Week 4 - CHT Analysis on Exhaust port

A CHT or Conjugate Heat Transfer analysis is used where there are multiple phases in a simulation and energy transfer in the form of heat occurs between the multiple phases. An example could be a condenser of any type, where the hot working fluid transfers its heat energy to a coolant. A CHT analysis can be used to calculate the heat transfer coefficient of any part of the condenser system. Further examples include: cooling of an exhaust pipe, cooling of a computer graphics card and heating a moving fluid using a heating coil.

In this project, I will be simulating an exhaust port which receives constant streams of hot exhaust gases which converge into a single outlet, the pipe will be made of aluminium and the heat transfer coefficient between the pipe and the fluid will be calculated.

Geometry

The geometry for this project was imported into SpaceClaim. The geometry consits of 4 inlets circular in cross section, each converging into single outlet, circular in cross section as well. The imported geometry was modified quite a bit by the following commands:

1. Removal of Duplicate Edges

Some duplicate edges were present in the geometry, these were removed by going to: Prepare -> Extra Edges

2. Extraction of Volume

Since flow of a fluid was going to be simulated inside the pipes, the volume must be extracted by going to: Prepare -> Volume Extract

3. Sharing Topology

The extracted volume and existing geometry has to be merged so that a body fitted mesh can be generated later, this is done by selecting FFF under Structure -> Analysis and set Share Topology to Share. Then, go to Workbench -> Share to start the sharing process. After this process is complete, the geometry is ready for meshing.

This is a picture of the completed geometry:

Meshing

The base size is 0.15m. There are multiple mesh controls used to generate the mesh for this geometry, they are:

1. Mesh -> Inflation

This option is used to accurately capture the boundary layers and to properly calculate the heat coefficient.

According to https://www.pointwise.com/yplus/index.html, for an inlet velocity of 5m/s, the wall spacing is 1.91mm. ie. The size of the first element on the walls of the pipe should be 1.9mm high. If the initial thickness is 1.91mm and if number of layers are 5 for a growth rate of 1.2 then the total thickness is 12.5mm. (recall geometric progession)

2. Sizing -> Body Sizing

This control is used to refine the mesh on the outer wall of the pipe.

3. Sizing -> Body Sizing -> Sphere of Influence

This control introduces a sphere of finer mesh in the elbow near the outlet.

This is the location of the sphere, and the body sizing applied to it.

This is the final mesh and its metrics below:

Looking at the inflation layers,

The mesh metrics are mixed, but most of the lower quality cells lie in the solid region (thickness of the pipe), conduction occurs here and there is less dependence on mesh quality for conduction due to the simple equations solved. Hence mesh quality is satisfactory.

The numbers of nodes are 134704 and elements 375578.

Setup

Boundaries

inlet - inlet with 5m/s velocity normal to the boundary

outlet - pressure outlet

outer-wall - wall (no slip)

others - they were left unchanged, they are set to convection with 0 heat transfer (adiabatic)

Materials

The existing materials' (air and aluminium) properties were used and were left unchanged.

Density of Air: `1.225 kg//m^3`

Specific Heat of Air: `1006.43 J//kg.K`

Thermal Conductivity of Air: `0.0242 W//m.K`

Viscosity of Air: `1.7894 * 10^-5 kg//m.s`

Density of Aluminium: `2719 kg//m^3`

Specific Heat of Aluminium: `871 J//kg.K`

Thermal Conductivity of Aluminium: `202.4 W//m.K`

Viscous

k-epsilon standard with standard near wall treatment was the viscous model used. This model requires the y+ to be above 30.

 Solution - Methods

Simulation Results

The simulation ran for 100 iterations using the steady state solver and a hybrid initialisation. The results are below:

Residuals

This was taken in Fluent.

Velocity Contour along the outlet

A plane parallel to the XY plane with z offset = 0 was created in CFD-Post to view the velocity distriubtion near the outlet.

Temperature Contour along the outlet

A plane parallel to the XY plane with z offset = 0 was created in CFD-Post to view the temperature distriubtion near the outlet.

Wall Surface Heat Transfer Coefficient

A plane parallel to the XY plane with z offset = 0 was created in CFD-Post to view the wall surface heat transfer coefficient distribution near the outlet.

Zooming in,

The wall heat transfer coefficient is `230.853 W//m^2.K`

This results gives us the amount of heat emitted by the inner wall into the thickness of the pipe. The value depends on the reynold's number of the flow. In the elbow, due to high velocities, the heat transfer coefficient is the highest

Surface Heat Transfer Coefficient

A plane parallel to the XY plane with z offset = 0 was created in CFD-Post to view the surface heat transfer distriubtion near the outlet.

Zooming in,

The surface heat transfer coefficient lies between `-51.24 W//m^2.K` and `51.24 W//m^2.K`

This result gives us the amount of heat received or emitted by the solid outer wall (thickness), the negative value indicates inflow of heat and positive value is outflow. Heat inflow occurs due to convection from the moving fluid in the pipe and outflow is just general convection with the surrounding air.

Velocity Streamlines along the port

These were taken in CFD Post

We can deduce from these streamlines that velocity is maximum at the elbow near the outlet.

The accuracy of the values obtained from the simulation depends on:

1. Size of Inflation Layers: the correct inflation layer size must be used to capture the boundary layer region correctly for the appropiate turbulence model

2. Element size and quality: the coarse the mesh becomes, the less accurate the solution becomes.

3. Conforming Mesh at solid-fluid interface: If the topology is not shared, a conforming mesh will not be generated,

Verification of Simulation Predictions

The results can be verified using the Nusselt Number, it is the ratio of conductive to convective heat transfer at the boundary of a fluid.

It is given by: `Nu = (h*L)/k`

Rearranging,

`h = (Nu * k)/L`

The Nusselt Number is a function of Prandtl Number and Rayleigh Number, the Prandtl Number is given by: `Pr = (c_p * mu)/k`

For forced convection through a pipe, the nusselt number is given by:

`Nu_D = ((f//8) (Re_D - 1000)Pr)/(1+12.7(f//8)^(1//2) (Pr^(2//3) - 1)`

Where, Re is the Reynold's Number given by:

`Re = (rho * u * D)/mu`

where,

`h`: Heat Transfer coefficient (`W//m^2.K`)

`L`: Length of pipe (`m`)

`k`: Thermal Conductivity of pipe (`W//m.K`)

`c_p`: Specific Heat of fluid (`J//kg.K`)

`f` : Darcy friction factor (to be calculated from a Moody Chart)

By substituting these values into these expressions, the theoretical heat transfer coefficient can be calculated.

Conclusions and Observations

1. The simulation runs well and produces the results expected, such as higher velocity near the elbow.

2. The results also concurrent with expected general trends, the higher velocity near the elbow also increases heat transfer.

3. The increased heat transfer also caused lower temperature (when compared to the rest of the pipe) near the elbow region.