Conjugate Heat Transfer Simulation and Understanding wall function and Y

Objective: To simulate the flow through a solid pipe \"Conjugate Heat Transfer\" and understand super-cycling.

1. Run grid dependence test on 3 grids
2. Show that the outlet temperature converges to a particular value
3. Effect of supercycle stage interval
4. How does the total simulation time compare against the baseline configuration

Given: 1. Inlet Reynolds number= 7000
           2. Velocity calculated at Inlet BC based on Reynold\'s Number

                      Re = (rho*V*D)/(Dynamic viscosity)

           3. Turbulence modeling - RNG K-Epsilon
           4. Supercycle stage interval to 0.01,0.02 and 0.03

Geometry is as:

Inner Dia: 0.03m
Thickness of pipe: 0.01m
Length of pipe: 0.2m

Theory:

                                       CONJUGATE HEAT TRANSFER
The term conjugate heat transfer (CHT) is used to describe processes that involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids.
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. Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers. Forced convection is the most common way to achieve a high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapor phase change).
Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls and because solids are usually immersed in a fluid.

Some of the examples are: 

1. Streamlines and temperature profile around a heat sink cooling by forced convection.
2. Temperature profile induced by natural convection in a glass of cold water in contact with a hot surface.
3. Flow and temperature field in a shell and tube heat exchanger illustrating heat transfer between two fluids separated by the thin metallic wall.

Case Setup:

Before going to case setup, geometry cleanup and boundary flagging should be done properly. All surface errors need to be removed, the only error Nonmanifold problem will there and that will be automatically clear once we setup conjugate Heat transfer case

`**`We are going to perform Conjugate Heat transfer simulation with General Flow Application.
`**`In materials we select Solid simulation as both solid and fluid involved. Air mixture is going to flow through solid pipe Species also selected to tell the converge what are participating species for solid it is Aluminium and for gas, it is O2 and N2.
For the solid part, \'ALUMINIUM\' is selected from Predefined solids.

`**` Run Parameter:
Solver- Transient
Simulation mode- Full-hydrodynamic
Gas flow solver- Compressible
`**`Simulation time Parameter:
Start time- 0
End time- 0.5 sec
Initial timestep- 1e-7 sec
Minimum timestep- 1e-7 sec
Maximum timestep- 1 sec

`**`Initial condition and Events:

Since we are dealing with two different materials we have to specify the regions as:

For fluid part-

For solid part-

`**`Boundary:
Boundaries are assigned as below based on the participating domain.

Solid Outer wall: 
Region Name- Solid Region
Boundary type- Wall
Velocity B.C.:
Wall motion type- Stationary
Select \"Slip\", since it is made up of solid there is no boundary for fluid so setting up the Law of wall for a solid part will not make a sense. The law of wall is basically a boundary condition for fluid. 
Temperature B.C.:
Select \"Heat Flux\", since we are dealing with conjugate heat transfer problem where the external surface of the pipe is heating with constant heat flux.
Flux- 10000.0 w/m2 (-ve sign indicates heat is flowing into the system)

Solid side wall: (Adiabatic wall) 
Region Name- Solid Region
Boundary type- Wall
Velocity B.C.:
Wall motion type- Stationary
Select \"Slip\".
Temperature B.C.:
Select \"Zero normal gradients (NE)\" because the wall is adiabatic which means no heat transfer takes place through this boundary.

Inlet:
Region Name- Fluid Region
Boundary type- INFLOW
Pressure B.C.:
Select \"Zero normal gradients (NE)\"
Velocity B.C.:

Where Velocity will be calculated as

Temperature B.C.:
Specified Value (DI)- 300K
Species B.C.: AIR

Outlet:
Region Name- Fluid Region
Boundary type- Outflow
Pressure B.C.:
Specified Value (DI)- 101325 Pa
Velocity B.C.:
Select \"Zero normal gradients (NE)\".
Temperature B.C.:
Specified Value (DI)- 300K

Interface:
Boundary type- INTERFACE
Velocity B.C.:
Wall motion type- Stationary

Here, as we know this boundary is the interface between solid and fluid regions, Two different boundaries we need to set. The boundary which is in the direction of normal of interface boundary called \'FORWARD Boundary\' and the boundary opposite of normal of interface boundary called \'REVERSE Boundary\'.

`**`Turbulence Modelling: RNG k-epsilon

`**`Super cycling Modelling:

Super-Cycling:
The time-scale necessary to resolve solid heat transfer is usually much greater than that for fluid heat transfer. It takes many engine cycles for the solid temperature to reach a steady-state. Super-cycling in CONVERGE is an acceleration method that solves time-dependent CHT problems to a steady-state in a solid with fewer engine cycles. Super cycling iterates between fully-coupled transient and steady-state solvers

`**`Base grid:
We will be working out on 0.001, 0.002 & 0.003 base grids along all directions.

`**`Output/ Post-processing:

Y+ data selection will be made as
Post variable selection `->`Combustion/Turbulence `->` Y+

The y+ value is a non-dimensional term that can be used to understand how coarse or fine our grid is. This can then be used to determine if wall functions need to be used or not.

Post-Processing Results:

1. Mesh Comparision:

The baseline is considered as 0.004m

Time used to complete simulation by the program is as:

Mesh size: 0.004m

Mesh size: 0.001m

Mesh size: 0.002m

Mesh size: 0.003m

From the above details, we can say that due to the increase in the number of cells, the time required to solve transport equations, updating boundary conditions, writing output files etc. increases.

2. Temperature convergence:

Outlet Fluid Temperature(K) Vs Time(sec)

Solid Temperature(K) Vs Time(sec)

Here, we have performed a grid dependence test with 0.001m, 0.002m & 0.003m. From the above plots, we can clearly say that as we make mesh size finner, the accuracy in the results increases but at the same time computation time required to solve all governing and transport equations rises drastically.
Summery is as below:

As summarised above 0.001 mesh size is sufficient to get correct results. The values for both 0.002m and 0.001m grid size are somewhat closer to each other so, making grid size more finner than 0.001m will give you more accurate results but that will require more computational power.

3. Effect of supercycle stage interval:

We set supercycle stage interval i.e. time length for each cycle stage from Supercycle modeling to 0.01, 0.02 & 0.03. Here, CONVERGE continues to solve both the fluid and solid equations and stores heat transfer coefficients and near-wall fluid cell temperatures for a time equal to the supercycle_stage_interval.

As we know CONVERGE solves the fluid and solid equations together using the transient solver (but does not store the solid heat transfer data) from the start of the simulation until the supercycle_start_time in order to develop the fluid flow field. At supercycle_start_time, CONVERGE begins storing values for a heat transfer coefficient (HTC) and near-wall temperature for each cell at the solid/fluid interface, one value for each time-step.
From the plot, it is clear that setting up the supercycle stage interval to lower value convergence to the exact value in solid temperature will be faster. and also Convergence we achieved is irrespective of supercycle stage interval values.

Since we are interested in the effect of the supercycle stage interval we increase value from 0.01 to 0.03. Moreover, we achieved convergence to a particular value but storing supercycle data delayed as we increase interval values shown in the above plots.

4. Total simulation time compares against the baseline configuration:

Total simulation time is taken by each interval stages is as below:

No major difference we got in simulation time since we consider here mesh size is 0.003m for all supercycle stage interval. Simulation time only affected if we interfere with a grid size of the geometry.

Y+ Data:

Near-wall regions have larger gradients in the solution variables, and momentum and other scalar transports occur most vigorously. The wall y+ is a non-dimensional distance similar to local Reynolds number, often used in CFD to describe how coarse or fine a mesh is for a particular flow. It is the ratio between the turbulent and laminar influences in a cell.

Accurate presentation of the flow in the near-wall region determines the successful prediction of wall-bounded turbulent flows. Values of y+ close to the lower bound (y+≈30) are most
desirable for wall functions whereas y+≈1 are most desirable for near-wall modeling.

However, we have a problem when the y+ lies in the range between 10 and 30. Here, it is not easy to predict the solution in the transition region. The best practice here is to go finer to the laminar region and just use the no-slip condition or another idea would be to use a coarser grid and go for a wall function instead.

In our case, the following are results we got for Y+ data during performing grid dependence test is as:

The maximum value for Y+ for grid size 0.001, 0.002 & 0.003 are 6.4, 8.2 & 12 respectively. Hence, the values for Y+ for all grid sizes are less than 10 except for grid size 0.003, there is no need to use wall function for grid size 0.001 and 0.002.