Week 6: Conjugate Heat Transfer Simulation

Aim:

• To run the grid independence test and identified the obtained temperature
• To study the Super Cycling Stage interval and compare the simulation time for the corresponding results.
• Plot the Y+ results.

Conjugate Heat Transfer:

The term conjugate heat transfer (CHT) is used to describe processes which 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 high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapour 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.

Modes of Heat Transfer:

• Conduction: Diffusion of heat due to temperature gradients. A measure of the amount of conduction for a given gradient is the heat conductivity.
• Convection: When heat is carried away by moving fluid. The flow can either be caused by external influences, forced convection; or by buoyancy forces, natural convection. Convective heat transfer is tightly coupled to the fluid flow solution.
• Radiation: Transfer of energy by electromagnetic waves between surfaces with different temperatures, separated by a medium that is at least partially transparent to the (infrared) radiation. Radiation is especially important at high temperatures, e.g. during combustion processes, but can also have a measurable effect at room temperatures.

What is Y+ and its Importance:

The behaviour of the flow near the wall is a complicated phenomenon and to distinguish the different regions near the wall the concept of wall has been formulated. Thus is a dimensionless quantity, and is distance from the wall measured in terms of viscous lengths.

One of the reasons for the need of is to distinguish different regions near the wall or in the viscous region, however how exactly it helps in turbulence modelling or in general CFD modelling need to be well understood. In this case if we intend to resolve the effects near the wall i.e., in the viscous sub layer then the size of the mesh size should be small and dense enough near the wall so that almost all the effects are captured. But in some cases if the wall effects are negligible then there is option of including semi-empirical formulae to bridge between the viscosity affected region and fully turbulent region and in this case the mesh need not to be dense or small near the wall i.e., coarse mesh would work.

• If y+ is less than 10 then we are in the Vicious Sub layer
• If y+ is greater than 30 then we are in the Turbulent layer region
• If y+ is in between 10 and 30 then we are in the Transition state which is un desirable is still being researched.

What is Super Cycle:

Super-cycling is a method used by CONVERGE Studio in the case of conjugate heat transfer problems with a solid and liquid region. The integral problem here is that both solvers cannot run at the same speed since solving in the fluid domain is much faster owing to the time scale difference for heat transfer in liquids as compared to solids. This causes problems during the solution given that the solid side solver would not have reached a steady state/convergence in the time the liquid solver does. This is where the concept of super-cycling can be used.

Working and Importance:

• The basic idea of super-cycling is that the solver for the fluid domain is paused until the solver for the solid domain converges. This pausing is done in intervals that can be set by the user.
• Super-cycling is only meant to speed up the simulation and if the simulation is run without super-cycling, the convergence of the data will take a long time.

Calculating the Velocity:

Given data

Inner diameter, d=0.03 m

Reynold number, =7000

Density of air =1.161

Dynamic Viscosity

Velocity V =??

Creating Geometry:

• Go to geometry Create then shape and then Cylinder
• The dimensions of the cylinder are
• Inner Diameter=0.03m
• Outer Diameter=0.04 m
• Length in the Z-Direction=0.2 m

Make Some Changes in the geometry in order to obtain our desired geometry which is used for the simulation. Here are the below images where we done some operation by using the tools in the geometry.

Enable the vectors/ normal which are showing outside of the geometry and make sure them transform into the fluid domain.

Now make the naming of the boundaries for the Geometry.

Case setup for Simulation:

• Application Type – Time Based
• Enable the Gas Simulation, Solid Simulation and Species.
• The flow is general flow which contains the air as a Material.
• Go to the Solid Simulation then click on Predefined Solids select the Aluminium click ok.
• Air contains a Species mixture of O2 and N2 which will flow through the required geometry.
• Global Transport Parameters the Prandtl number is 0.9 and the Schmidt number is 0.78.
• Go to the Species and then select the Solid and then click on Query Available list select the aluminium and also Select the gas then add the N2 O2 Click ok.

Simulation Parameters:

• In the Run Parameter: Solver we used is Transient state and the simulation mode = Full hydrodynamic in the mic state we enable the Solver Momentum, Solve Species.
• In Simulation time Parameters we set the values for start time as 0 Seconds and end time 0.5 Seconds and the initial and Minimum time setup for 1e-9 and Maximum time setup =1 Seconds and remaining values are put to default.
• In the Solver Parameters, the Navier stock equation should be Density based solver and remaining should be default.

Initialization and Boundary Conditions:

• In the initialization region change the name of the Region as a Fluid region with the Stream ID=0 and the values assigned for the temperature and pressure is 300k and 101325 Pascal and add the species O2 and N2 with the mole fraction of 0.23 and 0.77.
• Add another region as Solid region make sure that change the Stream ID=1 and check the Solid box and enter the temperature value as 300k and add the species of Solid as Aluminium and Mass fraction Should be 1 click ok

Solid Outer Wall Boundary Conditions:

• The boundary type is Wall
• Wall motion type=Stationary
• UDF=Slip
• In the Temperature Boundary conditions, the UDF should be Heat flux and the value should be -10000 W/m^2.
• Region: Solid

Solid Side Boundary Conditions:

• The boundary type is Wall
• Wall motion type=Stationary
• UDF=Slip
• Temperature Boundary conditions should be Zero Normal Gradient
• Region: Solid

Inlet Boundary Conditions:

• The boundary type is INFLOW
• Pressure Boundary Conditions- Zero Normal Gradient (Neumann Boundary)
• Velocity Boundary Conditions- Dirichlet Condition and the value should be the 3.71 m/sec in the Z direction.
• The temperature should be 300 k and
• Add species 02=0.23 N2=0.77
• Region: Fluid

Outlet Boundary Conditions:

• The boundary type is OUTFLOW
• Pressure Boundary Conditions- Dirichlet Condition and the value should be the 101325 Pascal.
• Velocity Boundary Conditions- Zero Normal Gradient (Neumann Boundary)
• The temperature should be 300 k and
• Add species 02=0.23 N2=0.77

• Region: Fluid

Interface Boundary Conditions:

• Forward side with the Fluid region and Velocity, Temperature Boundary Conditions should be the Law of wall
• Reverse side should be the Sold region and the Velocity Boundary Condition should be the Slip

Physical Models:

• In the physical models enable the Turbulence Modelling and the solver should be selected as RNG K-e and put the remaining values as a default.
• Enable the Super Cycling Modelling
• Begin Storing Super Cycle Data= 0.05 Seconds (these values are changed for the 0.002 mesh with 0.001,0.002,0.003 to study the effect of Super Cycle on the Simulation)
• Solid Side Heat Transfer Solver = Steady State
• Time length of each Cycle Stage =0.05 Seconds
• Total number of Stages=1
• Conduction CFL number=100
• Sensible internal Energy Tolerance=1e-7
• Sensible Internal Energy Relaxation=1.4

Grid Control:

• Element size dx=dy=dz=0.004 m (0.003 and 0.002 to study the grid dependence test)

Output and Post Processing:

• In the Post variable Selection all are default values to this add the Y+ which is im Turbulence/Combustion.
• In the output files we have given time interval to write the 3D output data=0.005 sec, thus the outputs of the simulation files be stored after 0.005 seconds.

Post-Processing:

I have done the post processing of the results for all three cases using the converge studio and paraview. Post processing is actually used in order to get the desired Output by running the simulation

Results:

Case I: Mesh 0.004

Mesh Contour for Mesh 0.004:

Y+ for Mesh 0.004:

Velocity Contour for Mesh 0.004:

Velocity Animation for Mesh 0.004:

Temperature contour for Mesh 0.004:

Temperature Animation for Mesh 0.004:

Temperature for solid region of mesh 0.004:

The mean converged temperaturefor the Solid region is 870 k

Temperature for Fluid region of mesh 0.004:

The mean converged temperaturefor the Fluid region is 345 k

Total cells for the mesh 0.004:

The total cell count in the mesh Size of 0.004 is around 5000 cells

Case II: Mesh 0.003

Mesh Contour for Mesh 0.003:

Y+ for Mesh 0.003:

Velocity Contour for Mesh 0.003:

Velocity Animation for Mesh 0.003:

Temperature contour for Mesh 0.003:

Temperature Animation for Mesh 0.003:

Temperature for solid region of mesh 0.003:

The Mean temperature obtained for the Solid region of Mesh Size 0.003 is 820 k.

Temperature for Fluid region of mesh 0.003:

The Mean temperature obtained for the fluid region of Mesh Size 0.003 is 345 k.

Total cells for the mesh 0.003:

The Total number of cells obtained for the Mesh Size 0.003 is around 10,500 cells.

Case III: Mesh 0.002

Mesh Contour for Mesh 0.002:

Y+ for Mesh 0.002:

Velocity Contour for Mesh 0.002:

Velocity Animation for Mesh 0.002:

Temperature contour for Mesh 0.002:

Temperature Animation for Mesh 0.002:

Temperature for solid region of mesh 0.002:

The Mean temperature obtained for the Solid region of Mesh Size 0.002 is 750 k.

Temperature for Fluid region of mesh 0.002:

The Mean temperature obtained for the fluid region of Mesh Size 0.003 is 352 k.

Total cells for the mesh 0.002:

The Total number of cells obtained for the Mesh Size of 0.001 is around 38000 cells.

Grid Dependence Test:

Solid Temperature on Different Mesh types:

Fluid Temperature on Different Mesh types:

These above images show that mean outlet fluid temperature and the solid temperature for three different grid Sizes. Although they are not Converge at the same Specific point. The Mean temperature for the Solid is around 800 k and the mean temperature for the fluid should be 340k

In solid mean temperature, as the mesh grid size decreases the temperature also decreases because more refinement of the cells so the capture of temperature is accurately.

In Fluid mean temperature, as the mesh grid size decreases the temperature is increases because more refinement of cell so that we can capture the fluid temperature more appropriate.

Super Cycle Stage intervals for the Mesh 0.002:

Super cycle Stage Interval of 0.01:

Mesh Contour for the Super Cycle Stage Interval of 0.01:

Temperature Contour Super Cycle Stage Interval of 0.01:

Temperature Animation for Super Cycle Stage Interval of 0.01:

Velocity Contour Super Cycle Stage Interval of 0.01:

Velocity Animation for Super Cycle Stage Interval of 0.01:

Y+ Contour Super Cycle Stage Interval of 0.01:

Fluid region Temperature for Super Cycle Stage Interval of 0.01:

Solid region Temperature for Super Cycle Stage Interval of 0.01:

Super cycle Stage Interval of 0.02:

Mesh Contour for the Super Cycle Stage Interval of 0.02:

Velocity Contour Super Cycle Stage Interval of 0.02:

Velocity Animation for Super Cycle Stage Interval of 0.02:

Temperature Contour Super Cycle Stage Interval of 0.02:

Temperature Animation for Super Cycle Stage Interval of 0.02:

Y+ Contour Super Cycle Stage Interval of 0.02:

Fluid region Temperature for Super Cycle Stage Interval of 0.02:

Solid region Temperature for Super Cycle Stage Interval of 0.02:

Super cycle Stage Interval of 0.03:

Mesh Contour for the Super Cycle Stage Interval of 0.03:

Velocity Contour Super Cycle Stage Interval of 0.03:

Velocity Animation for Super Cycle Stage Interval of 0.03:

Temperature Contour Super Cycle Stage Interval of 0.03:

Temperature Animation for Super Cycle Stage Interval of 0.03:

Y+ Contour Super Cycle Stage Interval of 0.03:

Fluid region Temperature for Super Cycle Stage Interval of 0.03:

Solid region Temperature for Super Cycle Stage Interval of 0.03:

Fluid region Temperature for Different Super Cycle Stage Interval:

Solid region Temperature for Different Super Cycle Stage Interval:

From the above graph we can conclude that in the supercycling the intermediate values are not taken in consideration to determine the values for the Transient simulation of any problem.

In this case only final value should be considered because we have done the steady state and also observe the changes in temperatures at each and every second in Transient simulation which was shown in the graphs.

Effect of Super Cycle Stage Interval on simulation time

• The Super Cycle Stage interval of 0.01 the Simulation ran time is 10164.01 Seconds
• The Super Cycle Stage interval of 0.02 the Simulation ran time is 9528.01 seconds
• The Super Cycle Stage interval of 0.03 the Simulation ran time is 9331.76 seconds
• because we are simulating the all Super Cycles with a fine Mesh so that the time taken by each acuurate simulation is huge

Conclusion:

• CONVERGE solves the fluid and solid phases in the same simulation without requiring you to stop and restart the simulation.
• Super-cycling significantly reduces the computational cost of the CHT simulation.
• Successfully completely the Grid dependence test.