Conjugate Heat Transfer Simulation

In this challenge conjugate heat transfer simulation of the Pipe flow is studied using converge 3.0.

Geometry:

The geometry of the pipe is as shown below. The length of the pipe is 0.2m, the external diameter is 0.04m and the internal diameter is 0.03m. The fluid flowing is air and the pipe is made up of Aluminum.

Mesh Generation:

A base grid with three various sizes is studied to check for grid dependency.

Cases	Grid Size (m)
1	0.004
2	0.003
3	0.002

Physical Setup:

General	Transient
Model	RNG k-`ε` Super-cycle Modeling
Materials	Fluid: Air (77% N2, 23% O2) Solid: Aluminum
Monitors	The temperature at an arbitrary point in the solid domain
Boundary Conditions	Inlet: 3.676 m/s (Re = 7000) Outlet: 101325 Pa Outer Wall: slip & 10000 W/m2 flux (into the system) Interface: Interface Boundary

Inlet velocity is calculated based upon the given Reynolds number criterion.

`Re = (ρVD)/μ`

Re = 7000

`ρ` = 1.176 kg/m3

Diameter = 0.03 m

`μ`= 1.853e-5 N-s/m2

The calculated inlet velocity is 3.676 m/s.

Super Cycling:

Super cycling is a method used by Converge in the case of conjugate hear transfer problems with solid and liquid regions. The problem while solving the solid and liquid regions is both solvers cannot run at the same speed since solving in the fluid domain is much faster owing to the time scale difference for heat transfer in liquids as compared to solids. Here for the solid region for the given time interval, both the fluid and solid regions are solved together then, a fluid region solver is frozen and solid region is solved using a steady-state solver. Then the fluid solver is unfrozen and then both the solvers are solved. This is repeated until the end time of the simulation.

Flow of Project in Converge:

1. Provided geometry is designed in the Converge workspace.
2. Boundaries are named using appropriate names.
3. Normal directions are checked to be in line with the geometry and flow.
4. Diagnosis is performed to check any discrepancies in geometry.
5. Then appropriate species are selected for the fluid and solid domains.
6. Boundary conditions are set to the appropriate regions and their corresponding values.
7. The Super-cycling model is also selected in the physical models as this is a conjugate heat transfer problem.
8. The base grid of the considered step size is inserted along with respective directions.
9. Variables for post-processing and time intervals for writing the output and restart files are set and selected.
10. All the input files are stored at the desired location.
11. All the stored input files are executed using the command editor. These input files are executed by Converge Solver in the background.
12. Then the executed files generate the output folder in which data files after every selected interval are stored which are post-processed for the graphical results.

Results:

Case1:

Mesh:

Temperature Contour:

Pressure Contour:

Velocity Contour:

Velocity Vector:

y+ :

Case2:

Mesh:

Temperature Contour:

Pressure Contour:

Velocity Contour:

Velocity Vector:

y+ :

Case3:

Mesh:

Temperature Contour:

Pressure Contour:

Velocity Contour:

Velocity Vector:

y+ :

Comparative Results:

Mean Fluid Temperature:

Mean Solid Temperature:

Temperature at Monitor Point:

Effect of Super Cycle Interval:

The below results are obtained at the base grid of 0.004m

Animation of Temperature Variation:

Discussion:

From the above comparative results,

• It is evident that from the graphs of mean solid and mean fluid temperatures, none of the results are converged at 0.5 seconds, we need to run the simulation for a longer time.
• As far as, grid dependency is concerned none of the base grids yielded identical results, so, we need to run the simulation for the finer mesh.
• With the decrease in the super-cycle interval, the mean temperature for the solid is converged faster in comparison to the higher super-cycle interval but at the expense of computation time. The base grid used for comparison is 0.004m.

  Super Cycle Interval	Computation Time (seconds)
  0.03	172.783
  0.02	174.869
  0.01	239.294

• The y+ value is a dimensionless parameter used to determine the appropriate wall function to be used for simulation. In order to predict the nature and behavior of the fluid near the wall. If it is less than 10, it is in the viscous sublayer region. Between 10 and 30, it is in the transition region. Beyond 30, it is in the turbulent region.
• In cases 1 & 2, we have y+ between 0-16, whereas in case3 it is between 0-8. As case3 is for finer mesh and results are not satisfactory and we need to study for the much finer mesh. we can opt for no-slip boundary condition for the near-wall treatment.