Viscous Gas Flow Research Articles

INVESTIGATION OF BLADE ATTACK ANGLE VALUE ON VERTICAL AXIAL WIND POWER PLANT

In this paper, the efficiency of the vertical-axial wind power plant at various wind speeds depending on the angle of attack of the rotor blades was investigated. The object of the investigation was a three-bladed Darrieus rotor. During the modeling we used the viscous gas flow model with averaging of turbulent characteristics (Reynolds-averaged Navier–Stokes equations for an incompressible fluid. These investigations would allow us to develop new principles for constructing vertical-axial wind turbines with a variable angle of attack of the blades in order to increase the energy efficiency of vertical-axis wind turbine.

Mathematical Model of the Flow of a Liquid Film of Variable Thickness on a Flat Surface in a Viscous Gas Flow

The paper presents a mathematical model of the film flow over a half-plane directed at an angle to the horizon. In the cross section of the film, a quadratic law for the longitudinal velocity distribution is adopted, taking into account friction on the film surface. An approximate solution of the problem is obtained in the form of a series in powers of the small parameter. The solution is presented in the form of graphs of the film thickness and the average longitudinal velocity along the length of the plate.

A new model for calculating the apparent permeability of shale gas in the real state

In all the existing apparent permeability calculation models used for shale gas, the effect of surface diffusion of adsorbed gas is neglected and shale gas is assumed to be in an ideal state, so the calculation results may not reflect the real situations. In this paper, a new apparent permeability model suitable for the shale gas of real state was developed by seepage mechanics method. In this model, the influential factors (e.g. the viscous flow and Knudsen diffusion of free gas and the surface diffusion of adsorbed gas) are taken into account to present the real flowing situations of shale gas in nanopores. Then, the accuracy of this new apparent permeability model was verified by comparing its calculation results with the experimental data. Finally, all factors influencing the apparent permeability of shale gas were analyzed in this new model. It is shown that the apparent permeability of shale gas is most affected by pressure and pore radius, and less by relative molecular mass and blockage coefficient. Langmuir maximum adsorption capacity, Langmuir pressure and isothermal adsorption heat mainly affect the fraction of permeability contributed by surface diffusion. Besides, the effects of each factor on apparent permeability and permeability fraction under low pressure are different from those under high pressure. Under low pressure, the effects of temperature and pore radius on apparent permeability are more obvious, and the effects of temperature, pore radius, Langmuir maximum adsorption capacity, Langmuir pressure and isothermal adsorption heat on the fraction of permeability are also more obvious. Finally, when the pressure is low and the pore radius is small, the surface diffusion is dominant. When the pressure is high and the pore radius is large, the viscous flow is dominant. In the case of small pore radius or low pressure, the surface diffusion shall not be neglected.

Dependence of energy characteristics of ascending swirling air flow on velocity of vertical blowing

In the model of a compressible continuous medium, for the complete Navier-Stokes system of equations, an initial boundary problem is proposed that corresponds to the conducted and planned experiments and describes complex three-dimensional flows of a viscous compressible heat-conducting gas in ascending swirling flows that are initiated by a vertical cold blowing. Using parallelization methods, three-dimensional nonstationary flows of a polytropic viscous compressible heat-conducting gas are constructed numerically in different scaled ascending swirling flows under the condition when gravity and Coriolis forces act. With the help of explicit difference schemes and the proposed initial boundary conditions, approximate solutions of the complete system of Navier-Stokes equations are constructed as well as the velocity and energy characteristics of three-dimensional nonstationary gas flows in ascending swirling flows are determined.

Investigation of Flow past a Flat Plate in the Strong Interaction Regime

Viscous gas flow past a finite-length plate in the strong interaction regime is investigated. The expansions of the flow functions in the vicinity of the leading edge are derived and the boundary value problems for the viscous and inviscid flow regions are formulated and jointly solved. The effect of the adiabatic exponent and the temperature factor on the flow parameters in these regions and the eigenvalue determining the intensity of the upstream disturbance transfer is studied. It is shown that in the non-self-similar case a transitional layer arises at the outer edge of the boundary layer.

Study on the nonlinear coupling seepage model of shale reservoir with discrete networks

Gas shale is rich in natural fractures, in which the percolation mechanisms are complicated. Consequently, it’s the key scientific problem of accurately evaluating shale gas production to figure out the law of flow in fractured shale reservoirs. In this paper, a multi-continuum/discrete fracture model was built to describe the shale reservoir space after hydraulic fracturing, and a nonlinear coupled seepage flow mathematical model is established based on the adsorbed gas and free gas coupling, including the nonlinear non-equilibrium desorption and surface diffusion of adsorbed gas, viscous flow and Knudsen diffusion mechanism of free gas. The model believes that the surface diffusion of adsorbed gas occurs on the surface of the organic matter, and non-equilibrium desorption occurs between the adsorbed gas and the pores of the inorganic matrix. There are viscous flow and Knudsen diffusion in the pores of the inorganic matrix. But there is only viscous flow in natural and hydraulic fractures. Through the numerical simulation results of a fractured horizontal well, the time-space evolution process of the net desorption rate of the adsorbed gas in the hydraulic fractured shale reservoir was revealed. It was found that the region of the maximum net desorption rate gradually spread from the artificial network to the matrix. Through the analysis of multiple pressure systems, it was found that the diffusion of free gas in natural fractures, free gas in inorganic matrix pores and adsorbed gas in organic matter lagged successively. Through the flow analysis of natural fracture field, it is found that the flow patterns, outside the envelope of discrete fracture network, appear in succession with time: elliptical radial flow, linear flow and non-linear flow caused by primary fracture interference. This study reveals the percolation mechanism of fractured shale reservoirs and provides a scientific basis for the exploitation of the shale gas reservoir.

Numerical Study of the Supersonic Base Flow around Aircraft Model

This paper deals with a numerical study of the base part of the supersonic flow past an aircraft model. The simulation was carried out using the software developed by the authors for calculating 3D turbulent flow of viscous compressible gas in the framework of the unsteady Reynolds averaged Navier–Stokes equations (URANS) with the Spalart–Allmaras (SA) and Menter’s SST turbulence models. Flight modes with M = 2.5 and angle of attack α = 0°, 3° were considered. A comparison is made of the effect of the choice of the turbulence model on the base flow.

Geometric situation of points of division of regions of direct and return currency in channels with the presence of heating zone limited on the longitudinal coordinate

The analysis of energy balance equation for viscous laminar flow of fluid or gas in the cylindrical channel in the area (zone) of warm up bounded along the longitudinal coordinate is made. It was found that at laminar flow of fluid or gas in a round pipe, in each warm up area bounded along the longitudinal coordinate there are the areas of direct and reverse flows separated by a plane that is a locus of points where temperature is maximal for each fixed value of radial coordinate r.

Three mechanisms model of shale gas in real state transport through a single nanopore

At present, the apparent permeability models of shale gas consider only the viscous flow and Knudsen diffusion of free gas, but do not take into account the influence of surface diffusion. Moreover, it is assumed that shale gas is in ideal state. In this paper, shale gas is assumed in real state, a new apparent permeability model for shale gas transport through a single nanopore is developed that captures many important migration mechanisms, such as viscous flow and Knudsen diffusion of free gas, surface diffusion of adsorbed gas. According to experimental data, the accuracy of apparent permeability model was verified. What’s more, the effects of pressure and pore radius on apparent permeability, and the effects on the permeability fraction of viscous flow, Knudsen diffusion and surface diffusion were analysed, separately. Finally, the results indicate that the error of the developed model in this paper was 3.02%, which is less than the existing models. Pressure and pore radius seriously affect the apparent permeability of shale gas. When the pore radius is small or pressure is low, the surface diffusion cannot be ignored. When the pressure and the pore radius is big, the viscous flow occupies the main position.

High-Order Multioperator Compact Schemes for Numerical Simulation of Unsteady Subsonic Airfoil Flow

On the basis of high-order schemes, the viscous gas flow over the NACA2212 airfoil is numerically simulated at a free-stream Mach number of 0.3 and Reynolds numbers ranging from 103 to 107. Flow regimes sequentially varying due to variations in the free-stream viscosity are considered. Vortex structures developing on the airfoil surface are investigated, and a physical interpretation of this phenomenon is given.

Galactic structures in the viscous gas flow in the channel with solid walls

Galactic structures in the viscous gas flow in the channel with solid walls

Space-time discontinuous Galerkin method for the numerical simulation of viscous compressible gas flow with the k-omega turbulence model

In this article we deal with the numerical simulation of the non-stationary compressible turbulent flow described by the Reynolds-Averaged Navier-Stokes (RANS) equations. This RANS system is equipped with two-equation k-omega turbulence model. The discretization of these two systems is carried out separately by the space-time discontinuous Galerkin method. This method is based on the piecewise polynomial discontinuous approximation of the sought solution in space and in time. We use the numerical experiments to demonstrate the applicability of the shown approach. All presented results were computed with the own-developed code.

Phonon Hydrodynamic Heat Conduction and Knudsen Minimum in Graphite.

In the hydrodynamic regime, phonons drift with a nonzero collective velocity under a temperature gradient, reminiscent of viscous gas and fluid flow. The study of hydrodynamic phonon transport has spanned over half a century but has been mostly limited to cryogenic temperatures (∼1 K) and more recently to low-dimensional materials. Here, we identify graphite as a three-dimensional material that supports phonon hydrodynamics at significantly higher temperatures (∼100 K) based on first-principles calculations. In particular, by solving the Boltzmann equation for phonon transport in graphite ribbons, we predict that phonon Poiseuille flow and Knudsen minimum can be experimentally observed above liquid nitrogen temperature. Further, we reveal the microscopic origin of these intriguing phenomena in terms of the dependence of the effective boundary scattering rate on momentum-conserving phonon-phonon scattering processes and the collective motion of phonons. The significant hydrodynamic nature of phonon transport in graphite is attributed to its strong intralayer sp2 hybrid bonding and weak van der Waals interlayer interactions. More intriguingly, the reflection symmetry associated with a single graphene layer is broken in graphite, which opens up more momentum-conserving phonon-phonon scattering channels and results in stronger hydrodynamic features in graphite than graphene. As a boundary-sensitive transport regime, phonon hydrodynamics opens up new possibilities for thermal management and energy conversion.

MATHEMATICAL MODELING AND CALCULATION OF GAS DYNAMIC CHARACTERISTICS OF FREE THERMAL AIR VORTEX

The article analyzes experimental and analytical studies of ascending swirling air flows. In experimental works such flows are considered from the point of view of the direction of twist, the thermal regimes of heating the underlying surface, the estimation of integral parameters, the method of influence on them, and various methods of visualization. In analytical papers, by constructing solutions of the system of gas dynamics equations, the emergence of a twist of the corresponding direction is proven when there is a gas flow into a vertical cylinder of nonzero radius. In addition, in the numerical modeling of thermal ascending swirling flows, a feature was observed in the behavior of a moving gas at the initial moments of flow formation when the underlying surface was heated locally. This feature consists in the appearance on the boundary of the heating region of counter propagating gas flows with opposite directions of twist. The paper presents the results of numerical simulation of three-dimensional unsteady flows of a compressible viscous heat-conducting gas in thermal swirled vortices with local heating of the underlying surface, taking into account the action of gravity and Coriolis forces.

Numerical and experimental study of fuel pre-injection in the inlet of a high-velocity air-breathing engine

The effect of preliminary injection (pre-injection) of a gas (heated air, methane, or ethylene) ahead of the entrance of a three-dimensional inlet in a supersonic flow with Mach numbers M∞ = 2–4, stagnation temperature T * = 300 K, and flow rates of the injected gas corresponding to 0–6% of the flow rate of air through the inlet is numerically studied. The gas is injected through orifices located behind the base surfaces of pylons mounted upstream of the inlet entrance. The computations are performed by the ESI-FASTRAN software package, which allows one to calculate three-dimensional viscous turbulent gas flows by a time-dependent method with the use of the Reynolds-averaged Navier–Stokes equations. Experimental investigations of pre-injection are performed with the use of small-scale and large-scale inlet models at M∞ = 3–4 and 6. A positive effect of pre-injection on stable (without stalling) deceleration of the incident flow in the case of mass supply and on initiation of ignition and stable combustion in the combustion chamber is confirmed.

Bounds for solutions of isothermal equations of viscous gas dynamics

We consider the first boundary-value problem for the Navier- Stokes equations of isothermal viscous gas flows. We establish bounds for the flow density in negative Sobolev spaces and Lebesgue spaces. Bibliography: 8 titles.

Upscaling of gas transport in shale matrix based on homogenization theory

The shale matrix is composed of organic matrix with free gas and adsorbed, and inorganic matrix with only free gas. The gas transport mechanism in two different shale matrix is different. The conventional numerical model did not consider the different gas transport mechanism in the shale matrix and the influence of the distribution of the organic matter. In this paper we established a upscaled shale matrix model with considering these mechanisms. In the microscale region, the Knudsen diffusion and viscous flow of free gas and surface diffusion of adsorbed gas is considered in the microscale model of organic matrix, while only Knudsen diffusion and viscous flow of free gas is considered in the microscale model of inorganic matrix. We calculated the production and pressure of shale matrix have different organic matrix distribution and same TOC content in the microscale region while have same parameters in the macroscale model, the result shows that the macro-scale equations solved directly without homogenization process have the same pressure and production while with upscaling process the solved pressure and production are different in these macro-scale models.

Ejectors for pressure recovery systems of supersonic chemical lasers

Results of a numerical study of performance characteristics of supersonic ejectors with nozzles of different types are reported. The work was carried out with the aim of developing a high-performance ejector for pressure recovery systems of supersonic chemical lasers. A specific feature of the operation of ejectors in pressure recovery systems consists in that, in this case, the ejecting and ejected gases, as they undergo mixing, have different thermodynamic properties, and the ejection coefficient depends on the ratio between the temperatures of the gases and on the ratio of their molecular masses. Since the operation of an ejector is based on the mixing process, the task consisted in intensification of this process using nozzles of special geometries. The performance of ejectors was judged considering an integral parameter, the product of induction by compression ratio. The calculations of the 3D viscous gas flow in the ejector channel were performed using ANSYS software. In verifying the numerical model, a comparison with experimental data obtained earlier on a model ejector facility and during tests of real pressure recovery systems in operation with supersonic chemical lasers was performed.

Numerical Investigation of the Air Flows in the Cab of a Truck in Three Different Regimes of its Ventilation

Different variants of ventilation of the cab of a truck were investigated by numerical simulation methods. An unsteady viscous gas flow was numerically simulated using the VP2/3 package. In the process of numerical simulation of this flow, the Reynolds equations closed with the use of the differential k–ω model of turbulence in the SST modification of Menter were solved numerically. On the basis of analysis of the fields of the velocity, pressure, and turbulence characteristics of the air flows in the truck cab, obtained as a result of their numerical simulation, the efficiency of ventilation of this cab was estimated.

Rotationally symmetric viscous gas flows

The Dirichlet boundary value problem for the Navier–Stokes equations of a barotropic viscous compressible fluid is considered. The flow region and the data of the problem are assumed to be invariant under rotations about a fixed axis. The existence of rotationally symmetric weak solutions for all adiabatic exponents from the interval (γ*,∞) with a critical exponent γ* < 4/3 is proved.