Week 6: Conjugate Heat Transfer Simulation

AIM- 

To simulate a Conjugate Heat Transfer flow through a pipe, while the inlet Reynolds number should be 7000.

To run the grid independance test on 3 grids and show that the outlet temperature converges to a particular value

To observe the effect of various supercycle stage interval on the total simulation time.

Calculating the inlet Velocity:

Reynolds number (`R_e`)= 7000

Density of air (`rho`)= 1.184 `(kg)/m^3`

Viscosity of air (`mu`)= `1.849*10^-5  m^2/s`

diameter of tube (d)= 0.03 m

Using the formula

`R_e = (rho. V. d)/ mu`

then 

`V = (R_e.mu)/(rho.d)`

`V= (7000* 1.849*10^-5)/(1.184*0.03) = 3.6438 m/s`

Velocity at the inlet = 3.6438 m/s

 

Geometry:

Inner Diameter = 0.03 m

Thickness of the solid = 0.005 m

Length of pipe = 0.2 m

The Diagnosis shows no problems.

CASE SETUP

Application type - Time Based

Materials-

Gas Simualtion -Air

Solid Simulation - Aluminium

Species - Air(N2 & O2) and Aluminium (AL)

Simulation Parameters-

Run parameters-

Solver = Transient;

Simulation mode = Full Hydrodynamic;

The Simulation time parameters are set as following-

start time - 0 seconds

end time - 0.5 seconds

initial time step = 1e-07 seconds 

 

 

Solver parameters

Solver type =  density based

Boundary Conditions-

Boundaries

The outer wall of the solid is set as fixed wall with heat flux of 10000W/m^2 going into the wall. 

the solid side has agian fixed wall condition with derichlet temperature boundary condition.

At the inflow the inlet velocity is 3.6438 m/s as calculated to keep the renolds number at 7000. 

The oulet is set at the atomspheric condition for the pressure and the velocity is set as derichlet boundary.

For the interface the forward side is for the fluid region with temperature BC as law of wall.

the reverse side is set as solid region and the temp BC is set as Specified value.

 

Inital Conditions and Events-

here the two regions are set , first is the Fluid region at 300 K temp and 1 atm pressure and the species are Air with 77% of N2 and 23% of O2.

The solid region is at 300 K with 100% aluminum

Physical Models-

Turbulance modeling - RNG K espilon model is used.

Super-cycle  modeling-

Concept of Super Cycling:

Super cycling is a technique which is used in Converge studio in the case of conjugate heat transfer problems with a solid and liquid regions. Main poblem is that both solvers cannot run at the same speed since solving in fluid domain is much faster owing to the time scale difference for heat transfer in liquids as compared to the solids. This causes problems during the solution given that the solid side solver would not have reached a steady state/convergene in the time the liquid solver does. This is where the concept of super cycling is based.

The basic idea of super cycling is that the solver for the fluid domain is paused until the solver for the solid domain converges. The following steps are involved in performing the super cycling 

1. Solve the fluid and the solid together with the transient solver, store the instantaneous Heat transfer coefficients and temperature on the interface during process.
2. Freeze the fluid solver. Time-averages the Heat transfer coefficients and temperatures and applies them as boundary conditions at the interface.
3. Solves the solid temperature until it reaches steady-state.
4. Update the solid temp field and unfreezes the fluid solver.
5. Repets until the solid temp converges.

 

Here in this case,

begin storing SC data = 0.05 

time length of each cycle stage = 0.05

conduction CL = 100

SIE relaxaiton faction for supercycle = 1.4

 

Grid Control-

Base grid

Output/Post Processing-

Typical output variable= Density , pressure , temperature , viscosity, region ID,

Turbulence variables= Trubulent kinetic energy, turbulent viscocity,  y+,

Boundary variables= supercycling avergae heat transfer coefficient , supercycling avg temperature.

Output files

the output files are written at every 0.01 seconds so according to the simulation time a total of 50 output files will be available to create a good amination.

 

 

RESULTS:

 

GRID TEST:

To Perform the grid test the base grid sizes used is 0.004, 0.003, 0.002 and the results are compared.

Mesh-

For 4mm grid size

For grid size 3mm

For Grid size 2mm

 

Pressure Contour -

4mm mesh

3mm mesh

2mm mesh

Pressure contour for all the three mesh are almost similar

Velocity Contour -

4 mm mesh

3mm mesh

2mm mesh

 The maximum velocity increases with decreasing the grid size.

Temperature Contour -

4 mm mesh

3mm mesh

2mm mesh

 The maximum temp reduces with reducing the grid size.

Y-plus Contour -

4mm mesh

3mm mesh

2mm mesh

 The Y-plus values reduces with reduction in the grid size.

 

SC_AVG_HTC

4mm mesh

3mm mesh

2mm mesh

 The supercycling avgerage Heat transfer coefficient reduces with reduction in the grid size.

SC_AVG_TEMP

4mm mesh

3mm mesh

2mm mesh

 The supercycling average temp increses with increase in the grid size

 

Mean temprature plot for the solid region all the three grid sizes -

 

Mean Temperature plot for the fluid region for all the three grid sizes -

 

Temp plot at the moniter point  [0.017202, -0.003216, 0.18] -

Mesh Size (in m)	Y-plus value	Mean temp in Solid region (K)	Mean temp in Fluid region(K)	Temp at moniter point (K)	Simulation time(sec)
0.004	16	861.4	352.7	866.4	1393
0.003	16	827.2	346.1	832.7	3324
0.002	7.2	7493	345.2	759.1	15730

 

EFFECT OF SUPER CYCLE INTERVAL:

The Super Cycle interval values of 0.01, 0.02. 0.03 is used and the results are observed here.

Mean temp plot in the solid regions for all the three supercycling stage values -

 Mean temp plot in the fluid region for all the three supercycling stage values -

Mean temp plot for all the three supercycling stage interval values at the moniter point  [0.017202, -0.003216, 0.18] -

 

Super Cycle stage interval (sec)	Mean temp in the fluid region	Mean temp in the solid region	Mean temp at the moniter point	Simulation time(sec)
0.01	353.56	755.9	766.2	56295
0.02	353.52	755.5	765.9	29629
0.03	353.42	755.0	765.1	6800

 

 

CONCLUSION -

1. After performing the gird dependence test , it is observed that as the mesh becomes finer the accuracy of the results increases.

2. As the mesh becomes finer the simulation cost and time increases.

3. After performing the super cycle stage interval , it is observed that there not much difference in the temperature values and the results are almost similar.

4. There is a hug difference between the simulation time that is required when the supercycling stage inverval varies, as the value decreases the computation time and cost increases a lot.

 

 

VIDEO ANIMATIONS -