CHT Flow Simulation through a Pipe using Converge CFD

Introduction : 

          Conjugate heat transfer is a study of heat transfer between solids and fluids in combination. The heat transfer through solids is by conduction & convection in fluids. When both these phenomenon's occur simultaneously in a system together we call it CHT. CHT simulations help in capturing the heat transfer occuring in the system of the Part or the device. For example the exhaust port of the IC engine, Graphic card simulation. So developing these simulations help to improvise the design & material being utilized, the cooling methods either natural or forced, number of fins to use etc. 

A cht flow simulation through a pipe is done in this project using Converge CFD package from Convergent Science. Converge package allows the usage of Supercycling a CHT simulation and its effect is captured & studied under this project. The post-processing is done with Paraview software. 

Super-cylcing in Converge :

Super-cycling is used as a time control process. It uses clever averaging techniques to reach convergence quickly. The steps it follows : 

1. Solves the fluid and solid regions together with the transient solver during initial time steps. 

2. Stores the instantaneous heat transfer coefficients and temperatures on the Interface boundary during this process. 

3. Once it does that, then it freezes the Fluid solver (Transient) and Time-averages the htc's and temperatures and applies them as B.C at the interface. 

4. Then it solves for the solid region temperature until it reaches steady state using steady state solver. 

5. Updates the solid region temperature field and unfreezes the Fluid solver (transient) and repeats this process until solid temperature converges. 

Interface B.C in converge :

An interface boundary separates two different materials or phases. In converge Cht simulations require atleast one interface boundary.

Objectives : 

1. Perform CHT flow simulation through a pipe.

2. Perform grid dependence test & capture the convergence of pipe outlet temperature. 

3. Capture effect of supercycle stage interval with different cycle time & compare total simulation time.

4.  Y+ 3d output. 

Inlet velocity : 

We're setting up a turbulent flow simulation here and reynolds number assumed is 7000.

radius = 0.015 

rho = 1.184 kg/m^3 for 298k 

Mu = 1.849x10^-5 Kg/m-s

hence calculating the inlet velocity from the RE formula we have, 

`Re = ((rho*v*d)/(mu))`  

`7000 = (1.184 * v *0.03)/(1.849*10^-5) = 3.643 m/s`

Geometry in Converge Studio :

The geometry of cylinder was created in converge studio 3.0 using create option /  shape / cylinder . with inner circle radius 0.015 m and outer 0.02 m. the length of the cylinder is 0.2 m. After this boundary is flagged as per b.c's.  

Meshing : 

Meshing shown in paraview with their respective grid sizes on top. Different grid sizes are used to conduct grid dependence test. 

Total cells : 

These are the total cell elements created for different grid sizes. The highest number of cells is created for the finest refinement of 0.00275 m around 13351. 

Case Setup : 

1. Application type : Time Based

2. Material : Air mixture ( Gas simulation)  / Solid Simulation

3. Gas Species : 02 , N2 . 

    Solid Material : Aluminum

4. Solver :Transient , Time-based simulation , Fully hydrodynamic. 

5. Gas flow solver : Compressible.

6. Misc : Momentum , Energy on 

7. Simulation Time parameters : 

i. Start 0 s

ii. End : 0.5 s. 

iii. Initial Time-step : 1e-7s

iv. minimum Time-step  1e-7s

v. Max time-step 1s.

10. Solver scheme : Piso algorithm : Density Based

11. Boundary Conditions : 

i. Inlet (Fluid region) : Inflow ; velocity (z) : 3.643 m/s ;Temp : 300 k ; Species : o2 , N2 .

ii. Outlet (Fluid region) : Velocity : Zero Normal Gradient ; Species : O2, N2. ; Pressure : 101325 pa. 

iii. Solidwall outside (solid region) : WALL ; Stationary : Fixed - Slip & Heat flux - 10,000 w/m^2

iv. Solid thickness (Solid region) : WALL ; Stationary fixed, slip ; zero Normal gradient. 

v: Interface : INTERFACE , wall - Stationary . fwd - fluid region ; wall treatment : law of wall.

                    REV : Solid region ; wall treatment - Slip/ 

12. Regions & Initialization : 

13 Region 0 created (fluid) : Velocity Z dir - 3.643 m/s ; Pressure 101325 pa ; Temp : 300 K ; Species : O2,N2 .

     Region 1 (Solid) stream id1 : Temp : 300k . Species : Aluminum

14. Turbulence Model : RNG K-epsilon

15. Output Files : Time interval for writing 3D output data files : 0.01 s.

16. Max restart files saved : 3 

17. Post variable selection : Additional selection : Y + 

18. Super - cycling modeling : Time length for each cycle STAGE has been varied in Super cycling study.

Solution & Post processing : 

This is IDREG contour it displays the steam id selected during the solver settings with 1 being Solid region (red) and 0 being Fluid region (blue).

Grid Dependence test 

Temperature Contour : 

The temperature contour for all 3 grids are shown below, From the contour, if observed near the outlet side there are clear differences in all 3 grids. With more refinement the outlet temperature has converged to slightly different Values. Even the coloured profile observed in the base grid just below the solid region is less denser but as moved to grid 0.003 its more shaper and even more at the final grid 0.00275. 

Plot for Fluid & Solid regions for all 3 grids. 

These are mean temperature plots for all 3 grids for fluid and solid region separately. Theyre each converging to slightly different values. The effect of super cycling can be seen in the Solid region plot. The location where the value remains stable is being averaged from the transient solver and then steady state solver runs and averages it to a new converged value. Similarly Fluid profile is completely transient in nature. The grid is temperature dependent and further refinement would most likely give a highly refined output and maybe that limit can be considered as grid independent. 

Effect of Super cycle stage interval : 

The effect of Supercycle stage interval is checked for three SS intervals - 0.01, 0.02 & 0.03 for same base mesh of 0.004 meter element size. The Supercyle affects the time to solve the equations and reach convergence. 

The plot as can be seen the cycle stage starts at the second set for super cycling and converges to a same temperature at the end of convergence. This means that the solution for same mesh is supercycle independent for these particular values. However the time taken to solve these 3 varies and once we know this then we can use super cycling value interval to reach steady convergence faster in future. 

Super cycling total simulation time : 0.03 > 0.02 > 0.01  

0.01 is the fastest and 0.03 is the slowest in comparison. 

Velocity contour for 3 different grids : 

Y+ contours : 

Temperature Animation in Paraview : 

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