Conjugate Heat Transfer Simulation

Conjugate Heat Transfer(CHT) simulation using Super-Cycling in converge CFD and post processing in paraview

Aim:- the aim is to focus on analysing a conjugate heat transfer simulation through a pipe model which is made of aluminium any the flowing fluid is air, and checking for the grid dependency test whith 3 different grid size of 0.004m, 0.003m, 0.002m and also taking a look at the super cycling of the model at different stage interval of 0.01, 0.02, 0.03.

The body is modelled in converge itself, using the cylinder command with the outer dia as 0.02 and inner diameter as 0.015 below is the pictorial depiction of the body

Diagnosis

The body was diagnosed for few parameters like intersections, non-manifold problem, Open edges, Overlapping triangles, Normal orientation and isolated triangles , from all of the above there is a problem in non-manifold edges because the circular edges are shared by 3 triangles. As the different faces of the body is assigned the boundary condition and the inside face of the pipe which is the interaction between the solid and the fluid region is made as interface boundary , the solver understands that its an CHT problem then the non manifold edges problem is washed out

Case setup

• here a time based setup was used
• aluminium was used as the solid material and air was used as the fluid passing through the pipe.reaction mechanism(mech.dat) was unchecked and species(not in mech.dat) was checked.gas simulation was used with the preconfined values.solid simulation was done using aluminium, global transport parameters were kept as it was, in the species tab for the soild section aluminium was selected and for gas section O2 and N2 was used.
• For run parameters transient simulation was used full hydrodynamic and compressible was used also unchecking steady state monitor and used shared memory.
• Start time was 0.0 sec and end time was 0.5 s, the initial and the minimum time step was 1e-7 rest all other values were kept as it is.
• Boundary conditions were provided for different faces of the geometry as written above.
• In region and initialization 2 regions were selected 1 for each solid and fluid , for solid region stream ID 1 was selected which is a very important step. In the boundary condition the velocity was assigned by using the formula

`Re = (rhovL)/mu`

where `Re`= renold nos = 7000

`rho`= Density used is 1.225 kg/m^3

`mu`= The dynamic viscosity = 1.81 x 10^-5 Pa.s

Length = 0.015

The velocity is obtained as 6.895 m/s

Which is used in the simulations

• RNG k-episolon is used for turbulence modelling , for super cycling the outer points are claculated at a distance of 0.18m along the length axis to know the heat transfer characteristic.
• For Output files , time interval for writing the 3D output files is 0.01s and time interval for writing text output and restart output is taken as 1e-6
• Then all the inputs are validated and then exported to a folder and then processed using the CYGWIN terminal window

Governing equation

The solution for CFD simulation is obtained by solving the Navier-Stokes (NS) equations. The equations comprise of 5 equations, namely the continuity, momentum (3 equations), and energy equations. The continuity and momentum equations are solved for all flow problems with the energy equation are optional and can be used only when heat transfer is taking place to save computation time.

Super-Cycling

Super-cycling is a method used by CONVERGE Studio in the case of conjugate heat transfer problems with a solid and liquid regions.The integral problem here is that 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. This causes problems during the solution given that the solid side solver would not have reached a steady state/convergence in the time the liquid solver does. This is where the concept of super-cycling can be used.The basic idea 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

Significance of y+

Wall functions are useful in telling the solver how to approach the solution near a wall. These are used to predict near wall results accurately even at coarse grids. There are multiple wall functions out there for each turbulence model, but the most basic is the standard wall function. Before going into wall functions, there are 2 terms to understand. The first is boundary layer and the second is y+. To understand boundary layer, let us go into the boundary layer theory. The image attached shows the boundary layer development. We first start at the laminar region, then transition to the turbulent region. Near wall, due to the viscous forces, the velocity is dragged to zero and as the boundary layer develops, the velocity will reach free-stream velocity. This is termed as the no-slip condition.

We can use the no-slip condition if we know the flow is completely laminar. This would mean that we are resolving the flow in the laminar region whatever the grid size. This however, doesn’t hold if the flow is turbulent. Turbulent flows have a smaller laminar region near the wall and if we are to resolve the gradients at such a small region, we’d need a very small grid size.This is where the y+ value comes handy. The y+ value is a non-dimensional term that can be used to understand how coarse or fine our grid is. This can then be used to determine if wall functions need to be used or not. From the image attached above, we need to either be in the viscous sub-layer or the turbulent region.If we were in the viscous sub-layer, that would mean a y+ of less than 10 and if we were in the turbulent region, it would mean a y+ of greater than 30. This is very significant in our making the decision of using or not using a wall function.

Post processing

the files are then post processed using CYGWIN terminal window, and converted to .vtm files which are readable by the paraview . as the no of grid size increases the processing takes a high time to complete.

Analysis at 0.004m mesh size at stage interval of 0.05

Velocity animation at 0.004m grid

temperature animation at 0.004m grid

y+ animation at 0.004m grid

Analysis at 0.003m mesh size at stage interval of 0.05

Velocity animation at 0.003m grid

temperature animation at 0.003m grid

y+ animation at 0.003m grid

Analysis at 0.002m mesh size at stage interval of 0.05

Animation of velocity at 0.002m grid

Animation of temperature at 0.002m grid

Animation of y+ at 0.002m grid

comparision of plots of super cycling at 0.03, 0.02, 0.01 s

Here we see that as the cycle time decreases the graph of the mean temp fro the start takes less time to reach a temp of approx. 600K

Observations of the test conducted

The CHT test which was conducted by a pipe flow of aluminium material and air as the working fluid shows that as the base grid size decreases the number of cells increases, which increases the computing timing. The comparision plot for the mean temperature at 0.004m base grid with super cycling time as 0.03, 0.02 and 0.01 s shows that there is a sharp rize in the in temperature as the cycling time decreases this indicates the super cycling effects. As we check for the 3 y+ datas for 0.004, 0.003, 0.002m grid we get to know that the value of y+ goes on increasing as the grid size decreases