Differentially weighted direct simulation Monte Carlo method for particle collision in gas-solid flows

In gas-solid flows, particle-particle interaction （typical, particle collision） is highly significant, despite the small particles fractional volume. Widely distributed polydisperse particle population is a typical characteristic during dynamic evolution of particles （e.g., agglomeration and fragmentation） in spite of their initial monodisperse particle distribution. The conventional direct simulation Monte Carlo （DSMC） method for particle collision tracks equally weighted simulation particles, which results in high statistical noise for particle fields if there are insufficient simulation particles in less-populated regions. In this study, a new differentially weighted DSMC （DW-DSMC） method for collisions of particles with different number weight is proposed within the framework of the general Eulerian-Lagrangian models for hydrodynamics. Three schemes （mass, momentum and energy conservation） were developed to restore the numbers of simulation particle while keeping total mass, momentum or energy of the whole system unchanged respectively. A limiting case of high-inertia particle flow was numerically simulated to validate the DW-DSMC method in terms of computational precision and efficiency. The momentum conservation scheme which leads to little fluctuation around the mass and energy of the whole system performed best. Improved resolution in particle fields and dynamic behavior could be attained simultaneously using DW-DSMC, compared with the equally weighted DSMC. Meanwhile, computational cost can be largely reduced in contrast with direct numerical simulation.

Convergence Detection in Direct Simulation Monte Carlo Calculations for Steady State Flows

A new criterion is presented to detect global convergence to steady state,and to identify local transient characteristics,during rarefied gas flow simulations performed using the direct simulation Monte Carlo(DSMC)method.Unlike deterministic computational fluid dynamics(CFD)schemes,DSMC is generally subject to large statistical scatter in instantaneous flow property evaluations,which prevents the use of residual tracking procedures as are often employed in CFD simulations.However,reliable prediction of the time to reach steady state is necessary for initialization of DSMC sampling operations.Techniques currently used in DSMC to identify steady state convergence are usually insensitive to weak transient behavior in small regions of relatively low density or recirculating flow.The proposed convergence criterion is developed with the goal of properly identifying such weak transient behavior,while adding negligible computational expense and allowing simple implementation in any existing DSMC code.Benefits of the proposed technique over existing convergence detection methods are demonstrated for representative nozzle/plume expansion flow,hypersonic blunt body flow and driven cavity flow problems.

DSMC: Fast direct simulation Monte Carlo solver for the Boltzmann equation by Multi-Chain Markov Chain and multicore programming

Direct Simulation Monte Carlo(DSMC)solves the Boltzmann equation with large Knudsen number.The Boltzmann equation generally consists of three terms:the force term,the diffusion term and the collision term.While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method,the third term can be approximated by DSMC,and DSMC simulates the physical behaviors of gas molecules.However,because of the low sampling efficiency of Monte Carlo Simulation in DSMC,this part usually occupies large portion of computational costs to solve the Boltzmann equation.In this paper,by Markov Chain Monte Carlo(MCMC)and multicore programming,we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo(DSMC3):a fast solver to calculate the numerical solution for the Boltzmann equation.Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

Elbow precision machining technology by abrasive flow based on direct Monte Carlo method

The investigation was carried out on the technical problems of finishing the inner surface of elbow parts and the action mechanism of particles in elbow precision machining by abrasive flow.This work was analyzed and researched by combining theory,numerical and experimental methods.The direct simulation Monte Carlo(DSMC)method and the finite element analysis method were combined to reveal the random collision of particles during the precision machining of abrasive flow.Under different inlet velocity,volume fraction and abrasive particle size,the dynamic pressure and turbulence flow energy of abrasive flow in elbow were analyzed,and the machining mechanism of particles on the wall and the influence of different machining parameters on the precision machining quality of abrasive flow were obtained.The test results show the order of the influence of different parameters on the quality of abrasive flow precision machining and establish the optimal process parameters.The results of the surface morphology before and after the precision machining of the inner surface of the elbow are discussed,and the surface roughness Ra value is reduced from 1.125μm to 0.295μm after the precision machining of the abrasive flow.The application of DSMC method provides special insights for the development of abrasive flow technology.

Spacecraft aerodynamics and trajectory simulation during aerobraking

This paper uses a direct simulation Monte Carlo （DSMC） approach to simulate rarefied aerodynamic characteristics during the aerobraking process of the NASA Mars Global Surveyor （MGS） spacecraft. The research focuses on the flowfield and aerodynamic characteristics distribution under various free stream densities. The vari- ation regularity of aerodynamic coefficients is analyzed. The paper also develops an aerodynamics-aeroheating-trajectory integrative simulation model to preliminarily calculate the aerobraking orbit transfer by combining the DSMC technique and the classical kinematics theory. The results show that the effect of the planetary atmospheric density, the spacecraft yaw, and the pitch attitudes on the spacecraft aerodynamics is significant. The numerical results are in good agreement with the existing results reported in the literature. The aerodynamics-aeroheating-trajectory integrative simulation model can simulate the orbit transfer in the complete aerobraking mission. The current results of the spacecraft trajectory show that the aerobraking maneuvers have good performance of attitude control.

Convergence ofADistributional Monte Carlo Method for the Boltzmann Equation

Direct Simulation Monte Carlo(DSMC)methods for the Boltzmann equation employ a point measure approximation to the distribution function,as simulated particles may possess only a single velocity.This representation limits the method to converge only weakly to the solution of the Boltzmann equation.Utilizing kernel density estimation we have developed a stochastic Boltzmann solver which possesses strong convergence for bounded and L∞solutions of the Boltzmann equation.This is facilitated by distributing the velocity of each simulated particle instead of using the point measure approximation inherent to DSMC.We propose that the development of a distributional method which incorporates distributed velocities in collision selection and modeling should improve convergence and potentially result in a substantial reduction of the variance in comparison to DSMC methods.Toward this end,we also report initial findings of modeling collisions distributionally using the Bhatnagar-Gross-Krook collision operator.

Employing Per-Component Time Step in DSMC Simulations of Disparate Mass and Cross-Section Gas Mixtures

A new approach to simulation of stationary flows by Direct Simulation Monte Carlo method is proposed.The idea is to specify an individual time step for each component of a gas mixture.The approach consists of modifications mainly to collision phase simulation and recommendations on choosing time step ratios.It allows lowering the demands on the computational resources for cases of disparate collision diameters of molecules and/or disparate molecular masses.These are cases important e.g.,in vacuum deposition technologies.Few tests of the new approach are made.Finally,the usage of new approach is demonstrated on a problem of silver nanocluster diffusion in argon carrier gas under conditions of silver deposition experiments.

Slip boundary conditions for rough surfaces

The velocity slip and temperature jump for a two-dimensional rough plate under hypersonic conditions were analyzed using the Direct Simulation Monte Carlo(DSMC)method.Surface roughness was explicitly modeled by introducing various structures on the flat plate.The influences of relative roughness height,which involves the roughness height,roughness spacing,incoming velocity,and the degree of rarefaction,were analyzed and discussed.It is found that with the increase of the relative roughness height,the jump temperature increases,while the slip velocity decreases gradually.The effects of surface roughness on the slip coefficients can be attributed to the change of accommodation coefficients.A new slip model for rough surfaces was established in this paper,which accounts for the coupling effects of gas rarefaction and surface roughness,without the effort to model the surface roughness explicitly.The nitrogen flows in the microchannel,and flows over a blunt cone and an axisymmetric bi-conic body,were simulated under the modified and conventional slip boundary conditions,respectively.The numerical solutions were validated with experimental data.It can be safely concluded that compared with the traditional first-order slip boundary conditions,the modified slip model improves the accuracy of macroscopic properties,especially the heat transfer coefficient.

Boosting the convergence of low-variance DSMC by GSIS

The low-variance direct simulation Monte Carlo(LVDSMC)is a powerful method to simulate low-speed rarefied gas flows.However,in the near-continuum flow regime,due to limitations on the time step and spatial cell size,it takes plenty of time to find the steady-state solution.Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme(GSIS)which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale.As a proof of concept,we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model.First,macroscopic synthetic equations are derived exactly from the kinetic equation,which not only contain the Navier-Stokes-Fourier constitutive relation,but also encompass the higher-order terms describing the rarefaction effects.Then,the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict the macroscopic properties which are closer to the steady-state solution than LVDSMC.Finally,the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties.As a result,the convergence to steady state is greatly accelerated,and the restrictions on cell size and the time step are removed.We conduct the Fourier stability analysis and simulate several canonical rarefied gas flows to demonstrate the advantages of LVDSMC-GSIS:when the Knudsen number is lower than 0.1,it can use the grid size about 10 times larger than that in traditional DSMC,and it can reduce the computational cost by two orders of magnitude in the flow regime.

Rarefied gas effect in hypersonic shear flows

Recently,as aerodynamics was applied to flying vehicles with very high speed and flying at high altitude,the numerical simulation based on the Navier-Stokes(NS)equations was found that cannot correctly predict certain aero-thermo-dynamic properties in a certain range of velocity and altitude while the Knudsen number indicates that the flow is still in the continuum regime.As first noted by Zhou and Zhang(Science in China,2015),the invalidity of NS equations for such flows might be attributed to an non-equilibrium effect originating from the combined effects of gas rarefaction and strong shear in the boundary-layer flows.In this paper,we present the scope,physical concept,mathematical model of this shear non-equilibrium effect in hypersonic flows,as well as the way of considering this effect in conventional computational fluid mechanics(CFD)for engineering applications.Several hypersonic flows over sharp bodies and blunt bodies are analyzed by the proposed new continuum model,named direct simulation Monte Carlo(DSMC)data-improved Navier-Stokes(DiNS)model.

Numerical study of conduction and radiation heat losses from vacuum annulus in parabolic trough receivers

Parabolic trough receiver is a key component to convert solar energy into thermal energy in the parabolic trough solar system.The heat loss of the receiver has an important influence on the thermal efficiency and the operating cost of the power station.In this paper,conduction and radiation heat losses are analyzed respectively to identify the heat loss mechanism of the receiver.A 2-D heat transfer model is established by using the direct simulation Monte Carlo method for rarefied gas flow and heat transfer within the annulus of the receiver to predict the conduction heat loss caused by residual gases.The numerical results conform to the experimental results,and show the temperature of the glass envelope and heat loss for various conditions in detail.The effects of annulus pressure,gas species,temperature of heat transfer fluid,and annulus size on the conduction and radiation heat losses are systematically analyzed.Besides,the main factors that cause heat loss are analyzed,providing a theoretical basis for guiding the improvement of receiver,as well as the operation and maintenance strategy to reduce heat loss.