## Conjugate Heat Transfer - A study of Converge capabilities and the effect of Supercycling time intervals on simulation time

Objective

• To implement and understand super-cycling in a conjugate heat transfer problem
• Verify the simulated result with analytical calculations

Geometry

The geometry is a hollow cylindrical pipe made of Aluminium

Outer Diameter = 4 mm

Inner Diameter = 3 mm

Length = 200 mm

Boundary Conditions

The inlet is a velocity inflow condition of 5.23 m/s which gives a Reynolds number of 10000.

The outlet is at atmospheric pressure. The fluid region is initialised at 300K. The solid material is Aluminium. Thermodynamic properties of air are obtained from the internet for analytical calculations.

The model used is RNG k-ε. The simulation was conducted on two geometries, complete geometry and a quarter section of the geometry. This was done since simulation of the complete geometry was resource intensive. A base grid size of 4mm was chosen and grid refinement of 11% was performed. The quarter-sized geometry was initialised for a grid size of 3mm and refined until the mesh size was 1.18 mm.

A monitor point was placed at 0.0125,0.0125,0.18 m inside the solid pipe to measure the temperature.

The supercycle data was generated at 0.02 s interval, the generation of supercycle data started at 0.02s after the simulation began.

The plot shows the temperature at the monitor point for the grid sizes mentioned.

Plot comparing temperatures for the quarter section of the geometry.

The Simulation was allowed to run until the change in temperature at the monitor point was less than 2% for 11% mesh refinement.

Simulation Parameters

Starting from 0 seconds the simulations was allowed to run for 0.5 seconds.

A transient simulation was set up and used RNG K-ε with variable time step size. A minimum step size of 1e-7 seconds and maximum of 1 seconds was set up.

Effect of Supercycling

The effect of supercycling is studied.

A shorter interval leads to faster convergence of the wall temperature.

The comparison of total simulation time to baseline configuration is inconclusive and therefore not added.

Grid Dependency

The simulation was initially run on the complete geometry.

After reducing the mesh size to 3.24 mm, a further reduction in mesh size led to a significant increase in simulation time. Therefore a quarter section of geometry was created and setup to be able to run finer meshes.

The initial mesh size for this geometry was 3 mm. After which the mesh was reduced by 10% for the next iteration, up to 1.18 mm.

The threshold for grid dependency test was a change in temperature within 5%.

The value obtained for the wall temperature from the simulation is 653.3 K and the value obtained from analytical calculations is 658.87 K which is a difference of 0.8%.

Y+

The Y+ results were calculated for all the simulations.

The maximum Y+ at 0.5s for the mesh size of 1.18 mm is around 8. This is between the buffer layer and unsuitable for the turbulence model used.

The Y+ value for the base grid size of 4mm at 0.5s is 20 which is again in the log-law region.

It is to be noted that the temperature and velocity values obtained for these set of simulations are prone to error, and whose verification is beyond the scope of this study,

The series of simulations were carried out to study and get a feel for capabilities of Converge as a tool. Part of this study was to run a grid dependency test, while another was to understand the effect of changing time interval values of Supercycling. These have been achieved.

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