Unified Gas Research Articles

Construction of a NiFe-LDH catalyst with a three-dimensional unified gas diffusion layer structure via a facile acid etching route for the oxygen evolution reaction

A simple acid etching method is proposed to prepare a three-dimensional unified NiFe-LDH gas diffusion layer. Moreover, the experiment proved that the electrode followed the lattice oxygen mechanism and exhibited high electrocatalytic activity.

Optimized discrete unified gas kinetic scheme for continuum and rarefied flows

In this paper, an optimized discrete unified gas kinetic scheme (DUGKS) is presented for both continuum and rarefied flows. The present scheme can be considered as a new version of the DUGKS. At first, we follow the original DUGKS to obtain the evolution equation by finite volume method. Then, we propose a new method to evaluate the flux. Different from the original DUGKS, the flux is evaluated by the distribution function at the node instead of the interface center. This makes the present scheme easier to implement and more efficient than the original DUGKS. To validate the present scheme, several numerical tests are performed, including the doubly periodic shear layers, the canonical two-dimension, and three-dimension Taylor–Green vortex flows, as well as the pressure-driven Couette flow and micro-Couette flow. Numerical results demonstrate that the present scheme preserves almost the same accuracy as compared with the original DUGKS, while it exhibits a lower numerical dissipation, and the computational efficiency and numerical stability can be significantly improved.

A discrete unified gas kinetic scheme on unstructured grids for viscid compressible flows and its parallel algorithm

<abstract><p>In this paper, we present a discrete unified gas kinetic scheme (DUGKS) on unstructured grids for high-speed viscid compressible flows on the basis of double distribution function (the density and the total energy distribution functions) Boltzmann-BGK equations. In the DUGKS, the discrete equilibrium distribution functions are constructed based on a D2Q17 circular function. In order to accelerate the simulation, we also illustrate a corresponding parallel algorithm. The DUGKS is validated by two benchmark problems, i.e., flows around the NACA0012 airfoil and flows past a circular cylinder with the Mach numbers range from 0.5 to 2.5. Good agreements with the referenced results are observed from the numerical results. The results of parallel test indicate that the DUGKS is highly parallel scalable, in which the parallel efficiency achieves $ 93.88\% $ on a supercomputer using up to $ 4800 $ processors. The proposed method can be utilized for high-resolution numerical simulation of complex and high Mach number flows.</p></abstract>

Modified steady discrete unified gas kinetic scheme for multiscale radiative heat transfer

In this work, a steady discrete unified gas kinetic scheme (SDUGKS) is proposed to solve the steady radiative transfer equation (RTE), which is an improvement of the original SDUGKS [X. F. Zhou et al., J. Comput. Phys. 423, 109767 (2020)]. The trapezoidal rule other than the rectangular rule used in the original SDUGKS is adopted in the proposed method in the reconstruction of energy flux across cell interface, just as the unsteady DUGKS. By this way, the length of the characteristic line of the modified SDUGKS establishes a relationship with the Courant-Friedrichs-Lewy (CFL) number in the transient DUGKS, which guarantees the accuracy of the modified SDUGKS. Furthermore, the length of the characteristic line is no longer limited by the extinction coefficient like in the original SDUGKS. As a result, the modified SDUGKS is more accurate than the original SDUGKS, and more efficient than the transient DUGKS for steady radiation problems. Furthermore, the smooth linear interpolation and the van Leer limiter are used for problems with smooth and discontinuous optical thicknesses, respectively. Several numerical tests with optical thickness varying from optical thin to thick are conducted to validate the present scheme. Numerical results demonstrate that the modified SDUGKS can serve as an effective tool in the study of multiscale steady radiative heat transfer in participating media.

Boundary vorticity dynamics of two-phase viscous flow

From the Navier–Stokes–Korteweg equations, the exact relations between the fundamental surface physical quantities for the two-phase viscous flow with the diffuse interface are derived, including density gradient, shear stress, vorticity, pressure, enstrophy flux, and surface curvature. These theoretical results provide a solid foundation of the boundary/interfacial vorticity dynamics and a new tool for the analysis of complex interfacial phenomena in two-phase viscous flows. To demonstrate the application of the developed results, simulation of a droplet impacting and spreading on a solid wall is conducted by using a recently developed well-balanced discrete unified gas kinetic scheme, focusing on the spreading process when the separation bubbles form inside the droplet. The distributions of shear stress, pressure, and enstrophy flux at the interface and the wall are analyzed, particularly near the moving contact points and other characteristic points. This example gives an unique perspective to the physics of droplet impingement on a wall.

On the Rarefied Thermally-Driven Flows in Cavities and Bends

This study examined rarefied thermally-driven flow in a square cavity (Case 1) and rectangular bend (Case 2), with various uniform wall temperatures in two dimensions. We employed the direct simulation Monte Carlo (DSMC) to solve problems with a wide range of Knudsen numbers Kn = 0.01 to 10, and the discrete unified gas kinetic scheme (DUGKS) solver was used at Kn = 0.01. The scenario was that, in case 1, the bottom side and its opposite were set hot, and the other sides were set cold. Diffuse reflector boundary conditions were set for all walls. The imposed temperature differences created four primary vortices. The results of the continuum set of equations of the slow non-isothermal flow (SNIT) solver proved that the primary vortices in the square cavity were caused by nonlinear thermal stress effects, and other smaller vortices appearing at Kn = 0.01, 0.1 were brought about by thermal creep processes. As the Kn increased, vortices generated by thermal creep disappeared, and eddies created by nonlinear thermal stress occupied the cavity. In case 2, i.e., a rectangular bend, two sides were set cold, and the others were hot. Two primary vortices were formed, which were caused by nonlinear thermal stress effects. The direction of streamlines in the two main vortices was opposite, from the warm to the cold zone, as some eddies on the left were counterclockwise, and others were clockwise.

Interface-resolved simulation of solid-liquid phase change with thermal convection using discrete unified gas kinetic scheme

This work presents an interface-resolved model for simulating the solid-liquid phase transition problems. In the method, the natural convection flow is handled by the recently proposed discrete unified gas kinetic scheme (DUGKS). Compared with the conventional lattice Boltzmann equation, DUGKS has more advantages on numerical stability and multiscale computation. On the other hand, the ghost-cell (GC) immersed boundary scheme is applied to capturing the solid-liquid interface of pure material. In contrast to the phase-field or enthalpy-based method, the interface here with zero thickness is resolved and explicitly tracked on the fixed Cartesian grid. It is worth noting that due to the adsorption or release of latent heat, the phase front should be evolved according to the Stefan condition. Since compatible with the GC method, the position of the melting front is directly identified by the intersection point, and the complicated treatment of marker inserting and/or deleting in the previous studies is removed. Three numerical examples, including the one-dimension conduction melting, convection melting in a square cavity and melting in a circular cavity with natural convection are conducted to test the present model. The result demonstrates the accuracy of the method for solid-liquid phase change problems.

A sharp interface immersed boundary-discrete unified gas kinetic scheme for fluid-solid flows with heat transfer

Particulate flow with thermal convection involves lots of moving and complex fluid-solid interfaces, and hence generally sheets a great challenge to numerical methods. For interface-resolved simulation of that flow, we present a ghost-cell (GC) method in the framework of discrete unified gas kinetic scheme (DUGKS) in this study. As a sharp interface immersed boundary model, the particle surface is considered to be of zero thickness in GC. A computation cell with its center located inside the particle and intersected by the interface is transformed into the fictitious cell, and its information is reconstructed from neighboring fields. The fluid motion with heat transfer is solved by the recently proposed DUGKS. For updating the position of particles, we evaluate the hydrodynamic forces of fluid-solid interaction through the mesoscopic momentum flux. The particle-particle interaction is described by the repulsive force model. The accuracy of the method is corroborated by five benchmark cases of flow past a heated cylinder, sedimentation of a cold particle in a channel, a catalyst particle migrating in a box, drafting-kissing-tumbling process of two hot particles, and a group of particles settling in an enclosure. It is observed that GC-DUGKS well captures the character of the thermal particulate flows.

A parallel discrete unified gas kinetic scheme on unstructured grid for inviscid high-speed compressible flow simulation

The discrete unified gas kinetic scheme (DUGKS) is a recently devised approach to simulate multiscale flows based on the kinetic models, which also shows distinct features for continuum flows. Most of the existing DUGKS are sequential or based on structured grids, thus limiting their scope of application in engineering. In this paper, a parallel DUGKS for inviscid high-speed compressible flows on unstructured grids is proposed. In the framework of the DUGKS, the gradients of the distribution functions are calculated by a least-square method. To parallelize the method, a graph-based partitioning method is employed to guarantee the load balancing and minimize the communication among processors. The method is validated by several benchmark problems, i.e., a two-dimensional (2D) Riemann problem, 2D subsonic flows passing two benchmark airfoils, a 2D regular shock reflection problem, 2D supersonic flows (Mach numbers are 3 and 5) around a cylinder, an explosion in a three-dimensional (3D) box, a 3D subsonic flow around the Office National d'Etudes et de Recherches Aérospatiales M6 wing, a 3D hypersonic flow (Mach number is 10) around a hemisphere, and a supersonic flow over the Northrop YF-17 fighter model. The numerical results show good agreement with the published results, and the present method is robust for a wide range of Mach numbers, from subsonic to hypersonic. The parallel performance results show that the proposed method is highly parallel scalable, where an almost linear scalability with 93% parallel efficiency is achieved for a 3D problem with over 55 × 106 tetrahedrons on a supercomputer with up to 4800 processors.

Pseudopotential-based discrete unified gas kinetic scheme for modeling multiphase fluid flows

To directly incorporate the intermolecular interaction effects into the discrete unified gas-kinetic scheme (DUGKS) for simulations of multiphase fluid flow, we developed a pseudopotential-based DUGKS by coupling the pseudopotential model that mimics the intermolecular interaction into DUGKS. Due to the flux reconstruction procedure, additional terms that break the isotropic requirements of the pseudopotential model will be introduced. To eliminate the influences of nonisotropic terms, the expression of equilibrium distribution functions is reformulated in a moment-based form. With the isotropy-preserving parameter appropriately tuned, the nonisotropic effects can be properly canceled out. The fundamental capabilities are validated by the flat interface test and the quiescent droplet test. It has been proved that the proposed pseudopotential-based DUGKS managed to produce and maintain isotropic interfaces. The isotropy-preserving property of pseudopotential-based DUGKS in transient conditions is further confirmed by the spinodal decomposition. Stability superiority of the pseudopotential-based DUGKS over the lattice Boltzmann method is also demonstrated by predicting the coexistence densities complying with the van der Waals equation of state. By directly incorporating the intermolecular interactions, the pseudopotential-based DUGKS offers a mesoscopic perspective of understanding multiphase behaviors, which could help gain fresh insights into multiphase fluid flow.

Simulation of two-phase flows at large density ratios and high Reynolds numbers using a discrete unified gas kinetic scheme

In order to treat immiscible two-phase flows at large density ratios and high Reynolds numbers, a three-dimensional code based on the discrete unified gas kinetic scheme (DUGKS) is developed, incorporating two major improvements. First, the particle distribution functions at cell interfaces are reconstructed using a weighted essentially non-oscillatory scheme. Second, the conservative lower-order Allen–Cahn equation is chosen instead of the higher-order Cahn–Hilliard equation to evolve the free-energy-based phase field governing the dynamics of two-phase interfaces. Five benchmark problems are simulated to demonstrate the capability of the approach in treating two-phase flows at large density ratios and high Reynolds numbers, including three two-dimensional problems (a stationary droplet, Rayleigh–Taylor instability, and a droplet splashing on a thin liquid film) and two three-dimensional problems (binary droplets collision and Rayleigh–Taylor instability). All results agree well with the previous numerical and experimental results. In these simulations, the density ratio and the Reynolds number can reach a large value of O(1000). Our improved approach sets the stage for the DUGKS scheme to handle realistic two-phase flow problems.

Arbitrary Lagrangian-Eulerian-type conserved discrete unified gas kinetic scheme for the simulations of transonic continuum and rarefied gas flows with moving boundaries

In this paper, an arbitrary Lagrangian-Eulerian (ALE) framework is incorporated into the conserved discrete unified gas-kinetic scheme (CDUGKS) to solve the transonic continuum and rarefied gas flows with moving boundary. This is a continuation of our earlier work [Y. Wang et al., Phys. Rev. E, 100(6), 063310 (2019)]. Compared to the original low-speed ALE-DUGKS, in which only the governing equation of the distribution function is solved, the mesh motion velocity is introduced in the proposed ALE-CDUGKS for updating both the distribution function and the conservative flow variables. For a flow in the continuum regime, the potential energy double-distribution-functions framework and the circle equilibrium distribution function model are incorporated for inviscid and viscous flows. In the rarefied flow regime, the technique of unstructured velocity-space mesh is introduced to decrease the total number of discrete particle-velocity points and reduce the computational load. In addition, a loosely-coupled algorithm for simulating the fluid-structure interaction problem (airfoil flutter) is also presented. As a result, under this unified framework based on the distribution function, the numerical simulations have relatively high computational efficiency for flows in both continuum and rarefied regimes. A series of flows around a stationary or moving airfoil in the continuum regime is simulated, and a plunging airfoil in rarefied gas flow is also studied. The consistent and good results obtained from the above test cases demonstrate the capability of the proposed ALE-CDUGKS for solving the compressible moving boundary problems with the rarefied gas effect.

Exponential Bhatnagar-Gross-Krook integrator for multiscale particle-based kinetic simulations.

Despite the development of an extensive toolbox of multiscale rarefied flow simulators, such simulations remain challenging due to the significant disparity of collisional and macroscopic spatiotemporal scales. Our study offers a novel and consistent numerical scheme for a coupled treatment of particles advection and collision governed by the BGK evolution, honoring positivity of the velocity distribution. Our method shares its framework, in spirit, with the unified gas kinetic class of multiscale schemes. Yet it provides attractive features for particle-based stochastic simulations, readily implementable to existing direct simulation Monte Carlo codes. Two main innovations are integrated in the presented BGK particle method. The first ingredient is a high-order time integration that can be interpreted probabilistically, independent of the time step size. The next one is identifying modified particle distributions that remain invariant under the advection-relaxation evolution. We demonstrate accuracy and performance of the devised scheme for prototypic gas flows over a wide range of rarefaction parameters. Due to the resulting robustness and flexibility of the devised exponential BGK integrator, the scheme paves the way towards more affordable simulations of large-scale and multiscale rarefied gas phenomena.

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

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.

Утилизация попутного нефтяного газа в России: методы и перспективы производства продуктов газохимии.

From an economic point of view, the flaring of associated petroleum gas (APG) entails significant losses of a resource that can be usefully used. In addition, it has a negative impact on the environment. Russian oil and gas companies are actively engaged in the APG utilization, but the question of choosing the most effective and reasonable solutions for its useful use remains open. The purpose of the study is to analyze the known and used methods of APG utilization in the world, the level and directions of APG utilization by Russian oil and gas companies, as well as to assess the prospects for the development of APG deep processing projects based on Russian oil and gas companies to produce gas chemistry products. The general situation on the utilization of APG in Russia was considered, the study showed that the volume of flaring has been increasing in absolute terms over the past 5 years, due to the fact that companies do not have time to develop infrastructure for gas utilization, as well as with the growth of oil production in Russia. The analysis of the level and main trends of APG utilization by the largest Russian oil and gas companies was carried out, which showed that companies are already engaged in the development of the gas chemical segment, however, they often use simpler methods of utilization (injection of APG into the reservoir, generation of electricity, injection of APG into Unified Gas Supply System). The study of the gas chemistry market showed the prospects for growth in demand for gas chemistry products at least until 2030, which confirms the relevance of the development of this direction. For a complex assessment of the prospects for the creation of gas chemical production facilities on the basis of Russian oil and gas companies, a SWOT analysis was carried out, which helped to systematize ideas about the potential for the development of the gas chemical direction by oil and gas companies. Methods of statistical research, methods of comparative and causal analysis, strategic and managerial analysis, as well as the method of SWOT analysis were used to conduct the study.

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

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.

Unified X-space parallelization algorithm for conserved discrete unified gas kinetic scheme

In this paper, the open source multiscale flow solver dugksFoam is optimized with a newly proposed parallelization strategy and conserved algorithm. A novel X-space parallel framework is introduced. In contrast to traditional discrete physical/velocity space decomposition parallelization methods, it can decompose each space in a hybrid manner and efficiently parallelize the computation. For better conservation of the macroscopic physical variables, flow properties in each cell are updated by moments of microscopic variable fluxes, which preserves particle multiscale information under sparse velocity space mesh. Several test cases, which include 2D lid-driven cavity flow in the transition flow regime, hypersonic rarefied flow past a 3D sphere, are carried out to verify the accuracy of the conserved discrete unified gas kinetic scheme to simulate the flows in all flow regimes. A large-scale parallel computational test case of 3D sphere with 101,600 physical mesh cells and 62,744 velocity mesh cells is conducted to measure the parallel efficiency of the conserved dugksFoam code. A significant superlinear speedup of 1631.87 has been achieved on 1120 cores.

On the nonlinear thermal stress, thermal creep, and thermal edge flows in triangular cavities

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.

Rarefaction Effect, Heat Transfer, and Drag Coefficient for Gas Flow Around Square Cylinder in Transition Flow Regime

Abstract In this work, rarefaction effect, heat transfer, and drag coefficient for gas flow around a square cylinder in transition flow regime are numerically studied using unified gas kinetic scheme (UGKS). To reduce computational cost, a mirror symmetry boundary treatment for UGKS is proposed and applied in this study. It is found that: (1) velocity slip is not obvious on upwind and downwind surfaces of square cylinder due to the tangential gas flow being weak in these surfaces; (2) with the increase of local Knudsen number, velocity slip on upper surface always increases, but temperature jump can decrease, which indicates that Knudsen number is not the decisive parameter to characterize temperature jump; (3) the heat transfer between gas and square cylinder enhances with the increase of inflow Knudsen number and cylinder temperature due to the increase of temperature jump and deteriorates with the increase of inflow Mach number on account of gas stagnation; and (4) the drag coefficient increases with the increase of inflow Knudsen number, the decrease of inflow Mach number, and the increase of cylinder temperature. To further predict the variation of average Nusselt number and drag coefficient, correlations for average Nusselt number and drag coefficient with inflow Mach number ranging from 0.05 to 0.3, inflow Knudsen number ranging from 0.1 to 10, and cylinder temperature ranging from 320 K to 380 K are proposed. This research can improve the understanding for mechanisms of gas flow and heat transfer in micro-electromechanical system (MEMS) devices.

Investigation of nonlinear squeeze-film damping involving rarefied gas effect in micro-electro-mechanical systems

In this paper, the nonlinear squeeze-film damping (SFD) involving rarefied gas effect in the micro-electro-mechanical systems (MEMS) is investigated. Considering the motion of structures (beam, cantilever, and membrane) in MEMS, the dynamic response of the structure is affected greatly by the SFD. In the traditional model, a viscous damping assumption that the damping force is linear with the moving velocity is used. As the nonlinear damping phenomenon is observed for a micro-structure oscillating at a high velocity, this assumption does not hold and will cause error results for predicting the response of the micro-structure. Meanwhile, due to the small size of the device and the low pressure of the encapsulation, the gas in MEMS is usually rarefied gas. Therefore, to correctly predict the damping force, the rarefied gas effect must be considered. To study the nonlinear SFD problem involving the rarefied gas effect, a kinetic method, i.e., discrete unified gas kinetic scheme (DUGKS), is introduced in this paper. Also, based on the DUGKS, two solving methods, i.e., a traditional decoupled method (Eulerian scheme) and a coupled framework (arbitrary Lagrangian-Eulerian scheme), are adopted. With these two methods, two basic motion forms, i.e., linear (perpendicular) and tilting motions of a rigid micro-beam, are studied under forced and free oscillations. For a forced oscillation, the nonlinear SFD phenomenon is investigated. For a free oscillation, in the resonance regime, some numerical results at different maximum oscillating velocities are presented and discussed. Besides, the influence of oscillation frequency on the damping force or torque is also studied, and the cause of the nonlinear damping phenomenon is investigated.