Dimensionless analysis of the influence of secondary water level on the single-phase reverse flow in the inverted U-tube of steam generators with natural circulation

[Background]: The single-phase reversed flow in inverted U-tubes of the steam generator (SG) in nuclear power plants leads to increasing flow resistance and decreasing heat transfer area, so it is meaningful to study this phenomenon. [Purpose]: This study aims to clarify the influence mechanism of the secondary side water level in SG on the single-phase reversed flow from a more general viewpoint. [Methods]:  The dimensionless conservation equations were derived first based on the mass, momentum, and energy equations. Based on the dimensionless conservation equations and the parameter of the AP1000 inverted U-tubes, the curves of dimensionless total and gravitational pressure drop with respect to flow velocity were obtained with the MATLAB code. Then the curves of different water levels were compared. Meanwhile, the extreme point was obtained with the partial derivative being zero concerning flow velocity. Then the effect of the water level on the secondary side under the conditions of different lengths, dimensionless resistance number, and dimensionless heat transfer number was analyzed by using the model of extreme point. Finally, the above theoretical results have been validated by the simulational results of the system analysis code for single-phase reverse flow in the SG of AP1000. [Results]: The decrease in the water level leads to the critical point of the single-phase reversed flow gradually approaching the origin, and the negative slope zone of the curves gradually decreases, Meanwhile, the gravitational pressure drop decreases, and its negative slope zone reduces. The above results mean that the reversed flow is becoming more and more easy to emerge. With the increase in pipe length, the dimensionless characteristic pressure drop increases, and the dimensionless characteristic velocity decreases, which means the reverse flow occurs more easily in the longer pipe. When the dimensionless resistance number increases, the dimensionless characteristic velocity decreases, and the dimensionless characteristic pressure drop increases, which means the reverse flow occurs more difficult. As the water level decreases, the effect of the dimensionless resistance number becomes weaker. As for the dimensionless heat transfer number, the dimensionless characteristic velocity is not affected by its value, and the dimensionless characteristic pressure drop increases with its increase, which means the reverse flow occurs more easily. Moreover, the effect of the dimensionless resistance number becomes weaker with the decreases of the water level. Hence, the influence law of the water level is the same under different pipe length conditions. As the water level decreases, the influence of the dimensionless resistance number and dimensionless heat transfer number on the critical point gradually reduces. [Conclusions]: This study theoretically proves that the effect of secondary water level on single-phase reversed flow is conducive to the occurrence of backflow, and explains the reasons from a mechanistic perspective, which can assist in accident analysis of related nuclear power plants.