Convergence problems unsteady conjugate heat flow problem when refining mesh

Sven_netherlands · December 2, 2020, 04:32

Hello,
I'am trying to solve an incompressible unsteady conjugate heat flow problem for an uniformly heated cylinder in a laminar flow of water using Comsol. The cylinder is located at the centerline and the inlet boundary is located at

and outlet boundary at

. The height of the domain is equal to

.

All differential equations are dimensionless and are dependent on the Reynolds, Prandtl and Richardson numbers. In this case these numbers are equal to 20, 7 and 1 respectively.
Note that the equations are nondimensionlized by setting $\rho$ and $\mu$ equal to 1 and $\frac{1}{Re}$ respectively for the laminar flow module. Furthermore, bouyancy is added by using the boussinesq approximation and is included in the y term of the volume force as $Ri \Theta$ for which, $\Theta = (T - T_0)/(T_w - T_0)$ is the dimensionless temperature.

For the heat transfer module

is set to 1 and

to $\frac{1}{Pr Re}$

The boundary conditions are:

Inlet
Uniform inlet velocity of 1
And inflow temperature of

Upper and lower boundary
Slip boundary conditions and heat conduction normal to the wall set to 0

Cylinder

No slip condition

Temperature of the wall

Outlet conditions

Zero pressure outlet condition

Conduction normal to the wall set to 0

Mesh

The mesh is mapped with quads elements and are non uniformly distributed. The statistics are shown below:

Number of elements 133200

Minimum skewness 0.4995, average 0.9889

Minimum volume versus circumradius 0.2049, average 0.774

Minimum condition number 0.2692, average 0.7876

Minimum growth rate 0.9628, average 0.9849

Boundary minimum element size 0.0134

Solver

I'am using a seggregated solver

Convergence

Up to around 100000 elements the convergence is good but for finer meshes the error of the segregated solvers shows a fluctuating error after a time of around 40 seconds. The residuals also increase significantly in this period of time. These plots can be found in the attachment. Furthermore, after the error appears ''May have reached a singularity.
Time: 40.593993119146752 s.Last time step is not converged.'' A plot containing undefined values of the variable comp1.T appears and is also included in the attachment. Just before the simulation quits the timestep also decreases significantly. The reciprocal of the time step plot is included in the attachment.

Can anybody help me with this problem. The effort is greatly appreciated.

Best regards,

Sven Beekers
Master student University of Technology Eindhoven

residuals.png

undefined values.png

seggregated solver error.jpg

reciprocal time step.jpg

December 2, 2020, 04:32	Convergence problems unsteady conjugate heat flow problem when refining mesh	#1
Sven_netherlands New Member Join Date: Dec 2020 Posts: 1 Rep Power: 0	Hello, I'am trying to solve an incompressible unsteady conjugate heat flow problem for an uniformly heated cylinder in a laminar flow of water using Comsol. The cylinder is located at the centerline and the inlet boundary is located at and outlet boundary at . The height of the domain is equal to . All differential equations are dimensionless and are dependent on the Reynolds, Prandtl and Richardson numbers. In this case these numbers are equal to 20, 7 and 1 respectively. Note that the equations are nondimensionlized by setting $\rho$ and $\mu$ equal to 1 and $\frac{1}{Re}$ respectively for the laminar flow module. Furthermore, bouyancy is added by using the boussinesq approximation and is included in the y term of the volume force as $Ri \Theta$ for which, $\Theta = (T - T_0)/(T_w - T_0)$ is the dimensionless temperature. For the heat transfer module is set to 1 and to $\frac{1}{Pr Re}$ The boundary conditions are: Inlet Uniform inlet velocity of 1 And inflow temperature of Upper and lower boundary Slip boundary conditions and heat conduction normal to the wall set to 0 Cylinder No slip condition Temperature of the wall Outlet conditions Zero pressure outlet condition Conduction normal to the wall set to 0 Mesh The mesh is mapped with quads elements and are non uniformly distributed. The statistics are shown below: Number of elements 133200 Minimum skewness 0.4995, average 0.9889 Minimum volume versus circumradius 0.2049, average 0.774 Minimum condition number 0.2692, average 0.7876 Minimum growth rate 0.9628, average 0.9849 Boundary minimum element size 0.0134 Solver I'am using a seggregated solver Convergence Up to around 100000 elements the convergence is good but for finer meshes the error of the segregated solvers shows a fluctuating error after a time of around 40 seconds. The residuals also increase significantly in this period of time. These plots can be found in the attachment. Furthermore, after the error appears ''May have reached a singularity. Time: 40.593993119146752 s.Last time step is not converged.'' A plot containing undefined values of the variable comp1.T appears and is also included in the attachment. Just before the simulation quits the timestep also decreases significantly. The reciprocal of the time step plot is included in the attachment. Can anybody help me with this problem. The effort is greatly appreciated. Best regards, Sven Beekers Master student University of Technology Eindhoven residuals.png undefined values.png seggregated solver error.jpg reciprocal time step.jpg

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