Supersonic Rarefied Flow Research Articles

Data Parallelization Algorithms for the Direct Simulation Monte Carlo Method for Rarefied Gas Flows on the Basis of OpenMP Technology

A data parallelization algorithm for the direct simulation Monte Carlo method for rarefied gas flows is considered. The scaling of performance of the main algorithm procedures are analyzed. Satisfactory performance scaling of the parallel particle indexing procedure is shown, and an algorithm for speeding up the operation of this procedure is proposed. Using examples of solving problems of free flow and flow around a cone for a 28-core node with shared memory, an acceptable speedup of the entire algorithm was obtained. The efficiency of the data parallelization algorithm and the computational domain decomposition algorithm for free flow is compared. Using the developed parallel code, a study of the supersonic rarefied flow around a cone is carried out.

Numerical simulation of rarefied supersonic flows using a fourth-order maximum-entropy moment method with interpolative closure

Maximum-entropy moment methods allow for the modeling of gases from the continuum regime to strongly rarefied conditions. The development of approximated solutions to the entropy maximization problem has made these methods computationally affordable. In this work, we apply a fourth-order maximum-entropy moment method to the study of supersonic rarefied flows. For such conditions, we compare the maximum-entropy solutions to results obtained from the kinetic theory of gases at different Knudsen numbers. The analysis is performed for both a simplified model of a gas with a single translational degree of freedom (5-moment system) and for a typical gas with three degrees of freedom (14-moment system). The maximum-entropy method is applied to the study of the Sod shock-tube problem at various rarefaction levels, and to the simulation of two-dimensional low-collisional crossed supersonic jets. We show that, in rarefied supersonic conditions, it is important to employ accurate estimates of the wave speeds. Since analytical expressions are not presently available, we propose an approximation, valid for the 14-moment system. In these conditions, the solution of the maximum-entropy system is shown to realize large degrees of non-equilibrium and to approach the Junk subspace, yet provides a good overall accuracy and agreement with the kinetic theory. Numerical procedures for reaching second-order accurate discretizations are discussed, as well as the implementation of the 14-moment solver on Graphics Processing Units (GPUs).

Investigation of shock/shock interferences on the aerodynamics of a fragment in the wake of debris in a rarefied regime/at high altitude

This work presents an experimental investigation focused on the analysis of aerodynamic properties between two interacting spheres in a supersonic rarefied flow. Atmospheric re-entries of space debris, whether natural or man-made, begin at altitude 120 km, and observations of historical re-entries have shown that fragmentation occurs between 90 and 50 km. The resulting fragments interact with each other, altering their own trajectories while traversing the different flow regimes between the free molecular and continuum regimes. This study focuses on the intermediate slip regime, where viscous effects of varying magnitude can influence the nature of the interactions of the shocks and modify them from the already known behaviour in the continuum regime. Specifically, this study examines how two spheres interact with each other upon re-entry into the atmosphere, focusing particularly on the six types of shock/shock interactions identified by Edney. The experiments were performed in the MARHy wind tunnel, in a steady Mach 4 laminar flow with static pressure 2.67 Pa. To highlight the differences between the six types of interferences, a variety of set-ups and devices were used: flow-field visualization, aerodynamic forces (through two diagnoses, aerodynamic balance and the swinging sphere technique) and wall pressure measurements. Results demonstrate the identification of differences according to the type of interference observed, showing in particular the viscous effect of rarefied flows by making a comparison with the continuum regime.

Information preservation optimization method based on the advection upstream splitting method in supersonic rarefied flow simulation

Here, we propose an information preservation (IP) optimization approach for supersonic flow simulations. Based on the conversion of variables integrated in a half-space and analogical analysis, we obtained a relationship between the integrated variables, used in the governing equations of the preserved information, and the macroscopic variables used in Navier–Stokes equations. Computationally, the flux for the correlation terms is reconstructed using the Advection Upstream Splitting Method (AUSM) scheme, giving the IP method windward characteristics. Additionally, the pressure boundary treatment is modified to improve the stability and accuracy of the IP method in the simulation of rarefied supersonic flows driven by high pressures. The particle number threshold method is proposed to solve the “carbuncle point” problem, which is caused by insufficient local collisions. The IP optimization method combines the advantages of the AUSM scheme and low statistical scatter method. Thus, it can be used to investigate the real-time variations in a rarefied supersonic flow through simulations of the supersonic microscale jet flow and hypersonic macroscale nozzle flow. The results indicate that the real-time statistical accuracy of the IP optimization method is significantly higher than that of the direct-simulation Monte Carlo method, and the correctness and accuracy of this method are satisfactory as well. Therefore, the proposed method can unveil the mechanisms underlying the variations and unsteadiness in rarefied supersonic flows on different scales.

Unified gas-kinetic scheme with simplified multi-scale numerical flux for thermodynamic non-equilibrium flow in all flow regimes

In this paper, a BGK-type kinetic model for diatomic gases is proposed to describe the high-temperature thermodynamic non-equilibrium effect, which is a phenomenological relaxation model with continuous distribution modes of rotational and vibrational energies. In order to obtain the correct Prandtl number and reasonable relaxation rate of heat fluxes, the equilibrium distribution function is constructed by using a multi-dimensional Hermitian expansion around Maxwellian distribution. Based on this kinetic model equation, a unified gas-kinetic scheme (UGKS) with simplified multi-scale numerical flux is proposed for thermodynamic non-equilibrium flows involving the excitation of molecular vibrational degrees of freedom in all flow regimes. The present UGKS keeps the basic conservation laws of the macroscopic flow variables and microscopic gas distribution function in a discretized space. In order to improve the efficiency of UGKS, a simplified multi-scale numerical flux is directly constructed from the characteristic difference solution of complex kinetic model equation. Furthermore, the applications of unstructured discrete velocity space (DVS) and a simple integration error correction reduce the number of velocity mesh significantly and make the present method be rather efficient for flow simulation in all flow regimes. The new scheme is examined in a series of cases, such as Sod’s shock tube, high non-equilibrium shock structure, hypersonic flow around a circular cylinder with Knudsen (Kn) number Kn=0.01, supersonic rarefied flow over a flat plate with a sharp leading edge, and hypersonic rarefied flow past a blunt wedge. The present UGKS results agree well with the benchmark data of DSMC and other validated methods.

A novel hybrid framework coupling the discrete velocity based-method, the particle-based method and the Grad's distribution function-based method for supersonic rarefied flows

Supersonic rarefied flow has an intrinsically multiple-scale nature due to the large variations of density and characteristic length of the flow structures. Although particle-based methods such as direct Monte Carlo simulation (DSMC) present efficient performance in supersonic rarefied flows, the statistical noise as the nature of stochastic method causes a large amount of averaging steps to be required. To minimise the contamination of statistical noise and preserve the efficiency of capturing the multiscale rarefied effects, a finite volume based hybrid framework is proposed to couple the discrete velocity method (DVM), the particle-based method and the Grad's distribution function-based moment gas kinetic method (G13-MGKS). Benefiting from the coupled treatment both in the spatial and velocity space, the DVM-based method is applied to low-velocity areas close to the wall, which greatly eases the statistical noise and numerous steps of statistical averages can be avoided. Besides, the partition of different sub-methods conveniently determined by the initial flow field from conventional CFD solver has been verified without compromising any accuracy. Further applying the Grad's distribution function-based method in the area with moderate rarefied effect, the present hybrid DVM-Particle-Grad (HDPG) method exhibits the high efficiency and achieves a tenfold speedup ratio compared to the DVM.

Correlation between waverider shock waves and aerodynamic forces in supersonic rarefied flow, experimental investigation in the wind tunnel MARHy

This paper presents an experimental study of the influence of viscous flows on the aerodynamic behaviour of waveriders. This investigation was carried out in the MARHy facility, under supersonic and rarefied flow conditions. Three supersonic and low density flow conditions were tested operating at Mach 2 and 4 with free stream pressures of 8 Pa and 2.67 Pa giving slip regime flows. Knudsen numbers associated with these flow conditions and this test model are between 2.79 × 10-3 and 7.33 × 10-4. In terms of pressure, these conditions are similar at altitudes between 50 km and 80 km. The studied waverider has a geometry proposed in the literature and optimised for a Mach 10 flow and an altitude of 50 km. The purpose of this work is to experimentally analyse how viscous effects will affect the aerodynamic performances of the waverider in off-design conditions. This work is based on the analysis of the upper and lower shock wave angles obtained from glow discharge imaging technique for different angles of attack and the three operating conditions. Results showed that the evolution of shock wave angles are Mach number dependent, as predicted by the inviscid shock relations, but also strongly depends on the flow pressure. From these experimental results, fitting equations have been established to predict the variation of upper and lower shock angles with the flow density, Mach number as a function of the angle of attack in continuum and especially in slip regime. Shock wave angles behaviour are compared to measured Lift-to-Drag ratio. Comparison presents a similar behaviour with flows conditions and shows that viscous layers appearing at low densities have a great influence on aerodynamic forces.

A simple hydrodynamic-particle method for supersonic rarefied flows

In the practical aerospace industry, the supersonic rarefied effect presents multiscale characteristics from the near-continuum regime to the free molecular regime. In this paper, a simple hydrodynamic-particle method (SHPM) is proposed to efficiently capture the multiscale properties for the supersonic rarefied flow. To combine the conventional computational fluid dynamics solver with the particle-based method, the weights are theoretically derived from the integral solution of the Boltzmann Bhatnagar–Gross–Krook equation. The present numerical method is validated by test cases of supersonic shock wave structure, Sod shock-tube, and supersonic flow around the circular cylinder. Numerical results demonstrate that the SHPM could capture the multiscale properties from the continuum regime to the rarefied regime.

Information Preservation Optimization Method Based on the Advection Upstream Splitting Method in Supersonic Rarefied Flow Simulation

Information Preservation Optimization Method Based on the Advection Upstream Splitting Method in Supersonic Rarefied Flow Simulation

Shock/shock interferences in a supersonic rarefied flow: experimental investigation

Shock/shock interferences in a supersonic rarefied flow: experimental investigation

DC Discharge Electronic Non-equilibrium Effects Investigations on a M = 2 Rarefied Supersonic Flow Over a Flat Plate

This work aims at studying the effects of a low-pressure Argon discharge (P = 0.5 Torr) on a supersonic Argon flow (M = 2) around a flat plate. The observed phenomena during high speed-flow control with a plasma discharge are exhaustively described. The present investigation is of great interest not only to aviation but also to numerous other areas like the wind power industry. The computations have been carried out using the DC discharge and the High Mach Number Flow Comsol Multiphysics modules. To simulate the DC discharge, chemical reactions near the cathode region along with their corresponding Townsend coefficients need to be defined. The latter are calculated using the Bolsig + computer code. The other reactions cross sections are imported from the LXCAT data base. The imported data are used to calculate the reactions rates. The plasma discharge effects on the rarefied supersonic flow are described using a 2D hydrodynamical model under the Drift–Diffusion approximation. The hydrodynamical model was validated by comparing its results for a supersonic air flow with experiments. The main results on an Argon supersonic flow coupled to an Argon discharge show an increase in the pitot pressure and the shock angle.

Experimental investigation of the properties of a glow discharge used as plasma actuator applied to rarefied supersonic flow control around a flat plate

This paper describes experimental investigations focused on the glow discharge created by a plasma actuator and used to shock wave modification over a flat plate in a Mach 2 air flow. The model is equipped with a plasma actuator composed of two electrodes. A weakly ionized plasma is created above the plate by generating a glow discharge with a negative dc potential applied to the upstream electrode. ICCD images of the discharge without and with the Mach 2 flow show the influence of the flow field on the discharge morphology. In addition, ICCD images of the modified flow revealed that when the discharge is ignited, the shock wave angle increased with the applied voltage. Thermal measurements of the flat plate surface carried out with an IR camera showed that the spatial temperature distribution is not uniform along the plate and its maximum, near the leading edge, increases with the applied voltage. Previous results showed that surface heating is responsible for roughly 50% of the shock wave angle increase, meaning that purely plasma effects must also be considered to fully explain the flow modifications observed. The focus of this paper is the study of the properties of the glow discharge to better understand the interaction between the supersonic flow and the purely plasma effects which are responsible of flow field modifications, in particular ionization degree and thermal disequilibrium upstream the model.

Aerodynamic analysis of the aerospaceplane HyPlane in supersonic rarefied flow

HyPlane is the Italian aerospaceplane proposal targeting, at the same time, both the space tourism and point-to-point intercontinental hypersonic flights. Unlike other aerospaceplane projects, relying on boosters or mother airplanes that bring the vehicle to high altitude, HyPlane will take off and land horizontally from common runways. According to the current project, HyPlane will fly sub-orbital trajectories under high-supersonic/low-hypersonic continuum flow regimes. It can go beyond the von Karman line at 100km altitude for a short time, then starting the descending leg of the trajectory. Its aerodynamic behavior up to 70km have already been studied and the results published in previous works. In the present paper some aspects of the aerodynamic behavior of HyPlane have been analyzed at 80, 90 and 100km. Computer tests, calculating the aerodynamic parameters, have been carried out by a Direct Simulation Monte Carlo code. The effects of the Knudsen, Mach and Reynolds numbers have been evaluated in clean configuration. The effects of the aerodynamic surfaces on the rolling, pitching and yawing moments, and therefore on the capability to control attitude, have been analyzed at 100km altitude. The aerodynamic behavior has been compared also with that of another aerospaceplane at 100km both in clean and flapped configuration.

Kinetic analysis of thermally relativistic flow with dissipation. II. Relativistic Boltzmann equation versus its kinetic models

Thermally relativistic flow with dissipation was analyzed by solving the rarefied supersonic flow of thermally relativistic matter around a triangle prism by Yano and Suzuki [Phys. Rev. D 83, 023517 (2011)], where the Anderson-Witting (AW) model was used as a solver. In this paper, we solve the same problem, which was analyzed by Yano and Suzuki, using the relativistic Boltzmann equation (RBE). To solve the RBE, the conventional direct simulation Monte Carlo method for the nonrelativistic Boltzmann equation is extended to a new direct simulation Monte Carlo method for the RBE. Additionally, we solve the modified Marle (MM) model proposed by Yano-Suzuki-Kuroda for comparisons. The solution of the thermally relativistic shock layer around the triangle prism obtained using the relativistic Boltzmann equation is considered by focusing on profiles of macroscopic quantities, such as the density, velocity, temperature, heat flux and dynamic pressure along the stagnation streamline (SSL). Differences among profiles of the number density, velocity and temperature along the SSL obtained using the RBE, the AW and MM. models are described in the framework of the relativistic Navier-Stokes-Fourier law. Finally, distribution functions on the SSL obtained using the RBE are compared with those obtained using the AW and MM models. The distribution function inside the shock wave obtained using the RBE does not indicate a bimodal form, which is obtained using the AW and MM models, but a smooth deceleration of thermally relativistic matter inside a shock wave.

Kinetic analysis of thermally relativistic flow with dissipation

Nonequilibrium flow of thermally relativistic matter with dissipation is considered in the framework of the relativistic kinetic theory. As an object of the analysis, the supersonic rarefied flow of thermally relativistic matter around the triangle prism is analyzed using the Anderson-Witting model. Obtained numerical results indicate that the flow field changes in accordance with the flow velocity and temperature of the uniform flow owing to both effects derived from the Lorentz contraction and thermally relativistic effects, even when the Mach number of the uniform flow is fixed. The profiles of the heat flux along the stagnation streamline can be approximated on the basis of the relativistic Navier-Stokes-Fourier (NSF) law except for a strong nonequilibrium regime such as the middle of the shock wave and the vicinity of the wall, whereas the profile of the heat flux behind the triangle prism cannot be approximated on the basis of the relativistic NSF law owing to rarefied effects via the expansion behind the triangle prism. Additionally, the heat flux via the gradient of the static pressure is non-negligible owing to thermally relativistic effects. The profile of the dynamic pressure is different from that approximated on the basis of the NSF law, which ismore » obtained by the Eckart decomposition. Finally, variations of convections of the mass and momentum owing to the effects derived from the Lorentz contraction and thermally relativistic effects are numerically confirmed.« less

Investigation of rarefied supersonic flows into rectangular nanochannels using a three-dimensional direct simulation Monte Carlo method

The rarefied flow of nitrogen with speed ratio (mean speed over most probable speed) of S=2,5,10, pressure of 10.132 kPa into rectangular nanochannels with height of 100, 500, and 1000 nm is investigated using a three-dimensional, unstructured, direct simulation Monte Carlo method. The parametric computational investigation considers rarefaction effects with Knudsen number Kn=0.481,0.962,4.81, geometric effects with nanochannel aspect ratios of (L/H) from AR=1,10,100, and back-pressure effects with imposed pressures from 0 to 200 kPa. The computational domain features a buffer region upstream of the inlet and the nanochannel walls are assumed to be diffusively reflecting at the free stream temperature of 273 K. The flow analysis is based on the phase space distributions while macroscopic flow variables sampled in cells along the centerline are used to corroborate the microscopic analysis. The phase-space distributions show the formation of a disturbance region ahead of the inlet due to slow particles backstreaming through the inlet and the formation of a density enhancement with its maximum inside the nanochannel. Velocity phase-space distributions show a low-speed particle population generated inside the nanochannel due to wall collisions which is superimposed with the free stream high-speed population. The mean velocity decreases, while the number density increases in the buffer region. The translational temperature increases in the buffer region and reaches its maximum near the inlet. For AR=10,100 nanochannels the gas reaches near equilibrium with the wall temperature. The heat transfer rate is largest near the inlet region where nonequilibrium effects are dominant. For Kn=0.481,0.962,4.81, vacuum back pressure, and AR=1, the nanoflow is supersonic throughout the nanochannel, while for AR=10,100, the nanoflow is subsonic at the inlet and becomes sonic at the outlet. For Kn=0.962, AR=1, and imposed back pressure of 120 and 200 kPa, the nanoflow becomes subsonic at the outlet. For Kn=0.962 and AR=10, the outlet pressure nearly matches the imposed back pressure with the nanoflow becoming sonic at 40 kPa and subsonic at 100 kPa. Heat transfer rates at the inlet and mass flow rates at the outlet are in good agreement with those obtained from theoretical free-molecular models. The flows in these nanochannels share qualitatively characteristics found in microflows and continuum compressible flows in channels with friction and heat loss.

Transformation of energy and composition of gas mixtures in a collision of rarefied supersonic flows

Transformation of energy and composition of gas mixtures in a convergent flow from a strip source on a cylindrical surface toward the axis is systematically studied with the use of the direct simulation Monte Carlo method. Information on the influence of gas-flow rarefaction and system geometry on the temperature and concentration of the heavy gas in a dense cloud formed on the axis is obtained. The use of convergent supersonic flows is demonstrated to offer new possibilities for research in the field of physical gas dynamics.

Supersonic Rarefied Flow Past a Cascade of Transverse Flat Plates

The results of numerical calculations of the supersonic rarefied flow through an infinite, periodic cascade of flat plates set transverse to the incident flow are presented. The flow in the vicinity of the cascade is described on the basis of the kinetic Boltzmann equation. The Knudsen numbers, based on the plate span, the distances between the plates and the scalelength of the flow under consideration, range from 0.2 to 0.003. Both steady-state regimes with a shock attached to the cascade and time-dependent ones with an upstream-traveling shock are investigated.

Monte Carlo computation of rarefied supersonic flow into a pitot probe

Pitot probes are commonly used to make measurements in high-speed gas flows in wind tunnels and vacuum chambers. In supersonic flow, a shock wave forms in front of the probe. In the continuum flow regime, the Rayleigh pitot probe equation is used to describe nonisentropic pressure losses across this shock. Under the rarefied flow conditions typical of supersonic plumes produced by spacecraft propulsion systems, the continuum theory is inaccurate. Hence, pressure corrections are needed to make use of pitot probe measurements in these flows. Currently, there is no general analytical theory describing this behavior. In the present study, the direct simulation Monte Carlo method is used to simulate rarefied, supersonic flow of nitrogen into a representative pitot probe geometry in order to predict these pressure corrections. Numerical results are compared with experimental data and are found to show good agreement qualitatively and quantitatively. Pressure corrections computed at very low probe Reynolds numbers are found to be consistent with free molecular limits calculated using collisionless gas theory.

Rarefied gas flow analysis by direct simulation Monte Carlo method in body-fitted coordinate system

A new method is proposed for the rarefied gas flow analysis by the direct simulation Monte Carlo (DSMC) method in a multidimensional flow. In this method, a body-fitted coordinate system is used and therefore the DSMC method can be applicable to a flow-field analysis around the body of arbitrary configuration. Through an application to the rarefied supersonic flow around the circular cylinder, the present method was found to be reliable and time-saving in computation time.