Numerical and experimental investigation of rarefied hypersonic flow in a nozzle

A combined computational/experimental study is performed to investigate hypersonic low-density internal gas flows in a convergent-divergent nozzle over a wide range of Knudsen numbers. The numerical solutions are obtained using the direct simulation Monte Carlo (DSMC) method and the experimental measurement is conducted in the hypersonic low-density wind tunnel FengDong-19 (FD-19) at China Academy of Aerospace Aerodynamics. Rarefaction effects are found to play an important role in pressure disturbance propagation, flow separation (vortex formation), mass flow rate, velocity slip, and thermally nonequilibrium effect. Pressure disturbance propagates farther upstream with increasing free-stream Knudsen number Kn∞. Although there is no flow separation near the nozzle surface for Kn∞ = 0.1, the slip velocity is such anomalously small that it cannot suppress flow separation, thus, producing one small vortex for Kn∞ = 0.2, 0.5 and 1. Due to the presence of the continuous sheet of two-order Moffatt vortices, the skin friction coefficient does not change sign (positive to negative) in the small separated region. This indicates that the incipient and small separated flows with second-order vortices may not be discerned by examining the sign of the skin friction. As Kn∞ grows to 2, this small vortex disappears. However, with further increase in Kn∞, a large vortex nearly fills the compression section of the nozzle due to the backflow effect. As Kn∞ increases from continuum to free molecular regime, the dimensionless mass flow rate mfr/mfr∞ rises first to its maximum at Kn∞ ∼ 0.2 resulting from the weaker flow blockage effect. After the maximum point, mfr/mfr∞ dwindles first because of the stronger backflow effect and rises again to its free molecular limit, obtaining its minimum (the so-called Knudsen minimum) at Kn∞ ∼ 10. DSMC results and experimental data obtained from FD-19 wind tunnel are in good agreement, achieving a mutual validation between computation and experiment. This indicates that our experiment provides valuable data that can server as “benchmark” case to support computational code evaluation and validation.