# Conjugate Heat Transfer through solid pipe using Converge CFD

**OBJECTIVE-**

-Using conjugate heat transfer simulate flow through a solid pipe and understand super-cycling.

-Perform Grid dependence test

-Analyze the effect of supercycle stage interval

**Geometry-**

**Calculation of inlet velocity:**

Inlet Reynolds number =7000

Diameter of pipe=0.03 m

Dynamic viscocity of air=1.81*10^-5 pa.s

density=1.225 kg/m3

Re=ρvdμ

v=Re.μρd

=(7000*1.81*10^-5)/1.225*0.03

=3.45 m/s

**Setup-**

**Applications-**

-General flow

**Materials-**

**Case setup-****Gas Simulation,Solid Simulation,Species**

**Species-Gas-O2,N2 Solid- Aluminium**

-Air

**Simulation Parameters:**

-Transient solver

-Start time-0, End time-0.5 s

-Intial time step=minimum time step=1e-7 s

-Maximum time step=1 s

**Boundary conditions- **

-Inlet- INFLOW-velocity-3.45 m/s

-Outlet- OUTFLOW-Total pressure-101325 pa

-Solid outer wall- WALL, Heat flux= -10000 W/m2

-Solid wall -WALL velocity-slip , Temperature-zero normal gradient

-Interface- INTERFACE

Forward boundary-velocity and temperature-Law of wall ,region-fluid

Reverse boundary-velocity and temperature-slip and specified value ,region-solid

**Regions & Initialization:**

Boundaries are assigned to region

Temperature and pressure set to 300K and 101325pa

Species-Air

**Grid Dependence test:**

**Case-1: **Grid size- dx=0.04 m, dy=0.04 m, dz=0.04 m

**Case-2:** Grid size- dx=0.03 m, dy=0.03 m, dz=0.03 m

**Case-3:** Grid size- dx=0.02 m, dy=0.02 m, dz=0.02 m

**Total cell count for different grid size:**

The total cell count is increasing with decrease in element size.

**Case-1: Grid size- dx=0.04 m, dy=0.04 m, dz=0.04 m**

**Mesh-**

**Temperature Contours:**

**Velocity Contours:**

**Yplus plot:**

The maximum range of ypus contour is 13 for the mesh size of 0.04 m

**Case-2: Grid size- dx=0.03 m, dy=0.03 m, dz=0.03 m**

**Mesh-**

**Temperature Contours:**

**Velocity Contours:**

**Yplus plot:**

The maximum range of ypus contour is 12 for the mesh size of 0.03 m.So we can see that with decrease in mesh size the ypus value is also decreasing.

**Case-3: Grid size- dx=0.02 m, dy=0.02 m, dz=0.02 m**

**Mesh-**

**Temperature Contours:**

**Velocity Contours:**

**Yplus plot:**

The maximum range of ypus contour is 7.9 for the mesh size of 0.02 m.So we can see that with decrease in mesh size the ypus value is also decreasing. The lowest ypus value is noticed for grid size of 0.02 m.

**Grid Dependence test:**

**Mean temperature in fluid region vs time:**

The mean temperature for fluid region converged to around 348 kelvin for 0.04m and 0.03m grid size.Whereas for 0.02m size the value is 357K.

So it can be said that with decrease in mesh size we are aproaching grid indipendency.

**Mean temperature in solid region vs time:**

The mean temperature for solid region converged to around 900 kelvin for 0.04m grid size.Whereas for 0.03m and 0.02m size the value is 800 K and 750 k respectively.

So it can be said that with decrease in mesh size we are aproaching grid indipendency

**Temperature at monitor point vs time:**

The outlet temperature converged to around 900 kelvin for 0.04m grid size.Whereas for 0.03m and 0.02m size the value is 800 K and 750 k respectively.

So it can be said that with decrease in mesh size we are aproaching grid indipendency.

**Effect of supercycle stage interval:**

Super-cycling is a method used by CONVERGE in the case of conjugate heat transfer problems with a solid and liquid regions.The solver for fluid and solid doesnt run at same speed as heat transfer in fluid region is faster than solid region.

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.Super-cycling is only meant to speed up the simulation and if the simulation.

**Three supercyle stage interval was set for comparision 0.01,0.02 and 0.03 respectively.**

**Mean temperature in fluid region vs time:**

The mean temperature for fluid region converged to around 345 kelvin.

We can see from the below graph that supercyle stage interval of 0.01 coverged faster than stage interval with 0.02 and 0.03.

**Mean temperature in solid region vs time:**

The mean temperature for solid region converged to around 900 kelvin.

We can see from the below graph that supercyle stage interval of 0.01 coverged faster than stage interval with 0.02 and 0.03.

**Temperature at monitor point vs time:**

The temperature at outlet monitor point converged to 900 kelvin.

We can see from the below graph that supercyle stage interval of 0.01 coverged faster than stage interval with 0.02 and 0.03.

From the above three graphs it is seen that temperature is converging to a particular value at the end.

But for supercyle stage interval of 0.01 the convergence is the fastest in all the cases followed by 0.02 and 0.003 stage interval.So it can be concluded that lower value of supercycle stage inverval gives faster convergence.

**Time of simulation for different supercycle stage inverval **

**Stage interval Time of simulation**

** **0.03 987.9 s

0.02 980.6 s

0.01 911.4 s

**Animation:**

**Conclusion:**

1. Conjugate heat transfer simulation for flow through a solid pipe was successfully performed.

2. The grid dependency test showed that the temperature values aproached a closed value when we decreased the mesh size and the solution was almost grid independent.

2. From the effect of supercycling it can be concluded that lower value of supercycle stage inverval gave faster convergence.