/D>10.

And the value of heat transfer coefficient is varying between 0 to 1006 W/m²k.

Factors affecting accuracy of prediction:

There are several factors which affects the accuracy of prediction of heat thransfer such as the meshing near wall tp get accurate HTC,proper boundary conditions etc.