Conjugate Heat Transfer Simulation
Problem Statement:
The aim of this project is to model the conjugate heat transfer problem, which deals with the interaction between a solid and a liquid. In this case, air flows through a heated aluminum pipe. The effect of grid size and super cycling is to be studied and also the variation of y+ values are to be investigated.
Case Setup:
A cylinder of inner diameter 30 mm and a thickness of 10 mm is created using the create tool in converge. The boundaries for inlet, outlet and cylinder wall are then flagged accordingly. There are two regions in the simulation: Solid Region, which is the aluminum tube and Liquid Region, which is the air flowing through the tube. Air is flowing in at atmospheric conditions and the cylinder is initially at 300 K. The velocity of air flow, if it has to follow the given condition of Reynolds Number=10000 will be 0.7845 m/s. For calculating the velocity properties of air were taken at 300 K.
The mesh sizes used were 2mm, 3mm, and 4mm to elucidate the grid independence. A view of 2mm grid generation developed in paraview:
The simulation was run for 1.5 seconds and super cycling was added for an interval of 0.05 seconds. Later, the effect of variation in super cycling values was checked by using super cycle intervals of 0.01, 0.02 and 0.03 seconds.
Heat is transferred to the tube at a rate of 10000 W/m2 and the change in temperature can be observed from the animations.
Boundary Conditions:
Inlet boundary: Inflow condition. Air at Atmospheric conditions and velocity 0.7845 m/s is given.
Cylinder Walls: treated as wall boundaries following the law of wall.
Outflow: Air at atmospheric conditions.
Interface: This boundary is the one where the two regions, i.e. fluid and solid interact with each other. Since the air is flowing inside the pipe, it is given as the forward boundary with roughness constant 0.5 and the solid pipe is treated as a slip boundary.
Turbulence model used is RNG k-epsilon. A transient solver is used and the CFL numbers used are default.
Results and Observation:
Grid Independence:
The temperature of the solid region for grid sizes 2mm, 3mm and 4mm are shown above. We can see that the profiles are almost the same. The temperature starts to converge at the same time in all three cases. They converge at a value around 750-800 K. They might not have exactly the same values as the increase in grid size decreases the accuracy. Apart from a minor discrepancy in values, the temperature seems to converge around the same value and thus we can prove the grid independence.
Y+ Value:
The Y+ value is a measure of how turbulent a flow is at a particular point. It is a non-dimensional quantity and it purely depends upon the grid size. The Y+ values seem to be low as the flow is not very turbulent near the walls and as time progresses the flow smoothens out. We can see that the y+ value is lower for lower grid sizes.
Y+ values for 2,3 and 4mm are shown.
Effect of Supercycling:
The effect of super cycling can be directly seen on the convergence time. A comparison of 3 super cycle values for 4mm grid size was done. From the graph, we can see that for 0.01s super cycle interval the temperature converges the fastest. Owing to a faster convergence the simulation also takes a shorter duration. The simulation takes longest for a 0.05 s interval. This can be seen from an earlier graph of 0.05 s interval where convergence takes close to 0.04 s for a 4mm grid size.
The link to the animations: