Conjugate Heat Transfer Simulation

Objective:

Simulate flow through a solid pipe and understand the effect of Super-Cycling

Introduction:

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. The exchange of thermal energy between the two physical bodies is called study of Heat Transfer, the rate of transferred heat is directly proportional to the temperature difference between the bodies. A typical example is the heating or cooling of a solid object by the flow of air in which it is immersed and some other example includes conduction through solids, free and forced convection in the gases/fluids and thermal radiation.

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. Efficiently combining heat transfer in fluids and solids is the key to designing effective coolers, heaters, or heat exchangers. Forced convection is the most common way to achieve 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).

Heat transfer in solids and heat transfer in fluids are combined in the majority of applications. This is because fluids flow around solids or between solid walls, and because solids are usually immersed in a fluid.

Simulation Setup:

The geometry used is a solid pipe. It has inner radius of 0.015m and outer radius of 0.02m. The length of the pipe is 0.2m. Solid pipe is made of Aliminium and fluid used is air. For gas simulation we have used the Redlich-Kwong equation of state because it accounts for non-ideal gas behavior, which may be significant at high pressures and temperatures.

Boundary Conditions:

Te outer curved solid surface has slip wall type boundary condition and temperature boundary condition is set to \"heat flux\" equal to -10000 W/m^2. The negative sign indicates that the heat is flowing inside the geometry. Inlet has a Reynolds number of 7000. Density of air at 300K is 1.177kg/m^3, hydraulic diameter is equal to 0.03m, dynamic viscosity of air is 1.846×10^-5 kg/ms. By using the formula Re = (rho*V*D)/(Dynamic viscosity) we get inlet velocity equal to 3.65 m/s. Outlet has pressure boundary condition of 101325.0 Pa. In CHT we apply interface BC where fluid and solid suface meet. The inner solid wall is set to interface BC. The normals are pointing towards the fluid region hence it is a forward boundary for fluid region having \"law of wall\" for velocity and temperature. Similarly solid has reverse BC with slip wall treatment for velocity and specified value ID for temperature. The solid side wall thickness has slip wall BC and \"zero normal gradient(NE)\"(adiabatic) for temperature. In \"region and initialization tab\'we have added two regions one for fliud and one for solid. Temperature for fluid is 300K and pressure equal to 101325 Pa. Solid has a stream ID of 1. Turbulence modelling used is K-Epsilon.

Running Simulation Using Cygwin:

Post Processing Results Using ParaView:

Grid Dependence Test:

The grid dependence test was carried out for four grid sizes and the following Outlet temperature (vs) Time graph shows for which grid size the convergence is good.

• Grid Size = 0.004 m

• Temperature Contour

• Grid Size = 0.003 m

• Temperature Contour

• Grid Size = 0.002 m

• Temperature Contour

• Grid Size = 0.0015 m

• Temperature Contour

• Plot of average Temperature for different grid size vs Time

From the above contours and the mean temperature (vs) time graph it can be seen that the outlet mean temperature does not converges at the same value for all the four grid sizes. The convergence of outlet mean temperature for the grid size 4 mm and 3 mm is good.

Effect of Supercycle Stage Interval:

Super-cycling is a method used by CONVERGE Studio in the case of conjugate heat transfer problems with a solid and liquid regions.The integral problem here is that both solvers cannot run at the same speed since solving in the fluid domain is much faster owing to the time scale difference for heat transfer in liquids as compared to solids. 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.

The basic idea of super-cycling is that the solver for the fluid domain is paused until the solver for the solid domain converges. This pausing is done in intervals that can be set by the user.

• Plot of Mean temperature for solids with different super-cycling values vs Time

The plot shows more steps for lower value of super-cycle stage interval time and it starts taking average earlier.

Simulation Time Comparision:

• Super-Cycle stage Interval = 0.01s

Program Used 252.26 seconds

Load Balance = 0.06 seconds (0.02%)

Solving Transport Equations = 223.85 seconds (88.74%)

Move Surface and Update Grid = 2.95 seconds (1.97%)

Update Boundary Conditions = 5.89 seconds (2.33%)

Writing Output files = 15.81 seconds (6.27%)

• Super-Cycle stage Interval = 0.02s

Program Used 246.21 seconds

Load Balance = 0.06 seconds (0.02%)

Solving Transport Equations = 223.39 seconds (90.73%)

Move Surface and Update Grid = 2.42 seconds (0.98%)

Update Boundary Conditions = 5.10 seconds (2.07%)

Writing Output files = 11.83 seconds (4.81%)

• Super-Cycle stage Interval = 0.03s

Program Used 224.93 seconds

Load Balance = 0.06 seconds (0.02%)

Solving Transport Equations = 203.54 seconds (90.48%)

Move Surface and Update Grid = 2.21 seconds (0.98%)

Update Boundary Conditions = 4.70 seconds (2.09%)

Writing Output files = 11.00 seconds (4.89%)

Thus from the above values it is observed that as the super-cycle stage interval increases the simulation time decreases.

The Simulation can be visualized from the animation below

Conclusion:

From this conjugate heat transfer simulation, one can understand the transfer of heat occurring between the solid and fluid regions. The technique of supercycling is used here. The supercycling method first solves the fluid part and the solid interface part together. Then it makes the results as the boundary condition at the interface to solve the solid part as a steady state by freezing the fluid solver. Then the solid temperature is updated and the fluid part in unfreezed. This cycle takes place till the solid temperature converges. The conjugate heat transfer simulation is used for efficiently combining heat transfer in fluids and solids for designing effective coolers, heaters, or heat exchangers. Heat transfer in fluids and solids can also be combined to minimize heat losses in various devices.