Three-dimensional large eddy simulations of high-pressure jets at the same nozzle pressure ratio of 5.60 but issuing from different nozzles are conducted. Four different nozzle geometries, i.e., the circular, elliptic, square, and rectangular nozzles, are used to investigate the effect of the nozzle geometry on the near-field jet flow behavior. A high-resolution, hexahedral, and block-structured grid containing about 31.8 million computational cells is applied. The compressible flow solver, astroFoam, which is developed based on the OpenFOAM C++ library, is used to perform the simulations. The time-averaged near-field shock structures and the mean axial density are compared with the experiment data to validate the fidelity of the LES results, and the reasonable agreement is observed. The results indicate that the remarkable differences exist in the near-field flow structures of the jets. In particular, the circular and square jets correspond to a three-dimensional helical instability mode, while the elliptic and rectangular jets have a two-dimensional lateral instability in their minor axis planes. A subsonic flow zone exists after the Mach disk in the circular and square jets, but is lacking in the elliptic and rectangular jets. The intercepting shocks in the circular jet originate near the nozzle exit, and appear to be circular in cross-section. The intercepting shocks in the square jet originate at the four corners of the nozzle exit at first, and then are observed along the major axis plane some distance downstream of the nozzle exit. However, the formation of the intercepting shock is observed in the major axis planes but is lacking in the minor axis planes for the elliptic and rectangular jets. In addition, the real mass flow rates and discharge coefficients for different jets are computed based on the LES modeling, and their differences are explored.

Safety relief valve (SRV) is still the ultimate security component of pressure vessels or piping equipment. It does not take the place of a regulating or control valve but it aims to protect devices and people by preventing damage due to overpressure in the system. This is ensured by discharging an amount of fluid when excessive rising pressure occurs. For the incompressible flows, the discharge coefficient of the relief valve can be modified by cavitation development under specific operating conditions. Then, the sizing of the valve doesn’t correspond to the flow discharged resulting in severe damage. This study aims to demonstrate the capability of numerical modeling to predict the evolution of discharge coefficient under cavitation conditions. URANS simulations have been performed with ANSYS CFX 13.0 using Shear Stress Transport modeling. A Rayleigh-Plessey model is used to predict the development of cavitation in the relief valve. A modification of the saturation vapor pressure is proposed in the cavitation model to take into account the turbulent effects on the cavitation development. Additionally a Plexiglas mock-up has been built for flow visualization and two valve discs are used to measure the discharge coefficient or the flow force acting on the valve. Numerical and experimental approaches are compared first by analyzing qualitative results through flow visualization and also by evaluating hydraulic characteristics of the SRV.

The assessment of the seismic scrammability, which means the control rod insertability during a seismic event, is one of the most important design tasks for ensuring the seismic safety of nuclear power plants in Japan. This paper discusses the dynamic modeling of the control rod insertion behavior of a boiling water reactor (BWR) during an earthquake. A dynamic model of a control rod insertion system for BWR was developed based on multi-body dynamics. The coupled vibration behavior of the fuel assemblies in the fluid was modeled as an inertial coupling system. The effect of the interaction force between the control rod and the fuel assemblies was considered in a three-dimensional contact analysis. The hydraulic control unit and the control rod drive, which provide the control rod with drive force, were modeled in the concentrated parameter system. The model parameters, such as the friction coefficient between the control rod and the fuel assembly and the discharge coefficient of the scram piping, were obtained by conducting experiments. The validity of the model was confirmed by comparing the analytical results with the experimental ones. First, the validity of the fuel assembly model was verified through a comparison with the vibration testing in an underwater condition. It was confirmed that the calculation results for the frequency response of the fuel assembly were in good agreement with the experimental ones. Second, the validity of the modeling method of the drive system consisting of the hydraulic control unit and the control rod drive was verified through a comparison with the scram testing under non-vibration condition. The calculation results for the time history of the control rod insertion, the accumulator pressure, and the flow through the scram piping were in good agreement with the experimental ones. Finally, the validity of the modeling method of the whole system consisting of the fuel assemblies, the control rod, and the drive system was verified through a comparison with the scram testing under vibration condition. The calculation results for the time history of the control rod insertion stroke and the time delay of the insertion motion during an earthquake were in good agreement with the experimental ones. The results of these comparisons show that the developed analysis model can simulate the control rod insertion behavior during an earthquake.

A multiple steam generator tube rupture (MSGTR) event in APR1400, an advanced pressurized water reactor, is investigated using the best estimate thermal hydraulic system code, MARS1.4. The effects of parameters such as the number of ruptured tubes, rupture location, affected steam generator on analysis of the MSGTR event in APR1400 are taken into account. In particular, the effects of tube rupture modeling are compared. In the present study, single tube (STM) and double tube modeling (DTM) are examined for assessment on the main steam safety valve (MSSV) lift time. Nuclear steam supply system (NSSS) and several safety systems that are relevant to the APR1400 are modeled. Automatic safety systems are assumed to mitigate the MSGTR events including the reactor protection trip, reactor coolant pump trip, the pressurizer heaters, high-pressure safety injection (HPSI) pumps, and the valves for atmospheric dump, main steam safety, main steam isolation, and turbine stop and bypass. When five tubes are ruptured, the STM permits the operator response time of 2085 seconds before lifting of MSSVs. The effects of rupture location on the MSSV lift time is not significant in case of STM, while the MSSV lift time for tube-top rupture is found to be 25.3% larger than that for rupture at hog-leg side tube sheet in case of DTM. The MSSV lift time for the cases that both steam generators are affected (4C5x, 4C23x) are found to be larger than that for the single steam generator cases (4A5x, 4B5x) due to a bifurcation of the primary leak flow. The discharge coefficient of C d is found to affect the MSSV lift time only for smaller value of C d below 0.5. For larger values of C d than 0.5, its effect on the leak flow rates as well as the MSSV lift time become negligible. It is found that the most dominant parameter governing the MSSV lift time is the leak flow rate. Whichever modeling method is used, it gives the similar MSSV lift time if the leak flow rate is similar, except the case of both steam generators are affected. Therefore, the system performance and the MSSV lift time of the APR1400 are strongly dependent on the break flow model used in the best estimate system code.

The paper presents the results of an extensive experimental research programme performed on safety valves in order to clarify the effects of back pressure and valve size on the flow capacity of a valve. As well known, back pressure strongly influences valve operating characteristics and can also reduce the discharge coefficient. This flow rate reduction can be related to the occurrence of a subsonic flow regime along the flow path and to insufficient disc lift. Last mentioned features can play a different role on different valve sizes because of the non exact geometrical scaling within the same valve size range. This happens because the requirements of typical application design standards, such as the API Standard 526, are such that the valve inlet, valve outlet and face to face dimension are not exactly scaled with respect to the orifice diameter. Moreover, face to face dimension can limit the body bowl volume leading to different device performances the same operational conditions. In order to clarify and evaluate the influence of the above mentioned parameters on the flow capacity of safety valves, many tests were carried on a single valve for different pressure ratios, disc lifts and for different valve outlet areas and body volumes representing different sizes derived from API Standard 526. Test results show significant differences on the flow capacity of safety valves under back pressure regime. This would suggest testing every valve size of the considered valve size range at different expansion ratios to confirm performance. Since this procedure leads to an excessive number of experimental tests, a sensitivity analysis on the influence of the most important geometrical parameters has been carried out. In order to minimize the number of experimental tests required for characterizing the flowing capacity of the whole valve size range, the paper proposes an experimental correlation for the prediction of the above mentioned non similarity effects.

This paper provides design examples and summarizes a study on the determination of multiple free discharge orifice coefficients in a circular walled manifold for a variety of shapes and area projections. A simplified design procedure is presented which allows engineers to accurately maintain a given pressure and flow at the entrance to the sparger. The design provides for uniform flow across the cooling tower basin, and prevents an increase in back pressure or open channel flow within the sparger, minimizing the effect on upstream performance.