CHT SIMULATION THROUGH A CIRCULAR PIPE

AIM

To perform a CHT simulation between solid and liquid interface for a flow with Reynolds Number 7000.

INTRODUCTION

1. The exchange of thermal energy between the two physical bodies is called studyof Heat Transfer where the rate of transferred heat is directly proportional to the temperature difference between the bodies.
2. The term conjugate heat transfer (CHT) is used to describe processes which involve variations of temperature within solids and fluids, due to thermal interaction between the solids and fluids.
3. Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids.
4. In solids, conduction often dominates whereas in fluids, convection usually dominates. Efficiently combining heat transfer in fluids and solids is the key to designing an effective system.
5. Typical applications of this analysis type are the simulation of heat exchangers, cooling of electronic equipment, and general-purpose cooling and heating systems.
6. But there are several challenges when solving the fluid and solid domains together i.e. to overcome the difference in time-scales associated with the fluid and solid.
7. In general, the heat transfer in the solid occurs more slowly than the convective and diffusive time-scales dictated by the fluid flow in the solid geometry.
8. This kind of disparity in time-scales is problematic for CFD simulation because each cycle can be computationally expensive. Here Converge Studio offers super—cycling approach to overcome this issue.
9. In super-cycling, the fluid solver is frozen periodically while the heat transfer in the solid is allowed to progress to steady-state and the studio suite solves the fluid and solid phases in the same simulation without requiring the user to stop and restart the simulation.

GEOMETRY

FLUID DOMAIN

SOLID DOMAIN

COMBINED PIPE

1. Red - Solid Domain
2. Blue - Fluid Domain
3. Total length of the pipe :- 0.2 m
4. Inner & Outer Diameter :- 0.03 m and 0.04 m
5. Material of Solid :- Aluminium

MESHING

CASE 1: dx=dy=dz=0.004m

CASE 2: dx=dy=dz=0.003m

CASE 3: dx=dy=dz=0.002m

GRID SIZE IN METERS	CELL COUNT
0.004	6018
0.003	13736
0.002	41006

SIMULATION SETUP

The simulation is a transient simulation run for 0.5 sec . The fluid used for the simulation is \'Air\'

(mixture of O2 and N2), and the solid used is \'Aluminum\'. The RNG k - ε model is used to simulate the

turbulence in the flow. The boundary conditions for different boundaries are listed below:

Inlet

Neumann Condition for pressure and Dirchelet condition for velocity.

Velocity calculated using the Reynolds Number Formula given above in the problem.

Boundary Type: Inflow

Velocity: 3.5 m/s (corresponding to Re = 7000 )

Temperature: 300 K

Outlet

Neuman Condition for pressure and Dirchelet condition for pressure.

Boundary Type: Outflow

Pressure: 101325 Pa (Standard Atmospheric Pressure)

Backflow Temperature: 300 K

Outer Wall of Solid Domain

Boundary Type: Wall

Heat Flux: − 10000 W /m 2

Interface between fluid and solid domain

Boundary Type: Interface

Velocity formulation on fluid side: Law of wall

Velocity formulation on solid side: Slip

In addition to the boundary conditions, the super-cycling is enabled as well. The super-cycling is set to

activate after 0.05 sec of the simulation time. The super-cycle stage interval (SSI) is set to 0.05 sec .

A comparison is also done for the simulation time for the baseline mesh by varying the SSI to 0.03

0.02 and 0.01 sec .

SIMULATION OUTPUT CONTOURS

CASE 1: dx=dy=dz=0.004m

A. 0.03 s

TEMPERATURE

VELOCITY MAGNITUDE

Y+ WALL DISTANCE

B. 0.02 s

TEMPERATURE

VELOCITY MAGNITUDE

Y+ WALL DISTANCE

C. 0.01 s

TEMPERATURE

VELOCITY MAGNITUDE

Y+ WALL DISTANCE

CASE 2: dx=dy=dz=0.003m

TEMPERATURE

VELOCITY MAGNITUDE

Y+ WALL DISTANCE

CASE 3: dx=dy=dz=0.002m

TEMPERATURE

VELOCITY MAGNITUDE

Y+ WALL DISTANCE

SIMULATION OUTPUT PLOTS

1. GRID DEPENDENCE TEST

1.1. SOLID REGION AT DIFFERENT MESH SIZES AT SUPERCYCLE OF 0.03s

1.2. FLUID REGION AT DIFFERENT MESH SIZES AT SUPERCYCLE OF 0.03s

• It can be observed that coarser mesh converges at faster rate but a finer meshprovides accurate results.
• We can see that for finer mesh the solid region mean temperature is low, whereas liquid region mean temperature is high for a finer mesh.
• Here the temperatures are sensitive to changes in mesh grids and hencewe can reduce the mesh size further to obtain high level accuracy until these results become independent of the mesh.

2. EFFECT OF CHANGE IN SUPERCYCLE VALUES

2.1. FLUID REGION AT MESH SIZE 0.004 m AT SUPERCYCLE OF 0.05s (baseline configuration), 0.03s, 0.02s & 0.01s

2.2. SOLID REGION AT MESH SIZE 0.004 m AT SUPERCYCLE OF 0.05s (baseline configuration), 0.03s, 0.02s & 0.01s

2.3. SUPERCYCLE TEMPERATURE AT FLUID REGION

As supercycle valuesare reduced higher the time is taken for processing it (i.e. comparision to

baseline configuration of 0.05s with 0.03s, 0.02s & 0.01s). The above temperature curve attains

convergence early at lowest value of supercycle amongst the values given. This could be employed

for finer mesh where convergence delays to attain it at a faster rate. Hence, thereby the end time

could be shortened which could save the solving time.

ANIMATION

NOTE: The \'Pressure Contours\' in the video is actually velocity magnitude contours. That part has not been edited correctly.

INFERENCES

1. Y+ VALUES (text from wikipedia, table values from Simulation)

Y+ is a non-dimensional length scale that is normalized using wall shearstress. Since, each turbulence model simulates the boundary condition, so the value of Y+ is an important parameter to predict the flow field of boundary layer. The turbulent boundary layer consists of 3 layers (Viscous sub layer, logarithmic region and the Buffer layer) wherein different relations are observed between the average velocity and this non dimensional distance y+.

S.No.	MESH SIZE IN METERS	MAX Y+ VALUE
1	0.004	14
2	0.003	12
3	0.002	8.2

The above table gives us values of y+ in different mesh grids which are independent of supercycle values at same mesh size. Below image from wikipedia assigns regions to different values of y+.

• Viscous sub layer lies for y+ <=5.
• Buffer layer lies in 5<y+<30
• Logarithmic layer y+ = 30-100, up to 500.

Hence we can say that for this simulation the flow regime lies in the buffer layer.

2. PURPOSE/SIGNIFICANCE OF SUPER CYCLING

• The difference between the time scales of solid region and fluid region wasovercome by supercycling with basic idea that the solver for the fluid domain is paused (done in intervals) until the solver for the solid domain converges.
• The effect of supercycle can be observed that at lower supercycle stage interval values the flow converges early (i.e. comparision to baseline configuration of 0.05s with 0.03s, 0.02s & 0.01s) which can be employed to solving finer mesh for reducing solver time by reducing end time in seconds.

Super-cycling significantly reduces the computational cost of the CHT simulation.

3. GRID BDEPENDENCE TEST

• We can observe that as mesh size is reduced to 0.002m we can observe finer flow contour of temperature, velocity and y+ boundary value. This is demonstrated by the velocity glyph below.

• Further interesting point to note is that as the mesh is made to finer from coarser one the y+ wall distance decreases which is explained above.

Finer mesh gives precise details of changes in flow pattern.