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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]

The motivation of the current paper is to provide a detailed review of crucial topics in micro- and nanoscale gas flows, i.e., velocity slip and temperature jump phenomena and their modeling, Knudsen minimum, and thermally-driven flows with application in Knudsen pumps. Non-equilibrium gas flows at the micro and nano scales exhibit peculiarities different from the intuition of macroscopic continuum fluid dynamics and heat transfer. Rarefied gas flows experience unique features such as slip and jump boundary effects , Knudsen paradox , pumping effect , , anti-Fourier heat transfer , thermal critical Knudsen number , and rarefied gas shock polars. This paper reviews the latest advancements and investigations on the gas–surface velocity and temperature inequalities, named velocity slip and temperature jump , in rarefied gas flows. Thermodynamic non-equilibrium effects are localized in the Knudsen layer within a width of a few gas mean free path near the surfaces. These particular features result in inequalities between the velocity and temperature of the gas concerning the surface. Experimental investigations of the slip and jump conditions from the first observation to the recent studies are reviewed. Next, a comprehensive review of the different categories of velocity slip models from the Maxwell model up to the recently developed models will be performed. For the first time, all the current models on the viscosity of rarefied gas are classified and compared in the present paper. Progress in the derivation of the models describing the temperature jump of rarefied gas over a solid surface will be performed. Next, a unique behavior of rarefied gas named the Knudsen paradox or Knudsen minimum is introduced and reviewed based on the different viewpoints. Different possible reasons for the origin of the Knudsen paradox phenomena are reviewed. A complete set of experimental and numerical works which detected the Knudsen paradox feature will be historically reviewed. Then, the closed-form relations obtained from the numerical simulations and experimental measurements indicating and predicting the occurrence of the Knudsen paradox phenomenon are reviewed and compared. The end section of this paper focuses on deemed physical and real-world applications of the rarefied flows at small scales utilizing thermally driven gas flows, i.e., the pumping effect of the rarefied gas. The pumping effect of the rarefied gas under temperature gradient leads to the Knudsen pump or Knudsen compressor concept. The main advantage over macro-scale pumps is that these sorts of pumps do not suffer from reduced life cycles due to various modes of mechanical failure because they do not have any rotating and moving parts. Moreover, the pumps mentioned above could find applications in gas chromatography, spectroscopy, moving gases on a chip, forced convection cooling, and micro-nano scale actuators. Different classes of thermally-induced flows with their origins are proposed and discussed, containing the recently detected thermally-driven flows. Based on that, a critical and comprehensive review of the different types and configurations of Knudsen pumps will be presented in detail. The newest published research containing new designs of Knudsen pumps has been considered in this review. Different numerical techniques developed or employed to simulate Knudsen pumps will be extensively reviewed. Besides, all published experimental investigations on Knudsen pumps will be reviewed and classified. Overall, this review will provide insights into the emerging physical science and engineering application of micro- and nanoscale gas flows. [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]

The narratives of the reign of the last Amorian emperor, Michael III (r. 842–867), and the government of his uncle, Caesar Bardas (r. 856–866), were mostly authored by hostile Macedonian chroniclers living a century or so following the events they describe. This fact poses considerable difficulties for the historiographical assessment of this period. Recently brought to scholarly attention, a Shīʿī Arabic account has been presented in previous scholarship as a counter-narrative to Byzantine historians' portrayal of the period of interest. The present study sets out to, first, re-appraise, in the light of fresh historical testimonies, the extent of Byzantine records' affinities with this "ignored Arabic account" and second, to gauge whether this Arabic evidence can be an aid in filling the historiographical lacuna created by the Byzantine chroniclers' and hagiographers' one-sided depiction of the late Amorian period. The latter aim will be pursued via analysis of the rival representations of a traumatic event which happened during Bardas's rule, namely the earthquake of Constantinople. [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]

This numerical investigation employs advanced computational fluid dynamics techniques to examine the intricate physics of cavitating flows around a pitching NACA 66 hydrofoil. Unsteady simulations are conducted using both large eddy simulation (LES) and K-Omega SST turbulence models. The pitching motions range from 0 to 15°, encompassing four cavitation numbers (3.25, 3.5, 3.75, 4) and a Reynolds number of 750,000. The study comprehensively analyzes various flow field characteristics, including pressure distribution, velocity, vorticity, shear stress, vapor volume fraction, and turbulence kinetic energy. The kinematics of pitching significantly influence hydrodynamic loads and the surrounding flow structures in cavitating conditions. Flow visualizations illustrate the evolution of sheet/cloud cavitation, reentrant jet, and vortex dynamics throughout a pitching cycle. Notable findings demonstrate the impact of cavitation number on cavity shape and the relationship between angle of attack, reentrant jet location, and vortex size. Additionally, negative vorticity dilatation is observed to be correlated with cavity size. • The cavitation and supercavitation structure around a 2D, 3D pitching hydrofoil is studied using LES. • The impact of cavitation number on cavity shape and the relationship between angle of attack, reentrant jet location, and vortex size was studied. • Determination of the effect of pitching motion in cavitation flow on hydrodynamic coefficients and surrounding flow structure [ABSTRACT FROM AUTHOR]

Cooling of electronic devices is one of the critical challenges that the electronics industry is facing towards sustainable development. Aiming at lowering the surface temperature of the heat sink to limit thermally induced deformations, corrugated channels and nanofluids are employed to improve the thermal and hydraulic performances of a heat sink. Three-dimensional simulations based on the finite-volume approach are carried out to study conjugated heat transfer in the heat sink. Water-based nanofluids containing Al 2 O 3 nanoparticles with two different particle sizes (29 nm and 40 nm) and volume fractions less than 4% are employed as the coolant, and their influence on the thermal and hydraulic performance of the heat sink is compared with the base fluid (i.e. water). An empirical model is utilised to approximate the effective transport properties of the nanofluids. Employing corrugated channels instead of straight channels in the heat sink results in an enhancement of 24–36% in the heat transfer performance at the cost of 20–31% increase in the required pumping power leading to an enhancement of 16–24% in the overall performance of the heat sink. Additionally, the numerical predictions indicate that the overall performance of the proposed heat sink design with corrugated channels and water– Al 2 O 3 nanofluids is 22–40% higher than that of the water-cooled heat sink with straight channels. It is demonstrated that the overall performance of the heat sink cooled with water– Al 2 O 3 nanofluids increases with reducing the average nanoparticle size. Additionally, the maximum temperature rise in the heat sinks is determined for different thermal loads. [ABSTRACT FROM AUTHOR]

The impetus of the this study is to investigate flow and thermal field in rarefied gas flows inside a trapezoidal micro/nano-cavity using the direct simulation Monte Carlo (DSMC) technique. The investigation covers the hydrodynamic properties and thermal behavior of the flow. The selected Knudsen numbers for this study are arranged in the slip and transition regimes. The results show the center of the vortex location moves by variation in the Knudsen numbers. Also, as the Knudsen number increases, the non-dimensional shear stress increases, but the distribution deviates from a symmetrical profile. The cold to hot transfer, which is in contrast with the conventional Fourier law, is observed. We show that the heat transfer is affected by the second derivative of the velocity. By increasing the Knudsen number, the transferred heat through the walls decreases, but the contraction/expansion effects on the temperature in the corner of the cavity become higher. [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]

The impetus of this study is to evaluate the performance of the anisotropic minimum-dissipation (AMD) subgrid-scale model (SGS) for flow over a gently-curved backward-facing step (BFS) at a Reynolds number of 13 700. Minimum-dissipation sub-grid models were developed as simple alternatives to the dynamic eddy-viscosity SGS models. AMD model is a static type of eddy-viscosity SGS model incorporating anisotropic SGS effects into numerical predictions through the large-eddy simulation (LES) approach. The open-source CFD package of OpenFOAM was used to implement the AMD model. Before focusing on the BFS flow, we investigated the impact of the AMD model coefficient magnitude on the numerical predictions of the decaying isotropic turbulence flow. In the next step, numerical solutions were obtained for the curved backward-facing step using the AMD model and Dynamic Smagorinsky model (DSM). The curved backward-facing step was considered here for the evaluation of the SGS model predictions due to its weak adverse pressure gradient and high sensitive flow mechanism. The rescaling/recycling method was employed as a turbulent inflow generation technique. The AMD model results were compared with the prediction of the DSM and Vreman model. Moreover, AMD model predictions were compared with the reported solutions obtained using different turbulent inflow generation methods. The assessments revealed the high capability of the AMD model to capture decaying turbulence and predict velocity profiles and resolved flow statistics turbulent parameters in the gently-curved backward step flow. [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]

Imperial and aristocratic Byzantine women had a wide variety of roles with a spectrum of importance. One possible way to enrich our information about Byzantine royal women is to consult the historical and cultural heritage of Byzantium's adjacent territories. The primary aim of this article is thus to trace Byzantine women in the Arabic Shīʿī literature, as exemplified by the underutilised autobiography of a hitherto unidentified Roman princess named Malīka. Probably because Malīka's autobiography, along with its hagiographic and miraculous elements, is found in a source from the Shīʿī Ḥadīth tradition, the account's potential historical value has escaped the notice of previous Byzantinists. Despite its hagiographic character, Malīka's story has a historical core. Through an intertextual study between the Arabic and Byzantine historical texts, the present study seeks to shed light on the identification of Malīka and her paternal ancestry. [ABSTRACT FROM AUTHOR]

In this paper we numerically evaluate the recently developed Aoki et al. slip and jump conditions in high-speed rarefied gas flows for the first time. These slip and jump conditions are developed to be employed with the Navier–Stokes–Fourier equations. They were derived based on the Boltzmann equation with the first order Chapman–Enskog solution, and the analysis of the Knudsen layer. Four aerodynamic configurations are selected for a comprehensive evaluation of these conditions such as sharp-leading-edge flat plate, vertical plate, wedge and circular cylinder in cross-flow with the Knudsen number varying from 0.004 to 0.07, and argon as the working gas. The simulation results using the Aoki et al. boundary conditions show suitable agreement with the DSMC data for slip velocity and surface gas temperature. The accuracy of these boundary conditions is superior to the conventional Maxwell, Smoluchowski and Le boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, wavelet analysis of the cavitating flow over a sphere is reported. Unsteady and dynamic behaviors of cavitation were captured using large eddy simulation (LES) turbulence approach and Sauer mass transfer models. Numerical simulation is implemented under the framework of OpenFOAM within the interPhaseChangeFoam solver. The simulation is conducted over a wide range of cavitation numbers. Two more essential variations, pressures and kinetic energies, were considered at specific points in front and behind of the sphere's body for sufficient simulation period. The oscillations global frequency modes and spectral content of the cavity cloud are computed and analyzed using Fourier and continuous wavelet transformations. The computed results show that the flow fluctuations enhance by increasing the cavitation number. The low-frequency fluctuations play a pivotal role in the cavitating flow and possess almost the same magnitude in all investigated cavitation numbers. The frequencies enhance as the simulation time increases in all cases. One of the primary frequencies that happened in all cavitation numbers in the cavity cloud separation is due to a Strouhal number within the range of 0.046 and 0.05. Therefore, this Strouhal number can be used for the purpose of cloud cavitation detection. • LES simulation of cavitating flow around sphere in OpenFOAM. • Providing a thorough understanding of the wavelet analysis around a sphere for the first time. • Reporting the oscillations global frequency modes and spectral content of the sphere cavity cloud. [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]

Rarefied isothermal gaseous flow through long diverging micro and nanochannels is investigated in this paper using the two-relaxation-time (TRT) lattice Boltzmann method (LBM). The simulations are performed over a wide range of Knudsen number, pressure ratio, and divergence angle. The Bounce-Back Specular Reflection (BSR) slip boundary condition is applied and is connected to the second-order slip boundary condition coefficients by means of the antisymmetric relaxation time and the bounce-back portion parameter. The effects of the slip coefficients on the wall and centerline Mach numbers, as well as the mass flow rates, are investigated. The numerical results are validated with those of the direct simulation Monte Carlo (DSMC) reported in the literature. The results show that the local pressure distributions are almost independent of the slip coefficients with excellent agreements with DSMC over a wide range of the divergence angle. Our results demonstrate that there is a specific divergence angle at each pressure ratio where the local unbounded Knudsen and, as a result, Mach numbers remain constant along the channel. This observation is almost independent of the slip coefficients, and the underlying reason is that the pressure drop is compensated by an increase in the channel area. [ABSTRACT FROM AUTHOR]

Recently, a new family of subgrid-scale (SGS) models, termed as gradient-based models, has been introduced to calculate the SGS stresses in large eddy simulation (LES). In the present work, the modulated gradient model (MGM) was implemented in the OpenFOAM package, and the pimpleFoam solver was improved to be adopted with non-eddy viscosity models. The MGM is a new, nonlinear model that uses the local equilibrium hypothesis to assess the SGS kinetic energy and the velocity gradient tensor to calculate the relative weight of the different components of the SGS stress tensor. To evaluate the accuracy of the MGM along with the modified pimpleFoam solver, a turbulent channel flow was simulated at the three different frictional Reynolds numbers of 180, 395 and 590. Furthermore, the results were compared with direct numerical simulation data, as well as the numerical results obtained by the established SGS models such as the dynamic Smagorinsky model (DSM). A suitable accuracy for the first- and second-order turbulence parameters was reported. Moreover, it was demonstrated that MGM is computationally efficient compared to the DSM in treating channel flow. [ABSTRACT FROM AUTHOR]

Rarefied gas flows in nano-scale isosceles triangular cavities with a motion away from the square corner are considered over a wide range of flow rarefactions regimes, i.e., 0.01 ≤ Kn ≤ 10, using the direct simulation Monte Carlo (DSMC) method. We put emphasis to the rarefaction effects on the vortical behaviors and heat transfer patterns of rarefied monatomic and diatomic gases. We show that the primary vortices appearing in the triangular cavity are Moffat-type vortices, which disappear as velocity slip increases over the walls. However, an additional vortex is observed at Kn > 1 on the inclined wall attributable to the balance of the thermally driven flows from the cold to the hot region and flow induced by the primary vortex. We also report variations in the effective length scale of the fluid circulation with the Knudsen number. Our investigations specify that the competition between the Fourier term and shear stress gradient component of the heat flux constitutive relation results in the cold-to-hot transfer in triangular cavities. Also, heat flux patterns predicted by the asymptotic theory of the Boltzmann equation for the weakly non-linear flow and by the linearized form of the Regularized 13 moments (R13) equations are compared with the DSMC solution suitably at low Knudsen number regimes. [ABSTRACT FROM AUTHOR]

The impetus of this research is to present a generalized Bernoulli Trial collision scheme in the context of the direct simulation Monte Carlo (DSMC) method. Previously, a subsequent of several collision schemes have been put forward, which were mathematically based on the Kac stochastic model. These include Bernoulli Trial (BT), Ballot Box (BB), Simplified Bernoulli Trial (SBT) and Intelligent Simplified Bernoulli Trial (ISBT) schemes. The number of considered pairs for a possible collision in the above-mentioned schemes varies between N ( l ) ( N ( l ) − 1 ) / 2 in BT, 1 in BB, and ( N ( l ) − 1 ) in SBT or ISBT, where N ( l ) is the instantaneous number of particles in the l th cell. Here, we derive a generalized form of the Bernoulli Trial collision scheme (GBT) where the number of selected pairs is any desired value smaller than ( N ( l ) − 1 ), i.e., N sel < ( N ( l ) − 1 ) , keeping the same the collision frequency and accuracy of the solution as the original SBT and BT models. We derive two distinct formulas for the GBT scheme, where both formula recover BB and SBT limits if N sel is set as 1 and N ( l ) − 1 , respectively, and provide accurate solutions for a wide set of test cases. The present generalization further improves the computational efficiency of the BT-based collision models compared to the standard no time counter (NTC) and nearest neighbor (NN) collision models. [ABSTRACT FROM AUTHOR]

Here we examine partial and supercavitation over a sphere at a constant Reynolds number of 1.5 × 10 6 and a broad range of cavitation numbers (0.36 <σ< 1). Large eddy simulation (LES) and Sauer mass transfer model were used to simulate the dynamic and unsteady cavitation around the sphere. Also, the compressive volume of fluid (VOF) method is used to track the cavity interface. The two-phase flow solver of the OpenFOAM package, intephaseChangeFoam is employed. Large-eddy simulation of cavitating flow over the sphere is compared with the non-cavitating flow at the same Reynolds number. This work provides a thorough understanding of the fluid dynamic characteristics of the sphere cavitation such as vorticity field, turbulent kinetic energy, pressure, velocity, streamlines and boundary layer. Also, detailed analyses of the instantaneous cavity leading edge and separation point location, vortex shedding, streamwise velocity fluctuation and evolution of the cavity are reported. Characteristics of the wake of the cavitating flows are compared with the single-phase results. We report that cavitation suppresses instability in the near wake region and delays the three-dimensional breakdown of the vortices. The volume fraction contours of the cavity cloud obtained from the numerical simulations are compared with the experimental data at the same working condition with a suitable quantitative accuracy. [ABSTRACT FROM AUTHOR]

A detailed study on thermally driven flows through divergent micro/nanochannels is presented. Rarefied gas flow behavior and thermal mass flow rate were investigated with different divergence angles ranging between 0 and 7 at two aspect ratios () using particle-based direct simulation Monte-Carlo (DSMC) method. We compare our DSMC solutions for normalized thermal mass flow rate with the numerical solution of the Boltzmann-Krook-Walender (BKW) model and Bhatnagar-Gross-Krook (BGK) model and asymptotic theory over a wide range of Knudsen number in the transition regime. The flow field properties including Mach number, pressure, overall temperature and magnitude of shear stress are examined in detail. Based on our analysis, we observed an approximately constant velocity and pressure distribution at a microchannel with a small opening angle. Our results also demonstrate that the heat lines from weakly nonlinear form of Sone constitutive law and DSMC show good agreement at low Knudsen numbers. Moreover, we show that the effect of divergence angle is influential in increasing normalized thermal mass flow rate at early transition regime. [ABSTRACT FROM AUTHOR]

In this study we use the direct simulation Monte Carlo (DSMC) to elaborate on the heat transfer patterns in the pressure-driven rarefied flow through micro/nanochannels. Finite length planar micro/nanochannels are considered using with symmetrical wall heat flux boundary conditions, and the gas flow is considered to be in slip and transition regimes. When considering zero-conductive or cooled walls, the DSMC solution predicts a possibility of the anti-Fourier heat transfer, i.e., the transfer of heat from cold-to-hot regions of the flow field. It turns out that the competition between the contributions of temperature gradient and pressure gradient (shear stress) in the heat flux results in three different heat transfer regimes. The regimes consist of complete hot-to-cold heat transfer regime, the entire anti-Fourier regime, and localized anti-Fourier regime. While the heat flux due to the shear stress is directed from the outlet towards the inlet, the Fourier term is strongly influenced by viscous slip heating, which then acts as a heat source, and contributes to patterns of heat flux on the fluid layer adjacent to the walls. Furthermore, the heat flux regimes for complete or localized cold-to-hot transfer are classified according to the magnitude of the normalized heat flux and the Knudsen number. Additionally, effects of heat flux condition on the mass flow rate are discussed. [ABSTRACT FROM AUTHOR]

The aim of the current work is to evaluate the accuracy and efficiency of a newly suggested collision scheme in the Direct Simulation Monte Carlo (DSMC) method; Simplified Bernoulli Trials implemented over transient adaptive subcells, SBT-TAS, for two different unsteady flow test cases. First, the performance of the SBT-TAS scheme is evaluated via simulating the shock-tube test case through a broad range of Knudsen numbers. The shock-tube investigations indicated that the SBT-TAS scheme could predict solutions as accurate as the nearest neighbor (NN) scheme. We show that the implemented SBT-TAS scheme requires at least 3–4 particles per each subcell to predict intermolecular collision frequency accurately. Then, a two-dimensional cylinder at Mach number of 0.6 is considered to investigate the accuracy and efficiency of the SBT-TAS in the prediction of the unsteady vortexes shedding. On the same grid and using the same number of particles per cell (PPC), the SBT and No Time Counter (NTC) collisions schemes fail to predict the correct vortex shedding behind the cylinder accurately and the structure of vortices are smeared out while the SBT-TAS and NN collisions schemes predict the strength of the vortices and their oscillation frequency with the same level of accuracy. Our results indicate that SBT-TAS preserves its accuracy in prediction of the aforementioned phenomenon while it uses relatively the same sample sizes and number of particles compared with its NN counterpart. [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]

The motivation of this review paper is to present a detailed summary of different collision models developed in the framework of the direct simulation Monte Carlo (DSMC) method. The emphasis is put on a newly developed collision model, i.e., the Simplified Bernoulli trial (SBT), which permits efficient low-memory simulation of rarefied gas flows. The paper starts with a brief review of the governing equations of the rarefied gas dynamics including Boltzmann and Kac master equations and reiterates that the linear Kac equation reduces to a non-linear Boltzmann equation under the assumption of molecular chaos. An introduction to the DSMC method is provided, and principles of collision algorithms in the DSMC are discussed. A distinction is made between those collision models that are based on classical kinetic theory (time counter, no time counter (NTC), and nearest neighbor (NN)) and the other class that could be derived mathematically from the Kac master equation (pseudo-Poisson process, ballot box, majorant frequency, null collision, Bernoulli trials scheme and its variants). To provide a deeper insight, the derivation of both collision models, either from the principles of the kinetic theory or the Kac master equation, is provided with sufficient details. Some discussions on the importance of subcells in the DSMC collision procedure are also provided and different types of subcells are presented. The paper then focuses on the simplified version of the Bernoulli trials algorithm (SBT) and presents a detailed summary of validation of the SBT family collision schemes (SBT on transient adaptive subcells: SBT-TAS, and intelligent SBT: ISBT) in a broad spectrum of rarefied gas-flow test cases, ranging from low speed, internal micro and nano flows to external hypersonic flow, emphasizing first the accuracy of these new collision models and second, demonstrating that the SBT family scheme, if compared to other conventional and recent collision models, requires smaller number of particles per cell to obtain sufficiently accurate solutions. [ABSTRACT FROM AUTHOR]

The present work is related to the study of the nitrogen gas flow through diverging micro/nano-channels. The direct simulation Monte-Carlo (DSMC) method has been used to study the flow. The Simplified Bernoulli Trials (SBT) collision scheme has been employed to reduce the computational costs and required amounts of the computer resources. The effects of various divergence angles on flow and thermal fields have been studied for different Knudsen numbers in late-slip and early-transition regimes. The inlet-to-outlet pressure ratio has been set to 2.5 for micro/nano-channels with a uniform constant wall temperature. By analyzing the numerical results no flow separation has been found due to slip at the wall which is different than flow behavior in continuum regime. The results indicate that the viscous component has a relatively large contribution in the overall pressure drop and flow behavior. It observed that for low divergence angles the effects of pressure forces dominate the effects of shear stress and divergence angle and cause the flow to accelerate along the channel while by increasing the divergence angle and therefore the effects of flow expansion, the flow decelerates along the channel. The mass flow rate through channel increases by increasing the divergence angle. Cold-to-hot heat transfer has been observed in diverging micro/nano-channels. In order to investigate the thermal behavior in diverging micro/nano-channels, the results have been compared to weakly non-linear constitutive laws derived from Boltzmann's equation. [ABSTRACT FROM AUTHOR]

In this paper, cavitation and supercavitation around 3D hemispherical head-form body and a conical cavitator were simulated. Dynamic and unsteady behaviors of cavitation were solved using large eddy simulation (LES) and k-ω SST turbulence models, as well as Kunz and Sauer mass transfer models. In addition, the compressive volume of fluid (VOF) method is used to track the cavity interface. Simulation is performed under the framework of the OpenFOAM package. The main contribution of this work is to present a correlation between the cavity length and diameter for hemispherical head-form bodies for the first time. Moreover, we provide a detailed comparison between different turbulence and mass transfer models over a broad range of cavitation numbers, especially in small cavitation numbers, including σ =0.07, 0.05, 0.02 for two cases, which is not reported previously. Our numerical results are compared with the available experimental data and a broad set of analytic relations for the cavity characteristics such as cavity length and diameter with suitable accuracy. Discussions on boundary layer separation and re-entrant jet behavior, which play a significant role in the bubble shedding in the cavity closure region, are presented. [ABSTRACT FROM AUTHOR]

In this study, we performed numerical investigations of the cavitating and supercavitating flow behind a three-dimensional disk with a particular emphasis on detailed comparisons of various turbulence and mass transfer models. Simulations were performed using the OpenFOAM package and flows at three different cavitation numbers, ( σ = 0.2, 0.1, and 0.05) were considered. Large eddy simulation (LES) and k – ω shear stress transport turbulence approaches were coupled with various mass transfer model types (e.g., Kunz, Schnerr–Sauer, and Zwart models). The Zwart mass transfer model was added to the standard OpenFOAM package. A compressive volume of fluid method was used to track the interface between the liquid and vapor phases. Our numerical results in terms of the cavity length, diameter, and drag coefficient compared fairly well with experimental data and a broad set of analytical relations. Moreover, this study provides a better understanding of the cavitation dynamics behind disk cavitators. Our results indicate that the most accurate solutions will be obtained by applying an LES turbulence approach combined with the Kunz mass transfer model. [ABSTRACT FROM AUTHOR]

The current paper examines a new DSMC approach to hypersonic flow simulation consisting of a combination between the Simplified Bernoulli Trials (SBT) collision algorithm and the transient adaptive subcell (TAS) selection procedure. The SBT collision algorithm has already been introduced as a scheme that provides accurate results with a quite small number of particles per cells and its combination with the transient adaptive subcell (TAS) technique will enable SBT to have coarser grid sizes as well. In the current research, the no-time-counter (NTC) collision algorithm and nearest neighbor (NN) pair selection procedure of Bird DS2V code are substituted by the SBT-TAS and comparisons between the new algorithm and NTC-NN are made considering appropriate test cases including hypersonic cylinder flow and axisymmetric biconic flow. Hypersonic cylinder flow is a well-known benchmark problem with a wide collision frequency range while the biconic flow exhibits laminar shock/shock and shock/boundary-layer interactions. Improvements implemented in the SBT-TAS technique, including subcell volume estimation, surface properties filter, and time controller, are discussed in detail. The simulations of these hypersonic test cases demonstrated that from the viewpoint of consumed sample-size, SBT-TAS is an efficient collision technique. [ABSTRACT FROM AUTHOR]

Flow patterns and heat transfer inside mini twisted oval tubes (TOTs) heated by constant-temperature walls are numerically investigated. Different configurations of tubes are simulated using water as the working fluid with temperature-dependent thermo-physical properties at Reynolds numbers ranging between 500 and 1100. After validating the numerical method with the published correlations and available experimental results, the performance of TOTs is compared to a smooth circular tube. The overall performance of TOTs is evaluated by investigating the thermal-hydraulic performance and the results are analyzed in terms of the field synergy principle and entropy generation. Enhanced heat transfer performance for TOTs is observed at the expense of a higher pressure drop. Additionally, the secondary flow generated by the tube-wall twist is concluded to play a critical role in the augmentation of convective heat transfer, and consequently, better heat transfer performance. It is also observed that the improvement of synergy between velocity and temperature gradient and lower irreversibility cause heat transfer enhancement for TOTs. [ABSTRACT FROM AUTHOR]

The accuracy of numerical simulations of rarefied gas flows, in particular the Navier-Stokes-Fourier (N–S–F) equations, depends on the employed surface boundary conditions. In the literature, the combination of the second-order slip/jump conditions has primarily been used for either the Burnett or the BGK Burnett equations for hypersonic gas flows. In this work, we suggest the second-order temperature jump condition in a new form. The second-order slip/jump conditions are implemented in the framework of OpenFOAM to employ with the N–S–F equations for low-speed nanoscale and hypersonic rarefied gas flows. We investigate both the first and second-order slip/jump boundary conditions for low speed rarefied gas flow in the pressure-driven backward facing step nanochannel as well as hypersonic gas flows over the flat plate and past a circular cylinder in cross-flow. Simulation results show that the combination of the second-order slip/jump (in new form) conditions predicts better surface properties than those of the first-order slip/jump conditions for all cases studied by comparing the Burnett and DSMC data. Especially, the N–S–F simulation results of the second-order slip/jump (in new form) conditions of the cylinder case can capture the Burnett data at Kn = 0.1, while those of the first-order conditions do not. [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]

Flow regimes through micro/nano nozzles experience the continuum behavior as well as the rarefied condition. The occurrence of broad rarefaction regimes due to unique geometry/flow conditions makes the particle-based simulation of micro/nano nozzles computationally expensive. Therefore, the primary aim of the present study is to implement the Simplified Bernoulli trials (SBT) collision algorithm in place of the conventional “No-Time-Counter” scheme in the direct simulation Monte Carlo (DSMC) method, thus reducing the required particle number. We show that the SBT scheme employed on the proper number of grid cells could reduce the computational costs and memory of micro/nano nozzle flow simulations. We also investigated the physical behavior of gas flows in micro/nano nozzles. We report the bimodal behavior of the velocity, temperature and Mach number at the throat at lower Knudsen numbers and the occurrence of Mach < 1 in the throat. We also considered back pressure effects on the flow field and the impact of gas species on the micro/nano nozzle performance. We identified an efficiency reduction due to rarefaction and improvements of the micro/nano nozzle performance due to increasing of the throat dimension. Performance reduction at the nanoscale is also discussed. [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]

The impetus of this study is to provide an in-depth insight into the unsteady hydrodynamic characteristics of the cavitating flow, effects of the wavy leading edge (WLE) on the noise suppression mechanism due to a cavity cloud formation, which contains condensation, detachment, collapse, spanwise flow, streamwise velocity fluctuation, and shedding phenomenon. NACA 634-021 hydrofoil was considered with WLE having a wavelength of 25% and an amplitude of 5% of the mean chord length and was compared to a straight-leading-edge (SLE) hydrofoil at cavitation numbers of σ = 0. 8 and a chord-based Reynolds number of 7. 2 × 1 0 5 . Counter-rotation vortices were produced between the peaks of the WLE hydrofoil by destroying the horseshoe vortex and delaying the tail vortex, changing the frequency. Here, the hydrodynamic forces have also been discussed in addition to the noise. The results showed that the leading-edge vortex formation and flow separation dynamics fundamentally differed between the SLE and the WLE hydrofoil. The main difference between the WLE and SLE hydrofoil turbulent flow is the formation of counter-rotating streamwise vortices pairs. We solved the cavitating flow using the large eddy simulation (LES) approach, as well as the Kunz mass transfer model, which is performed under the framework of the OpenFOAM package. [ABSTRACT FROM AUTHOR]