Projects and Objectives

The objective of the project entrusted to BSIM was to determine the airflow rate and temperature at the inlet of a double-door display refrigerator.

The airflow had to ensure a temperature of 4°C inside the refrigerated volume. The position and size of the ventilation vents were already defined, as was the rest of the geometry, including the inevitable gaps leading to the outside that remain even when the doors are closed.

This was a fairly typical request from our client, where the team responsible for the gas-cycle components asks the CFD specialist for fixed parameters to implement, which for the refrigerator designer will serve as the boundary conditions for the subsequent simulation.

The refrigerator with doors closed, doors open, and the gaps above the doors.

Approach to the analysis

The simulation includes detailed modeling of the various layers of material that make up the insulation and the refrigerator casing, the presence of a heat source such as the motor located in the lower technical compartment, and standard ambient conditions in the operating environment.

A preliminary simulation was performed with an airflow rate of 200 l/min at 4°C, resulting in the following:

Clearly, the 4°C airflow was not sufficient to ensure the proper temperature inside the refrigerated volume. However, this steady-state simulation was useful in understanding the extent of the losses within the fridge and identifying the key parameters to monitor (fluid velocity, fluid temperature, flow trajectories, wall temperatures).

The next step was to determine: “What is the air temperature at the inlet of the channel that achieves the target temperature inside the volume?”

Using dedicated optimization tools within the 3D CFD software we employ (Simcenter FLOEFD), it was possible to find the following iterative solution by varying the inlet temperature, resulting in:

We found that an airflow rate of 200 l/min at -7.37°C achieves 4°C inside the volume.

This optimized solution suggests a consistent value for both flow rate and temperature. However, it is important to emphasize that the two solutions presented so far were limited by being steady-state solutions, meaning they represent the conditions obtainable over infinite time. Their function is to highlight the thermal behavior of the refrigerator: understanding how much the refrigerator loses, whether the selected materials are suitable, if one configuration is better than another, and so on.

Once this task is complete, the steady-state simulation can and must give way to a time-dependent simulation, which provides insights into the system’s dynamics and, more importantly, addresses the designer’s key question:

“Are the optimal temperature and flow rate, which were satisfactory from a steady-state perspective, equally effective from a dynamic standpoint?”

After 10 hours, the system has reached approximately 5°C, and based on the current trend, it may take many more hours to finally approach the promised 4°C.

As expected, the flow rate estimated in the steady-state simulation, even at a theoretically appropriate temperature, was not sufficient to ensure the correct performance of the system. How should we proceed in this case? One approach would be to use the Goal Optimization Tool again, this time perhaps fixing the temperature and allowing the system to iterate by adjusting the airflow rate. In this case, the goal would not just be achieving a certain temperature but also specifying when that temperature should be reached. It would be up to the designer to define a specific criterion, for example:

“I would like the refrigerator to be able to reach 4°C within a maximum time of 1 hour.”

Thus, the decision was made to iterate again, this time not on the air temperature but on the airflow rate. By allowing the tool to iterate up to 1000 l/min, the optimal solution was found:

We discovered that with an airflow rate of 920 l/min at an inlet temperature of -7.37°C, our system was able to bring the refrigerated volume to 4°C within one hour. But what would happen if we allowed the simulation to continue beyond the one-hour mark? The temperature would certainly drop well below the 4°C just achieved. However, as we know, all refrigeration systems have a thermostatic mechanism that deactivates the cooling circuit once a certain temperature is reached.

This brings us to the final step of the CFD design process: translating the data into energy terms and asking the key question:

“I want my refrigerator to turn off when it reaches 4°C: how often will my compressor need to activate?”

To simulate this cycle, we implemented a control logic on the time-dependent boundary conditions, such as:

The logical formulation could have been much more complex than this, for example, trying to replicate a behavior with a whole range of shutdown temperatures (e.g., from 3°C to 5°C). However, for the level of analysis conducted, this was sufficient. A feasible approach in this case would have been the combined use of a 3D CFD software and a 0D-1D tool, such as Simcenter Amesim, which is much more specialized in control system development and can therefore be used to manage the external components of the refrigerator system.

In more advanced developments, co-simulation can become fully integrated, assigning the refrigeration cycle, including the details of recirculation channels, heat exchangers, gases, compressors, etc., to the 0D-1D tool, as well as the aforementioned control system. Meanwhile, the 3D CFD tool continues to focus on the volumetric fluid dynamics and heat exchange.

That said, with the simulation set up according to the logic described above, we obtained a time-dependent trend that looked like:

Conclusion

With the airflow set, the refrigerator reaches 4°C after exactly 3600 seconds. At that point, the refrigeration system shuts off for the first time, and we can observe how, due to thermal losses, the temperature begins to rise almost immediately. After just a few dozen seconds, the temperature reaches 4°C again, causing the airflow to restart. However, for several more seconds, the effects are not immediately noticeable, at least until the airflow once again influences the majority of the volume.

It can also be observed that the behavior repeats almost identically with each cycle. The slight differences between one cycle and the next are due to the instantaneous time-step, which does not always coincide perfectly with the moment the temperature thresholds are crossed.

This is how we supported the client in completing the fluid design of the refrigerator using 3D CFD simulation.