Simcenter STAR-CCM+ Switching To Adiabatic Wall When The Wall Heat Transfer Rate To A Wall Boundary Exceeds A Value (Schmitt Trigger)

The method of Schmit Trigger applied in Simcenter STAR-CCM+ has been described here. But can this concept be applied in this simple 2D heat transfer by conduction simulation? The 2D heat conduction model is shown in the picture below. The heat sources 25 W and 50 W are applied on these marked boundaries. The heat source 25 Watts is applied to half a circle boundaries and 50 Watts to the full circle boundaries as indicated in the picture below.

Convective heat transfer is applied to the remainder of the boundaries, as shown in the picture below. But one boundary will have a conditional heat transfer coefficient. When the wall heat transfer rate on that boundary is below five Watts, heat transfer coefficient is 326 W/m²-K. But once the wall heat transfer rate exceeds five Watts, the heat transfer coefficient will drop to 0 and will remain to be zero for the rest of the simulation.

One can simply apply a conditional statement on the boundary condition itself, like shown in the picture below. But this will not work. When the wall heat transfer rate exceeds five Watts, the heat trasnfer coefficient will drop to 0. But this will cause the wall heat transfer rate to drop below five Watts, which then in the next iteration the heat transfer coefficient will go back up to 326 W/m²-K again. The whole process will repeat and will result in fluctuating wall heat transfer rate on the boundary, which is not what we want. We want the heat transfer coefficient to remain 0 W/m²-K througout the simulation once the condition is met for the first time.

Unlike the Schmitt Trigger method described in this article here, the result from this heat conduction simulation is being fed back into the boundary condition of the model. It should be noted that any expressions defined on the boundary, in this case the Heat Transfer Coefficient, can only accept a single value. Therefore you cannot enter a field function into the expression, except for field function Iteration. Therefore we will be using Reports and Monitors.

The way it works is in this way: Let us assume that at iteration 301 for the first time the wall heat transfer rate at the boundary is slightly above five Watts. When the code is solving the model for iteration 302, it will use a heat transfer coefficient of 0.0 W/m²-K. This will return a wall heat transfer of 0.0 W for iteration 302. When the code is solving iteration 303, the code will use the heat transfer coefficient of 326.0 W/m²-K because the wall heat transfer rate at iteration 302 is 0.0 Watts, which is less than five Watts. The wall heat transfer at iteration 303 will return a value that is above five Watts. As the iteration continues, the wall heat transfer will fluctuating up and down between 0 Watts and a value above five Watts. In order to keep the heat transfer coefficient to remain 0.0 right after the first time the wall heat transfer drops to 0.0 Watts, we need to add one or more additional conditional statement that checks the wall heat transfer from previous the Iteration.

In order to keep track the wall heat transfer from the previous Iteration, you need to create three reports. The first two reports are Statistics Report. The third report is an Expression report. The first Statistics Report is named HP1(N+1). It returns the value of the summation of wall heat tranfer rate from the current and the previous iterations, see the picture below for the properties of this report. The second Statistics Report is named HP1(N), which returns heat transfer rate from the current iteration (Sample count in the property window is set to 1 for this report). The third report is named HP1(N-1), and it is an Expression report. The third report performs an arithmetic operation from the two previously mentioned Statistics Reports: HP1(N+1) - HP1(N). This report will return wall heat transfer rate from the previous iteration. 

The next step is to create one more Expression report, named Flag, that will return one of the two values: 1.0 and 0.0. It will return a value of 1.0 if one of these conditions are met: the current or the previous wall heat transfer rate is 0.0 Watts. This conditional statement should look like in the picture below. The first part of the conditional statement "${Iteration} <= 1 : 0.0" is added for a safety measure when iteration is equal or less than 1.

Now that we have everything in place, we can enter a proper expression in the definition for the boundary heat transfer coefficient, see picture below. 

The plot of the wall heat transfer rate is shown in the picture below.

The plot of wall heat transfer rate with the wrong setup is shown in the picture below.