Conjugate Heat Transfer Analysis through a pipe using CONVERGE CFD

Objective:

To set up flow simulation through a pipe and to run a grid independence test and find the effect of grid size on the Y-plus value and study the effect of super cycling interval on the simulation.

Introduction to the Conjugate heat transfer analysis:

Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas, in fluids, convection usually dominates. Conjugate heat transfer is observed in many situations.

For example:

Heat sinks are optimized to combine heat transfer by conduction in the heat sink with the convection in the surrounding fluid.

It can be used for the following reasons:

1.Measurement of heat transfer in solid regions by conduction.

2.Identification of the solid domain fluid parameters.

3.Measurement of both the heat transfer from the solid to the fluid environment.

4. Determine the capacity of the material for heat transfer.

5.Optimization of heat transfer frequency and refreshment capability improvement.

Conjugate heat transfer Applications:

Effective Heat Transfer:

Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers.

The fluid usually plays the role of energy carrier on large distances. Forced convection is the most common way to achieve a high heat transfer rate. In some applications, the performances are further improved by combining convection with phase change (for example liquid water to vapor phase change).

Even so, solids are also needed, in particular, to separate fluids in a heat exchanger so that fluids exchange energy without being mixed.

Flow and temperature field in a shell-and-tube heat exchanger illustrating heat transfer between two fluids separated by the thin metallic wall.

Super-cycling:

Super-cycling is used by Converge studio in CHT problems, to make up for the time scale difference between the fluid and solid. The solid takes longer to reach a steady-state while compared to that of the fluid, thus creating a difference in the time scales. Hence the solver pauses the fluid solver at intervals defined by the user until the solid domain converges. Thus the simulation time can be reduced.

Y-plus value :

Y-plus is a non-dimensional distance. It is often used to describe how coarse or fine a mesh is for a particular flow pattern. It is important in turbulence modeling to determine the proper size of the cells near domain walls. The turbulence model wall laws have restrictions on the y-plus value at the wall.

Calculation:

Case Setup

Geometry:

The geometry is created in Converge studio using the create option. The dimensions are as follows:

Inner diameter = 0.03m

Outer diameter = 0.04m

Length of pipe = 0.2m

Pipe Material = Aluminium

Circulating Fluid = Air

Boundary Conditions:

The boundary conditions assigned to the above geometry are as follow

Inlet = Inflow type

Velocity = 3.64 m/sec as the Z-axis component .{Dirchlet boundary condition}

Pressure = Neumann Boundary condition

Outlet = Outflow type

Velocity = Neumann Boundary condition

Pressure = 101325 Pa.{Dirchlet boundary condition}

Outerwall = Wall Type

Wall Type = Stationary wall with slip condition

Temperature = Heat flux 10000W/m^2

Sidewall = Wall Type

Wall Type = Stationary wall with slip condition

Temperature = Neumann

Interface = Interface

The Fluid region is taken as the Forward Region with the law of the wall condition.

The solid region is used as the Reverse Region with slip condition

Simulation Parameters:

A transient simulation is carried out for 0.5sec

RNG K-Epsilon turbulence model is used.

Two regions are setup the fluid and solid region, with air as fluid and Aluminium as Solid

The supercycle model is enabled with supercycle intervals of 0.03,0.02 and 0.01 seconds.

Grid Independence Test:

Three different base grid size is chosen for the test

1. 0.004m

2. 0.003m

3. 0.002m

case-1:

Base mesh 0.004

Temperature contour with the baseline mesh 0.004

The temperature contour with the baseline mesh of 0.004 with a super-cycling of 0.03 is provided below.

And we can see the mesh is coarse and for the refinement, we have used the grid independences for the remaining cases.

Velocity contour with the baseline mesh 0.004

The Velocity contour with the baseline mesh of 0.004 with a super-cycling of 0.03 is provided below.

And we can see the mesh is coarse and for the refinement, we have used the grid independences for the remaining cases.

Y-plus contour with the baseline mesh 0.004

The Y-plus contour with the baseline mesh of 0.004 with a super-cycling of 0.03 is provided below.

And we can see the mesh is coarse and for the refinement, we have used the grid independences for the remaining cases.

Animation for the Temperature with the baseline mesh 0.004

The animation for the temperature contour with the baseline mesh of 0.004 with a super-cycling of 0.03 is provided above.

case-2:

Base mesh 0.003

Temperature contour with the baseline mesh 0.003.

The temperature contour with the baseline mesh of 0.003 with a super-cycling of 0.02 is provided below.

And we can see some refinement, we have used the grid independences when compared with the case-1.

Velocity contours with the baseline mesh 0.003.

The Velocity contour with the baseline mesh of 0.003 with a super-cycling of 0.02 is provided below.

And we can see some refinement, we have used the grid independences when compared with the case-1.

Y-plus contour with the baseline mesh 0.003.

The Y-plus contour with the baseline mesh of 0.003 with a super-cycling of 0.02 is provided below.

And we can see some refinement, we have used the grid independences when compared with the case-1.

Animation for the Temperature with the baseline mesh 0.003.

The animation for the temperature contour with the baseline mesh of 0.003 with a super-cycling of 0.02 is provided above.

case-3 :

Base mesh 0.002

Temperature contour with the baseline mesh 0.002.

The Temperature contour with the baseline mesh of 0.002 with a super-cycling of 0.01 is provided below.

In this case-3 the mesh is refined very much and a finer mesh is used to get an accurate result for the Temperature.

Velocity contours with the baseline mesh 0.002.

The Velocity contour with the baseline mesh of 0.002 with a super-cycling of 0.01 is provided below.

In this case-3 the mesh is refined very much and a finer mesh is used to get an accurate result for the velocity.

Y-plus contour with the baseline mesh 0.002.

The Y-plus contour with the baseline mesh of 0.002 with a super-cycling of 0.01 is provided below.

In this case-3 the mesh is refined very much and a finer mesh is used to get an accurate result for the Y-plus.

Animation for the Temperature with the baseline mesh 0.002.

The animation for the temperature contour with the baseline mesh of 0.002 with a super-cycling of 0.01 is provided above.

Effect of the Different super-cycle Time intervals on the temperature based on the base meshes:

case-1:

The base mesh 0.004 with a supercycle stage interval of 0.03 seconds was been used and the graph below shows the solid max_temperature reaches the constant temperature of 900 k after a flow time of 0.5 seconds.

case-2:

Base mesh 0.003 with a supercycle stage interval of 0.02 seconds was been used and the graph below shows the solid max_temperature reaches the constant temperature of 790 k after a flow time of 0.5 seconds.

case-3:

Base mesh 0.002 with a supercycle stage interval of 0.01 seconds was been used and the graph below shows the solid max_temperature reaches the constant temperature of 750 k after a flow time of 0.5 seconds.

Supercycle Interval:

Three intervals are chosen for testing the effect of supercycle interval.

• 0.03
• 0.02
• 0.01

Supercycle temperature at a different base mesh size.

case-1 base mesh 0.004 with a supercycle stage interval of 0.03 seconds.

case-2 base mesh 0.003 with a supercycle stage interval of 0.02 seconds.

case-3 base mesh 0.002 with a supercycle stage interval of 0.01 seconds.

Effect of the Max Temperature at Different base meshes with the different supercycle stage intervals.

In the previous picture, we can see how the supercycle stage interval does not affect the final value of the fluid or solid temperatures. there we as the expected change in the transient as the solid heat transfer is computed as different steady states. However, note the intermediate values at this simulation are not valid to determine the real transient state of the problem. In this case, where only the final steady solution is important, all of the different supercycle stages would be valid as they all reach the solution. however, what impact does change the supercycle interval have in the simulation.

The computational time for the different valued is shown here

case-1: Base mesh 0.004 with a supercycle stage interval of 0.03 seconds.

Summary of total time for:
           load balance                    =      0.05 seconds ( 0.02%)
           solving transport equations     =    182.90 seconds (87.27%)
           move surface and update grid    =      2.34 seconds ( 1.12%)
           update boundary conditions      =      4.69 seconds ( 2.24%)
           combustion                      =      0.00 seconds ( 0.00%)
           spray                           =      0.00 seconds ( 0.00%)
           writing output files            =     13.88 seconds ( 6.62%)

case-2: Base mesh 0.003 with a supercycle stage interval of 0.02 seconds.

Summary of total time for:
           load balance                    =      0.10 seconds ( 0.02%)
           solving transport equations     =    363.31 seconds (82.48%)
           move surface and update grid    =      5.93 seconds ( 1.35%)
           update boundary conditions      =     19.22 seconds ( 4.36%)
           combustion                      =      0.00 seconds ( 0.00%)
           spray                           =      0.01 seconds ( 0.00%)
           writing output files            =     36.19 seconds ( 8.22%)

case-3 Base mesh 0.002 with a supercycle stage interval of 0.01 seconds.

Summary of total time for:
           load balance                    =      0.23 seconds ( 0.01%)
           solving transport equations     =   1508.10 seconds (88.14%)
           move surface and update grid    =     10.23 seconds ( 0.60%)
           update boundary conditions      =     62.89 seconds ( 3.68%)
           combustion                      =      0.01 seconds ( 0.00%)
           spray                           =      0.01 seconds ( 0.00%)
           writing output files            =     97.12 seconds ( 5.68%)

Although the time difference here might not be huge, it is important to notice that we are simulating a coarse mesh, knowingly that an accurate simulation would take hours. Therefore, a 10-20% difference is quite relevant when trying t solve a thinner mesh. Noticing that the higher supercycle stage interval does not lead to the smallest computational time as it could be expected.

Conclusion:

1. The difference in temperature between the solid and the fluid reduces with the reduction in grid size.

2. The y+ value increases with increases in the grid size.

3. The simulation time is higher for the higher supercycle intervals, thus smaller intervals can be given to speed up the simulation.