Numerical Simulation Of Gas Flow Research Articles

Modeling gas flow in low-permeability formations: An efficient combination of mixed finite elements and high order time integration schemes

Numerical simulation of gas flow in low permeability formations is a challenging task due to the high nonlinearity induced by (i) the compressibility of the gas, (ii) the Klinkenberg slippage effect and (iii) the Langmuir adsorption of the gas on the pore surface. Because of these nonlinearities, modeling gas flow in low permeability formations requires a great deal of computational effort. In this work, we develop an efficient numerical model using advanced spatial and temporal discretization methods for a simultaneous solution of the coupled equations of gas flow, cubic Peng-Robinson equation of state, slippage effect and Langmuir adsorption. The spatial discretization is performed with the lumped hybrid formulation of the mixed finite element method which is well adapted for fluid flow in heterogeneous porous media. The time integration is performed with high-order methods via the method of lines (MOL) which allows large time steps and efficient solution of the nonlinear system of equations. Numerical experiments, performed for gas extraction in a heterogeneous domain, point out the high efficiency of the new model since it can be until 10 times more efficient than the classical first-order time discretization method. Results of global sensitivity analysis show that the intrinsic gas-phase permeability and the Klinkenberg factor are the most influential parameters controlling the pumping rate in the case of gas extraction in a homogeneous domain.

An energy-stable and conservative numerical method for multicomponent Maxwell–Stefan model with rock compressibility

Numerical simulation of gas flow in porous media is becoming increasingly attractive due to its importance in shale and natural gas production and carbon dioxide sequestration. In this paper, taking molar densities as the primary unknowns rather than the pressure and molar fractions, we propose an alternative formulation of multicomponent Maxwell–Stefan (MS) model with rock compressibility. Benefiting from the definitions of gas and solid free energies, this MS formulation has a distinct feature that it follows an energy dissipation law, and namely, it is consistent with the second law of thermodynamics. Additionally, the formulation obeys the famous Onsager's reciprocal principle. An efficient energy-stable numerical scheme is constructed using the stabilized energy factorization approach for the Helmholtz free energy density and certain carefully designed formulations involving explicit and implicit mixed treatments for the coupling between molar densities, pressure, and porosity. We rigorously prove that the scheme inherits the energy dissipation law at the discrete level. The fully discrete scheme has the ability to ensure the mass conservation law for each component as well as preserve the Onsager's reciprocal principle. Numerical tests are conducted to verify our theories, and in particular, to demonstrate the good performance of the proposed scheme in energy stability and mass conservation as expected from our theories.

Numerical Simulation of Gas Flow through a Cylindrical Grain Storage

This study is concerned with a process known as fumigation in the grain industry. During this process, fumigant is injected at the inlet of storage and is expected to distribute throughout the stored grain to kill the insects in it. The present research focuses on the study of the fumigant (phosphine) flow distribution based on mathematical modelling and numerical simulation through available Computational Fluid Dynamic (CFD) software. In particular, the mathematical modelling is translated into the CFD and simulation is ran to determine areas where insects might find refuge. Hence provide information for conducting more effective fumigation. Numerical simulation using CFD software, for example, FLUENT, is widely known as cost and time effective. However, the numerical simulation needs to be verified before conducting such studies. For a simple case, the analytical solution exists. Therefore, the analytic solution for a simple case, can be used for verification and serve as a basis for adopting a CFD software, FLUENT for an extended geometry and boundary conditions. The numerical results are found to agree well with the analytical results. Overall, the fumigant gas flows towards the outlet regardless of the position of the outlet.

Direct numerical simulations for assessment of gas-solid drag models in two-dimensional random arrays of particles

The momentum exchange between the phases plays a vital role in modelling of gas–solid flows and it is mathematically described by drag models. However, no consensus exists on which drag model gives the most accurate prediction of the drag force, and, despite the increase in available computing power, the same drag models are used in two-dimensional and three-dimensional simulations. In this study, direct numerical simulations of gas flow through multiple random configurations of static monodisperse particles are performed. The variations of solid volume fraction and particle Reynolds number are in the ranges of 0.05–0.4 and 13.7–136.9, respectively. The drag force exerted on particles is calculated and properly averaged. Based on the simulation results, thirteen drag models are compared and correction factors are introduced using the stochastic gradient descent algorithm. The correction factors provide a simple adjustment for the models to be used in 2D modelling.

NUMERICAL STUDY OF THE BALANCE OF KINETIC ENERGY LOSSES IN THE FLOW PART OF A LOW-CONSUMPTION INFLOW TURBINE

The development of marine power engineering and automation, due to qualitative and quantitative changes by a significant increase in the capacity of modern power plants is considered in the paper. The object of this study is the flow part of a low-consumption inflow turbine, the subject of the study is the loss of kinetic energy in the stage of a low-consumption inflow turbine. The method of investigation is numerical simulation of gas flow using computational gas dynamics; the purpose of the study is to compare the values of kinetic energy loss coefficients in the nozzle diaphragm, impeller and output velocity losses obtained during physical and numerical experiments. The main objective of the study is to compare the values of kinetic energy loss coefficients in the turbine stage obtained during a physical experiment with the results of a numerical experiment. It is noted that low-consumption turbines are characterized by small dimensions, which do not allow to fully carrying out a physical experiment. A balance of losses of a low-consumption inflow turbine is performed in the study. A good convergence of the loss coefficients values obtained by the numerical method with the results of the physical experiment has been established. Conclusions about the possibility of applying numerical modeling for identical types of turbine stages are made.

Energy Stable and Mass Conservative Numerical Method for Gas Flow in Porous Media with Rock Compressibility

Taking rock compressibility into consideration brings up a quite challenging issue to modeling and numerical simulation of gas flow in porous media. To develop efficient numerical methods for such a problem, on the basis of the existing model, we, for the first time, propose an alternative formulation by introducing a free energy accounting for rock compressibility and by using chemical potential gradient instead of pressure gradient as the primary driving force. This formulation has a distinct feature that it is proved to satisfy an energy dissipation law. We further propose an efficient energy stable time discrete scheme using the improved energy factorization approach to tackle the Helmholtz free energy density determined by the Peng--Robinson equation of state. The discrete pressure is taken carefully using the discrete chemical potential and free energy such that the discrete energy dissipation law can be preserved. The fully discrete scheme is constructed based on the cell-centered finite difference method with the upwind strategy, which features full mass conservation and positivity preservation of molar density under proper conditions. Numerical results are also provided to show the performance of the proposed scheme and validate theoretical analysis.

Influence of the shape on the hydraulic resistance of bypass channels inside a smart pig for low pressure gas pipeline inspection

The in-line smart pig for gas pipeline diagnostics is driven by the pumped gas and performs quality diagnostics only if its speed is constant, when the information reading is uniform along the length of the pipeline. In a low-pressure gas pipeline, if there are inhomogeneities on its walls, the condition of the pig speed constancy is easily broken, as the force of resistance to the pig movement on the stoppers is comparable with the difference of pressure forces acting on its ends. A central bypass channel of constant cross-section is usually used to control the pig velocity. The paper shows insufficiency of such method of regulation, leading to noticeable flow pulsations at the outlet of the channel. The use of variable cross-section of the bypass channel along its length in the form of a Laval nozzle to reduce flow pulsations is proposed. The numerical simulation of gas flow in Laval nozzles of different configuration is performed; it is shown that for all considered nozzles, the pressure pulsation at the channel outlet is 20-30 times less than that in the cylindrical channel, which simplifies the velocity control of such pig. However, it is not possible to completely avoid detachment of the flow from the walls of the expanding part of the nozzle, so in order to reduce the area of the detachment zone and reduce the flow resistance force, additional peripheral bypass channels connecting the inlet end of the pig with the diffuser section of the central bypass are added. Thus, a 40% reduction of gas flow resistance force through the bypass compared to the cylindrical bypass is obtained.

Numerical Simulation of Gas Flow Passing through Slots of Various Shapes in Labyrinth Seals

Labyrinth seals are widely used in centrifugal compressors, turbines, and many other pneumatic systems due to their simplicity of design, reliability, and low cost. The calculation scheme for the movement of the working medium in a labyrinth seal is constructed by analogy with the movement of the working medium through holes with a sharp edge. Annular and flat slots, holes, and such a factor as the shaft rotation with a calculated sector of 3 degrees were studied. The purpose of the study is to determine the flow coefficient when the working medium flows through slots of various shapes. To achieve this purpose, modeling of the working medium flow in the FlowVision software was performed. The mass flow and flow coefficients are determined for the studied slot shapes. The convergence of the calculation results was determined by comparing the values of the mass flow rate at the inlet and outlet of the slot. Differences in visualizations of the flow for the studied variants of slots were established. The resulting difference should be taken into account in practical calculations of the working medium mass flow through the slot using a conditional flow rate factor which is determined by the slot design.

Parametric study of the influence of location and extension height of the rod interceptor on jet engine nozzle characteristics

Modern aircraft need increased maneuverability to maintain a competitive position. One way to improve this characteristic is to use methods to adjust the thrust vectors of a jet engine nozzle. One method of controlling nozzle thrust is the use of nozzle interceptors devices of various shapes that extend into the nozzle channel and cause an uneven distribution of pressure along the walls of the channel. The extension of the rod interceptor near the critical section of the nozzle creates a greater lateral force than the extension of the rod near the exit section. The dependence of the lateral force on the extension height is nonlinear. The article presents a description of a nozzle interceptor of a cylindrical shape extended from the channel wall. Numerical simulation of gas flow in the nozzle with a cylindrical interceptor was carried out. The patterns of gas flow in the channel and in the environment outside the nozzle are presented. The plots of the lateral and axial components of the thrust force against the interceptor rod length are also presented for both cases of the rod location. Rod interceptors can be used in combination with other correcting devices.

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The subject of the research is modern marine turbomachines which differ in many types, designs, purposes, materials and working bodies. It is noted that this diversity is guaranteed by the use of modern computer technologies from the stage of preliminary preparation of production to the release of final products. The design stage of turbine units taking into account the external characteristics of the turbine stage - power, speed, efficiency, shaft torque and others is considered. The efficiency of the stage is expressed by the efficiency coefficient, which is determined by the energy losses available in the stage. Losses, in turn, are expressed by losses in each individual element of the turbine stage design. At the same time, it is noted that the losses in the nozzle apparatus are decomposed into friction losses, edge and end losses. The object of the study is the nozzle apparatus of a low-consumption inflow turbine. The subject of the study is the velocity coefficient of the nozzle apparatus of a low-consumption inflow turbine. The research method is numerical simulation of gas flow using computational gas dynamics. The purpose of the study is to compare the value of the speed coefficient of the nozzle apparatus obtained during a physical experiment with the results of numerical modeling of the nozzle apparatus with subsonic (narrowing) channels. The conducted studies have shown that low-consumption inflow turbines are characterized by small sizes that do not allow us to fully carry out a physical experiment. A graph of the dependence of the velocity coefficient of the nozzle apparatus on the Mach number is provided in the study. A good convergence of the values of the velocity coefficient of the nozzle apparatus obtained by the numerical method with the results of the physical experiment has been established. The velocity fields of the flow part of the nozzle apparatus are obtained in the range of the Mach number ranging from 0.66 to 0.88. The possibility of using numerical modeling for this type of nozzle apparatus is concluded.

Coupled modeling and numerical simulation of gas flows laden with solid particles in de Laval nozzles

Coupled modeling and numerical simulation of gas flows laden with solid particles in de Laval nozzles

Керування газо-масопотоками в струминному обладнанні

Based on a numerical simulation of gas flows in an ejector unit and an analysis of grinding chamber acoustic signals, this paper shows ways to increase the efficiency of jet grinding. To prevent ejector speed-up tube wear and to obtain a ground product without impurities, the effect of feeding an additional energy carrier flow on the flow pattern in the speed-up tube of a jet mill was studied. A comparative analysis of the ejector flow pattern as a function of the presence of an additional feed and the speed-up tube shape was carried out. It was shown that the use of a conical nozzle offers a more uniform flow at the ejector outlet. The additional energy carrier feed provides a uniform increase in flow speed and reduces speed-up tube wall wear. The acoustic signals of the mill working zones were related to the jet grinding process parameters, around which a ground product quality control method was developed. The paper presents a technique for determining the material particle size in the energy carrier flow from the results of acoustic monitoring of the process. The technique uses the established relationship between the dispersion of the acoustic signal characteristic frequency and the mass of the corresponding fracture of the mixture in in-flow material transportation. The technique speeds up material particle size determination and improves the finished product quality. An automatic system was developed to control the grinding process by controlling the loading process according to the characteristics of the grinding zone acoustic signals. An operating model of a controlled hopper of a gas jet mill was made. The operability of the control system was verified on a simulation model, which includes a control objet (mill) model and a control system model. It was shown that the system of mill loading automatic control by the characteristics of the grinding zone acoustic signals offers an up to 10 percent increase in mill capacity, which was verified in industrial conditions at Vilnohorsk Mining and Metallurgical Plant.

Numerical simulation of gas flow in nozzle channels with a central body

The development of a reusable launch system is one of the most promising directions in the development of cosmonautics. World rocket companies are striving to create a space vehicle with improved tactical and technical characteristics. The main task is to ensure the most efficient flight mode of the reusable spacecraft from the point of view of the full load of the injection system. Since the main costs are spent on transporting the fuel of the rocket and its own design, the developers strive to fully load such a system not only when sending into orbit, but also when returning back. The implementation of the idea of a reusable spacecraft entails large energy losses, which suggests the idea of creating a single-stage reusable launch system.

Моделювання газодинамічних процесів в елементах імпульсного ежектора

The paper presents the numerical results on gas-dynamic processes in various elements of the impulse ejector, including pre-chamber, supersonic nozzle and mixing chamber, to determine optimal geometric parameters providing the given flow rate characteristics. At an extra-high pressure of the ejecting gas (>100 bar) it is impossible to create a nozzle design with continuously changing cross-sectional area and limited nozzle length. So, it is necessary to place a pre-chamber between the gas generator and the ejector nozzle for throttling full gas pressure. In order to optimize the pre-chamber parameters in the ejector with discrete holes of the gas generator and the operating pressure in the range of 400÷1000 bar, a series of calculations were performed to determine the pre-chamber parameters, ensuring stable operation of the supersonic annular nozzle at the high pressure of 35÷45 bar and the flow rate of 0.5÷0.6 kg/s. 3D numerical simulation of the gas flow into the pre-chamber through the gas generator holes shows the degree of the flow pattern non-uniformity in the pre-chamber at the ejector nozzle inlet is quite low. This justifies the numerical simulation of gas flow in the ejector in axisymmetric formulation and allows restricting the number of the gas generator holes without inducing significant non-uniformity in the azimuthal direction.

Experimental Investigation and Numerical Simulation of Gas Flow Through Wastegated Turbine of Gasoline Turbocharger

Turbochargers are generally used in the combustion engine due to their capability to increase the specific power. This paper investigates the performance of the turbocharger turbine, which is mounted in a gasoline engine. Different working points, including close and open wastegate positions, are studied in a steady-state condition. The experimental test of this article has been performed on an engine test cell. The movement of the wastegate linkage in different working conditions of the engine was measured in the test cell. Furthermore, the static pressure was measured at the different positions of the turbine housing. Simulation results show that as the wastegate starts to open, maximum loading happens. However, increasing the waste-gate opening angle will decrease the force, which is caused by the passing gas. It was found that at 2 degrees opening angle of the wastegate, there is an 80 kPa pressure difference between two sides of the wastegate valve. When the wastegate has a small opening angle, the pressure distribution on the flat surface of the valve is not symmetric, which means the gas does not provide a 360° flow distribution around the valve. Moreover, streamlines show that the high-speed flow passing bypass passage disturbs the flow exiting the turbine blades. Results show that the opening of the wastegate flap can reduce the turbine’s power. The 6 degrees opening of the wastegate causes a 30 percent power reduction. Moreover, the simulation results of the turbine’s map show that at the constant mass flow rate, the opening of the wastegate from the closed position to 6 degrees causes the pressure ratio to decrease 26 percent.

Two-component galaxy models with a central BH – II. The ellipsoidal case

ABSTRACTRecently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an r−3 law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in the presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh k-decomposition. Finally, we present the analytical formulae for velocity fields near the centre and at large radii, together with the various terms entering the virial theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behaviour of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics and in numerical simulations of gas flows in galaxies.

Analysis of noise sources in the acoustic field of a combine harvester’s rotating thresher drum

The main goal of the current research is to analyze the acoustic field of the threshing unit of a combine harvester. This research implements a numerical simulation of gas flow based on the Navier-Stokes equations with discretization of equations by the finite volume method. The finite element mesh used in the idealized model allows one to adequately analyze noise sources up to a frequency of 2500 Hz based on the broadband noise source models of Curl and Proudman. In this paper, the analysis of the flow around the threshing unit at two rotation speeds of 500 rpm and 980 rpm was performed in order to point out elements contributing the most to the noise environment of a combine harvester in operation. As a result of the analysis, the spectra of maximum acoustic pressure and intensity were obtained. Based on this data, there were obtained design refinement areas and areas of increased technological control of a typical thresher drum for the practical implementation in the noise reduction strategies.

Pore-scale simulation of gas flow in microscopic permeable media with complex geometries

Lattice Boltzmann method (LBM) is an efficient tool to perform direct numerical simulation of gas flow in micro-size pores. Despite great advances in LBM and its use in describing gas flow in micro-size channels in slip and transitional flow regimes, exploring formulations that are able to capture flow behavior in domains with complex boundary geometries remains a challenging task. As a result, the impact of complexities in pore structures on gas flow may not be fully explored using LBM. In this study, we propose to use the combined bounce-back and Maxwellian diffusive reflection scheme to capture the slip velocity with a new set of slip coefficients. Optimal values of slip coefficients are determined using a gradient based method, where the results from the linearized Boltzmann equation is used as the reference solution. The proposed formulation is further validated against predictions from molecular dynamics simulation in the presence of complex geometries by introducing obstacles of different shapes in straight channels. LBM with the proposed boundary treatment is then used to investigate gas flow in a synthetic microscopic permeable medium. Results indicate that gas exhibits different flow configurations as Knudsen number varies, and apparent gas permeability appears to have up to a second-order dependency on the reciprocal mean pressure in slip and transitional flow regimes.

Numerical simulation of gas flow through the flow part of a multi-stage turbomolecular vacuum pump

The modeling of gas flow through a multi-stage flowing part of a turbomolecular vacuum pump to optimize the parameters of rotor and stator impeller wheels is considered. The developed program of statistical modeling by the Monte Carlo method allows us to determine the influence of the geometric parameters of the stages on the pump performance indicators. Keywords turbomolecular pump, impeller wheels, maximum action speed, maximum pressure ratio, Monte Carlo method. marc081939@gmail.com

Collecting finely-dispersed particles from the gas flow in a centrifugal separator with coaxially arranged pipes

The article deals with the problem of increasing the efficiency of dedusting the gas flow from the finely dispersed particles smaller than 10 μm. In order to solve this problem, a design of centrifugal separator with coaxially arranged pipes is proposed. The described principle of operation includes the large values of centrifugal forces, which take place inside the device when the flow is swirled, and these forces throw the finely dispersed particles to the walls of device. This scientific paper shows a numerical simulation of gas flow dedusting process by means of ANSYS Fluent software package. The efficiency of dedusting the gas from the finely dispersed particles of up to 10 μm in the device is on average within the range of 53.8–76.7%. The exponential function, describing the changes in the pressure loss from the input gas rate, is obtained. In the course of studies, it was found that the pressure loss in the device is not more than 800 Pa at the input gas rate from 3 to 19 m/s.