E. V. Titov

Extension of the DSMC method to high pressure flows

A collision-limiter method, designated as equilibrium direct simulation Monte Carlo (eDSMC), is proposed to extend the DSMC technique to high pressure flows. The method is similar to collision-limiter schemes considered in the past with the important distinction that for inviscid flows, equilibrium is enforced in the entire flow by providing a sufficient number of collisions, based on pre-simulation testing. To test the method with standard DSMC and Navier–Stokes (NS) methods, axi-symmetric nozzle and embedded-channel flows are simulated and compared with experimental temperature data and pre-existing calculations, respectively. The method is shown to agree with third-order Eulerian nozzle flows and first-order channel flows. Chapman–Enskog theory is utilized to predict the range of initial conditions where eDSMC is potentially useful for modeling flows that contain viscous boundary layer regions. Comparison with supersonic nozzle data suggests that the eDSMC method is not adequate for capturing the large variation in flow length scales occurring in supersonic expansions into a vacuum. However, when eDSMC is used in combination with the baseline-DSMC method a near-exact solution is obtained with a considerable computational savings compared to the exact DSMC solution. Viscous flow channel calculations are found to agree well with an exact Navier–Stokes (NS) calculation for a small Knudsen number case as predicted by Chapman–Enskog theory.

Examination of a Collision-Limiter Direct Simulation Monte Carlo Method for Micropropulsion Applications

A wide range of flow regimes occur in micronozzles, from the transitional to the continuum regime, which prevents the use of a single computational method such as direct simulation Monte Carlo or computational fluid dynamics and Navier-Stokes. A collision-limiter approach is proposed that extends the applicability of direct simulation Monte Carlo to the continuum regime and can be used to solve a wide range of microelectromechanical system flows when it is coupled with the baseline direct simulation Monte Carlo. A comparison of the results obtained with this computational technique with new experimental data and Navier-Stokes results suggests consistency between experimental and computational methods for three-dimensional microelectromechanical system micronozzles with stagnation pressures on the order of 5 atm. However, the level of agreement was found to vary with the nozzle geometry, suggesting that additional research is needed for both computations and experiments in this flow regime.

Assessment of Bhatnagar-Gross-Krook Approaches for Near Continuum Regime Nozzle Flows

Accurate and numerically efficient modeling of low-to-moderate Reynolds number nozzle flow expansions to vacuum can be difficult due to the presence of multiple flow length scales. Such simulations are important for the prediction of propulsive thrust as well as spacecraft contamination, both of which can be difficult to measure in ground-based facilities. To that end, conical nozzle flows were studied for Reynolds numbers of 1230 and 12,300 using the direct simulation Monte Carlo method, Navier―Stokes with velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of the Bhatnagar―Gross―Krook and ellipsoidal-statistical Bhatnagar―Gross―Krook equations. The deterministic and statistical solutions of the Bhatnagar―Gross―Krook equation were found to be in good agreement with the benchmark direct simulation Monte Carlo results. Statistical Bhatnagar―Gross―Krook and ellipsoidal-statistical Bhatnagar―Gross―Krook methods were also found to be more efficient methods than direct simulation Monte Carlo in the continuum and near-continuum regime, and more accurate than the Navier―Stokes equations in the portions of the flow with rarefaction, such as the boundary layer and the flow around the nozzle lip.

Reconsideration of Planar Couette Flows Using the Statistical Bhatnagar-Gross-Krook Approach

DOI: 10.2514/1.44409 Anumberofresearchershaveconsideredtransitional-flowgasdynamicapproachestothewell-knowncaseof flow through moving parallel plates. The papers consider different initial conditions and different aspects of the problem and, in some cases, reach conclusions that will be shown to be contradictory to careful numerical simulations. The purpose of this paper is to reexamine some of these key works on planar Couette flow, one of the most fundamental fluid-dynamics problems, particularly with respect to the calibration of the statistical Bhatnagar–Gross–Krook and ellipsoidalstatisticalBhatnagar–Gross–Krookmethods.ThepaperwillpresentbenchmarkdirectsimulationMonte Carlo solutions, by which analytic and Bhatnagar–Gross–Krook/ellipsoidal statistical Bhatnagar–Gross–Krook simulationsmaybecomparedfor flowvelocities,temperatures,heat fluxes,andshearingcoefficients.Thedifferences among the solutions obtained by the direct simulation Monte Carlo, Bhatnagar–Gross–Krook, and ellipsoidal statistical Bhatnagar–Gross–Krook methods will be examined from a microscopic point of view, and the statistical Bhatnagar–Gross–Krook and ellipsoidal statistical Bhatnagar–Gross–Krook methods will be shown to be numericallymoreefficientthanthedirectsimulationMonteCarlomethodfora flowconditionthatispresentlyatthe comfort-levellimitfordirectsimulationMonteCarlocomputations.Finally,itwillbeshownthatananalyticsolution for incompressible, argon, transitional flow (Knudsennumber 0:01) remains valid beyond the applicability ranges suggested in the original work.

Development of a Particle–Particle Hybrid Scheme to Simulate Multiscale Transitional Flows

In the present work, a new particle–particle hybrid method that combines the statistical ellipsoidal-statistical Bhatnagar–Gross–Krook and direct simulation Monte Carlo methods is developed. The switching criterion between the two methods is based on the deviation of the cumulative velocity distribution function from Maxwellian as measured by the Kolmogorov–Smirnov statistical test. Unlike other hybrid approaches that use switching criteria based on macroscopic properties, the selection of a particular particle method in a cell is determined by the local Kolmogorov–Smirnov parameter value with respect to a preset global switching criterion. A numerically efficient technique to compute the Kolmogorov–Smirnov parameter was developed to enable the efficient calculation of the degree of nonequilibrium. Two well-known fluid-flow problems, expanding argon flow through a nozzle and hypersonic flow over a blunt body, were studied. The Kolmogorov–Smirnov parameter is shown to demarcate the regions of nonequilibriu...

Analysis of Fractal-Like Spore Aggregates Using Direct Simulation Monte Carlo

DOI: 10.2514/1.T3824 The work presented in this paper is a continuation of the authors’ previous efforts to develop a realistic bioengineering model for predicting the survivability of anthrax spores subjected to a high-temperature gas environment. One of the major mechanisms of deactivating spores is to expose them to elevated temperatures, and careful, exposure-tube experiments have been carried out to ascertain the deactivation mechanism. Spores typically exist in nature as aggregates, but simulating the heat transfer to clumps of spores is difficult because of the highly irregular geometry of spore clumps. In this work, the tunable particle-cluster and cluster-cluster algorithms are implemented to generate fractal-like spore aggregates. The algorithm output as a function of algorithm parameter input is compared with a typical spore-clump image. Because the spore aggregate size is small and is on the order of the mean free path even at atmospheric conditions, the direct simulation Monte Carlo method is used to model the heat transfer to each of the spores in the aggregate. The shielding effect of aggregate spores on a single spore in the clump is studied, revealing that, for aggregates on the order of 100, the shielding effect is about 25% 45% compared with a single, isolated spore.

Compressible laminar boundary-layer flows with statistical Bhatnagar-Gross-Krook approaches

DOI: 10.2514/1.45699 In this work, we study the well-known, fundamental viscous fluid problem of compressible, laminar boundarylayer flowovera flatplate.Thepaperinvestigatesthemodelingofsuch flowsusingtheBhatnagar–Gross–Krookand ellipsoidal statistical Bhatnagar–Gross–Krook model kinetic equations for the supersonic flow of argon gas over a flat plate in the semirarefied regime. The Bhatnagar–Gross–Krook and ellipsoidal statistical Bhatnagar–Gross– Krook solutions are compared with the exact, well-known direct simulation Monte Carlo method as well as the theoretical solution of the boundary-layer equations that include velocity slip and temperature jump boundary conditions for adiabatic and isothermal wall boundary conditions. It is found that the solutions obtained by the statistical Bhatnagar–Gross–KrookandellipsoidalstatisticalBhatnagar–Gross–Krookmethodsagreewell withthe theoretical and the benchmark direct simulation Monte Carlo solutions. Both approaches capture the shock wave appearing at the leading edge of the flat plate, but the ellipsoidal statistical Bhatnagar–Gross–Krook approach is shown to be in better agreement with the benchmark direct simulation Monte Carlo method solutions as well as the theoreticalresults.Inaddition,thestatistical Bhatnagar–Gross–Krookandellipsoidalstatistical Bhatnagar–Gross– Krook methods are shown to be numerically more efficient than the direct simulation Monte Carlo method.

Application of Statistical-BGK Approach to Modeling of Nozzle Flows in the Near Continuum Regime

Conical nozzle flows are studied for Reynolds numbers of 1,230 and 12,300 using different numerical techniques: DSMC Method, Navier-Stokes with velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of the BGK and ES-BGK equations. Detailed comparison of the accuracy and convergence of the employed numerical techniques provides better understanding of their benefits and deficiencies, and assists in selecting the most appropriate technique for a particular nozzle flow application and available computational resources. The deterministic and statistical solutions of the BGK equation were found to be in good agreement with the benchmark DSMC results. The Navier-Stokes solution was found to differ from DSMC in the boundary layer. Statistical BGK and ES-BGK methods are shown to be more efficient methods than DSMC in the continuum and near-continuum regime, and more accurate than the solution of the Navier-Stokes equations in the transition regime.

Towards the development of a hybrid statistical method for modeling reentry flows about blunt bodies

Non-equilibrium features of the reentry flows at moderately high altitudes between 95 and 80 km for a vehicle of a shape of the Crew Exploration Vehicle (CEV) were studied by Direct Simulation Monte Carlo Method (DSMC) and the Kolmogorov-Smirnov statistical test. The locations of the regions of non-equilibrium recognized by the test were compared with the locations of chemically active areas in the flow to establish the criteria for switching between different computational methods applied to different areas in the flow. Application of an accurate kinetic computational technique, such as DSMC is suggested for areas with strong non-equilibrium features and with active flow state chemistry. The near equilibrium as well as chemically inactive portions of the flow can be solved with either statistical BGK method or with CFD approaches. It was found that both thermal non-equilibrium portions of the flow as well as areas of active molecular nitrogen dissociation (chemical non-equilibrium) become narrower as the altitude decreases. An the same time, these two areas do not coincide making reliance on only one switching criteria problematic. A combined criterion that includes both the Kolmogoriov-Smirnov test and computed or estimated dissociation rates is suggested.

Analysis of Different Approaches to Modeling of Nozzle Flows in the Near Continuum Regime

Conical nozzle flows are studied for Reynolds numbers of 1,230 and 12,300 using different numerical techniques: DSMC Method, Navier‐Stokes/CFD accounting for velocity slip and temperature jump boundary conditions, and statistical and deterministic approaches to the solution of BGK equation. Detailed comparison of the stability, accuracy, and convergence of the employed numerical techniques provides better understanding of their benefits and deficiencies, and assists in selecting the most appropriate technique for a particular nozzle and flow application. The deterministic and statistical solutions of the BGK equation were found to be in good agreement with the benchmark DSMC results. The Navier‐Stokes solution differs from DSMC in the boundary layer.