Week 6: Conjugate Heat Transfer Simulation

AIM:

• To simulate a Conjugate Heat transfer simulation across a pipe. The impacts of 3 grid sizes and super cycling on the results will be examined.

THEORY:

Meaning of Conjugate Heat Transfer:

• The heat transfer between a body and the fluid flowing past it is governed by Fourier's equation, whereas the flow in the liquid is governed by the Navier-Stokes equation. The temperature and heat flux distributions at the interface are given by the solution to such an equation. The conjugate heat transfer is used when a solid and a fluid interact and we need to know the thermal exchange between the solids and liquids.

Meaning of Supercycling:

• In super-cycling, the fluid solver is frozen periodically while the heat transfer in the solid is allowed to progress to a steady state. CONVERGE solves the fluid and solid phases in the same simulation without requiring you to stop and restart the simulation. Super-cycling significantly reduces the computational cost of the CHT simulation.

A. CASE SETUP:

1. Creation of geometry. A concentric pipe with an internal diameter of 0.03m and an external diameter of 0.04m was created for the analysis.

2. After creating the geometry, a diagnosis check was performed with intersection errors noticed. These were rectified by selecting the Repair option under Geometry. The Front two faces and the rear faces were selected and deleted.

3. Boundaries were created as listed below,

3. The direction of the normals was found to be incorrect and was rectified to ensure the normals are pointing inwards to the direction of fluid flow.

4. After completion of the above steps a diagnosis check was again performed. Non-manifold edges were observed and this was a result of an interface between solid and fluid.

B. CASE SETUP:

i) Materials:- Gas simulation, Solid Simulation and Species were selected.

ii) Gas Simulation:- Default retained,

iii) Solid Simulation:- The Material used was Aluminium,

iv) Global Transport Parameters:- Default values retained,

v) Species:-

a) Gas:- O2 and N2,

For Solid,

- Simulation Parameters

i) Run Parameters:- Simulation set to Transient.

ii) Simulation Time Parameters:- Values set as shown below,

iii) Solver Parameters (Transient):- Defaults value retained,

iv) Boundary:

- Solid Outer Wall:- A Heat Flux of -10000 W/m^2 is introduced. The negative sign indicates that heat flux is flowing into the pipe.

- Solid Side:- Wall motion type is set to stationary, surface movement fixed,

-Outlet:- Pressure Value set to 101325 Pa at the outlet,

- Inlet:- In the problem, it is given that the inlet Reynolds number should be 7000.

- Interface. The normals on the interface point towards the fluid region and this is referred to as the forward side. The opposite direction which points towards the solid direction referred to as the reverse direction.

• Velocity and Temperature boundary conditions in forwarding region set to the Law of the Wall
• In the Reverse region Velocity and temperature are set to slip and specified values respectively,

-Regions and Initialization:

i) Fluid Region:- Values set as shown below,

ii) Solid Region:- Stream Id set to 1 and a solid box checked,

Turbulence Modelling:- k epsilon model is used,

-Super cycling was enabled to reduce the computational time required for CHT analysis. A monitor point was created at the outlet. Time length was initially set to 0.05 and then reduced to 0.03,0.02 and 0.01.

• The base grid size was set to 0.004, 0.003,0.0025.

• In post-variable selection, apart from the usual default, wall plus and heat transfer coefficient were enabled. The time intervals for writing output files were set as given below.

• To execute the simulation, the directory in which these input files were stored was accessed in Cygwin and the following command was typed "mpiexec.exe -n 4 converge.exe"
• After the Simulation was executed, the results were converted into a form which would be compatible with Paraview. This was done using the post_convert.exe command.

RESULTS:

CASE -1 ( GRID SIZE - 0.004):

1. Mesh. dx=dy=dz= 0.004m . The total number of Cells is 5386.

• MESH VIEW:

• VELOCITY CONTOUR:

• PRESSURE CONTOUR:

• TEMPERATURE CONTOUR:

- Since, Velocity profile development looks similar in all cases it is not shown in the animated file.

• PRESSURE PROFILE DEVELOPMENT:

CASE -2 ( GRID SIZE - 0.003):

1. Mesh. dx=dy=dz= 0.003m . The total number of Cells is 11932.

• MESH VIEW:

• VELOCITY CONTOUR:

• PRESSURE CONTOUR:

• TEMPERATURE CONTOUR:

- Since, Velocity profile development looks similar in all cases it is not shown in the animated file.

• PRESSURE PROFILE DEVELOPMENT:

CASE -3 ( GRID SIZE - 0.0025):

1. Mesh. dx=dy=dz= 0.003m . The total number of Cells is 22691.

• MESH VIEW:

• VELOCITY CONTOUR:

• PRESSURE CONTOUR:

• TEMPERATURE CONTOUR:

- Since, Velocity profile development looks similar in all cases it is not shown in the animated file.

• PRESSURE PROFILE DEVELOPMENT:

Comparison between different Meshes:

• With the refinement of the grid, it is seen that gradients in temperature, and pressure are observed more clearly. However, there is a significant increase in computational time as can be noted in the below table.

Grid Size (m)	Super cycling (time interval)	Time (seconds)
0.004	0.05	291.4
0.003	0.05	861.2
0.0025	0.05	1102.9

Effect of Super cycling:

• By reducing the Supercycling time interval from 0.03 to 0.01, we note that computational time decreases

Super cycling	Grid Size	Time (seconds)
0.03	0.004	291.3
0.02	0.004	222.7
0.01	0.004	198.4

Significance of Y-Plus:

• The Y-plus values obtained for different grids are given below. With the refinement of the grid, we note that the y-plus value decreases.
• We need to use wall functions for grids 0.004 and 0.003. For the other two grid sizes, the values are below 10 and therefore we are in the viscous sublayer.

Grid Size (m)	y plus
0.004	16
0.003	15
0.0025	10

OTHER PLOTS:

• From the above plot, we note that there is a variation in the solid side Mean temperature with the refinement of the grid. It varies between 780 K for a grid with 0.004m and 800K for a grid with 0.0025 m.

• The Fluid Side Mean Temperature is shown above, The variance is much lesser when compared to the solid Mean temperature.

• The temperature at the monitor point is shown above for various intervals of super cycling. The value varies from 850K for a coarse grid to 0.0025m for a fine grid.

CONCLUSION:

From the above analysis, we note that

i) Refinement of grid results in clearer plots however at the expense of computational time

ii) Decreasing the SUpercycling time interval results in the reduction of computational time

iii)Irrespective of grid size, fluid values converge to a particular value. (380 K)