The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.

A basic model of unconventional gas microscale flow based on the lattice Boltzmann method

A new method for selecting dimensionless relaxation time in the lattice Boltzmann model was proposed based on similarity criterion and gas true physical parameters.At the same time,the dimensionless relaxation time was modified by considering the influence of the boundary Knudsen layer.On this basis,the second-order slip boundary condition of the wall was considered,and the key parameters in the corresponding combined bounce-back/specular-reflection boundary condition were deduced to build a new model of unconventional gas microscale flow simulation based on the lattice Boltzmann method suitable for high temperatures and high pressures.The simulation results of methane gas flow driven by body force in infinite micro-channels and flow driven by inlet-outlet pressure differential in long straight channels were compared with the numerical and analytical solutions in the literature to verify the accuracy of the model,and the dimensionless relaxation time modification was formally optimized.The results show that the new model can effectively characterize the slippage effect,compression effect,gas density and the effect of boundary Knudsen layer in the micro-scale flow of unconventional natural gas.The new model can achieve a more comprehensive characterization of the real gas flow conditions and can be used as a basic model for the simulation of unconventional gas flow on the micro-nano scale.

Partitioning characteristics of gas channel of coal-rock mass in mining space and gas orientation method

In order to research the influence of coal-rock mass morphology of mining space on the flow law of gas,the laboratory physical model and numerical computation methods were adopted to simulate coal mining activities.The simulation results indicate that,after coal seam mining,the loose rock accumulation body of free caving,ordered rock arrangement body of plate damage rich in longitudinal and transverse fractures and horizontal fissure body formed by rock mass deformation imbalance are formed from bottom to top in the mining space.For these three types of accumulation bodies,there are essential differences in the accumulation state,rock size and gas breakover characteristics.According to this,the coal-rock mass in the mining space is classified into gas turbulence channel area,gas transitional flow channel area and gas seepage channel area.In the turbulence channel area,the gas is distributed transversely and longitudinally and gas diffuses in the form of convection with Reynolds number R_e more than100;in the transitional flow channel area,one-way or two-way gas channels are crisscross and gas is of transitional flow regime with R,.between 10 and 100.In the seepage channel area,there are a few vertical gas channels with R,.less than 10.In this paper,the researches on the gas orientation method in different partitions were further carried out,gas orientation methods of low-level pipe burying,middle-level interception and high-level extraction were determined and an on-site industrial test was conducted,achieving the effective diversion of gas and verifying the reasonableness of gas channel partition.

A liquid loading prediction method of gas pipeline based on machine learning

The liquid loading is one of the most frequently encountered phenomena in the transportation of gas pipeline,reducing the transmission efficiency and threatening the flow assurance.However,most of the traditional mechanism models are semi-empirical models,and have to be resolved under different working conditions with complex calculation process.The development of big data technology and artificial intelligence provides the possibility to establish data-driven models.This paper aims to establish a liquid loading prediction model for natural gas pipeline with high generalization ability based on machine learning.First,according to the characteristics of actual gas pipeline,a variety of reasonable combinations of working conditions such as different gas velocity,pipe diameters,water contents and outlet pressures were set,and multiple undulating pipeline topography with different elevation differences was established.Then a large number of simulations were performed by simulator OLGA to obtain the data required for machine learning.After data preprocessing,six supervised learning algorithms,including support vector machine(SVM),decision tree(DT),random forest(RF),artificial neural network(ANN),plain Bayesian classification(NBC),and K nearest neighbor algorithm(KNN),were compared to evaluate the performance of liquid loading prediction.Finally,the RF and KNN with better performance were selected for parameter tuning and then used to the actual pipeline for liquid loading location prediction.Compared with OLGA simulation,the established data-driven model not only improves calculation efficiency and reduces workload,but also can provide technical support for gas pipeline flow assurance.

Parametric study of gas−liquid two-phase flow field in horizontal stirred tank

Based on Fluent software,the gas−liquid two-phase flow in the horizontal stirred tank was simulated with SST k−ωturbulence model,Eulerian−Eulerian two-fluid model,and multi-reference flame method.The mixing process in the tank was calculated by tracer method.The results show that increasing the rotating speed or gas flow is conducive to a more uniform distribution of the gas phase and accelerates the mixing of the liquid phase.When the rotating speed exceeds 93 r/min,the relative power demand remains basically constant.The change in the inclination angle of the upper impeller has minimal effect on the gas phase distribution.When the inclination angle is 50°,the relative power demand reaches the maximum.An appropriate increase in the impeller distance from the bottom improves the gas holdup and gas phase distribution but increases the liquid phase mixing time.

Delivery of inert gas through a vertical borehole using inert gas generator: A theoretical study

The delivery of the inert gas through a vertical borehole using inert gas generator or IGG is investigated.Potential limitations and/or transient effects are highlighted.During the analysis,the borehole diameter,borehole length,type of borehole and partial condensation prior to entering the borehole were varied.A choked flow will occur for a contraction exit or borehole of 0.3 m in diameter if no condensation prior to the contraction occurs.If partial condensation takes place,a borehole diameter of 0.3 m will be possible if almost 50%of the water vapour condensates.However,pressure losses along boreholes with a diameter of 0.3 or 0.4 m are significant and could pose a challenge if trying to mitigate the pressure losses.Adding a booster fan prior to the inlet of the 0.4 m lined borehole would still be a challenge.The corresponding case with a 0.5 m borehole presents much more favourable pressure losses.The 0.5 m diameter lined borehole should be regarded as the lower threshold.The rapid heating of the unlined borehole surface will increase the risk of thermal spallation and possibly imposing restrictions.Understanding the mechanisms during gas delivery will increase the likelihood of a successful inertisation.

Numerical simulation of a gas pipeline network using computational fluid dynamics simulators

This article describes numerical simulation of gas pipeline network operation using high-accuracy computational fluid dynamics (CFD) simulators of the modes of gas mixture transmission through long, multi-line pipeline systems (CFD-simulator). The approach used in CFD-simulators for modeling gas mixture transmission through long, branched, multi-section pipelines is based on tailoring the full system of fluid dynamics equations to conditions of unsteady, non-isothermal processes of the gas mixture flow. Identification, in a CFD-simulator, of safe parameters for gas transmission through compressor stations amounts to finding the interior points of admissible sets described by systems of nonlinear algebraic equalities and inequalities. Such systems of equalities and inequalities comprise a formal statement of technological, design, operational and other constraints to which operation of the network equipment is subject. To illustrate the practicability of the method of numerical simulation of a gas transmission network, we compare computation results and gas flow parameters measured on-site at the gas transmission enter-prise.

Simplified graphical correlation for determining flow rate in tight gas wells in the Sulige gas field

The Sulige tight gas reservoir is characterized by low-pressure, low-permeability and lowabundance. During production, gas flow rate and reservoir pressure decrease sharply; and in the shut- in period, reservoir pressure builds up slowly. Many conventional methods, such as the indicative curve method, systematic analysis method and numerical simulation, are not applicable to determining an appropriate gas flow rate. Static data and dynamic performance show permeability capacity, kh is the most sensitive factor influencing well productivity, so criteria based on kh were proposed to classify vertical wells. All gas wells were classified into 4 groups. A multi-objective fuzzy optimization method, in which dimensionless gas flow rate, period of stable production, and recovery at the end of the stable production period were selected as optimizing objectives, was established to determine the reasonable range of gas flow rate. In this method, membership functions of above-mentioned optimizing factors and their weights were given. Moreover, to simplify calculation and facilitate field use, a simplified graphical illustration （or correlation） was given for the four classes of wells. Case study illustrates the applicability of the proposed method and graphical correlation, and an increase in cumulative gas production up to 37% is achieved and the well can produce at a constant flow rate for a long time.

DIRECT NUMERICAL TEST OF THE B-G-K MODEL EQUATION BY THE DSMC METHOD

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

NUMERICAL SIMULATION OF 1-D UNSTEADY TWO-PHASE FLOWS WITH SHOCKS

In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the flow parameters for the gas and particle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.

Mathematical simulation of burden distribution in COREX 3000 shaft by discrete element method

The distribution of reducing gas in a shaft furnace dominates the temperature profile,gas utilization ratio,metallization degree and is the overwhelming factor for stable,high productivities and low-energy-consumption operation.At the same time,the distribution of gas flow is mainly determined by the position of gas inlet,the packed bed porosity distribution as well as its change due to the difference on the mode of top charge and bottom discharge.When injecting position of the process is fixed,the charge mode is the only means for regulating the gas flow distribution.In this paper,a numerical simulation model of burden distribution in the shaft furnace of COREX 3000 has been developed to analyze the porosity distribution under the different charge modes by means of Discrete Element Method(DEM).The effects of the particle size and its distribution under conditions of different charge batches,chute angle,stoke line on the burden surface shape and burden bed particle size distribution and segregation were investigated,and then the porosity distribution in the shaft of corresponding charging pattern was quantitatively accessed.Therefore,the results can be used to optimize the charge patterns base on required gas distribution.

Gas kinetic flux solver based finite volume weighted essentially non-oscillatory scheme for inviscid compressible flows

A high-order gas kinetic flux solver(GKFS)is presented for simulating inviscid compressible flows.The weighted essentially non-oscillatory(WENO)scheme on a uniform mesh in the finite volume formulation is combined with the circular function-based GKFS(C-GKFS)to capture more details of the flow fields with fewer grids.Different from most of the current GKFSs,which are constructed based on the Maxwellian distribution function or its equivalent form,the C-GKFS simplifies the Maxwellian distribution function into the circular function,which ensures that the Euler or Navier-Stokes equations can be recovered correctly.This improves the efficiency of the GKFS and reduces its complexity to facilitate the practical application of engineering.Several benchmark cases are simulated,and good agreement can be obtained in comparison with the references,which demonstrates that the high-order C-GKFS can achieve the desired accuracy.

Numerical simulation on gas-solid flow during circulating fluidized roasting of bauxite by a computational particle fluid dynamics method

A full-cycle numerical simulation of a circulating fluidized bed(CFB)by the use of the computational particle fluid dynamics(CPFD)method has been developed.The effects of the presence or absence of the secondary air,different secondary air positions,and different secondary air ratios on the gas–solid flow characteristics were explored.The results show that the presence of the secondary air makes a core-annular structure of the velocity distribution of particles in the fluidized bed,which enhances the uniformity of particles’distribution and the stability of fluidization.The position and the ratio of the secondary air have a significant impact on the particle distribution,particle flow rate,and gas flow rate in the fluidized bed.When the secondary air position and ratio are optimal,the particles,particle flow rate,and air flow rate in the CFB are evenly distributed,the gas–solid flow state is good,and the CFB can operate stably.

A numerical study on dispersion of particles from the surface of a circular cylinder placed in a gas flow using discrete vortex method

The dispersion of particles emitted from the surface of a circular cylinder placed in a gas flow at the Reynolds number of 200 000 is numerically investigated using the discrete vortex method coupled with a Lagrangian approach for solid particle tracking. The wake vortex patterns, the temporal-spatial distributions and trajectories as well as the dispersion functions for particles with various Stokes numbers（St） ranging from 0.001 to 1.0 are obtained. The numerical results reveal that：（1） Solid particles on the cylinder surface are picked up and then transported away from the cylinder by the wake vortex flow.（2） Solid particles emitted from the cylinder surface always follow the vortices in the cylinder wake, and the response of particles to wake vortices is directly related to their Stokes numbers（particles with St= 0.001, 0.0038, 0.01 can distribute both in the vortex core and around the vortex periphery, whereas those with St= 0.1, 1.0 can not enter the vortex core and congregate mainly around the vortex periphery）.（3） The particles move in rolling state in the wake region, and the dispersion intensity of particles in the lateral direction decreases remarkably as the Stokes number of particles is increased from 0.001 to 1.0.

Analysis of gas-solid flow and shaft-injected gas distribution in an oxygen blast furnace using a discrete element method and computational fluid dynamics coupled model

lronmaking using an oxygen blast furnace is an attractive approach for reducing energy consumption in the iron and steel industry. This paper presents a numerical study of gas-solid flow in an oxygen blast fur- nace by coupling the discrete element method with computational fluid dynamics. The model reliability was verified by previous experimental results. The influences of particle diameter, shaft tuyere size, and specific ratio （X） of shaft-injected gas （51G） flowrate to total gas flowrate on the SIC penetration behavior and pressure field in the furnace were investigated. The results showed that gas penetration capacity in the furnace gradually decreased as the particle diameter decreased from 100 to 40 mm. Decreasing particle diameter and increasing shaft tuyere size both slightly increased the SIG concentration near the furnace wall but decreased it at the furnace center. The value of X has a significant impact on the SIG distribution. According to the pressure fields obtained under different conditions, the key factor affecting SIG penetration depth is the pressure difference between the upper and lower levels of the shaft tuyere. If the pressure difference is small, the SIG can easily penetrate to the furnace center.

Particle-based hybrid and multiscale methods for nonequilibrium gas flows

Over the past half century,a variety of computational fluid dynamics(CFD)methods and the direct simulation Monte Carlo(DSMC)method have been widely and successfully applied to the simulation of gas flows for the continuum and rarefied regime,respectively.However,they both encounter difficulties when dealing with multiscale gas flows in modern engineering problems,where the whole system is on the macroscopic scale but the nonequilibrium effects play an important role.In this paper,we review two particle-based strategies developed for the simulation of multiscale nonequilibrium gas flows,i.e.,DSMC-CFD hybrid methods and multiscale particle methods.The principles,advantages,disadvantages,and applications for each method are described.The latest progress in the modelling of multiscale gas flows including the unified multiscale particle method proposed by the authors is presented.

A transient method for measuring the gas volume fraction in a mixed gas-liquid flow using acoustic resonance spectroscopy

In this paper, the feasibility of measuring the gas volume fraction in a mixed gas-liquid flow by using an acoustic resonant spectroscopy (ARS) method in a transient way is studied theoretically and experimentally. Firstly, the effects of sizes and locations of a single air bubble in a cylindrical cavity with two open ends on resonant frequencies are investigated numerically. Then, a transient measurement system for ARS is established, and the trends of the resonant frequencies (RFs) and resonant amplitudes (RAs) in the cylindrical cavity with gas flux inside are investigated experimentally. The measurement results by the proposed transient method are compared with those by steady-state ones and numerical ones. The numerical results show that the RFs of the cavity are highly sensitive to the volume of the single air bubble. A tiny bubble volume perturbation may cause a prominent RF shift even though the volume of the air bubble is smaller than 0.1% of that of the cavity. When the small air bubble moves, the RF shift will change and reach its maximum value as it is located at the middle of the cavity. As the gas volume fraction of the two-phase flow is low, both the RFs and RAs from the measurement results decrease dramatically with the increasing gas volume, and this decreasing trend gradually becomes even as the gas volume fraction increases further. These experimental results agree with the theoretical ones qualitatively. In addition, the transient method for ARS is more suitable for measuring the gas volume fraction with randomness and instantaneity than the steady-state one, because the latter could not reflect the random and instant characteristics of the mixed fluid due to the time consumption for frequency sweeping. This study will play a very important role in the quantitative measurement of the gas volume fraction of multiphase flows.

An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow

We study efficient simulation of steady state for multi-dimensional rarefied gas flow,which is modeled by the Boltzmann equation with BGK-type collision term.A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following approaches.The unified framework of numerical regularized moment method is first adopted to derive the high-quality discretization of the underlying problem.A fast sweeping iteration is introduced to solve the derived discrete problem more efficiently than the usual time-integration scheme on a single level grid.Taking it as the smoother,the nonlinear multigrid solver is then established to significantly improve the convergence rate.The OpenMP-based parallelization is applied in the implementation to further accelerate the computation.Numerical experiments for two lid-driven cavity flows and a bottom-heated cavity flow are carried out to investigate the performance of the resulting nonlinear multigrid solver.All results show the wonderful efficiency and robustness of the solver for both first-and second-order spatial discretization.

Generalized Boltzmann solution for non-equilibrium flows and the computation of flowfields of binary gas mixture

Hypersonic flows about space vehicles produce flowfields in thermodynamic non-equilibrium with the local Knudsen numbers Kn which may lie in all the three regimes:continuum,transition and rarefied.Continuum flows can be modeled accurately by solving the Navier–Stokes(NS)equations;however,the flows in transition and rarefied regimes require a kinetic approach such as the direct simulation Monte Carlo(DSMC)method or the solution of the Boltzmann equation.The Boltzmann equation and the general solution approach,using the splitting method,will be introduced in this paper.Details of the method used for solving both the classical Boltzmann equation(CBE)and the generalized Boltzmann equation(GBE)are also provided.The gas mixture discussed in this paper may consist of both monoatomic and diatomic gases.In particular,the method is applied to simulate two of the three primary constituents of air(N_(2),O_(2),and Ar)in a binary mixture at 1:1 density ratio at Mach 2 and 5,with gases in translational,rotational and vibrational non-equilibrium.

An Efficient Hybrid DSMC/MD Algorithm for Accurate Modeling of Micro Gas Flows

Aiming at simulating micro gas flows with accurate boundary conditions,an efficient hybrid algorithm is developed by combining the molecular dynamics(MD)method with the direct simulation Monte Carlo(DSMC)method.The efficiency comes from the fact that the MD method is applied only within the gas-wall interaction layer,characterized by the cut-off distance of the gas-solid interaction potential,to resolve accurately the gas-wall interaction process,while the DSMC method is employed in the remaining portion of the flow field to efficiently simulate rarefied gas transport outside the gas-wall interaction layer.A unique feature about the present scheme is that the coupling between the two methods is realized by matching the molecular velocity distribution function at the DSMC/MD interface,hence there is no need for one-toone mapping between a MD gas molecule and a DSMC simulation particle.Further improvement in efficiency is achieved by taking advantage of gas rarefaction inside the gas-wall interaction layer and by employing the“smart-wall model”proposed by Barisik et al.The developed hybrid algorithm is validated on two classical benchmarks namely 1-D Fourier thermal problem and Couette shear flow problem.Both the accuracy and efficiency of the hybrid algorithm are discussed.As an application,the hybrid algorithm is employed to simulate thermal transpiration coefficient in the free-molecule regime for a system with atomically smooth surface.Result is utilized to validate the coefficients calculated from the pure DSMC simulation with Maxwell and Cercignani-Lampis gas-wall interaction models.