Conjugate Heat Transfer Simulation
Objectives:
- Setup the case to simulate flow through a solid pipe using CONVERGE and visualize the conjugate heat transfer between the pipe walls and the fluid flowing inside the pipe using ParaVIEW.
- Perform grid dependency test
- Study the effect of supercycle stage interval on the simulation time
Background:
Conjugate heat transfer (CHT) is the term used when the heat transfer occurs simultaneously within and between solid and fluid regions during their thermal interaction. In solids, the predominant mode of heat transfer is conduction whereas in the fluid, its convection. CHT is applicable whenever fluid interacts with solids. For example, heat transfer from the engine block to the coolant, heat transfer from combustion gasses to the cylinder.
Simulating both the solid and the fluid domain is challenging, given that in the solid region an additional solid heat equation needs to be solved along with all the fluid equations solved in fluid region. This leads to the time scale difference associated with the solid and fluid. CONVERGE offers a time control approach known as Super-Cycling to overcome the time-scale disparity.
First, the CONVERGE solves the solid and fluid equations together using transient solver for a particular time know as supercycle stage interval and stores all the instantaneous heat temperature coefficients(HTCs) and temperatures on the interfaces. After which the fluid solver is freezed and the time averages of the HTCs and temperatures are provided as the boundary conditions at the interface to solve the solid state equation using steady solver. Once the solid temperature reaches the steady state, the solid side temperature is updated and the fluid side solver is unfrozen and the cycle continues till the solid temperature converges.
To summarize super-cycling, the fluid solver is frozen periodically while the heat transfer in the solid is allowed to progress to steady-state. CONVERGE solves the fluid and solid phases in the same simulation without requiring you to stop and restart the simulation; also significantly reducing the computational cost of the CHT simulation.
Geometry:
A solid pipe was constructed using the create option in CONVERGE and the geometry was inspected for any surface errors, after which the boundaries were flagged.
Pipe Specifications:
Length of the pipe = 0.2 m
Outer Diameter = 0.04 m
Inner Diameter = 0.03 m
Material = Aluminium
Initial conditions and Regions:
Fluid Region
Air (N2 + O2)
Stream ID = 0
Temperature = 300K
Pressure = 101325Pa
Solid Region
Material:Aluminium
Stream ID = 1
Temperature = 300K
The above image represenst the different domains in the problem, Red denotes solid region whereas blue denotes fluid region.
Boundary Conditions:
@Inlet
Neuman boundary condition for Pressure
Dirichlet boundary condition for velocity which was obtained from the given Reynolds Number.
`Re = (V.D)/nu`
Where
`Re rarr "Reynolds" " Number"= 7000`
`V rarr "Flow "Velocity`
`D rarr " Inner " Diameter = 0.03 m`
`nu rarr " Kinematic Viscosity" =1.608 xx10^-5 m^2s^-1 " for air at " 300K`
Solving for V
We get, V = 3.752 m/s
Which was provided as the velocity boundary condition along z axis
Dirichlet boundary condition for Temperature : T= 300 K
@Outlet
Dirichlet boundary condition for Pressure: P = 101325 Pa
Neuman boundary condition for Velocity
@Solid Outer Wall - Stationary Wall
Heat Flux = -10000 W/m2 (-ve because heat is flowing into the system)
@Solid side Wall - Slip Wall
Neuman boundary condition for Temperature (Adiabatic Wall)
@Interface
Forward Boundary Region (where the interface normal is pointing towards) -Fluid Region
Law of the wall velocity and temperature boundary condition
Reverse Boundary Region (where the interface normal is pointing away from) -Solid Region
Velocity slip boundary condition
Dirichlet Temperature boundary condition
Simulation Time Parameters:
Start Time: 0 sec
End Time : 0.5 sec
Solver: Transient Solver
Physical Models:
Turbulence Model - RNG K-`epsilon`
Supercycle Model
Geometry Mesh:
Mesh size of 4mm was provided in X, Y, Z directions as shown below.
Results:
1.Temperature variation in the pipe for baseline configuration
The effect of the external heat flux on the solid wall and the flowing fluid can be visualized from the below animation. Solid wall takes few seconds to heat up, after which it transfers heat to the fluid in contact, raising their temperature. The mean temperature in the solid reaches up to 870K whereas the mean fluid temperature was found to be 342K.
2.Velocity Glyph
The velocity of the fluid can be visualized with the help of the below velocity glyph.
Understandably, the maximum velocity of 5.1 m/s was recorded at the centre of the pipe and relatively lower velocities at the walls.
3. Grid dependency Test
In order to make sure that the solutions obtained are not dependent on the base mesh size, the simulation was repeated for different mesh sizes i.e 3mm and 2mm; and the results are as follows.
A monitor point was placed at 0.0078,0.015665,0.18 m inside the solid pipe to measure the temperature and the results were recorded.
Reduction in the grid sizes has resulted in noticeable changes in the output meaning that the obtained solution is grid dependent. In order to make the solution grid independent, the simulation needs to be repeated with a more finer mesh sizes, which is resource intensive.
4. Effect of supercycle stage interval
The Initial simulation was run with a supercycle stage interval of 0.05s. In order to study the effect of supercycle stage interval on simulation time, the simulation was repeated with different supercycle stage intervals of 0.01,0.02 and 0.03.
A shorter interval leads to faster convergence of the wall temperature.The comparison of total simulation time to baseline configuration is inconclusive and therefore not added.
5. Y+
The maximum Y+ obtained at 0.5s for mesh size 0.004 m was around 14.3, which means that the centre of the first cell layer lies in the buffer layer. Whereas the turbulence model RNG K-`epsilon`is applicable when the y+ is between 30 to 100 where the first cell centre lies in the turbulence region of the boundary layer. Due to this mismatch, the results obtained are prone to error and its verification is beyond the scope of this project.