Week 6: Conjugate Heat Transfer Simulation

Introduction:

Conjugate Heat Transfer (CHT) is used to refer as a process which involves a heat transfer occurs within and between the solid and fluid region. Conjugate heat transfer corresponds with a combination of heat transfer in fluid and solid. In solids, conduction often dominates whereas, in liquids, the convection often dominates.

Heat transfer in Solids:

In most cases, heat transfer in solids only due to the conduction. CONVERGE uses 3D Solid heat conduction equation to solve the heat transfer within solids.

`c_p*rho*(delT)/(delt) = grad.(kgradT)+S_h`

`c_p` - Specific heat

`rho` - Density

`S_h` - Volumetric heat source

Heat transfer in Fluids:

In fluids, the convection often dominates. CONVERGE uses the Navier Stokes equation to solve the heat transfer in the fluid region. The energy equation takes care of the fluid heat transfer.

Application of CHT:

• Heat transfer from the engine block to the coolant.
• Engine block heating due to combustion.
• Forced convection cooling of engine blocks.
• Heat exchangers.

Super-cycling process:

Super-cycling is a useful process for conducting CHT analysis. The time duration for heat to transfer the entire solid region usually takes much longer time than heat transfer in a fluid. Because in fluids, heat will be carried by fluid molecules whereas, in solids, molecules are immovable. Hence the time duration for conducting CHT analysis will take a longer time due to slow heat transfer in solids. In this kind of situation, super-cycling will be way more useful. In the super-cycling process, the solid part is simulated by the steady-state process whereas in the fluid region is solved by the transient solver.

Steps involved in Super-cycling Process:

1. Solves the fluid and solid together with the transient solver. Stores the instantaneous Heat Transfer Coefficient's and Temperatures on the interface during this process.
2. Freezes the fluid solver. Time averages of the HTC's and Temperatures will be applied as a Boundary condition at the Interface.
3. Solves the solid temperature until it reaches steady-state.
4. Updates the solid temperature field and unfreezes the fluid solver
5. Repeat until the solid temperature converges.

Objective:

To conduct the Conjugate Heat Transfer analysis on the flow over a circular cross-section pipe with a constant heat flux on the outer surface of the pipe using CONVERGE software.

Problem Definition:

In this challenge, the air is sent through the circular cross-sectional pipe which is made of Aluminum material with a constant heat flux of 10000 W/m^2 applied on the outer surface of the solid pipe. The good solution should have grid independence. The grid independence test was conducted with different grid sizes of 4 mm, 3 mm and 2 mm. The efficiency of the super-cycling process was measured in the form of total simulation time. It was measured by conducting simulations with different values of Time length of each stage value (0.05 s, 0.03 s, 0.02 s, 0.01 s).

The geometry of the setup

The dimension of the circular cross-sectional pipe:

The outer diameter of the pipe = 40 mm

The inner diameter of the pipe = 30 mm

Length of the cylinder = 200 mm

Mesh Details:

Three sizes of grid size were used to conduct the grid independence test.

Grid size = 4mm

Grid size = 3mm

Grid size = 2mm

Boundary Condition:

1) Inlet: INFLOW (Air Inlet)

Velocity Boundary condition: `u_z` = 3.52 m/s

[ Inlet velocity calculation: Reynolds number of the flow = 7000

`Re=(rho*v*D)/mu`

Density of the Air = 1.225 `(Kg)/(m^3)`

Dynamic viscosity of the Air = `1.81*10^-5 (Kg)/(m*s)`

`7000 = (1.225*v*0.03)/(1.81*10^-5)`

v = 3.52 m/s]

Pressure Boundary condition: Zero Normal gradient (NE)

2) Outlet: OUTFLOW

Velocity Boundary condition: Zero Normal gradient (NE)

Pressure Boundary condition: 101325 Pa (DI)

3) Solid side: WALL

Wall motion type: Stationary

Surface Movement: Fixed

Temperature Boundary Condition: Zero normal Gradient (NE)

4) Outer Solid Wall: WALL

Wall motion type: Stationary

Surface Movement: Fixed

Temperature Boundary Condition: Heat Flux = - 10000 `W/(m^2)` ( -ve sign indicates heat flux passing inside the domain)

5) Interface: INTERFACE

INTERFACE boundary separates the two different types of material or phase. In this setup, the air region is separated from the aluminium pipe region by using INTERFACE Boundary condition.

Interface BC

Forward Boundary: The boundary facing the direction of the normal vector. In our case, the forward boundary is facing towards the fluid region.

Velocity Boundary condition: Law of Wall treatment

Pressure boundary condition: Law of wall treatment

Reverse Boundary: The boundary facing the opposite direction of the normal vector. In our case, the reverse boundary is facing towards the solid region.

Velocity Boundary condition: Slip

Pressure boundary condition: Specified Value (DI)

Regions and Initialization:

A Stream is a collection of connected regions of the same phase.

Fluid Region: Stream Id= 0

O2 = 23%

N2 = 77%

Solid Region: Stream Id= 1

Aluminium = 100%

Solver Parameters:

1) Solver: Transient

Simulation mode: Full hydrodynamic

2) Turbulence Model: Reynolds Averaged Navier Stokes (RANS)

RNG K−ε

3) Simulation Time Parameters:

Start time = 0 s

End time = 0.5 s

Initial time step = 1e-7 s

Minimum time step = 1e-7 s

Maximum time step = 1 s

Procedure:

1) The above condition has been given to Converge Studio to create input data files.

2) 12 input data files are accessed by using the Cygwin terminal.

3) The simulation has been performed by using Converge-3.0 executable. To decrease the simulation time, 2 cores are used with the help of MSMPI.

4) The output files are converted into Paraview VTK in-line binary format by using Converge Studio Post Processing 3D to see the results in Paraview.

Results:

1) Grid Independence test:

Inference:

• Grid independence test was conducted with three different grid sizes of 2 mm, 3 mm, and 4 mm. The real objective of this test is to check the output result for different sizes of the mesh size. While changing the mesh size, the output should not vary more than an acceptable level of tolerance.
• From the above plot, It was clear that the outlet fluid temperatures did not vary so much. Hence, the minimum grid size can be selected as a mesh for an accurate solution.
• Outlet Fluid Temperature `T_(4 mm)` = 432.009 K `T_(3mm)` = 417.021 K `T_(2mm)` = 432.809 K

2) Y+ value:

Y+ value for a grid size of 4 mm

Y+ value for a grid size of 3 mm

Y+ value for a grid size of 2mm

Inference:

• Value of Y+ determines the choice of near-wall treatment. Y+ is the size of the grid cell nearest to the wall. `Y+= (y*u_tau)/nu`

Wall functions are the empirical functions that are fitted to the observed behaviour close to the wall. based on the Y+ value, the type of wall functions will be decided.

Types of layers:

• Viscous sub-layer `=>` Y+ < 5
• Buffer layer `=>` 5 < Y+ < 30
• Logarithmic layer `=>` 30 < Y+ < 200

If Y+ value lies in Viscous sub-layer, then the wall function will be Y+ = U+ which means the curve is linear.

If Y+ value lies in Logerthemic layer, then the wall function will follow the logarithmic function which is U+ = (1/K) log(E*Y+).

3) Effect of Super-Cycling process:

Mean Solid Temperature Vs Time Plot for different time interval:

Inference:

• All the above cases run the transient solver for the first 0.05 s for both solid and fluid region. Then the instantaneous HTC,s And Temperature value stored at the end of the beginning transient simulation.
• At the end of each time interval, the fluid solver is frozen. From the time-averaged Temperature data at the solid region, the steady-state solver solves the solid temperature until it reaches steady-state. The jumps in the above plots represent the update of the solid temperatures.
• After updating the solid temperature, fluid solver starts the transient simulation.
• 0.01 s time interval setup converges quicker than other time intervals.

Mean Fluid Temperature Vs Time Plot for different time interval:

Outlet Fluid Temperature Vs Time Plot for different time interval:

Inference:

• From the above plot, It was clear that the fluid temperatures converge quicker in 0.01 s time interval setup.
• Hence, the fluid temperature convergers quicker when we decrease the time interval.

Super-Cycling Interval (sec)	Total Simulation running time (sec)
0.01	900.4536
0.02	901.2008
0.03	922.87
0.05	923.1652

Inference:

• As the super-cycling stage interval decreases, The total simulation running time decreases.

4) Flow animation:

Inference:

• The above flow animation was obtained from 2 mm grid size setup. It represents the velocity contour at every time step.

5) Temperature contour animation:

Inference:

• The above temperature contour animation represents the flow and solid temperature contour at each time step.
• The maximum solid temperature is 772 K.

Conclusion:

• As the super-cycling stage interval decreases, The total simulation running time decreases.
• Hence, the super-cycling process for Conjugate heat transfer analysis reduces the total simulation time significantly.