Recent Research Activities

Verification of Neutronics-Thermalhydraulics Coupling Multi-Physics Method for Molten Salt Fast Reactor



  • Verification of the multi-physics analysis method to couple the neutronics and thermal-hydraulics on a computational fluid dynamics code.
  • Utilizing the reactivity input events when the fuel pump of the molten salt reactor operated at Oak Ridge National Laboratory was started and tripped.
  • It has been proved that the discretization method of the neutron kinetics equations is proper.


In a molten salt fast reactor, the fraction of delayed neutrons is lowered due to the outflow of delayed neutron precursors, and the fraction during reactor operation is lower than when there is no circulation. The neutron kinetic simultaneous differential equations taking into account the above characteristic are discretized with a prompt jump approximation, and a method for obtaining explicit solutions is incorporated into the computational fluid dynamics (CFD) code FLUENT using user defined function (UDF). This discretization method has been validated to be appropriate using measured data from the Molten Salt Reactor (MSRE) operated at Oak Ridge National Laboratory in the United States of America.


Molten fuel salt circulates in the core of a molten salt fast reactor, and the nuclear reaction and temperature distribution are closely linked.  It is in a so-called the neutronics and thermal-hydraulics coupling condition.  For this reason, it has been proposed that a method for evaluating the reactor power by analyzing the temperature distribution inside the molten salt fast reactor core in detail using a computational fluid dynamics (CFD) code combining with the nuclear kinetic equations.  The neutron kinetic equations represented by simultaneous differential equations are discretized under the prompt jump approximation so that they can be analyzed explicitly.  Therefore, it is necessary to validate the method.

Up to now, a molten salt thermal neutron reactor (MSRE) was in operation at Oak Ridge National Laboratory in the United States for four years since 1965.  In this reactor, delayed neutron precursors flowed out when the fuel pump was started, causing a change in reactivity.  The fuel pump startup and trip tests were carried out under the zero power conditions and the control rods were driven to maintain criticality.  The data at this time were disclosed and used for validation in this study.  The control rods were driven via a control circuit.  There have been several studies that analyzed these transients, but it is unclear whether the control circuit was properly simulated, and the analysis results did not sufficiently explain the test results.  In this study, a PID control circuit is incorporated into the FLUENT code as shown in Fig. 1 and two transients were analyzed.

Fig. 1 Schematic diagram of analysis model using the FLUENT code which incorporates neutron kinetic equations and PID control system


Figure 2 illustrates the reactivity change evaluated from the control rod (CR) movement when the fuel pump is started and tripped.  Although the behavior of CR movement is different depending on the PID control constants, the analysis results with a proportional gain of 1.0, an integration time of 4 s, and a derivative time of 0.2 s can almost simulate the measured results for startup and trip of the fuel pump.  When the pump is started, a negative reactivity of about 225 pcm is added to the core with nearly a stepwise change.  For this reason, the control rods are pulled out at the speed limit and pass through the setpoint position.  Therefore, the peak is a controller overshoot rather than a reactor physical characteristic.  This state differs depending on the control constants.  However, it has been verified that the discretization method of the kinetic equations was appropriate by the fact that the calculated reactivity matches the converged measured value.  In the case of the fuel pump trip, the added negative reactivity is eliminated.  When the pump is tripped, since the delayed neutron precursors are not discharged from the core, a positive reactivity is added to the core.  Since the pump does not stop instantly, the reactivity change rate is slower than when the pump is started.

From these analysis results, it was validated that the neutron kinetic equations and control program incorporated in FLUENT functioned correctly and that the neutron kinetics could be analyzed by the CFD code.

Fig. 2 Evolutions of measured and calculated reactivity changes for the fuel pump startup and trip of MSRE

Journal information

Author :
Title of original :
Verification of neutronics and thermal-hydraulics coupling method for FLUENT code using the MSRE pump startup, trip data
Journal :
Nuclear Engineering and Design, 378, 111191, (2021).
Affiliation :
Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute of Technology