Week 6: Conjugate Heat Transfer Simulation
Objective: Setup a 'Conjugate Heat Transfer' flow simulation through a pipe for given inlet boundary conditions.
To study the effect of change in the supercycle stage interval and record the observations for simulation time against the baseline configuration.
Run dependence test on different mesh grid values and show that the outlet temperature converges to a particular value.
Conjugate Heat Transfer Problem:
Conjugate heat transfer is a heat transfer which is a combination of heat transfer in solids and heat transfer in liquids. The heat transfer mode in solids is conduction while in fluids the mode is convection.
Heat transfer in solid:
The conduction mode of heat transfer in solids can be generally described by Fourier's law, which is given by
For a time-dependent transient heat transfer problem, the mathematical expression is given by
Heat transfer in a fluid:
The transport of fluid implies energy transport too, which appears in the heat equation as the convective contribution. Depending on the thermal properties on the fluid and on the flow regime, either the convective or the conductive heat transfer can dominate.
The transport of energy due to fluid flow appears in the heat equation as convection heat transfer. Dependening on the thermal properties of fluid, the heat transfer can be either convection or conduction. In addition to that, the viscosity of the fluid also contributes to the fluid getting heated. The contribution is cannot be neglected during fast flow in viscous fluids. The pressure work term also comes into picture if the fluid density is temperature dependent.
The following equation represents a transient heat equation for the temperature field in a fluid:
Solid-Fluid Interface:
The temperature field and the heat flux are continuous at the fluid/solid interface. But, the temperature field variation can be very rapid in fluid motion,with the fluid temperature being close to the solid temperature when the fluid is close to a solid, and far from the interface, the fluid temperature is close to the inlet or ambient fluid temperature.
The distance where the fluid temperature varies from the solid temperature to the fluid bulk temperature is called the thermal boundary layer.
Case Setup and Boundary Conditions:
General flow simualtion (Time-based)
Gas Simulation Fluid : Air
Solid Simulation Material: Aluminium
Species:Air- O2+N2, Solid- Aluminium
Simulation Parameters:
End Time: 0.05 s
Initial time-step: 1e-07 s
Minimum time step: 1e-07 s
Maximum time step: 1 s
Solver: Density based
Boundary conditions:
Inlet: Pressure- Zero Normal Gradient
Velocity at inlet calculations- In Positive Z direction
Temperature boundary condition: 300 K
Species: Air
Outlet:
Pressure : 101325 Pa
Velocity : Zero Normal Gradient
Temperature backflow: 300 K
Species: Air
Solid Outer Wall:
Velocity : Slip condition
Wall motion type: Stationary
Temperature: Heat flux -10,000 W/sqm
Thickness:
Velocity : Slip condition
Wall motion type: Stationary
Temperature: Zero normal gradient
Inner Wall:
Forward side ----->
Region- Fluid
Velocity: Law of wall
Temperature: Law of wall
Reverse side ----->
Region- Solid
Velocity: Slip
Temperature: Specified value (DI)
Regions:
Region 0 - Fluid (Air)
Velocity- 3.71 m/s
Temperature- 300 K
Pressure- 101325 Pa
Region 1 - Material (Aluminium)
Temperature- 300 K
Turbulence modelling - K-Epsilon
Super-cycle modeling:
Solids take more time than liquids to heat up. The difference in the time intervals is basically due to different equations governing heat transfer in both solids and liquids.
The solid outer wall gets heated as it is subjected to Heat flux of -10,000 W/sqm. The time required to increase the temperature of the solid wall is higher.
The super-cycle modeling feature allows to solve the the equations involving both solid and fluid interactions to solve faster.
Grid Dependency Test: For the grid dependency test the supercycling time of 0.05 s is kept constant.
The grid dependency is checked for three different base grid sizes of 0.006 m, 0.004 m,0.002 m
Grid Size: dx=0.004 m,dy=0.004 m,dz=0.004 m
Base Mesh Grid
Temperature Contour
Velocity contour
Pressure contour
Solid temperature variation plot
Fluid temperature variation plot
Y+ contour
Turbulent flows have a smaller laminar region near the wall and in order to resolve the gradients at such a small region, a very small grid size is required.The y+ value is a non-dimensional term that can be used to understand how coarse or fine the grid is.
Grid Size: dx=0.003 m,dy=0.003 m,dz=0.003 m
Base mesh grid
Temperature Contour
Velocity contour
Pressure contour
Solid temperature variation plot
Fluid temperature variation plot
Y+ plot
Grid Size: dx=0.002 m,dy=0.002 m,dz=0.002 m
Base mesh grid
Temperature Contour
Velocity contour
Pressure contour
Solid temperature variation plot
Fluid temperature variation plot
Y+ contour
Effect of Supercycle stage interval variation:
The base grid mesh size of 0.004 m is selected to observe the variation.
Temperature variation:
Simulation time variation :
Supercycling stage time interval 0.01 K : 404.5 s
Supercycling stage time interval 0.02 K : 374.42 s
Supercycling stage time interval 0.03 K : 386.78 s
The simulation time increases as the super-cycle stage time interval decreases.
Conclusion:
- The Y+ plus values increase with increase with coarser mesh sizes.
- Increase in super-cycle stage interval time length results in a fast converging rate as seen from the temperature plots for both solid outer wall and inner fluid.
- In the grid-dependency test, it can be seen that the temperature values are dependent on the size of base grid mesh. The temperatures are higher in case of coarser mesh size as against to the finer mesh sizes.Hence, dependency can be negligible only when a more number of trials are conducted with different mesh size and then arriving at a certain mesh size where less variation in results is obtained.