Week 6: Conjugate Heat Transfer Simulation

Objective: The objective of the challenge is to set up a Conjugate Heat Transfer analysis by performing a 2-D flow through simulation in an aluminum pipe of hydraulic diameter 0.03 m. Also, do a case study on grid independency study and a case study on the supercycle stage interval.

Introduction to the Conjugate Heat Transfer:

Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers.

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. The exchange of thermal energy between the two physical bodies is called the study of Heat Transfer, the rate of transferred heat is directly proportional to the temperature difference between the bodies.

Coming to the heat transfer concept, for the fluid region the convective heat transfer is dominant and for the solid region, the conductive heat transfer is dominant. 

To attain a steady-state condition, fluid takes less time where the solid region takes more time.

So, while doing this CHT case in the COnverge Studio software, a concept called super cycling is implemented to decrease the time to get a steady-state.

While we are doing the CHT, the solver divides the problem into domains fluid and solid. So, in the super cycling concept, the solver of the fluid domain is paused until the solid domains get its steady stare or convergence. Hence the solver pauses the fluid solver at intervals defined by the user until the solid domain converges. This way simulation time can be reduced. In this way, the supercycle helps in speeding up the CHT simulations.

So, this way the supercycle concept helps the user to save his computational time, and computational resources.

Y-Plus: 

The placement of the first node in our near-wall inflation mesh is very important.  The y+ value is a non-dimensional distance (based on local cell fluid velocity) from the wall to the first mesh node, as you can see in the image below.  To use a wall function approach for a particular turbulence model with confidence, we need to ensure that our y+ values are within a certain range.

Geometry:

• To perform this challenge, we consider a thick cylinder with a diameter of 0.04 m, in that the hydraulic diameter is 0.03 m.
• The length of the pipe is set to 0.2 m.

• The above picture tells us both the solid region and fluid region are activated to solve the case.
• The red-colored region is the solid part or solid thick cylinder. The blue-colored part indicates the fluid region. It is divided using the ID Region in the Paraview.

Finding Velocity Calculation:

The given Reynolds number to be maintained = 7000

Formula to find the velocity: `Re=(rho*v*D)/mu`

Re = Reynolds Number = 7000

rho = Density of the fluid = 1.184 kg/m3

v = velocity of the fluid stream = ?

D = hydraulic diameter of the cylinder = 0.03 m

mu = Kinematic viscosity = 1.849*10^-5 kg/m-s

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

                              `v=(7000*1.849*10^-5)/(1.184*0.03)`

                              `v=3.6438 m/s`

Case setup:

Application Type - Time-Based

Materials - Air (Mixture of O2 & N2)

Simulation Parameters:

• Run parameters: Solver - Transient
• Simulation time parameters:  Start time - 0

                                                   End time - 0.5

                                                   Initial time step - 1e-7

                                                   Minimum time step - 1e-7

                                                   Maximum time step - 1

Boundary Conditions:

1) Inlet:

• Boundary type: INFLOW
• Velocity: 3.64 m/s
• Fluid: Air (O2 - 23%, N2 - 77%)

2) Outlet:

• Boundary type: OUTFLOW
• Pressure: 101325 Pa
• Fluid: Air (O2 - 23%, N2 - 77%)

3) Solid-outer-wall:

• Boundary type: Wall
• Heat flux: -10000 W/m2

4) Solid-Thickness:

• Boundary type: Wall
• Slip Boundary Condition

5) Interface:

  a)Forward region: 

• Region: Fluid region
• wall-treatment: Law of wall

  b)Backward region:

• Region: Solid region
• Wall-treatment: Slip

Initial conditions and Events:

1) Fluid region:

2) Solid region:

• Stream ID: 1 (check the box with tick mark)
• Temperature: 300k
• Species: Aluminium

Physical Model:

• Turbulence Model: RNG K-Epsilon
• Super cycling: SSI (0.05), provide a monitor output point inside the length of the cylinder

Grid Control:

• Base grid: 0.004 m (dx,dy,dz)

Output/Post-processing:

1) Output files: 

• Time Interval for writing 3D files: 0.001 sec
• Max.number of restart files saved: 5

Results:

Effect of Grid dependency:

Case1: Base Grid = 0.004, SSI = 0.05 

Meshing: 

• Converge Software uses autonomous meshing. 
• Specifically, CONVERGE automatically creates the mesh at runtime, dynamically adapts the mesh throughout the simulation, and invokes Adaptive Mesh Refinement to maximize both accuracy and computational efficiency.

Temperature:

• The max. temperature is recorded on the surface of the solid aluminum cylindrical block.
• Inside the cylinder, we can also see the changes in temperature contour. This happens due to the heat transfer between the solid and liquid interfaces. 
• The change in temperature only records at the inner wall of the cylinder, what happens exactly is conduction from the inner wall to interface and then convection from the interface to the fluid domain.
• The Max. temperature obtained is nearly 870 k. The cause of the rise in temperature is heat flux we have applied on the surface.

• Here the stepped intervals represent the supercycle concept. As the solid takes more time comparatively, so we applied the supercycle and provide it with the time interval as 0.05 sec to calculate and throws a value.
• The max. temperature attained is 861.48 k.

Temperature Animation: https://youtu.be/zdChpqdxNgU

Velocity:

• The above contour represents the velocity contour. 
• The max. velocity recorded is about 5 m/s inside the cylinder at the end or outlet.
• The increase in temperature is because of the pressure difference at the outlet and due to some viscous forces.
• Due to the lack of cell count, we are not able to capture the development of the parabolic boundary layer.

Y-Plus:

•  The above contour is Y-Plus of the base grid size of 0.004.
• The max. y-plus recorded is 17 and it at the starting of the cylinder and min. y-plus recorded is about 10 at the end of the cylinder.

Case2: Base Grid = 0.003, SSI = 0.05 

Meshing: 

• Converge Software uses autonomous meshing. 
• Specifically, CONVERGE automatically creates the mesh at runtime, dynamically adapts the mesh throughout the simulation, and invokes Adaptive Mesh Refinement to maximize both accuracy and computational efficiency.

Temperature:

• The change in temperature only records at the inner wall of the cylinder, what happens exactly is conduction from the inner wall to interface and then convection from the interface to the fluid domain.
• The Max. temperature obtained is nearly 830 k. The cause of the rise in temperature is heat flux we have applied on the surface.

• Here the stepped intervals represent the supercycle concept. As the solid takes more time comparatively, so we applied the supercycle and provide it with the time interval as 0.05 sec to calculate and throws a value.
• The max. temperature attained is 827.7 k.

Temperature Animation:https://youtu.be/WefEeK5k1Uk

Velocity:

• The max. velocity recorded is about 5.1 m/s inside the cylinder at the end or outlet.
• The increase in temperature is because of the pressure difference at the outlet and due to some viscous forces.
• Due to the lack of cell count, we are not able to capture the development of the parabolic boundary layer.

Y-Plus:

•  The above contour is Y-Plus of the base grid size of 0.004.
• The max. y-plus recorded is 16 and it at the starting of the cylinder and min. y-plus recorded is about 12 at the end of the cylinder.

Case3: Base Grid = 0.0025, SSI = 0.05 

Meshing: 

• Converge Software uses autonomous meshing. 
• Specifically, CONVERGE automatically creates the mesh at runtime, dynamically adapts the mesh throughout the simulation, and invokes Adaptive Mesh Refinement to maximize both accuracy and computational efficiency.

Temperature:

• The change in temperature only records at the inner wall of the cylinder, what happens exactly is conduction from the inner wall to interface and then convection from the interface to the fluid domain.
• The Max. temperature obtained is nearly 810 k. The cause of the rise in temperature is heat flux we have applied on the surface.

• Here the stepped intervals represent the supercycle concept. As the solid takes more time comparatively, so we applied the supercycle and provide it with the time interval as 0.05 sec to calculate and throws a value.
• The max. temperature attained is 804.2 k.

Temperature Animation:https://youtu.be/cZqMrTh9mAQ

 

Velocity:

• The max. velocity recorded is about 5.2 m/s inside the cylinder at the end or outlet.
• The increase in temperature is because of the pressure difference at the outlet and due to some viscous forces.
• Here in this case we can see the development of the boundary layer on the interface of the wall.

Y-Plus:

•  The above contour is Y-Plus of the base grid size of 0.004.
• The max. y-plus recorded is 14 and it at the starting of the cylinder and min. y-plus recorded is about 10 at the end of the cylinder.
• What we can observe here is decreasing in the base grid size would decrease the Y-plus number which is a correct phenomenon.

Case4: Base Grid = 0.002, SSI = 0.05 

Meshing: 

• Converge Software uses autonomous meshing. 
• Specifically, CONVERGE automatically creates the mesh at runtime, dynamically adapts the mesh throughout the simulation, and invokes Adaptive Mesh Refinement to maximize both accuracy and computational efficiency.

• Here we can see how the size of Y-plus is decreased as we decreased the base grid size and it is represented above at the interface region.

Temperature:

• The change in temperature only records at the inner wall of the cylinder, what happens exactly is conduction from the inner wall to interface and then convection from the interface to the fluid domain.
• The Max. temperature obtained is nearly 760 k. The cause of the rise in temperature is heat flux we have applied on the surface.

• Here the stepped intervals represent the supercycle concept. As the solid takes more time comparatively, so we applied the supercycle and provide it with the time interval as 0.05 sec to calculate and throws a value.
• The max. temperature attained is 748.3 k.

Temperature Animation:https://youtu.be/mhd9iGKsdKk

Velocity:

• The max. velocity recorded is about 5.3 m/s inside the cylinder at the end or outlet.
• The increase in temperature is because of the pressure difference at the outlet and due to some viscous forces.
• Here in this case we can clearly see the development of the boundary layer on the interface of the wall.

Y-Plus:

•  The above contour is Y-Plus of the base grid size of 0.004.
• The max. y-plus recorded is 7.2 and it at the starting of the cylinder and min. y-plus recorded is about 3 at the end of the cylinder.
• It is always better to have our Y-plus values fall behind the 10.

Effect of SuperCycle Method:

Case1: Base Grid = 0.004, SSI = 0.03

• The above plot is with a base mesh 0.004 m with a supercycle method incorporated with SSI (interval) of 0.03 seconds. It shows Max. the temperature on the solid surface is 870 k with a flow time of 0.5 sec.

Temperature Animation:https://youtu.be/t8QPqTXOuCA

Case2: Base Grid = 0.004, SSI = 0.02

• As we decrease the SSI time or interval time of the supercycle, the solid surface tried to get steady-state early compare to the previous case.
• At the time of 0.2 seconds, it almost attains the steady-state.
• This can be observed by seeing the stepped profile in the graph.

Temperature Animation: https://youtu.be/9hFGHwXcf0E

Case3: Base Grid = 0.004, SSI = 0.01

• As we decrease the SSI time or interval time of the supercycle, the solid surface tried to get steady-state early compare to the previous case.
• At the time of 0.13 seconds, it almost attains the steady-state.
• This can be observed by seeing the stepped profile in the graph.

Temperature Animation: https://youtu.be/u2KTEP259QY

Conclusion:

• The solid domain reaches the steady-state faster as we decrease the supercycle time interval and also it takes less time to get converge. 
• This means as we decrease the time interval there is a faster convergence with less computational time compares to other cases studied in the effect of Supercycle Time Intervals.

SSI (seconds)	Run time (seconds)
0.05	451.77
0.03	377.60
0.02	363.57
0.01	362.88

• Here in the grid dependency test, we observe that a decrease in the grid size helps decrease the Y-Plus value also.
• In all the grid dependency tests, the observed minimum Y-plus number is 7 and it is in the simulation with grid size of 0.002.
• As we decrease the grid size from 0.004 to 0.002, the computational time increases from 451.77 seconds to 4775.54 seconds which is almost ten times.