Conjugate Heat Transfer Simulation

Objective:-

• Simulated the conjugate heat transfer analysis of fluid through a pipe.
• Run grid dependence test for three cases
• Plot Y+ values for each case
• Study the effect of supercyle stage interval

Before proceeding with the simualtion some important things we should which is explain below:

What is Conjugate Heat Transfer analysis?

• When ever their is a heat transfer from solid volume to fluid volume or vice-versa by exchaning their thermal properties at their interface in order to simulate this case conjugate heat transfer analysis is used.Conjugate heat transfer analysis basically describe the processes which involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids.

Applications:-

• It helps us to simulate & understand thermal systems like heat sinks,cooler,exhaust port of vehicle,HVAC,ICE etc.

What is Super-cycling?

Super-cycling is a method used by CONVERGE Studio in the case of conjugate heat transfer problems with a solid and liquid regions.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.

Steps of Super-cycling

• Converge solves the fluid and solid together with the tansient solver and during this it stores instantaneous HTCs and temperature on the interface during this process
• It freezes the fluid solver and time-averages the HTCs and temperature and applies them as boundary conditions at the interface.
• Then it solves the solid temperature until it reaches steady-state
• It updates the solid temperature and unfreezes the fluid solver
• This process it repeats until the solid temperature converges.

What is Y+?

The y+ value is a non-dimensional term that can be used to understand how coarse or fine our grid is. Before going to y+ we should know that in the boundary layer we have three layerThis can then be used to determine if wall functions need to be used or not. From the image attached below, we need to either be in the viscous sub-layer or the turbulent region.

If we were in the viscous sub-layer, that would mean a y+ of less than 10 and if we were in the turbulent region, it would mean a y+ of greater than 30. This is very significant in our making the decision of using or not using a wall function.

If y+ less then 10 which means we are in viscous sub-layer for this condition we can simply use no-slip condition.

If y+ value is between 10 to 30,its is undeseriable since over here transition zone is there.

If y+ above 30 which means we are in turbulent region for this condition we have to use wall function.

Given Data:

Reynolds number=7000

Kinematic viscosity at 25 degree celsius `nu=1.56xx10^-5frac{m^2}{s}`

D=Diamter of pipe

V=Velocity of flow

Calculation

Re=`frac{VxxD}{nu}`

7000=`frac{0.015xxV}{1.56xx10^-5}`

Inlet velocity:V=7.28m/s

Case

Step1.Geometry

The Pipe geometry has been created in converge by using below dimensions:

• Outer diameter:0.020m
• Inner diameter:0.015m
• L_z:0.2m

Boundary:Before proceeding for case setup we need to assing boundary selection which is shown below

Normal toggle

As we can see in above image normal toggle is pointing outward which is wrong its should point towards the fluid region and this can been done by using transform option.

Step2.Case Setup

• Application:General Flow
• Analysis:Transient State
• Type:Pressure type
• Material:Air for fluid volume & Aluminium for solid volume
• Species:O2 & N2
• Simualtion mode:Full hydrodynamic

Simulation time parameters:

• Start time:0sec
• End time:0.41sec
• Initial time step:1e-7sec
• Minimum time step:1e-7sec
• Maximum time step:1sec

Region & Initialization:

In this we have created two region is beacuse we have two different volume solid and fluid & also we have use two different stream id.Stream id 0 means solver will solve

• Region Name:Fluid of stream id 0
• Region Name:Solid of stream id 1

Boundary Conditions:

• Inlet
  • Type:Dirichlet condition
  • Velocity:7.28m/s in z-direction
  • Temperature:300k
  • Species condition:O2=0.23,N2=0.77
  • Region:Fluid

• Outlet
  • Type:Dirichlet condition
  • Pressure:101325.0Pa
  • Temperature:300k
  • Species condition:O2=0.23,N2=0.77
  • Region:Fluid

• Solid side
  • Boundary type:Wall
  • Velocity Boundary condition:Slip
  • Region:Solid

• Solid outer wall
  • Boundary type:Wall
  • Velocity Boundary condition:Slip
  • Heat flux:-10000.0W/m3
  • Region:Solid

• Interface
  • Forward side will be fluid region with law of wall boundary condition.
  • Reverse side will be Solid region with Slip boundary condition.

Physical Model

• Turbulence Model
  • K-e epslion

Output Files:

• Time interval for writing 3D output data files:0.0041sec(So,that we get atleast 100 3D output files)
• Time interval for writing text output:1e-6 sec(So,that we get every minute data)
• Time interval for writing restarting output:0.0041sec.
• Maximum number of restart file saved:3

Step5.Result

Mesh Plots

Grid size-3mm with supercycle-0.01

Grid size-2mm with supercycle-0.02

Grid size-2mm with supercycle-0.03

Temperature plots

As we can see in the above plot the temperature in solid region plot is decrease as we increase super-cycle stage interval this means more heat is transfering from solid domain to fluid domain.While in fluid region plot as we increase super-cycle stage interval mean temperature since fluid region is absorbing the temperature,but in both plot solution has not reach to converge for that further mesh refinement is need.

Total cell count

As we can see in the above plot the total number of cell is increases as we increase super-cycle stage interval.

Velocity Contours

Grid size-3mm with supercycle-0.01

Grid size-2mm with supercycle-0.02

Grid size-2mm with supercycle-0.03

From the above plot at the outlet we can see smooth parabolic profile of velocity get formed as we increase the super-cycle stage interval.

Y+ contour

Grid Size-3mm with supercycle-0.01

Grid Size-2mm with supercycle-0.02

Grid Size-2mm with supercycle-0.01

From above plot in all three cases we get y+ value between 10 to 30,which means center of the first layer lies in the buffer layer which is undesirable,because of this results obtained for such grids size which gives y+ in between 10 to 30 is void.

Velocity Animation

Grid size-3mm with supercycle-0.01

Grid size-2mm with supercycle-0.02

Grid size-2mm with supercycle-0.03

Conclusion

• Successfully did Conjugate heat transfer simulation
• Studied super-cycling and Y+ plus and also their effect.
• Results obtain in our simulation is completely void since we got y+ in the range of buffer region.