Conjugate Heat Transfer Simulation

Project objective:

To set up a case for flow through a solid pipe to study the effect of conjugate heat transfer, to perform grid dependency test on three different grid sizes and to study the effect of super-cycling.

Software tools used:

• Simulation - Converge CFD studio (v2.3)
• Command editor - Cygwin
• Post-processing - Paraview

Case setup:

• General flow gas simulation
• Solver type: Transient
• Species: Air (O2-23%,N2-77%)
• Solid material - Aluminium
• Turbulence model: RNG k-ε
• Simulation time - 0.5 seconds

Boundary conditions:

Inlet :

• Pressure - Zero normal gradient
• Velocity - 3.752 m/s
• Temperature - 300K

Outlet:

• Pressure - 101325 Pa
• Velocity - Zero normal gradient
• Temperature - 300K

Solid outer wall:

• Stationary
• Slip type
• Heat flux = -10000 W/meter square

Solid sidewall:

• Stationary
• Slip type
• Temperature: Zero normal gradient

The calculation of the above inlet velocity is given below -

Reynolds Number = Inertial Force / Viscous Force

The Reynolds number formula is expressed by,

`Re =rho*(V*D)/mu`

Where,

ρ = density of the fluid,

V = velocity of the fluid,

μ = viscosity of fluid,

D = diameter of the fluid.

`7000 = V* (0.015 *2)/(1.608*10^-5)`

Velocity V = 3.752 m/s

Geometry:

Grid dependency test:

• Mesh - 4mm

Mesh (surface with edges) - 4mm

Temperature contour - mesh 4mm

Velocity glyph

• Mesh - 3mm

Mesh (surface with edges) - 3mm

Temperature contour - 3mm mesh

Velocity glyph

• Mesh -2mm

Mesh (surface with edges) - 2mm

Temperature contour - 2mm mesh

Velocity glyph

In a solid, usually, conduction dominates. whereas with fluids convection dominates. A simulation in which the heat transfer between solid and fluid is done by exchanging thermal energy at their interfaces is known as Conjugate Heat Transfer (CHT). Some of the examples other than this simulation include engine cooling systems, heat sinks, etc.

From the above animations, it can be seen that initially, the conduction process takes up some time to heat the solid through heat flux. After that, the solid quickly reaches a steady state value of around 740K. In the case of fluid region, as there is a flow from inlet to outlet due to the pressure difference, the fluid flowing near the solid region gradually gets heated up to 360K.

Mean temperature vs time in the fluid region

Mean temperature vs time in solid region

Mean temperature at a monitor point(x = 0.0175, y = 0, z = 0.18) vs time

From the above plots it can be seen that, as the mesh becomes finer, the temperature value also decreases. So it is proven that the accuracy of simulation highly depends on the size of the mesh.

Effect of super-cycling:

In this type of conjugate heat transfer analysis, solving both the solid and fluid domain is tedious. To overcome this converge has a feature known as super-cycling in which the fluid solver is ceased for a particular period of time, while the solid solver solves the heat equations. And then the fluid solver is released to solve its fluid equations. This cycle continues until the temperature in solid domain converges to a steady value. From the above plot, it can be seen that as the super-cycle interval becomes shorter, the temperature converges sooner.

Y+ plot against the length of the tube:

The y+ reaches a maximum of 14.3 with 4mm mesh.