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In this study, we numerically examine the behavior of the NACA (National Advisory Committee for Aeronautics) 66 hydrofoil under combined oscillatory motion, considering different cavitation numbers. The large eddy simulation method is used for the turbulence modeling. The vertical oscillation (combined oscillation) creates an effective angle of attack, leading to reduced drag force. Our findings indicate that increasing the speed of hydrofoil oscillation leads to a delayed onset and increased production of cavity clouds. Moreover, an increase in the angle of attack during combined oscillatory motion decreases the detachment length of cavitation bubbles. Further investigations show that cavitation on the hydrofoil's surface can accelerate the shift from a laminar to turbulent boundary layer, reinforcing the turbulent boundary layer's strength and thereby delaying the onset of flow separation. Additionally, we accurately examine the terms of the vorticity transport equation in this research. It is evident that the vorticity dilatation term forms near the boundary layers close to the hydrofoil surface and correlates well with the vapor volume fraction. This term plays a vital role in the cavitation inception process. [ABSTRACT FROM AUTHOR]

This paper analyzes the mixing of gases in a plane channel at rarefied conditions. The direct simulation Monte Carlo method is employed to simulate gas mixing in parallel mixers working at different Knudsen numbers and having different values of wall accommodation coefficient. Results show that the normal-to-wall component of the mole fraction gradient may have the same sign as the corresponding component of the diffusive mass flux vector near the diffuse solid walls in contrast to the predictions of Fick's law for continuum conditions. This non-continuum behavior, which is called "inversion" in the present study, will become more pronounced at higher Knudsen numbers, whereas it will become less evident for smaller wall accommodation coefficients. To confirm that the observed phenomenon is consistent with the basic physical laws governing the rarefied gas dynamics and it is not an artifact of the numerical method, a new analytical model based on the kinetic theory of gases is developed for the parallel mixers that have diffuse walls and are working in the free-molecular regime. Excellent agreement is observed between the analytical and direct simulation Monte Carlo results in the free molecular flow regime. Both methods predict the occurrence of inversion near the diffuse walls at highly rarefied flow conditions. [ABSTRACT FROM AUTHOR]

The gas flow characteristics in lid-driven cavities are influenced by several factors, such as the cavity geometry, gas properties, and boundary conditions. In this study, the physics of heat and gas flow in cylindrical lid-driven cavities with various cross sections, including fully or partially rounded edges, is investigated through numerical simulations using the direct simulation Monte Carlo (DSMC) and the discrete unified gas kinetic scheme (DUGKS) methods. The thermal and fluid flow fields are systematically studied for both constant and oscillatory lid velocities, for various degrees of gas rarefaction ranging from the slip to the free-molecular regimes. The impact of expansion cooling and viscous dissipation on the thermal and flow fields, as well as the occurrence of counter-gradient heat transfer (also known as anti-Fourier heat transfer) under non-equilibrium conditions, is explained based on the results obtained from numerical simulations. Furthermore, the influence of the incomplete tangential accommodation coefficient on the thermal and fluid flow fields is discussed. A comparison is made between the thermal and fluid flow fields predicted in cylindrical cavities and those in square-shaped cavities. The present work contributes to the advancement of micro-/nano-electromechanical systems by providing valuable insight into rarefied gas flow and heat transfer in lid-driven cavities. [ABSTRACT FROM AUTHOR]

A novel hybrid transient adaptive subcell (TAS) direct simulation Monte Carlo (DSMC) algorithm is proposed to simulate rarefied gas flows in a wide range of Knudsen numbers. It is derived and analyzed by using a time and spatial discrete operator approach based on the non-homogeneous, local N-particle kinetic equation, first proposed by Stefanov. The novel algorithm is considered together with the standard and hybrid collision algorithms built on uniform grids. The standard collision algorithm uses only one single scheme—the NoTime Counter (NTC), or the Generalized or Simplified Bernoulli trials (GBT, SBT). The hybrid algorithm employs NTC, GBT, or SBT depending on the instantaneous number of particles in the considered cell. The novel hybrid TAS algorithm benefits from both the hybrid collision approach and the transient adaptive subcell grid covering each collision cell to achieve a uniform accuracy of order O(Δt, Δr) independently of the number of particles in the cells. To this aim, a local time step is defined as coherent with the TAS grid covering the corresponding collision cell. The novel hybrid TAS algorithm is tested on two-dimensional benchmark problems: supersonic rarefied gas flow past of a flat plate under an angle of incidence and pressure-driven gas flow in a microchannel. The results obtained by the hybrid TAS algorithm are compared to those obtained by the standard algorithms and the available Bird's DS2V code using nearest neighbor collision and open-source OpenFOAM code. The comparison shows an excellent accuracy of the suggested algorithm in predicting the flow field. [ABSTRACT FROM AUTHOR]

This study aimed to investigate the recirculation zone in a micro-step geometry using a hybrid molecular direct simulation Monte Carlo (DSMC) Fokker–Planck (FP) approach. As this hybrid approach benefits from the accuracy of the DSMC and reduced computational cost of FP, very low Knudsen number (Kn) and high Reynolds number (Re) cases were investigated for the first time. In particular, the role of Kn, specularity of walls, and Re was evaluated on the formation of concave and convex vortices. The Kn and Re ranges were from 0.0001 to 100 and from 0.04 to 5940, respectively. The latter considers a wide range of flow regimes from laminar to transitional flow. It is the first time that transitional flows have been treated in a micro-step using a rarefied flow solver. We demonstrated the formation of a vortex on the top wall of the micro-step geometry for low Kn conditions in the range of 0.0001 1. It was shown that making the junction and bottom wall of the step specular did not eliminate the concave vortex but rather led to an increase in its strength. In addition, cold-to-hot transfer could be observed in all cases due to the competition between the higher-order term of the heat flux formula with the Fourier term. [ABSTRACT FROM AUTHOR]

Here, rarefied thermally driven flow is investigated in two-dimensional equilateral triangular cavities with different uniform wall temperatures. We used three different solvers, i.e., the direct simulation Monte Carlo solver, discrete unified gas kinetic scheme solver, and continuum set of equations of a slow non-isothermal flow solver. Two main cases were considered; in the first case, the cavity's base is considered hot, and the other sides were set cold. In the second case, the right half of the bottom wall was regarded as a diffuse reflector with high temperature, while the left half of the bottom border was set as a specular reflector. The adjacent side walls were set cold with diffuse reflector boundary conditions. The imposed temperature difference/wall boundary condition induces various vortices in the geometry. In case 1, we observe that principal vortices appearing in the triangle are due to nonlinear thermal stress effects, and the thermal creep effects cause other smaller, confined ones. In case 2, a thermal edge flow is set up from the specular wall on the way to the diffusive hot wall, creating a large vortex in the geometry. As the Knudsen number decreases, another small vortex appears near the left cold border. [ABSTRACT FROM AUTHOR]

Here, a symmetrized and simplified Bernoulli trials (SSBT) scheme based on the probabilistic approach is introduced to provide less-restricted conditions in choosing selected pairs. Unlike the simplified Bernoulli trials (SBT) method, the SSBT scheme picks the second particle of a selected pair from a whole list of particles with equal probability; it prevents repetitive collisions by introducing a procedure to avoid duplicate colliding pairs. The efficiency of this newly introduced algorithm is investigated in benchmark problems such as a collision frequency test case, Fourier heat transfer, dissociation of simple gas, and hypersonic cylinder flow. Compared with SBT, no time counter (NTC), and nearest neighbor (NN) collision algorithms, the results show that the SSBT method predicts the solutions quite accurately. In the collision frequency test case and Fourier test case, we show that the SSBT scheme could work with few particles per cell (one or even less) if an appropriate space and time discretization is employed. The symmetrized algorithm of the SSBT scheme improves the quality of the selection process, which leads to a smaller sample size in the highly non-equilibrium problem of hypersonic cylinder flow to achieve the same convergence limit at that of the SBT and NN schemes. In addition, the SSBT scheme has inherently a lower separation of free paths in the stagnation point of the cylinder test case compared to the SBT scheme for the same grid test case. These features make SSBT a new, robust model that could be presented as an alternative to state-of-the-art models. [ABSTRACT FROM AUTHOR]

We provide the first direct calculation of the Knudsen layer (KL) thickness in rarefied gas flows based on the ballistic molecular motions in the direct simulation Monte Carlo simulations. Calculations reproduce a linear relation between the KL thickness and the mean free path (MFP) of the gas, which agrees with the classical gas kinetic theory statement. The ratio of the KL thickness and MFP is only a function of the gas molecular model at slight flow gradients. However, high flow gradient and high surface curvature effects destroy the linear relation between the KL thickness and MFP. [ABSTRACT FROM AUTHOR]

Well-known polars in classical shock wave theory, that is, flow deflection angle-shock angle (θ-β), hodograph (u*,v*), and pressure deflection (θ-P*) diagrams, are investigated for the rarefied gas flows using a recently proposed shock wave detection technique by Akhlaghi and coworkers. The agreement between the obtained polars with the analytical relations in classical shock wave theory has been shown in the continuum limit for the cases of supersonic flow over the wedge and cylinder geometries. Investigations are performed using the RGS2D direct simulation Monte Carlo solver for supersonic gas flows over a circular cylinder at continuum limit and Kn = 10−4, 10−3, 0.01, 0.03, 0.07, and 0.10. Two species of nitrogen and argon at various Mach numbers of 1.5, 3.0, and 10.0 are considered. The shock polars are investigated along bow shock waves in front of the cylinder. The results indicate that rarefaction significantly affects the shock polars. As Knudsen number increases, shock angle, maximum flow deflection angle, and aft shock pressure increase. However, velocity components after the shock wave decrease as the flow becomes more rarefied. These effects are stronger for θ-β polar under the weak shock condition. Meanwhile, they are stronger for θ-P* and hodograph polars in strong shock situations. [ABSTRACT FROM AUTHOR]

The impetus of this paper is to assess the newly suggested direct simulation Monte Carlo (DSMC) collision schemes, that is, the "Simplified Bernoulli Trails (SBT)" and "Generalized Bernoulli Trials (GBT)" schemes in the prediction of the higher-order moments of the velocity distribution function for both confined and non-confined gas flows. Two fundamental rarefied gas dynamics problems are considered: spatially homogeneous relaxation process of a gas flow from a non-Maxwellian condition given by Bobylev–Krook–Wu exact (analytical) solution of the Boltzmann equation and the stationary shock wave problem. To perform the relaxation test, SBT and GBT schemes were implemented in the DSMC0F program. For the shock wave test, changes were made in the DSMC1 code to include the SBT and GBT schemes. A detailed comparison of the SBT and GBT collision schemes in treating the higher-order moments of the velocity distribution function and comparison with theory and the solution of the standard No-Time-Counter (NTC) method and its new variant, nearest neighbor scheme, using the DS1 code, is reported. Some higher moments beyond the usual moments were computed. The results of the fourth moment of the velocity distribution function in the homogeneous relaxation problem show that while both collision schemes produce identical results at an ample time, the initial relaxation process indicates the difference between the schemes. Even though the NTC schemes required a large number of particles per cell to produce the same results as the theory, the SBT scheme successfully simulates the solution using a low number of particles per cell. [ABSTRACT FROM AUTHOR]

The present study numerically investigates nonlinear thermal stress in a rarefied gas flow between two coaxial elliptic cylinders with a hot outer wall. Monatomic argon is considered, and isothermal boundary conditions are implemented on the walls. Three different numerical methods are used to solve this problem, i.e., first, the direct simulation Monte Carlo (DSMC) method is used and validated against the numerical solution of the Boltzmann equation available in the literature. The results of the DSMC algorithm are compared with the results of the discrete unified gas kinetic scheme and the continuum set of equations of slow non-isothermal flows, which includes nonlinear thermal stress terms compared to the Navier–Stokes equations. For the first time, the flow is examined in a wide range of Knudsen numbers in the slip regime from the Knudsen number (Kn) of Kn = 0.005 to Kn = 0.1. At a minimal Knudsen number, there is just one vortex due to the nonlinear thermal stress flow; however, as Kn increases, the velocity peak near the inner cylinder is replaced with another vortex, which is created due to the second-order thermal creep effects on the inner wall of the cylinder. We show that as Kn increases, the inner vortex increases in size, while the outer vortex shrinks. The mechanisms of the formation of both vortices are described in detail. Other flow characteristics, including walls' velocity slip, shear stress, and vorticity, are discussed. [ABSTRACT FROM AUTHOR]

A new efficient direct simulation Monte Carlo (DSMC) method is proposed for the simulation of microporous media based on the dusty gas model (DGM). Instead of simulating gas flow through a microporous medium with a complex geometry of micropores that mimics the physical pore morphology, the DGM-DSMC method replaces it with the gas flow through a system of randomly distributed motionless virtual particles with simple spherical shapes confined in the considered domain. In addition, the interactions of gas molecules with the porous particles are simulated stochastically. For the aim of our study, the DGM is implemented in Bird's two-dimensional DSMC code. The obtained results for the average velocity of gas flow through microscale porous media with given porosity are verified for different pressure gradients with those reported in the literature where porous particles are modeled physically in the domain. Thereafter, the effective parameters in porous media such as porosity, particle diameter, and rarefaction on flow behavior including velocity profile, apparent gas permeability, and mass flow rate are investigated. A comparison with the results predicted by the Open source Field Operation and Manipulation (OpenFOAM) software suggests that the employed DGM-DSMC is more accurate in highly porous media and its computational cost is considerably low. [ABSTRACT FROM AUTHOR]

The objective of this work is to provide a detailed study on the convergence behavior of the Simplified Bernoulli Trials (SBT) collision scheme in the direct simulation Monte Carlo (DSMC) method. Onedimensional Fourier heat conduction problem of argon gas at the early slip regime is considered. The problem consists of rarefied gas confined between two infinite parallel plates with different temperature magnitudes. The investigations compare the SBT solution for the Sonine-polynomial coefficients with theoretical predictions of the Chapman-Enskog theory. Also, the convergence behavior of the wall heat flux and the DSMC-calculated bulk thermal conductivity (KDSMC) are studied. The numerical performance of the DSMC method is affected by the number of computational particles (simulators) per cell, time step, and cell size. The dependence of the SBT collision scheme on discretization errors has been examined and compared with the no time counter (NTC) collision algorithm. Our results show that SBT captures analytical solutions of the Sonine polynomials using a few particles per cell. Unlike the NTC scheme, the SBT algorithm is not so sensitive to the number of simulators per cell, and the effective parameter in the convergence is the cell size to time step ratio, Δx/Δt, which should be adjusted properly for any specific test case. With setting a constant Δx/Δt, the SBT algorithm accurately predicts the wall heat flux solution by decreasing the average number of particles per cell to one particle or even less. [ABSTRACT FROM AUTHOR]

This work deals with the development of an intelligent inter-particle collision scheme using the Direct Simulation Monte Carlo (DSMC) method. Conventional DSMC collision schemes cannot perceive collision distances by their own routines and, consequently, must rely on other techniques to provide a choice of collision pairs with a smaller inter-particle space. Here, we propose a modification of the Simplified Bernoulli Trials (SBT) scheme, called the Intelligent Simplified Bernoulli Trials (ISBT) scheme, which can create pseudo-circular subcells that reduce approximately 25%-32% of the mean collision separation distance. The ISBT scheme tries to arrange the particle indexing and collision acceptance-rejection of the SBT scheme in a way that leads to the formation of virtual clusters. These inner-cell clusters then will cause the selection of the "near-neighbor" pair, which leads to smaller mean collision separation distances. Different low- and high-speed test cases, e.g., lid-driven cavity flow, steady hypersonic flow over a two-dimensional cylinder, and Mach 15.6 nitrogen flow over a 25-55 axisymmetric biconic, are selected to assess the accuracy and efficiency of the ISBT collision scheme. [ABSTRACT FROM AUTHOR]

Nanosteps form once nanochannels of various diameters connect to each other. The focus of this paper is to investigate the heat transfer and hydro/thermal field behavior in nanostep geometries using direct simulation Monte Carlo. The effects of the hydrodynamics separation on the pressure field and heat lines are reported, i.e., we show that the length of the hydrodynamics separation zone is different from the positive pressure gradient and thermal separation zones. Interestingly, cold to hot transfer is observed when the wall temperatures and inlet temperature are close to each other. We show that cold to hot heat transfer appears due to the interplay between the higher order term of the heat flux formula, which is a function of the second derivate of the velocity, with the Fourier term; the cold to hot transfer effect is omitted as the wall temperature or Knudsen number increases. In addition, the impact of different parameters, such as pressure ratio, Knudsen number, and wall temperature adjacent to the separation zone, are investigated. The dependence of the mass flow rate and the length of the separation zone on the wall temperature and the channel pressure ratio is considered. We show that Knudsen minimum is not observed in the step geometry for both isothermal and non-isothermal wall conditions. [ABSTRACT FROM AUTHOR]

We investigate effects of wall heat transfer on the structure of pressure driven flow in micro/nanochannels using the Direct Simulation Monte Carlo method. The effects of non-zero wall heat flux on the pressure distribution, velocity profiles, heat flow patterns, and the mass flow rate are reported. The simulation results show that cooling decreases slip at the wall and pressure along the channel. Cooling changes the heat flow direction along the channel while heating does not. At higher degree of rarefaction, the direction of the heat flow is mainly axial along the channel. An existence of cold-to-hot heat transfer process is demonstrated in the cooling wall case. Cooling can also create a heat singularity point in the domain. There is a critical Knudsen number about unity for which heating or cooling does not affect the mass flow rate through the channel. Below the critical Knudsen number, heating decreases and cooling increases the mass flow rate. Above it, heating increases and cooling decreases the mass flow rate. [ABSTRACT FROM AUTHOR]

Fluids 33(1), 012009 (2021).10.1063/5.0036089 32 Y. Chen, Y. Zhu, and K. Xu, " A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes", Phys. Fluids 32(10), 102006 (2020).10.1063/5.0021704 37 S. Busuioc and L. Gibelli, " Mean-field kinetic theory approach to Langmuir evaporation of polyatomic liquids", Phys. Fluids 32(10), 102012 (2020).10.1063/5.0020082 14 A. Phan, D. Fan, and A. Striolo, " Fluid transport through heterogeneous pore matrices: Multiscale simulation approaches", Phys. [Extracted from the article]

The kinetic-theory-based numerical schemes, such as direct simulation Monte Carlo (DSMC) and information preservation (IP), can be readily used to solve transition flow regimes. However, their high computational cost still promotes the researchers to extend the Navier–Stokes (NS) equations beyond the slip flow and to the transition regime applications. Evidently, a suitable extension would accurately predict both the local velocity profiles and the mass flow rate magnitude as well as the streamwise pressure distribution. The second-order slip velocity model derived from kinetic theory can provide relatively accurate velocity profiles up to a Knudsen (Kn) number of around 0.5; however, its mass flow rate accuracy decreases as Knudsen number approaches the upper bound. One remedy is to consider the rarefaction effects in calculating the NS viscosity coefficient. In this work, we use the shear stress distribution derived from our IP simulations, extend an analytical expression for the viscosity coefficient, impose it in the NS equations, and evaluate it via solving the transition regime. Using the new viscosity coefficient, we also derive an analytical expression for the mass flow rate, which provides accurate solutions for Kn<0.5 and even beyond in micro- and nanochannel flows. We also show that the obtained streamwise pressure distribution agrees well with that of the DSMC-IP in this range. The current study is concerned with low speed diatomic gas flow through two-dimensional micro- and nanochannels. [ABSTRACT FROM AUTHOR]