Abstract:
The mixing coefficient is an important parameter of fuel assemblies, which has a significant impact on core design and safety analysis, and needs to be measured for each type of fuel assembly. But the mixing coefficient can’t be obtained directly by experiment. The common method is to conduct multiple subchannel analyses under the assumption of different mixing coefficients, and obtain the sum of squared errors
s between the measured temperature values and the corresponding calculated values for each subchannel. When
s is the minimum, the corresponding mixing coefficient is thought to be the actual measured mixing coefficient. Currently, there is a lack of an exact functional relationship between
s and the mixing coefficient, and the minimum
s can only be found through trial calculations. The whole process is quite complicated and costs a lot of time. In the paper, the maximum temperature difference
Tβ calculated by subchannel analysis was introduced as an intermediate variable, and the functional relationships for mixing coefficients were established through theoretical analysis, including the function of mixing coefficient and
Tβ, the function of
s and
Tβ, and the function of the
s and mixing coefficient. Among them,
Tβ decreases exponentially with the increase of the mixing coefficient, and
s is a quadratic function of
Tβ. These functions provide a clear theoretical basis for the mixing coefficient calculation. On this basis, a concise method for calculating the mixing coefficient from a single set experimental data was proposed, which can avoid tedious multiple trial calculations. Firstly, fit
s as a quadratic function of
Tβ. Then calculate
Tβ corresponding to the minimum value of
s based on the properties of the quadratic function. Finally, calculate the mixing coefficient according to the monotonic relationship between
Tβ and the mixing coefficient. The research also finds that when the mixing coefficient is a constant, the temperature rises of subchannels in different experimental data groups are proportional to the power-to-flow ratio. Based on this phenomenon, multiple sets of experimental data can be converted into one set, and the average mixing coefficient can be calculated directly, which can greatly reduce the computational load of subchannel analysis and improve the calculation accuracy of mixing coefficients. By comparing with the results obtained through traditional method, the correctness and efficiency of the new method were verified. A new method is also proposed to evaluate the uncertainty of the mixing coefficient test by subchannel temperature rise data, thereby avoiding error amplification in the calculation of the mixing coefficient.