Conjugate Heat Transfer Simulation

Objective 

This project aims to develop an understanding of super-cycle using a conjugate heat transfer simulation model. moreover, it will expand our knowledge on the grid dependency test and y+ method of checking the grid for wall functions.

Simulation setup

A pipe of diameter 0.03 m and a length of 0.2 m with a shell thickness of 0.01 m  is constructed for this problem and solid and gas species are taken as aluminum and air. the simulation is run till 0.5 s. 

For the value of the Reynolds number to be 7000, the inlet velocity is 3.71 calculated using the equation shown below:

                                       Re = (rho*V*D)/(Dynamic viscosity)

Slice of geometry with mesh.

Discussion on Y+

y+ is a non-dimensional number that gives us information about our grid size, whether it is coarse or fine. if the value of y+ is greater than 30 law of wall function is used to account for the turbulent boundary layer. 

in our case, the maximum value of y+ is 14 so it is not necessary to use the wall function. The contour for y+ is shown below:

Grid Dependency Test

This test is to determine the optimal grid size for which we spend less time on simulation and accuracy is not compromised. 

in this test, we reduce the base grid size until the difference between the consecutive mesh is negligible. this is when the solution becomes grid-independent and now reducing the grid size will not give a great difference in accuracy. 

In this case, the values of the base grid used are 0.006, 0.004, 0.003 and 0.002 the plot of temperature change with grid size is shown below:

As we can see from the graph that the difference reduces but not converges so we can say up till this mesh size the solution is grid-dependent. We can go on decreasing the grid size to get convergence. 

Understanding Supercycle

This section will focus on answering, what is super-cycle?

supercycle is basically a solution to the problem occurred due to difference in solving time of solid and fluid. In fluids, the steady-state is achieved much early as compared to solids. this is because in fluids heat transfer is fast and solved quickly. thus both solvers cant run at the same speed.

The concept of super-cycling is that the solver for the fluid domain is paused until the solver for the solid domain converges. This pausing is done in intervals that can be set by the user.

In this project, Super-Cycling is solved three times at different times intervals 0.01,0.02 and 0.03 to see the difference of total simulation time.

intervals - total simulation time

0.03       - 122.273 s 

0.02       - 126.521 s

0.01       - 121.590 s

The above graph shows the three-time intervals for temperature vs time for the solid region. As the time step decreases the value converges much earlier as compared to larger super-cycling time steps.

Outcome  

To solve conjugate Heat transfer the important Parameters learned is:

• The boundary conditions with interface boundary and how to set a heat flux. 
• Importance of y+ to determine the wall functions. 
• The technique of grid-independence to increase efficiency with accuracy.
• Concept of super-cycling and how it is used to solve the problem of different solving speeds of solid and fluid domains.