Conjugate Heat Transfer Simulation in Converge Studio
Objectives:
- Simulate flow of air through a solid pipe and study the heat transfer from the walls of the pipe to the fluid flowing inside the pipe.
- Run a grid dependence test to see the effect of changing grid size on the heat transfer.
- Study the effect of Supercycle stage interval and compare the simulation time in each case against the baseline configuration.
- Plot Y+ values for simulation in each case.
Introduction:
Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas, in fluids, convection usually dominates. Conjugate heat transfer is observed in many situations. For example, heat sinks are optimized to combine heat transfer by conduction in the heat sink with the convection in the surrounding fluid.
Super-cycling was used to perform the conjugate heat transfer simulation. The timescale associated with heat transfer in solids and fluids is different due to different specific heat and capacitance values. Solids have a higher value and as a result, takes more time to heat compared to fluids. So, if the simulation is carried out at the same time-step as that of fluid flow, the solid region temperature will change very slowly. Hence, super-cycling is used which performs a steady-state simulation of the solid region in periodic intervals.
Geometry:
- Length of Pipe = 0.2 m
- Inner Diameter = 0.03 m
- Outer Diameter = 0.04 m
- Material = Aluminum
Mesh Sizes:
Grid dependent analysis was carried out. The mesh sizes considered for analysis were-
- 0.002 m
- 0.003 m
- 0.004 m
Boundary Conditions:
(1) Inlet -
- INFLOW type boundary was selected.
- Neumann boundary condition for pressure.
- Dirichlet boundary condition for velocity. The value for velocity was calculated using Reynold's number formula.
- `Re=(rho*V*D)/mu`
- Reynold's number = 7000 as per the problem statement
- Density = 1.225 `kg*m^-3`
- Viscosity = 1.81e-5 `kg*(m*s)^-1`
- Hence, the Velocity = 3.45 `m*s^-1`
(2) Outlet -
- OUTFLOW type boundary was selected.
- Neumann boundary condition for velocity.
- Dirichlet boundary condition for pressure. Value of static pressure = 101325 Pa
(3) Outer Wall -
- WALL boundary type was selected.
- Stationary wall with Slip boundary condition as it is solid.
- A heat flux of 10000 `W*m^-2` into the system.
(4) Side Walls -
- WALL boundary type was selected.
- Stationary wall with Slip boundary condition as it is solid.
- Neumann boundary condition for temperature.
(5) Interface -
- INTERFACE type boundary was selected.
- Forward boundary consisted of the fluid region as the normals pointed in that direction. Backward boundary consisted of a solid region.
- Law of wall boundary condition was used for the forward boundary.
- Slip boundary condition was used for the backward boundary.
Initial Conditions:
Two regions, fluid and solid were set up.
Fluid Region -
- Velocity = 3.45 `m*s^-1`
- Temperature = 300 K
- Pressure = 101325 Pa
Solid Region -
- Temperature = 300 K
Supercycle modeling was enabled and a supercycle time-length of 0.05 sec was selected for the grid dependent test.
The simulation is run for a total of 0.5 sec. The RNG `k-epsilon` turbulence model is used.
CASE 1:
- Grid size = 0.002 m
Solid and Fluid region -
- Value of 1 is Solid region
- Value of 0 is Fluid region
Temperature Distribution in the pipe after 0.5 sec
Y+ value = 7.9028
Velocity distribution and Glyph plot in the pipe after 0.5 sec
CASE 2:
- Grid size = 0.003 m
Solid and Fluid region -
- Value of 1 is Solid region
- Value of 0 is Fluid region
Temperature Distribution in the pipe after 0.5 sec
Y+ value = 11.5687
Velocity distribution and Glyph plot in the pipe after 0.5 sec
CASE 3:
- Grid size = 0.004 m
Solid and Fluid region -
- Value of 1 is Solid region
- Value of 0 is Fluid region
Temperature Distribution in the pipe after 0.5 sec
Y+ value = 13.215
Velocity distribution and Glyph plot in the pipe after 0.5 sec
RESULTS:
Case 1:
Temperature converges to 743.4 K
Temperature converges to 355.46 K
Case 2:
Temperature converges to 788.62 K
Temperature converges to 346.65 K
Case 3:
Temperature converges to 900.511 K
Temperature converges to 345.84 K
CONCLUSION:
- Y+ value increases as the mesh become coarse.
- A steady-state is reached after roughly 0.3 seconds in each case.
- A large difference in Temperature of the solid region can be seen as mesh size is varied.
- The difference in temperature between the solid and fluid region is increased with an increase in grid size.
Animations:
(1) Conjugate Heat Transfer Simulation in a Pipe (Grid size=0.002 m)
(2) Conjugate Heat Transfer Simulation in a Pipe (Grid size=0.003 m)
(3) Conjugate Heat Transfer Simulation in a Pipe (Grid size=0.004 m)
Effect of Supercycle Stage Interval:
Supercycle time-length values considered-
- 0.01 sec
- 0.02 sec
- 0.03 sec
The base grid of 0.004 m was selected for all three cases.
Simulation time for the three scenarios-
- Simulation time for Supercycle time-length of 0.01 sec = 499.71 sec
- Simulation time for Supercycle time-length of 0.02 sec = 531.10 sec
- Simulation time for Supercycle time-length of 0.03 sec = 524.46 sec
RESULTS:
Temperature converges to 900.77 K
Temperature converges to 345.86 K
Temperature converges to 903.36 K
CONCLUSION:
- For low values of supercycle time-length, the simulation time is less.
- Temperature converges after 0.2 sec for all the three cases.
- The temperature value begins to change the earliest when the time-length is lowest.