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Kinetic Theory-Based Methods in Fluid Dynamics

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 19401

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Dr. Zhen Chen

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Guest Editor

School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Interests: Computational Fluid Dynamics; Lattice Boltzmann Method; Meshfree methods; Multiphase Flow; Fluid-structure Interaction

Dr. Liangqi Zhang

E-Mail Website
Guest Editor

College of Aerospace Engineering, Chongqing University, Chongqing 400044, China
Interests: computational fluid dynamics; gas kinetic scheme, discrete velocity method, lattice boltzmann method; fluid-structure interaction
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Prof. Dr. Liming Yang

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Guest Editor

Department of Aerodynamics, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Interests: computational fluid dynamics; gas kinetic scheme; discrete velocity method; lattice boltzmann method; fluid-structure interaction
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Kinetic theory stems from statistical mechanics established at the mesoscopic scale. In the area of fluid dynamics, kinetic theory outperforms macroscopic interpretations (represented by the Navier–Stokes equations) in theoretical generality, with no restrictions from the continuum assumption. Various methods have been developed within the framework of kinetic theory, including the lattice Boltzmann method (LBM), discrete velocity method (DVM), gas kinetic scheme (GKS), unified gas kinetic scheme (UGKS), and discrete unified gas kinetic scheme (DUGKS). These methods play unique and important roles in almost all studies of fluid dynamics.

Broader applications of kinetic theory-based methods in engineering problems are often hindered by their intrinsic limitations. In most circumstances, kinetic theory-based methods consume much larger virtual memory than macroscopic methods. Additionally, high-fidelity simulations of physical problems beyond the continuum regime are usually time-consuming. Therefore, developing and employing robust and efficient kinetic theory-based methods for various fluid dynamics problems are necessary in the research community.

This Special Issue aims to be a forum for presenting recent progress made in the very active area of kinetic theory-based methods in fluid dynamics. Papers dealing with the development of kinetic theory-related numerical schemes and their applications to fluid dynamics problems are particularly welcome.

Dr. Zhen Chen
Dr. Liangqi Zhang
Prof. Dr. Liming Yang
Guest Editors

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Keywords

lattice boltzmann method
discrete velocity method
gas kinetic scheme and others
kinetic theory-based flux solvers
high-order methods
multiphase/multiphysics flows
micro flows
rarefied flows
flows in porous media
particle-laden flows

Related Special Issue

Kinetic Theory-based Methods in Fluid Dynamics II in Entropy (6 articles)

Published Papers (13 papers)

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Editorial

Jump to: Research

2 pages, 168 KiB

Open AccessEditorial

Kinetic Theory-Based Methods in Fluid Dynamics

by Zhen Chen, Liangqi Zhang and Liming Yang

Entropy 2023, 25(2), 255; https://doi.org/10.3390/e25020255 - 31 Jan 2023

Viewed by 869

Abstract

Kinetic theory stems from the statistical mechanics established at the mesoscopic scale [...] Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

Research

Jump to: Editorial

16 pages, 3695 KiB

Open AccessArticle

Numerical Study on Heat-Transfer Characteristics of Convection Melting in Metal Foam under Sinusoidal Temperature Boundary Conditions

by Xiang-Bo Feng, Shi-Fan Huo, Xiao-Tao Xu, Fei Liu and Qing Liu

Entropy 2022, 24(12), 1779; https://doi.org/10.3390/e24121779 - 05 Dec 2022

Cited by 1 | Viewed by 1149

Abstract

Convection melting in metal foam under sinusoidal temperature boundary conditions is numerically studied in the present study. A multiple-relaxation-time lattice Boltzmann method, in conjunction with the enthalpy approach, is constructed to model the melting process without iteration steps. The effects of the porosity, phase deviation, and periodicity parameter on the heat-transfer characteristics are investigated. For the cases considered in this work, it is found that the effects of the phase deviation and periodicity parameter on the melting rate are weak, but the melting front can be significantly affected by the sinusoidal temperature boundary conditions. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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15 pages, 2422 KiB

Open AccessFeature PaperArticle

Planar Gas Expansion under Intensive Nanosecond Laser Evaporation into Vacuum as Applied to Time-of-Flight Analysis

by Alexey Morozov and Vladimir Titarev

Entropy 2022, 24(12), 1738; https://doi.org/10.3390/e24121738 - 28 Nov 2022

Cited by 4 | Viewed by 1062

Abstract

A computational investigation of the dynamics of gas expansion due to intense nanosecond laser evaporation into vacuum has been carried out. The problem is solved in a one-dimensional approximation, which simplifies calculations and at the same time allows one to analyze the main features of the expansion dynamics. For analysis we use three different approaches. Two of them are based on kinetic analysis via the direct simulation Monte Carlo (DSMC) method and numerical solution of the model Bhatnagar–Gross–Krook (BGK) equation. The third one focuses on derivation of an analytical continuum solution. Emphasis is placed on the analysis of the velocity distribution function and the average energy of particles passing through the time-of-flight detector on the normal to the evaporation surface, which is important for interpreting experimental measurements. The formulated problem is quite difficult as the considered flow is time-dependent, contains discontinuities in boundary conditions and involves large variations of local Knudsen numbers as well as steep gradients of the velocity distribution function. Data were obtained on the particle energy in the time-of-flight distribution for the range of regimes from the free molecular flow to continuum one. The maximum attainable average energy of particles in the time-of-flight distribution is determined. The non-monotonicity of the energy increase was found, which is explained based on analysis of the velocity distribution of particles. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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21 pages, 7152 KiB

Open AccessArticle

A Simplified Linearized Lattice Boltzmann Method for Acoustic Propagation Simulation

by Qiaochu Song, Rongqian Chen, Shuqi Cao, Jinhua Lou, Ningyu Zhan and Yancheng You

Entropy 2022, 24(11), 1622; https://doi.org/10.3390/e24111622 - 08 Nov 2022

Cited by 2 | Viewed by 1449

Abstract

A simplified linearized lattice Boltzmann method (SLLBM) suitable for the simulation of acoustic waves propagation in fluids was proposed herein. Through Chapman–Enskog expansion analysis, the linearized lattice Boltzmann equation (LLBE) was first recovered to linearized macroscopic equations. Then, using the fractional-step calculation technique, the solution of these linearized equations was divided into two steps: a predictor step and corrector step. Next, the evolution of the perturbation distribution function was transformed into the evolution of the perturbation equilibrium distribution function using second-order interpolation approximation of the latter at other positions and times to represent the nonequilibrium part of the former; additionally, the calculation formulas of SLLBM were deduced. SLLBM inherits the advantages of the linearized lattice Boltzmann method (LLBM), calculating acoustic disturbance and the mean flow separately so that macroscopic variables of the mean flow do not affect the calculation of acoustic disturbance. At the same time, it has other advantages: the calculation process is simpler, and the cost of computing memory is reduced. In addition, to simulate the acoustic scattering problem caused by the acoustic waves encountering objects, the immersed boundary method (IBM) and SLLBM were further combined so that the method can simulate the influence of complex geometries. Several cases were used to validate the feasibility of SLLBM for simulation of acoustic wave propagation under the mean flow. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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18 pages, 7575 KiB

Open AccessArticle

Thermal Lattice Boltzmann Flux Solver for Natural Convection of Nanofluid in a Square Enclosure

by Xiaodi Wu and Song Zhou

Entropy 2022, 24(10), 1448; https://doi.org/10.3390/e24101448 - 11 Oct 2022

Cited by 1 | Viewed by 1457

Abstract

In the present study, mathematical modeling was performed to simulate natural convection of a nanofluid in a square enclosure using the thermal lattice Boltzmann flux solver (TLBFS). Firstly, natural convection in a square enclosure, filled with pure fluid (air and water), was investigated to validate the accuracy and performance of the method. Then, influences of the Rayleigh number, of nanoparticle volume fraction on streamlines, isotherms and average Nusselt number were studied. The numerical results illustrated that heat transfer was enhanced with the augmentation of Rayleigh number and nanoparticle volume fraction. There was a linear relationship between the average Nusselt number and solid volume fraction. and there was an exponential relationship between the average Nusselt number and Ra. In view of the Cartesian grid used by the immersed boundary method and lattice model, the immersed boundary method was chosen to treat the no-slip boundary condition of the flow field, and the Dirichlet boundary condition of the temperature field, to facilitate natural convection around a bluff body in a square enclosure. The presented numerical algorithm and code implementation were validated by means of numerical examples of natural convection between a concentric circular cylinder and a square enclosure at different aspect ratios. Numerical simulations were conducted for natural convection around a cylinder and square in an enclosure. The results illustrated that nanoparticles enhance heat transfer in higher Rayleigh number, and the heat transfer of the inner cylinder is stronger than that of the square at the same perimeter. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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16 pages, 2504 KiB

Open AccessFeature PaperArticle

Kinetic Theory and Memory Effects of Homogeneous Inelastic Granular Gases under Nonlinear Drag

by Alberto Megías and Andrés Santos

Entropy 2022, 24(10), 1436; https://doi.org/10.3390/e24101436 - 09 Oct 2022

Cited by 3 | Viewed by 1777

Abstract

We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in collisions as accounted by a constant coefficient of normal restitution. The interaction with the thermal bath is modeled by a nonlinear drag force plus a white-noise stochastic force. The kinetic theory for this system is described by an Enskog–Fokker–Planck equation for the one-particle velocity distribution function. To get explicit results of the temperature aging and steady states, Maxwellian and first Sonine approximations are developed. The latter takes into account the coupling of the excess kurtosis with the temperature. Theoretical predictions are compared with direct simulation Monte Carlo and event-driven molecular dynamics simulations. While good results for the granular temperature are obtained from the Maxwellian approximation, a much better agreement, especially as inelasticity and drag nonlinearity increase, is found when using the first Sonine approximation. The latter approximation is, additionally, crucial to account for memory effects such as Mpemba and Kovacs-like ones. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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19 pages, 4581 KiB

Open AccessFeature PaperArticle

Application of a Gas-Kinetic BGK Scheme in Thermal Protection System Analysis for Hypersonic Vehicles

by Di Zhou, Bingchen Du, Tongqing Guo, Qiaozhong Li and Zhiliang Lu

Entropy 2022, 24(10), 1325; https://doi.org/10.3390/e24101325 - 21 Sep 2022

Cited by 1 | Viewed by 1051

Abstract

One major problem in the development of hypersonic vehicles is severe aerodynamic heating; thus, the implementation of a thermal protection system is required. A numerical investigation on the reduction of aerodynamic heating using different thermal protection systems is conducted using a novel gas-kinetic BGK scheme. This method adopts a different solution strategy from the conventional computational fluid dynamics technique, and has shown a lot of benefits in the simulation of hypersonic flows. To be specific, it is established based on solving the Boltzmann equation, and the obtained gas distribution function is used to reconstruct the macroscopic solution of the flow field. Within the finite volume framework, the present BGK scheme is specially designed for the evaluation of numerical fluxes across the cell interface. Two typical thermal protection systems are investigated by using spikes and opposing jets, separately. Both their effectiveness and mechanisms to protect the body surface from heating are analyzed. The predicted distributions of pressure and heat flux, and the unique flow characteristics brought by spikes of different shapes or opposing jets of different total pressure ratios all verify the reliability and accuracy of the BGK scheme in the thermal protection system analysis. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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13 pages, 10722 KiB

Open AccessArticle

Study of the Imbibition Phenomenon in Porous Media by the Smoothed Particle Hydrodynamic (SPH) Method

by Jie Liu, Tao Zhang and Shuyu Sun

Entropy 2022, 24(9), 1212; https://doi.org/10.3390/e24091212 - 29 Aug 2022

Cited by 10 | Viewed by 1504

Abstract

Over recent decades, studies in porous media have focused on many fields, typically in the development of oil and gas reservoirs. The imbibition phenomenon, a common mechanism affecting multi-phase flows in porous media, has shown more significant impacts on unconventional reservoir development, where the effect of the pore space increases with decreased pore sizes. In this paper, a comprehensive SPH method is applied, considering the binary interactions among the particles to study the imbibition phenomenon in porous media. The model is validated with physically meaningful results showing the effects of surface tension, contact angle, and pore structures. A heterogeneous porous medium is also constructed to study the effect of heterogeneity on the imbibition phenomenon; it can be referred from the results that the smaller pore throats and wetting surfaces are more preferred for the imbibition. The results show that the SPH method can be applied to solve the imbibition problems, but the unstable problem is still a sore point for the SPH method. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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22 pages, 4267 KiB

Open AccessArticle

Free-Energy-Based Discrete Unified Gas Kinetic Scheme for van der Waals Fluid

by Zeren Yang, Sha Liu, Congshan Zhuo and Chengwen Zhong

Entropy 2022, 24(9), 1202; https://doi.org/10.3390/e24091202 - 27 Aug 2022

Cited by 8 | Viewed by 1390

Abstract

The multiphase model based on free-energy theory has been experiencing long-term prosperity for its solid foundation and succinct implementation. To identify the main hindrance to developing a free-energy-based discrete unified gas-kinetic scheme (DUGKS), we introduced the classical lattice Boltzmann free-energy model into the DUGKS implemented with different flux reconstruction schemes. It is found that the force imbalance amplified by the reconstruction errors prevents the direct application of the free-energy model to the DUGKS. By coupling the well-balanced free-energy model with the DUGKS, the influences of the amplified force imbalance are entirely removed. Comparative results demonstrated a consistent performance of the well-balanced DUGKS despite the reconstruction schemes utilized. The capability of the DUGKS coupled with the well-balanced free-energy model was quantitatively validated by the coexisting density curves and Laplace’s law. In the quiescent droplet test, the magnitude of spurious currents is reduced to a machine accuracy of

10^{- 15}

. Aside from the excellent performance of the well-balanced DUGKS in predicting steady-state multiphase flows, the spinodal decomposition test and the droplet coalescence test revealed its stability problems in dealing with transient flows. Further improvements are required on this point. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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28 pages, 2634 KiB

Open AccessFeature PaperArticle

A Well-Balanced Unified Gas-Kinetic Scheme for Multicomponent Flows under External Force Field

by Tianbai Xiao

Entropy 2022, 24(8), 1110; https://doi.org/10.3390/e24081110 - 12 Aug 2022

Cited by 1 | Viewed by 1342

Abstract

The study of the evolution of the atmosphere requires careful consideration of multicomponent gaseous flows under gravity. The gas dynamics under an external force field is usually associated with an intrinsic multiscale nature due to large particle density variation along the direction of force. A wonderfully diverse set of behaviors of fluids can be observed in different flow regimes. This poses a great challenge for numerical algorithms to accurately and efficiently capture the scale-dependent flow physics. In this paper, a well-balanced unified gas-kinetic scheme (UGKS) for a gas mixture is developed, which can be used for the study of cross-scale multicomponent flows under an external force field. The well-balanced scheme here indicates the capability of a numerical method to evolve a gravitational system under any initial condition to the hydrostatic equilibrium and to keep such a solution. Such a property is crucial for an accurate description of multicomponent gas evolution under an external force field, especially for long-term evolving systems such as galaxy formation. Based on the Boltzmann model equation for gas mixtures, the UGKS leverages the space–time integral solution to construct numerical flux functions and, thus, provides a self-conditioned mechanism to recover typical flow dynamics in various flow regimes. We prove the well-balanced property of the current scheme formally through theoretical analysis and numerical validations. New physical phenomena, including the decoupled transport of different gas components in the transition regime, are presented and studied. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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34 pages, 9053 KiB

Open AccessArticle

Three-Dimensional Simulations of Anisotropic Slip Microflows Using the Discrete Unified Gas Kinetic Scheme

by Wenqiang Guo and Guoxiang Hou

Entropy 2022, 24(7), 907; https://doi.org/10.3390/e24070907 - 30 Jun 2022

Cited by 2 | Viewed by 1285

Abstract

The specific objective of the present work study is to propose an anisotropic slip boundary condition for three-dimensional (3D) simulations with adjustable streamwise and spanwise slip length by the discrete unified gas kinetic scheme (DUGKS). The present boundary condition is proposed based on the assumption of nonlinear velocity profiles near the wall instead of linear velocity profiles in a unidirectional steady flow. Moreover, a 3D corner boundary condition is introduced to the DUGKS to reduce the singularities. Numerical tests validate the effectiveness of the present method, which is more accurate than the bounce-back and specular reflection slip boundary condition in the lattice Boltzmann method. It is of significance to study the lid-driven cavity flow due to its applications and its capability in exhibiting important phenomena. Then, the present work explores, for the first time, the effects of anisotropic slip on the two-sided orthogonal oscillating micro-lid-driven cavity flow by adopting the present method. This work will generate fresh insight into the effects of anisotropic slip on the 3D flow in a two-sided orthogonal oscillating micro-lid-driven cavity. Some findings are obtained: The oscillating velocity of the wall has a weaker influence on the normal velocity component than on the tangential velocity component. In most cases, large slip length has a more significant influence on velocity profiles than small slip length. Compared with pure slip in both top and bottom walls, anisotropic slip on the top wall has a greater influence on flow, increasing the 3D mixing of flow. In short, the influence of slip on the flow field depends not only on slip length but also on the relative direction of the wall motion and the slip velocity. The findings can help in better understanding the anisotropic slip effect on the unsteady microflow and the design of microdevices. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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11 pages, 6745 KiB

Open AccessArticle

Hydrodynamic Behavior of Self-Propelled Particles in a Simple Shear Flow

by Tingting Qi, Jianzhong Lin and Zhenyu Ouyang

Entropy 2022, 24(7), 854; https://doi.org/10.3390/e24070854 - 22 Jun 2022

Cited by 7 | Viewed by 1449

Abstract

The hydrodynamic properties of a squirmer type of self-propelled particle in a simple shear flow are investigated using the immersed boundary-lattice Boltzmann method in the range of swimming Reynolds number 0.05 ≤ Re_s ≤ 2.0, flow Reynolds number 40 ≤ Re_p ≤ 160, blocking rate 0.2 ≤ κ ≤ 0.5. Some results are validated by comparing with available other results. The effects of Re_s, Re_p and κ on the hydrodynamic properties of squirmer are discussed. The results show that there exist four distinct motion modes for the squirmer, i.e., horizontal mode, attractive oscillation mode, oscillation mode, and chaotic mode. Increasing Re_s causes the motion mode of the squirmer to change from a constant tumbling near the centerline to a stable horizontal mode, even an oscillatory or appealing oscillatory mode near the wall. Increasing the swimming intensity of squirmer under the definite Re_s will induce the squirmer to make periodic and stable motion at a specific distance from the wall. Increasing Re_p will cause the squirmer to change from a stable swimming state to a spiral motion or continuous rotation. Increasing κ will strengthen the wall’s attraction to the squirmer. Increasing swimming intensity of squirmer will modify the strength and direction of the wall’s attraction to the squirmer if κ remains constant. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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18 pages, 5388 KiB

Open AccessArticle

Nonlinear Modeling Study of Aerodynamic Characteristics of an X38-like Vehicle at Strong Viscous Interaction Regions

by Dingwu Jiang, Pei Wang, Jin Li and Meiliang Mao

Entropy 2022, 24(6), 836; https://doi.org/10.3390/e24060836 - 17 Jun 2022

Cited by 3 | Viewed by 1629

Abstract

Strong viscous interaction and multiple flow regimes exist when vehicles fly at high altitude and high Mach number conditions. The Navier–Stokes(NS) solver is no longer applicable in the above situation. Instead, the direct simulation Monte Carlo (DSMC) method or Boltzmann model equation solvers are usually needed. However, they are computationally more expensive than the NS solver. Therefore, it is of great engineering value to establish the aerodynamic prediction model of vehicles at high altitude and high Mach number conditions. In this paper, the hypersonic aerodynamic characteristics of an X38-like vehicle in typical conditions from 70 km to 110 km are simulated using the unified gas kinetic scheme (UGKS), which is applicable for all flow regimes. The contributions of pressure and viscous stress on the force coefficients are analyzed. The viscous interaction parameters, Mach number, and angle of attack are used as independent variables, and the difference between the force coefficients calculated by UGKS and the Euler solver is used as a dependent variable to establish a nonlinear viscous interaction model between them in the range of 70–110 km. The evaluation of the model is completed using the correlation coefficient and the relative orthogonal distance. The conventional viscous interaction effect and rarefied effect are both taken into account in the model. The model can be used to quickly obtain the hypersonic aerodynamic characteristics of X38-like vehicle in a wide range, which is meaningful for engineering design. Full article

(This article belongs to the Special Issue Kinetic Theory-Based Methods in Fluid Dynamics)

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