Abstract
Numerical study is conducted to investigate the effects of free-stream Knudsen (Kn) number on rarefied flow field around a vertical plate employing an unstructured DSMC method, and an empirical method for fast prediction of flow-field structure at different Kn numbers in a given inflow velocity is proposed. First, the flow at a velocity 7500m/s is simulated using a perfect-gas model with free-stream Kn changing from 0.035 to 13.36. The flow-field characteristics in these cases with varying Kn numbers are analyzed and a linear-expansion phenomenon as a function of the square of Kn is discovered. An empirical method is proposed for fast flow-field prediction at different Kn based on the least-square-fitting method. Further, the effects of chemical reactions on flow field are investigated to verify the applicability of the empirical method in the real gas conditions. Three of the cases in perfect-gas flow are simulated again by introducing five-species air chemical module. The flow properties with and without chemical reactions are compared. In the end, the variation of chemical-reaction flow field as a function of Kn is analyzed and it is shown that the empirical method are also suitable when considering chemical reactions.
Highlights
With the rapid development of hypersonic vehicle technique, many researches are focused on the rarefied flow regime, where continuous medium hypothesis is no longer valid and a micro molecular model needs to be constructed
All simulations are performed using a Direct Simulation Monte-Carlo method (DSMC) code developed by our team from the Hypersonic Aerodynamics Research Center (HARC) in Nanjing University of Aeronautics & Astronautics (NUAA)[13]
Several important models and techniques in the simulations are chosen as follows: (1) Maxwell diffuse reflection model is used for gas-surface interaction; (2) surface temperature is supposed to be constant; (3) molecular mutual collisions are simulated using the variable hard sphere (VHS) model; (4) for possible collision partners selection, the no-time-counter (NTC) scheme is adopted, which decreases the requirement of algorithm to the mesh scale; (5) the energy exchange between kinetic and internal modes is controlled by the Larsen-Borgnakke statistical model; (6) five-species (O2, N2, O, N, NO) reacting air gas model is adopted with 23 chemical reactions[14], including dissociation, exchange and recombination; (7) for a fast and load-balancing computation, 1660155-2
Summary
With the rapid development of hypersonic vehicle technique, many researches are focused on the rarefied flow regime, where continuous medium hypothesis is no longer valid and a micro molecular model needs to be constructed. Kn is the ratio of the mean free path λ and the characteristic This is an Open Access article published by World Scientific Publishing Company. Ozawa et al found a bridging function to represent the aerodynamic characteristics of Mars explorer by carrying out a series of numerical simulations from the free-molecular flow to the continuum flow[11]. In these researches, variations of flow-field properties affected by gas rarefaction get little attention; neither do we have any empirical engineering method to predict the flow-field structure at different Kn rapidly. In a given-inflow-velocity condition, it is only needed to calculate rarefied flows at two Knudsen numbers and the flows in other Knudsen number condition can be predicted directly using the empirical method, instead of numerical simulation respectively
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