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A multistage (MS) gas–surface interaction model for a monatomic/diatomic gas molecule interacting with a solid surface is presented, based on the analysis of molecular dynamics (MD) simulations and a model equation derived from the classical theory of an ellipsoid hitting a hard cube. This model is developed for use with the direct simulation Monte Carlo (DSMC) method and belongs to the thermal scattering regime. The molecular dynamics method is used for the molecular-level understanding of the scattering of O2, N2, and Ar from a graphite surface. The basic idea of the model is to separate the collision into three stages. At stages 1 and 2, the energy and scattering direction are determined by the model equation. At stage 3, according to the translational energy, the molecule is determined to scatter, re-enter or be trapped by the surface. Re-entering molecules return to stage 1. The model parameters are determined from our MD database. Experiments are also performed by scattering a supersonic O2 molecular beam from a clean graphite surface in an ultrahigh vacuum chamber. The in-plane scattering distribution, out-of-plane scattering distribution, and in-plane velocity distribution of the model show good agreement with those of molecular beam experiments. A model equation was included in the MS model to maintain thermal equilibrium between a gas and a surface at the same temperature when applied to DSMC simulations and the results are also shown. The high accuracy of the model clearly shows that such multiple-scale analysis can lead to the development of realistic models of the gas–surface interaction.

Cavitation instability is a major vibration source in turbopump inducers, and its prevention is a critical design problem in rocket-engine development. As reported by Kang et al., (2009, “Cause of Cavitation Instabilities in Three Dimensional Inducer,” Int. J. Fluid Mach. Syst., 2(3), pp. 206–214), the flow coefficient plays an important role in the onset of cavitation instabilities such as rotating and asymmetric cavitation. At high flow rates, various cavitation instabilities occur; on the other hand, as the flow coefficient is reduced, these cavitation instabilities either become absent or may change in character. The purpose of the present study is to investigate the relationship between rotating cavitation and flow coefficient through numerical simulations using the Combustion Research Unstructured Navier-stokes solver with CHemistry (CRUNCH) computational fluid dynamics (CFD) code (Ahuja et al., 2001, “Simulations of Cavitating Flows Using Hybrid Unstructured Meshes,” J. Fluids Eng.Trans ASME, 123(2), pp. 331–340), and to investigate the internal flow. As a first step, the interaction between the tip vortex and inducer blade was investigated through steady-state simulations. The tip vortex was identified by a vortex detection variable, i.e., the Q-function, a second invariant of the velocity tensor, and the distance between the blade and Q-function peak was measured. For a better understanding of cavitation instabilities, unsteady simulations were also performed for two different flow coefficients. The internal flow was carefully investigated, and the relation between cavity collapse/growth and the change in angle of attack was evaluated. The tip-vortex interaction is not a primary cause of unsteady cavitation, but the negative flow divergence caused by cavity collapse has a great influence on the flow angle. Moreover, changes in flow angle also introduce backflow from the tip clearance; these two factors are primary causes of cavitation instability. When the flow coefficient is large, the backflow is weak, and the interaction with the cavity collapse is strong. In contrast, as the flow coefficient decreases, stronger backflow occurs, and the interaction between backflow, cavity collapse, and flow angle weakens.

Turbopump inducers often have swirling backflow under a wide range of flow rates because they are designed with a certain angle of attack even at the design point in order to attain high cavitation performance. When the flow rate is decreased, the backflow region extends upstream and may cause various problems by interacting with upstream elements. It is also known that the backflow vortex structure occurs in the shear layer between the main flow and the swirling backflow. Experimental studies on the backflow from an inducer have given us insight into the characteristics of backflow vortex structure, but the limited information has not lead to the complete understanding of the phenomena. Numerical studies based on Reynolds-averaged Navier-Stokes (RANS) computations usually deteriorate when the flow field of interest involves large-scale separations, as shown by a previous study by Tsujimoto et al. (2005). On the other hand, the numerical approach using the Large Eddy Simulation (LES) technique has the potential to predict unsteady flows and/or flow fields that include regions of large-scale separation much more accurately than RANS computations does in general. The present paper describes the application of the LES code developed by one of the authors (Kato) to further understand the backflow vortex structure at the inlet of an inducer. First, the internal flow of the inducer was simulated, as a way to evaluate the validity of the proposed method, under a wide range of inlet flow coefficients. The static pressure peformance and the length of the backflow region was compared with measured values, and good agreement was obtained. Second, using the validated LES code, the fundamental characteristics of the backflow vortex was investigated in detail. It was found that the backflow vortices are formed in a circumferentially twisted manner at the boundary between the swirling backflow and the straight inlet flow. Also, the backflow vortices rotate in the same direction as the inducer, but with half of the circumferential flow velocity in the backflow region. Another finding was that the backflow region expands toward the center of the flow field and the number of vortices decrease, as the flow coefficient decreases. To the best of our knowledge, this is the first computation of the backflow at the inducer inlet to achieve quantitative agreement with measured results, and give new findings to the complicated three-dimensional structure of the backflow, which was very limited under experimental studies.

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