Direct Simulation Monte Carlo Calculations Research Articles

Thin-airfoil aerodynamics in a rarefied gas wind tunnel: A theoretical study

We study the steady aerodynamic field and loadings about a thin flat plate placed in a wind tunnel under non-continuum conditions. Considering a two-dimensional straight tunnel configuration, the flow is driven by either density or temperature differences between the inlet and outlet tunnel reservoirs, producing a pressure gradient across the channel. Focusing on highly rarefied conditions, we derive a semi-analytic description for the gas flow field in the free-molecular limit for diffuse- and specular-wall configurations. The solution is valid at arbitrary differences between the inlet and outlet reservoirs as well as plate angles of attack α. The results are compared with direct simulation Monte Carlo calculations, indicating that the free-molecular description is valid through O(1) plate-size-based Knudsen numbers. The aerodynamic lift and drag forces are evaluated and their variations with α, reservoir conditions, and tunnel size are analyzed. At a fixed pressure ratio between the outlet and inlet reservoirs, the density-driven flow generates higher aerodynamic loads compared with its counterpart temperature-driven configuration, in line with the associated larger mass flow rate in the former. The results are discussed in light of the existing rarefied-gas description of the free-stream (non-confined) problem.

Validity of Stokes' hypothesis for near-continuum hypersonic flows

The alternative interpretation of Stokes' hypothesis provided by Buresti [Acta Mech. 226, 3555–3559 (2015)] is investigated by an analysis of a near-continuum, hypersonic flow of oxygen over a double cone obtained from a large-scale direct simulation Monte Carlo computation. We show that for molecular oxygen, which has comparable bulk and shear viscosity coefficients, the difference between mechanical and thermodynamic pressure is negligible throughout most of the flow. This result justifies neglecting viscous stresses in the normal stress tensor associated with fluid particle dilatation, as is often done in continuum descriptions of compressible flows. The violation of the revisited Stokes' hypothesis was only observed in highly nonequilibrium regions of the flow (shocks and strong expansions) and wherever non-continuum effects become significant. For nonequilibrium flows of gases with large bulk viscosity relative to their shear viscosity, the revisited Stokes' assumption may still breakdown and requires further investigation.

Non-continuum effects on the sound of a heated line source: from a monopole to non-isotropic radiation

We study the effect of continuum breakdown on the two-dimensional thermoacoustic radiation of a thin plate set in a perfect monatomic gas. The plate is heated harmonically in time and the acoustic field is investigated in the entire range of gas rarefaction rates. Analytical approximations are obtained in the limits of high (free-molecular) and low (continuum limit) gas rarefaction, accompanied by direct simulation Monte Carlo calculations at intermediate flow conditions. While the source acoustic field is of a monopole type in the continuum regime, it turns non-isotropic at non-continuum conditions, exhibiting dipole directivity and exponential decay rate in the collisionless limit. The combined effects of source heating frequency and gas Knudsen number on the far-field acoustic radiation are illustrated and rationalized.

Inflatable aerodynamic decelerator for CubeSat reentry and recovery: IAD geometrical effects on the flowfield structure

In this investigation, Direct Simulation Monte Carlo computations were carried out to assess the influence of Inflatable Aerodynamic Decelerator (IAD) geometrical configurations on the flowfield during the atmospheric reentry. The non-reacting hypersonic rarefied flow over three IAD configurations coupled to a CubeSat was simulated considering a 0∘ angle of attack at an altitude of 105 km. According to the results, it was observed the formation of a strong and diffuse shock wave for all geometries considered in this investigation. However, a lower inflatable aeroshell angle is associated with a thinner shock wave and a maximum shock wave temperature closer to the shield's surface. These differences decrease in the flow expansion over the IAD shoulder. In the rear of the inflatable shields, a low-temperature and low-velocity region is observed, indicating that the IADs geometries successfully mitigate the harsh reentry conditions experienced by the payload. Finally, it was noticed that the wake region is larger for aerodynamic elongated shapes, in contrast to blunt geometries with the expense of slightly higher gas temperature closer to the front surface of the shield. No recirculation zone was observed in any of the simulated IAD configurations considered in this investigation.

Aerodynamic drag analysis and reduction strategy for satellites in Very Low Earth Orbit

Research interest in operating satellites in Very Low Earth Orbit (VLEO) is growing due to their potential applications for high quality Earth observation and telecommunication. In VLEO, atmospheric drag is not only a critical issue affecting the attitude control and orbit prediction of satellites, but also a key factor limiting the operational life of satellites. In this work, we first employ the direct simulation Monte Carlo (DSMC) method to calculate the aerodynamic drag of elementary shapes including flat plate, cylinder, and sphere in the VLEO region, which are validated and compared with the free molecular flow (FMF) theory. Then, we calculate the aerodynamic drag of a conceptual VLEO satellite model, and the effects of the orbital altitude, accommodation coefficient of surfaces, and the molecular speed ratio on the aerodynamic drag coefficient are analyzed. Two drag reduction strategies, referred to as lateral side smoothing and shape optimization, are investigated in detail by DSMC calculations. We propose that combining these two drag reduction strategies can achieve better drag reduction effect. In addition, we modify the optimum aspect ratio theory by considering the rarefied gas effect to give a better prediction of the optimum aspect ratio for aerodynamic drag at lower orbital altitudes.

The Mott-Smith solution to the regular shock reflection problem

The classical Mott-Smith solution for one-dimensional normal shock wave structure is extended to the two-dimensional regular shock reflection problem. The solution for the non-equilibrium molecular velocity distribution function along the symmetry-plane streamline is obtained as a weighted sum of four Maxwellians. An analysis of applicability of the solution has been performed using the results of direct simulation Monte Carlo calculations for a range of incident shock wave intensities. Accuracy of the solution improves with increasing$Ma_n$, the Mach number normal to the shock front, so that the solution becomes rather accurate for strong shocks with$Ma_n>8$.

Non-continuum effects on a squeezed gas film in a two-dimensional acoustic resonator

We study the effect of gas rarefaction and wall confinement on the propagation of vibroacoustic disturbances in a microchannel, generated by non-uniform (localized) time-harmonic oscillations of one of the channel walls. The problem is studied in the entire range of gas rarefaction rates, combining continuum and free-molecular limit analyses with direct simulation Monte Carlo calculations. Gas rarefaction is found to strongly increase the signal decay rate, varying between a slowly decaying propagating wave parallel to the channel walls at continuum conditions, to a near-source confined acoustic perturbation in the free-molecular regime. The impact of the stationary scattering wall is examined in detail, and the effect of replacing between fully diffuse and specular boundary reflections is found to slightly reduce the decay rate of the signal. The frequency dependence of the force generated by the gas film on the channel walls is calculated. Here, gas rarefaction smooths the transition between resonance and antiresonance behaviours observed in the continuum regime. A model set-up of a fully specular channel with a point delta source is examined, for which closed-form expressions are found for the effect of the stationary wall on the hydrodynamic perturbations and the acoustic force. These expressions assist in rationalizing the fundamental effect of the scattering wall on the system response.

Aerodynamics Database for Aerocapture of a Conceptual Morphable Entry System at Mars

An aerodynamics database for aerocapture of a conceptual morphable entry system at Mars was developed. The vehicle is envisioned to employ deflections of its geometry to modulate angle of attack and sideslip angle for trajectory control. Modified Newtonian methods were used to compute hypersonic continuum aerodynamics. Direct simulation Monte Carlo calculations were carried out to compute data in the rarefied transitional regime. Free-molecular theory was used to compute values in the free-molecular regime. A bridging function method was then used to bridge data from all three flow regimes together and produce a database that can be used for future trajectory simulations to assess the vehicle’s performance. The vehicle was found to have the control authority in hypersonic continuum to effect an 18 deg change in the trim angle of attack using a 10 deg deflection of the pitching control surfaces. Similarly, a 6 deg change in the trim sideslip angle could be achieved with a 5 deg deflection of the yawing control surfaces. Different configurations of the vehicle were found to be statically stable in pitch and yaw in the continuum regime, but unstable in the rarefied and free-molecular regimes.

A kinetic approach to studying low-frequency molecular fluctuations in a one-dimensional shock

Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterized for the first time in a kinetic collisional framework in the Mach number range 2≤M≤10. Our analysis draws upon the well-known bimodal nature of the probability density function (PDF) of gas particles in the shock, as opposed to their Maxwellian distribution in the freestream, the latter exhibiting two orders of magnitude higher dominant frequencies than the former. Inside the (finite-thickness) shock region, the strong correlation between perturbations in the bimodal PDF and fluctuations in the normal stress suggests introducing a novel two-bin model to describe the reduced-order dynamics of a large number of collision interactions of gas particles. Our model correctly predicts two orders of magnitude differences in fluctuation frequencies in the shock vs those in the freestream and is consistent with the small-amplitude fluctuations obtained from the highly resolved direct simulation Monte Carlo computations of the same configuration. The variation of low-frequency fluctuations with changes in the conditions upstream of the shock revealed that these fluctuations can be described by a Strouhal number, based on the bulk velocity upstream of the shock and the shock-thickness based on the maximum density gradient inside the shock, that remains practically independent of Mach number in the range examined.

On the calculation of the electron temperature flowfield in the DSMC studies of ionized re-entry flows

Currently available procedures of electron temperature calculations in studying ionized flows around reentry spacecraft by the direct simulation Monte Carlo (DSMC) method are analyzed. It is shown that the heat conduction of electrons is not taken into account in these procedures. The contributions of various effects to the electron energy balance are calculated by an example of the RAM-C II capsule, and a numerical solution of the electron energy conservation equation is obtained, which refines the electron temperature distribution used in the DSMC computations. A method of coupled calculation of the electron temperature within the framework of the continuum approach and modelling of ionized gas flow by the DSMC method is proposed.

Free-molecular and near-free-molecular gas flows over backward facing steps

We consider the two-dimensional steady channel flow of a rarefied gas over a backward facing step in the limit of large Knudsen numbers. The free-molecular problem is solved analytically for both diffuse and specular-reflecting channel boundaries, and the solutions are validated through comparison with direct simulation Monte Carlo calculations. Prescribing the density and temperature differences between the inlet and outlet external equilibrium conditions, the results for the density- and temperature-drop-driven flows are analysed and contrasted, revealing higher flow velocities and mass flow rates in the former. While the flow rate is unaffected by the step geometry in the specular case, it increases with the step size in the diffuse-reflecting set-up. At conditions where small flow velocities occur, flow detachment is observed in the form of streamlines connecting the step edge stagnation points. Considering the problem at finite Knudsen numbers, the collisionless-flow regime breaks down at higher Knudsen numbers for lower gas speed flows, followed by the occurrence of step flow separation and recirculation.

Coarse-grain cross sections for rovibrational excitation and dissociation of the [formula omitted] system

We present a method to generate analytical coarse-grain cross sections for internal energy excitation and dissociation of nitrogen and apply it to the NASA Ames N2-Nab initio database. State-resolved cross sections from this database are reduced using the Uniform RoVibrational-Collisional bin model. With a 10-bin system as example we compare two sets of coarse-grain cross sections: one obtained by analytical inversion and another by direct binning. With analytical inversion we manage to compress the entire set of state-resolved data into a small set of parameters, sufficient to reconstruct the main features of the full database. This has the potential of massively reducing the computational cost in large-scale direct simulation Monte Carlo (DSMC) calculations, both concerning memory requirements and execution time. Combining this coarse-grain model with the N2-Nab initio database will enable much higher-fidelity DSMC simulation of nonequilibrium dissociation in shock-heated flows than is currently possible with conventional models.

Drag force on spherical particle moving near a plane wall in highly rarefied gas

The drag force on a sphere in tangential and normal motion to a plane wall is evaluated in the limit of large Knudsen number and small Mach (and Strouhal) number assuming isothermal conditions and diffuse reflection of gas molecules on walls. In the limit of free molecular flow, the molecular distribution function of the gas is evaluated using a set of coupled Fredholm integral equations. The results are compared with direct simulation Monte Carlo calculations and extended for finite Knudsen numbers. In all cases stronger dependence of the force on the width of the gap is found for normal compared to tangential motion. When the flow within the gap can be considered as essentially collisionless in nature, a similar dependence of the force on the gap width is observed at finite Knudsen numbers as in the free molecular case.

Numerical simulation of the Rayleigh-Taylor instability in rarefied Ar/He mixture using the Direct Simulation Monte Carlo method

The Direct Simulation Monte Carlo method is used to study the emergence and development of the Rayleigh-Taylor instability. At the initial time, the heavier gas (argon) was located above the lighter gas (helium). In the simulation, no initial perturbations were superimposed on the interface, the appearance of instability was caused by fluctuations of gas- dynamic parameters that are inherent in the Direct Simulation Monte Carlo calculations. The onset of large-scale movement and mixing processes are investigated. Quantitative characteristics of the evolution of the Rayleigh-Taylor instability in a rarefied mode are obtained.

Direct simulation Monte Carlo computations and experiments on leading-edge separation in rarefied hypersonic flow

A comprehensive study of the fundamental characteristics of leading-edge separation in rarefied hypersonic flows is undertaken and its salient features are elucidated. Separation of a boundary layer undergoing strong expansion is typical in many practical hypersonic applications such as base flows of re-entry vehicles and flows over deflected control surfaces. Boundary layer growth under such conditions is influenced by effects of rarefaction and thermal non-equilibrium, thereby differing significantly from the conventional no-slip Blasius type. A leading-edge separation configuration presents a fundamental case for studying the characteristics of such a flow separation but with minimal influence from a pre-existing boundary layer. In this work, direct simulation Monte Carlo computations have been performed to investigate flow separation and reattachment in a low-density hypersonic flow over such a configuration. Distinct features of leading-edge flow, limited boundary layer growth, separation, shear layer, flow structure in the recirculation region and reattachment are all explained in detail. The fully numerical shear layer profile after separation is compared against a semi-theoretical profile, which is obtained using the numerical separation profile as the initial condition on existing theoretical concepts of shear layer analysis based on continuum flow separation. Experimental studies have been carried out to determine the surface heat flux using thin-film gauges and computations showed good agreement with the experimental data. Flow visualisation experiments using the non-intrusive planar laser-induced fluorescence technique have been performed to image the fluorescence of nitric oxide, from which velocity and rotational temperature distributions of the separated flow region are determined.

Gas flow mechanism and pressure analysis in plates in micro scale gas film

PurposeThe purpose of this paper is to develop the micro-electro-mechanical systems (MEMS) technology has created the conditions for the study of microfluidic technology. Microfluidic technology has become a very large branch in the MEMS field over the past decade. For aerostatic thrust bearing, the micro-fluidic gas flow in a small-scale gas film between two parallel plates is the subject of many studies. Because of the thin gas in the film, velocity slip occurs at the interface, which causes the gas flow pattern to change in the lubricating film. So, it is important to clarify the mechanism and pressure characteristics in thin firm gas flow.Design/methodology/approachFirst, a new assumption and corresponding models for the flow regime were established by theoretical analysis. Second, computational simulations about pressure distribution and velocity were given by a large-scale atomic/molecular massively parallel simulator (LAMMPS). Third, comparison of the results of LAMMPS simulation and direct simulation Monte Carlo calculation were made to verify the reliability of above results.FindingsThe gas flow mechanism and corresponding regulations are significantly different from traditional pneumo dynamics, which can be described by Navier–Stokes equations accurately. Combining theatrical study and computational results, the stratification theory of the gas film was verified. The research shows that when the gas flow rate increased, the pressure of the gas film decreased, the thickness of the continuous flow layer increased, the thickness of the thin layer decreased and the layered pressure in the gas film disappeared. In this case, velocity slippage could be ignored.Originality/valueFirst, this paper established an analytical model of the gas film support and proposed a film stratification theory. The gas film was divided into the near wall layer, the thin layer and the continuous layer, which was proved by the calculation of LAMMPS flow simulation. The velocity slip boundary conditions theory is feasible. Second, the gas film size of the flat plate is at the micron level, which cannot be observed in its flow regimen, only determined by calculation and simulation. This paper proposes a new model and a new tool to analyze gas flow in gas films.

Computation of Hypersonic Flows over Flying Configurations Using a Nonlinear Constitutive Model

The linear Navier–Stokes–Fourier (NSF) constitutive relations are derived on the assumption of the small deviation from local thermodynamic equilibrium, and consequently they may fail in describing flows removed far from local equilibrium, like rarefied hypersonic flows. In this paper, a nonlinear constitutive model of diatomic gases named as “nonlinear coupled constitutive relations” (NCCR) is presented. The model conceptually starts from Eu’s generalized hydrodynamics and is developed for simulating rarefied hypersonic gas flows with a goal of recovering NSF’s solutions in near-continuum regime and more accurate in transition regime. To enhance stable computation, an undecomposed algorithm is further developed for the nonlinear constitutive model within finite volume framework. An analysis is carried out to compare the algorithm with Myong’s original decomposed algorithm. Local nonequilibrium flow regions are also investigated for rarefied hypersonic flows over a cone tip, a hollow cylinder-flare, and a hypersonic technology vehicle–type flying vehicle. The convergent solutions of NCCR model are compared with NSF, direct simulation Monte Carlo (DSMC) calculations, and experimental data. It is demonstrated from results of general flow-field and surface properties that the NCCR model is as computationally efficient as the NSF model in continuum regime, and, at the same time, more accurate in comparison with DSMC and experimental data than NSF in nonequilibrium flows.

Analysis of nonequilibrium effects characterizes shock wave-boundary layer interactions in hypersonic flow

The study combines direct simulation Monte Carlo calculations, linear global instability analysis and momentum potential theory to characterize nonequilibrium effects.

Parametric study of water vapor and water ice particle plumes based on DSMC calculations: Application to the Enceladus geysers

The field parameters – number density, velocity components and temperature – for the Enceladus geysers, and possibly similar jets from other bodies, such as Europa, Ceres or comets, are expensive to obtain using physically correct simulation methods, such as the Direct Simulation Monte Carlo (DSMC) approach. It would be very useful to be able to correctly reproduce all the different states that the flow is undergoing while expanding into vacuum, from a high density and collisional state near the surface to free-molecular and collisionless at high altitude without resorting to expensive DSMC simulations in every case. In this work, we consider a two-phase water vapor/grain mixture exiting a circular vent, assuming a uniform radius of the water ice grains, and study how the field parameters can be fitted at an altitude of 10 km, where the flow is collisionless. To do so, we define simple functional forms for each of these fitted parameters, and we study how their coefficients vary as a function of the vent exit parameters, i.e. the vent radius, the water mixture mass flow, the water vapor/water ice mass ratio, the water ice grain radius, the water vapor and water ice exit speed, the vent exit angle and flow temperature. We define polynomial approximations to model these variations. We show that all the vent parameters have nearly-independent influences on the radial profiles at 10 km, except for the water vapor and water ice exit speed, for which we considered cross-correlations. We finally show that the geyser field parameters can be reconstructed using our parametric study for variations of the vent parameters within the range considered here, and in a time frame of a few milliseconds. The results of the parametrizations presented in this study can now be used to propagate the geyser field parameters using computationally inexpensive free molecular/ballistic codes up to higher altitudes. The DSMC results that have been run for this paper are available at an online repository.

On the unsteadiness of shock–laminar boundary layer interactions of hypersonic flows over a double cone

Unsteadiness of axisymmetric shock-dominated hypersonic laminar separated flow over a double cone is studied for the first time using a combination of time accurate Direct Simulation Monte Carlo (DSMC) calculations, linear global instability analysis, and momentum potential theory (MPT). Close to steady state linear analysis reveals the spatial structure of the underlying temporally stable global modes. At all Reynolds numbers examined, the amplitude functions demonstrate the strong coupling between the separated flow region at the cone junction with the entire shock system, including pressure and temperature waves generated behind the shock and spatially amplified Kelvin-Helmholtz waves. In addition, as the Reynolds number is increased, temporally damped harmonic shock oscillations and multiple-reflected λ-shock patterns emerge in the eigenfunctions. Application of the MPT (valid for both linear and nonlinear signals) to the highest Reynolds number DSMC results shows that large acoustic and thermal potential variations exist in the vicinity of the separation shock, the λ-shock patterns, and the shear layers. It is further shown that the motion of the bow shock system is highly affected by non-uniformities in the acoustic field. At the highest Reynolds number considered here, the unsteadiness is characterized by Strouhal numbers in the shear layer and bow-shock regions and is found to be in qualitative agreement with earlier experimental and numerical work.