Conjugate Heat Transfer Simulation

Problem Statement:

Setting up a simulation in converge to model conjugate heat transfer.

• Adding Y+ to the post.in files.
• Verifying the grid independence of the case set up by running the simulation on three different mesh sizes.
• Observe and document the effect of supercycle on the total simulation time.

Setting up a simulation in converge to model conjugate heat transfer:

Geometry Setup:

The geometry is developed in converge studio and regions necessary for the conjugate heat transfer are created. After this surface preparation takes place and we eliminate the intersection and open edge errors. However manifold edges still remain in the geometry. The probable reason for this is the presence of edges at the interface of fluid and solid regions which share more than two triangles. Once the geometry is prepared we go our boundary flagging where boundaries are assigned to various geometric locations such that we can define the desired boundary conditions.

Boundary Conditions:

• Inlet: Pressure-Zero Normal gradient; Velocity at the inlet is 10.5 m/s in the Z direction.
• Outlet: Pressure at outlet 101325 Pa; Velocity Zero Normal gradient.
• Solid Cross-section: Wall boundary with slip condition.
• Solid outer wall: Wall boundary with slip condition. Along with this, we have a heat influx of -10000 W/m^2.

Interface: The interface boundary in Converge has two variations depending on the directions in which the normals are pointing. The direction in which they are pointing is called forward and the opposite is called reverse. Here the forward interface is in the fluid region and is a wall boundary following Law of the wall condition. The reverse boundary is in the solid region and is a wall boundary with slip boundary condition.

Note: The inlet conditions is defined in such a way that it meets the boundary condition mentioned in the challenge of a Reynolds number of 10000.

Grid Setup:

The initial base grid is 0.004 m in all directions. The base grid of 0.004 m produces an approximate cell count of 6000 cells

Case Setup:

• Here we have chosen a transient solver.
• In the materials tab of the case setup, we choose both solid and gas simulation as we are concerned with the variations in both the solid and fluid regions.
• We also input the participating species to converge using species option of Materials tab. Here the solid is aluminum and fluid is Air. Minimum timestep is 1e-07 s and the maximum is 1s.
• Default CFL values are used in this case setup.
• The turbulence model is RnG K-epsilon.

Results:

Velocity Profile:

Temperature Profile:

Vector Plot:

Regions diversification: Here 1 represents the solid region whereas 0 represents the fluid region.

Adding Y+ to the post.in files:

The Non-dimensionalization of distance Y and velocity U results in two non-dimensional quantities Y+ and U+.Here Y+ = [ρy(Uτ)]/μ and U+ = [(Τwall)/ρ]^0.5.The Y+ values give us an insight into the effectiveness of our model to capture Turbulence. The turbulence boundary layer as we know can be classified into two categories outer layer and inner layer. In the inner layer, the law of the wall is followed whereas in the outer layer it is not. The inner layer is further classified into three layers namely log layer buffer layer and viscous layer. Now Y+ gives us an estimate of the location of the first cell's cell centre. If Y+ is in between 30 to 300 then the cell centre is in log layer if it is less than 11 than it is in viscous sublayer and the cell centre will be in buffer layer if the Y+ range is 11 to 30. This information regarding the position of first cell centre is essential as it dictates the type wall treatment we must use. If we are selecting a standard wall treatment then we can maintain our cell centre in the log layer and can capture the turbulence satisfactorily to a given extent. However, if we want to capture turbulence and its effect much more accurately we move to enhanced wall treatment and maintain our cell centre in the viscous sublayer.

Note: The Y+ ranges mentioned above are for typical K-epsilon turbulence model.

The model which we have used is K-epsilon and wall treatment is standard wall treatment, therefore, the efficacy of our setup requires Y+ range of 30 to 300.

The Y+ value in our case:

Y+ value plot:

As we have been using standard wall functions the ideal range of Y+ values we require is between 30 - 300. From the plot and profile, we can see that the Y+ value lies in the ideal range for the most part of the pipe. The anomaly is near the inlet where the Y+ values are in the range of 17 to 30 which fall in the buffer layer of the turbulence boundary.

Observe and document the effect of the super cycling: