Researchers from the Moscow Institute of Physics and Technology, together with colleagues from Switzerland and the United States, determined the accuracy of popular turbulence models for calculating thermal conditions in advanced liquid-fueled nuclear reactors. This will help engineers more accurately predict the thermal state of a dual-fluid reactor operating in natural circulation mode. Such calculations are critically important for cooling systems that must function automatically — without external power supply or operator intervention.  The results of the study were published in the journal Nuclear Engineering and Design.

Most nuclear power plants in operation today use solid fuel elements — uranium dioxide pellets in zirconium cladding, according to Nauchnaya Rossiya.  In Generation IV dual-fluid reactors, the fuel is in a liquid state and circulates through a separate loop, while the coolant is molten lead.  This design has higher efficiency (30% higher compared with traditional pressurized water reactors) and makes it possible to continuously reprocess the fuel. However, it is precisely this feature that has created a serious mathematical problem for engineers.

Liquid fuel does not obey the heat transfer laws familiar from water and air. At low flow velocities, heat spreads through it not via turbulent mixing but through molecular forces. At the same time, all existing engineering turbulence models are designed specifically for water and air.

“In its characteristics, a liquid uranium-chromium alloy is something intermediate between traditional liquid metals (lead, sodium, and lead-bismuth) and air. This created uncertainty over whether turbulence models can be applied to a uranium-based liquid metal. This issue is especially important for natural circulation modes of the secondary loop — when the pumps providing lead flow are switched off and the flow moves slowly. If the model makes errors in temperature calculations, this can lead either to underestimating thermal loads or to excessively conservative design. And it is precisely in these cases that it is especially important to know exactly how the temperature is distributed so that safety systems operate reliably,” explained one of the study’s authors, Konstantin Sergeenko, a researcher at MIPT’s Laboratory of Supercomputer Methods in Condensed Matter Physics.

The object of the study was the experimental Dual Fluid Reactor. Using supercomputer modeling, the scientists obtained highly accurate “reference” data on the temperature and velocity of nuclear fuel as it flowed around heat-exchange rods. They then compared these data with the results produced by two common engineering turbulence models: the more complex Reynolds stress model RSM BSL and the simpler k-omega-SST model. Until now, it had been unknown how accurate they are for describing uranium-based liquid metals at low flow velocities.

“It turned out that the k-omega-SST turbulence model described the thermal hydraulics best. The RSM BSL model, despite its more detailed description of turbulent flow, showed no advantages in any of the calculation scenarios considered. The main reason is the lack of accounting for various mechanisms of turbulent flows, which operate differently in different parts of the flow. It was also found that in longitudinal flow over heat-exchange surfaces, the error in determining heat transfer increases with increasing velocity, while for transverse flow the error is small. The reason is that for transverse flow the velocities are relatively low, and turbulent heat transfer in liquid metals is harder to describe than in water or air, for which most engineering models were developed,” Konstantin Sergeenko said.

The authors of the work did not simply record these discrepancies — they quantitatively assessed the accuracy of each turbulence model for the studied modes. Engineers now know under what conditions each turbulence model provides reliable results and where special caution is required. This makes it possible to use simplified models in the operating modes where they have already been validated and to obtain accurate temperature forecasts without costly supercomputer modeling.

The data obtained will form the basis of designs for emergency decay heat removal systems for Generation IV dual-fluid reactors. It should be recalled that such installations are considered one of the most promising tools for closing the nuclear fuel cycle — that is, for the repeated use of uranium and reducing the amount of radioactive waste.