Week 6: Conjugate Heat Transfer Simulation

Aim: To set up a flow simulation through a pipe for visualizing conjugate heat transfer through a solid pipe over the walls. Also, perform a grid dependence test and analyzing the effect of supercycle interval.

Theory: Conjugate heat transfer (CHT) is a combination of heat transfer in solids and fluids. In solids, heat transfer takes place through conduction, and in fluids heat transfer takes place through convection. Whenever there is a heat transfer from solid volume to fluid volume or vice versa by exchanging their thermal properties, we use conjugate heat transfer analysis for the simulation. This kind of simulation helps in understanding thermal systems such as HVAC, Internal combustion engine, heat sinks, exhaust ports, etc.

Super-Cycling: It is a method used in Converge Studio in the case of CHT with solid and fluid regions. Usually solving the fluid domain is much faster due to its time scale difference for heat transfer in fluids as compared to that of the solids which are slow. Hence, both the solvers cannot run at the same speed causing problems during the solution as solid domain solver would not have reached a steady-state in the time compared to the fluid domain solver. Due to these kinds of problems we use the concept of super-cycling.

Y+: Y+ value is a non-dimensional distance (based on local cell fluid velocity) from the wall to the first mesh node as shown below. This parameter helps us in deciding if we have to use a wall function or not. If y+ value is less than 10 it is known as viscous sub-layer and we can use no-slip condition. If y+ value is between 10 to 30 it is in a transition zone. If y+ is above 30 it is in a turbulent region and for this condition, we have to use wall function.

Here 3 different cases are simulated based on grid size and supercycle stage interval.

Case1: Grid size: 3mm with a supercycle stage interval:0.01.

Case2: Grid size: 3mm with a supercycle stage interval:0.02.

Case3: Grid size: 2mm with a supercycle stage interval:0.03.

Methodology:

1) Pre-Processing:

We will be creating the geometry in Converge studio whose dimension will be scaled into meters and the dimensions are as follows:

• Length along x-direction (l_x) = 0.04 m.
• Length along y-direction (l_y) = 0.039 m.
• Length along z-direction (l_z) = 0.2 m.

We will be flagging the domain into 5 different boundaries namely Solid Outer Wall, Solid Side, Inlet, Outlet, Interface.

• Outer Diameter = 0.04 m.
• Inner diameter = 0.03 m.

The next step is we will be moving on to the case setup where we will be setting up all the parameters.

• In this project, we are interested in analyzing the heat transfer between solid and fluid regions. Hence we perform a Conjugate Heat Transfer (CHT) simulation using transient analysis.

• This is a general flow problem and hence we will be selecting a Time-based application type.

• Moving on to the Materials we will be using predefined air for the fluid region whose composition consists of nitrogen and oxygen. For the solid region, we will be using Aluminium. The transport properties are set to the default values. The species composition consists of N2 and O2.

• Simulation parameters are set in which the required transient solver is set up with a full hydrodynamic simulation mode. Also, simulation time parameters are set accordingly.

- Start time : 0 sec.

- End time : 0.5 sec.

- Initial time step : 1e-7 sec.

- Minimum time step : 1e-7 sec.

- Maximum time step : 1 sec.

• Now we will be creating a region in order to group various boundaries to define a volumetric region under initial conditions and initialization tab. We will be creating 2 regions as we have 2 different volume solid and fluid. We will be using 2 different stream id.

• Moving on, we flag different boundaries and assign respective boundary conditions to create a meaningful Volumetric region.

- Inlet :

1) Boundary Type: Inflow.

2) Velocity (Dirichlet condition): 3.752 m/s in z-direction.

`Re=(V*D)/nu`

V = Flow Velocity in 'm/s'.

D = Diameter of pipe at the inlet in 'm'.

v = Kinematic Viscosity `(1.608 * 10^-5 ) m^2/s`

3) Temperature (Dirichlet condition): 300 K.

4) Species BC: air.

5) Region:Fluid.

- Outlet Boundary :

1) Boundary Type: Outflow.

2) Pressure(Dirichlet condition): 101325 Pa.

3) Temperature (Dirichlet condition): 300 K.

4) Species BC: air.

5) Region: Fluid.

- Solid Side:

1) Boundary Type: Wall.

2) Velocity Boundary Condition: Slip.

3) Region: Solid.

- Solid Outer Wall:

1) Boundary Type: Wall.

2) Velocity Boundary Condition: Slip.

3) Heat Flux: -10000 W/m^3.

4) Region: Solid.

- Interface:

1) Forward side will be fluid region with law of wall boundary condition.

2) Reverse side will be solid region with Slip wall boundary condition.

• Turbulence Model: RNG k-epsilon.
• Finally, we will be setting up the parameters for printing the 3D and other output files in the post-processing tab. - Time interval for writing 3D output data files: 0.01 sec. - Time interval for writing text output:1e-6 sec. - Time interval for writing restart output:0.01 sec.

2) Running the solver:

• Once the case is setup we export the input files from the converge studio and save in a designated location.
• Then using Cygwin we will run the simulation.

3) Post-Processing:

• The output files are converted to a format in which ParaView can understand using Cygwin or converge studio.
• These converted files can be used for visualizing contours, animations, etc. using Paraview which is the post-processing software.

Post-Processing Results:

Geometry Mesh Plots:

Grid Size - 3mm with supercycle - 0.01

Grid Size - 3mm with supercycle - 0.02

Grid Size - 2mm with supercycle - 0.03

Temperature Plots

From the above solid region mean temperature plots, we can see that as the supercycle stage interval increases the mean temperature decreases. This means more heat is being transferred from the solid region to the fluid region as the time progress. Also, we can clearly see that the solution for the solid region is not converged and finer mesh is required to obtain accurate results.

From the above fluid region mean temperature plots, we can see that as the supercycle stage interval increases the mean temperature increases. This means more heat is being absorbed by the fluid region from the solid region as the time progress. Also, we can clearly see that the solution for the fluid region is not converged and finer mesh is required to obtain accurate results.

Total Cell Count Plot

We can see that for 0.01 and 0.02 supercycle stage interval the total cell is around 11,000 and for the supercycle stage interval 0.03, the total cell is around 36,000 as the grid is finer for this case (2mm) compared to 0.01 and 0.02 (3mm). As the grid is refined the total number of cells increases.

Velocity Contours:

Grid Size - 3mm with supercycle - 0.01

Grid Size - 3mm with supercycle - 0.02

Grid Size - 2mm with supercycle - 0.03

As we move along the flow direction, we observe that there is an increase in magnitude of the velocity leading to a smooth parabolic profile as momentum increases.

Velocity Glyph Contours:

Grid Size - 3mm with supercycle - 0.01

Grid Size - 3mm with supercycle - 0.02

Grid Size - 2mm with supercycle - 0.03

From the above glyph contours, we can observe the flow direction.

Y+ Contour:

Grid Size - 3mm with supercycle - 0.01

Grid Size - 3mm with supercycle - 0.02

Grid Size - 2mm with supercycle - 0.03

From the above Y+ contours, the average range of Y+ varies from 0 - 16. The range of Y+ becomes smaller as the mesh is refined. Refinement helps in determining the boundary layer near the wall more accurately.

Temperature Contour :

Grid Size - 3mm with supercycle - 0.01

Grid Size - 3mm with supercycle - 0.02

Grid Size - 2mm with supercycle - 0.03

From the above temperature contours, we can see that the stabilizing temperature decreases when the mesh is refined.

Velocity Animation:

Grid Size - 3mm with supercycle - 0.01

Grid Size - 3mm with supercycle - 0.02

Grid Size - 2mm with supercycle - 0.03

Conclusion:

• Successfully simulated a Conjugate Heat Transfer problem through a pipe.
• Performed grid dependency test.
• Observed and studied Y+ and super-cycling effects.