Conjugate Heat Transfer Simulation for an Aluminium Hollow Pipe

OBJECTIVE

The objective of this study is to set up a transient state flow simulation through a hollow pipe and understand the dependency of grid size on simulation time and results. Apart from this, the effect of supercycling stage interval on the simulation time will also be assessed in the study. The project includes the key results for three simulations setups based on the three different grid sizes and supercycling stage interval as per the table given below

Case	Grid Size	SuperCycling Stage Interval
Baseline	dx = 0.004 m; dy = 0.004 m; dz = 0.004 m	0.05
Case 1	dx = 0.004 m; dy = 0.004 m; dz = 0.004 m	0.03
Case 2	dx = 0.0025 m; dy = 0.0025 m; dz = 0.0025 m	0.03
Case 3	dx = 0.0015 m; dy = 0.0015 m; dz = 0.0015 m	0.03
Case 4	dx = 0.0025 m; dy = 0.0025 m; dz = 0.0025 m	0.02
Case 5	dx = 0.0025 m; dy = 0.0025 m; dz = 0.0025 m	0.01

The report includes the following steps taken to setup the conjugate heat transfer simulation:

1. Preprocessing

1.1. Geometry Creation

1.2. Diagnosis

1.3. Boundary Flagging

1.4. Case Setup

2. Solving

3. Post Processing

3.1. Mesh

3.2. Plots (Velocity, Inlet and Outlet Temperature, Mean Regional Temperature)

3.3. Contours (Velocity, Temperature)

3.4. Total Simulation Time vs Supercycling Stage Interval

3.5. Animation

PROCEDURE:

The procedure followed for setting up the simulation is provided below

1. Preprocessing

1.1. Geometry Creation

a. The geometry was created using following steps: Goto Geometry>Create>Shape> Click on cylinder button

i. Enter Center 1: 0,0,0

ii. Enter Center 2: 0,0,0.2

iii. Radius 1 and Radius 2: 0.015- This will create a solid pipe

iv. Click on create and repeat the process with new Radius 1 and Radius 2: 0.02- This will add the thickness to the pipe

v. Now select the Inlet and outlet faces traingles and delete those

vi. Goto create>traingles>loft edges>Select the concentric circles and click on create- This will create the thickness

vii. Goto Repair>patch>list of edges> select the inner circle on both the inlet stream and outlet stream side to create the traingles at these areas

Fig. 1: Geometry (All dimension are in m)

Fig. 2: Geometry (Section View)

c. A section cut was performed on the geomerty to inspect it again as shown in Fig.2.

d. Checked the normal orientation on surface and made sure the normals are pointing towards the fluid regime. In case it was poiting in the reverse direction, Goto Transform>Normal>Propagate Change from a single triangle>select any any traingle and click on apply

1.2. Diagnosis: The diagnosis tool helps in identifying the different problems in the geometry.

The Diagnosis tool looks for the following geometric issues

a. Intersection: Highlights number of triangles with piercing inbetween adjacent two triangles

b. Nonmanifold Vertices: Checks for number vertex which are being shared between two triangles

c. Open Edge: This highlights the number of edges of a triangle which not shared by any other triangle

d. Normal Orientation: This highlights the number of traingles whose normal vector is not pointing towards the interior of fluid domain

e. Isolated Triangles: This checks for the number of triangle surrounded by any neighbouring triangles that have different boundary ID number

Goto Diagnostics Dock>Find>

Since all the problem traingles are green ticked, there were no issues in the geometry

1.3. Boundary Flagging:

a. Goto Boundary>Flag>Create a New Boundary>Create Multiple Boundary>Enter 4 in \"Number of Multiple Boundaries\"

b. Select the triangles the assigned it to the respective boundaries

The figure below represent the boundaries flagged

1.4. Case Setup:

a. Clicked on \"Begin case Setup\" and entered the value provided below

Settings	Values to be Entered
Application	General Flow
Material	Select Air (predefined mixture) and Tick onto Species and Solid Simulation Gas simulation>No Change Solid Simulation>Click on Predefined Solid> select Aluminum>Add Selected Global Transport Paramters>No Change Species> Gas> add O2 and N2, Solid>Add Aluminum
Simulation Parameters	Run Paramters> Transient Simulation Time Parameter> Start Time: 0.5 s Initial time step: 1.0e-7 s Minimum time step: 1.0e-7 s Maximum time step: 0.5s Solver Parameters> No Change
Boundary Conditions	OuterWall Boundary Type>Wall, Wall Motion Type>Stationary, Select Slip from the list Temperature Boundary Condition> Select Heat Flux from the list & Assign the Flux value as -10000.0 W/m^2 Thickness Boundary Type>Wall, Wall Motion Type>Stationary, Select Slip from the list Temperature Boundary Condition> select Zero Normal Gradient Inlet Boundary Type> Inflow Pressure BC>Zero Normal Gradient Velocity BC>Specified Value, Assign Vz=0.37m/s* Temperature BC>Specified Value, Assign Temperature Value>300K Species BC> Add Air with Total Mass Fraction as 1, i.e., O2:0.23, N2:77 Outlet Boundary Type-OUTFLOW Pressure Boundary Condition>Specified Value, Enter a value of 101325.0 Pa Velocity Boundary Condition>Zero Normal Gradient (NE) Temperature Backflow>300k Species Backflow>Air InterfaceBoundary Boundary Type> Interface Velocity Boundary Condition> Stationary Forward Boundary>region>Fluid Velocity BC>Law of Wall Temperature BC>Law of Wall Backward Boundary>Region>Solid Velocity BC>Slip Temperature BC>Specified Value Assign Region Solid to OuterWall and Thickness, & Region Fluid to Inlet and Outlet
Initial Conditions & Events	Regions and Initialization Regions and Initialization Add region>\"Fluid\" Stream ID: 0 Temperature: 300k Enter Pressure value:101325.0Pa Species: Add Air Add region>\"Solid\" Stream ID: 1, Tick on the Solid Temperature: 300k Species: Add Aluminum
Physical Models	Physical Model> Tick on Supercycling Turbulence Modeling-RNG-K Eplison is selected Supercycling: Use the Settings as per the following: Note: The output coordinate should be within the thickness layer in the geometry For the case setups used the following interval values Case 1 :Supercyling Interval: 0.03 Case 2 :Supercyling Interval: 0.03 Case 3 :Supercyling Interval: 0.03 Case 4 :Supercyling Interval: 0.02 Case 5 :Supercyling Interval: 0.01
Grid Controls	Enter the grid values for (dx, dy, dz) as per the case Baseline Baseline: dx = 0.004 m; dy = 0.004 m; dz = 0.004 m For Case 1,2,3 use the following grid size Case 1 dx = 0.004 m; dy = 0.004 m; dz = 0.004 m Case 2 dx = 0.0025 m; dy = 0.0025 m; dz = 0.0025 m Case 3 dx = 0.0015 m; dy = 0.0015 m; dz = 0.0015 m For Case 4 & 5 used base grid size equivalent to case 2
Output/Post Processing	Post Variable Selection> Goto to the Combustion/Turbulence tab and tick on y+, No other change
Output Files	Time Interval for writing 3D output data files: 0.01 s Time Interval for writing text output: 1e-07 s Time Interval for restarting output: 0.1 s

After this all the input files was imported to a seperate folder. Converge creates .txt files which contains all the values entered while setting up the case for respective settings done above. These input files will be processed by converge using Message Passing Interface (MPI) standard

2. Solving:

For running the simulation, Cygwin tool was used instead of converge studio interface. Cygwin is a POSIX-compatible API which is based on command prompt is used to run the simulation

Steps:

a. Navigated to the folder location containing the input files

b. Entered the command> mpiexec.exe -n 2 converge.exe </dev/null> logfile & : This allows converge to run two processors (selection on number of processor cores present as per the system configuration, can use multiple cores if available) for the parallel processing and load balancing

c. Entered the command> taif -f logfile

d. After the simulation is over. Went back to converge studio>Post-Processing 3D

e. Enter Case Name>\"Test\", Change the File Type to Paraview VTK in-line binary format

d. Enter the address for the output files>Select all files>Select all Cell Variables>click on Convert

e. After the conversion of the post files to the binary output, open the Test.vtm (group file) file in Paraview

3. POST-PROCESSING:

After opening the group file in paraview, clicked on apply to load the results. Created slice, glyphs and other plots as required

3.1. Meshing:

Fig: Cell Count (Case 1, 2 & 3)

Fig: Case 1 Mesh View

Fig: Case 2 Mesh View

Fig: Case 3 Mesh View

3.2. Plots

Velocity Plots

Fig: Case 1: Inlet and Outlet Velocity Plots

Inlet and Outlet Temperature Plots

Fig: Baseline: Inlet and Outlet Temperature Plots

Fig: Case 1: Inlet and Outlet Temperature Plots

Fig: Case 2: Inlet and Outlet Temperature Plots

Fig: Case 3: Inlet and Outlet Temperature Plots

Fig: Case 4: Inlet and Outlet Temperature Plots

Fig: Case 5: Inlet and Outlet Temperature Plots

Mean Regionwise Temperature Plots

Fig: Baseline: Region 0 and Region 1 Temperature Plots

Fig: Case 1: Region 0 and Region 1 Temperature Plots

Fig: Case 2: Region 0 and Region 1 Temperature Plots

Fig: Case 3: Region 0 and Region 1 Temperature Plots

Fig: Case 4: Region 0 and Region 1 Temperature Plots

Fig: Case 5: Region 0 and Region 1 Temperature Plots

3.3. Total Simulation Time vs Supercycling Stage Interval

Note: Here the baseline case was run with grid size of dx=dy=dz=0.0025m for capturing the proper comparison of the simulation time which is independent of the grid size

3.4. Contours:

Case 1:

Fig: Velocity and Temperature Contour Plot (Case 1-Output 10)

Fig: Pressure and yPlus Contour Plot (Case 1-Output 10)

Case 2:

Fig: Velocity and Temperature Contour Plot (Case 2-Output 10)

Fig: Pressure and yPlus Contour Plot (Case 2-Output 10)

Case 3:

Fig: Velocity and Temperature Contour Plot (Case 3-Output 10)

Fig: Pressure and yPlus Contour Plot (Case 3-Output 10)

3.5. Animation :

Case 2

Case 3

Key Conclusions

1.With the decrease in grid size the total cell increases and the simulation time as well, since more number of equations are being solved

2. The rise in the outlet temperature curve increase sharply and then slowly reaches the steady state after some time. The increase in cell count the thereby, results in more accurate capture of the temperature rise

3. Grid dependency test was conducted to obtain the optimal grid size i.e., a tradeoff between the simulation time and results. It also assists in understanding the grid size and time to achieve converged state of results, which inturn influences the grid selection decision. In our case, the grid size of dx=dy=dz=0.0025m was selected, for further assesstment of the supercycling stage interval on the total simulation time

4. Activating the yplus results in the smooth acquisition of the velocity profile near the solid interface or the inner wall

5. By reducing the supercycling stage interval, the simuation took less time and the optimal results were also obtained, which is one of the key objectives of using this concept. Lower stage interval results in more frequent update of the temperature values in the solid domain which thereby overcomes the time scale differences at a faster pace