Flow Of Ideal Gas Research Articles

Numerical analysis of blade row aeroelastic behaviour of axial turbomachine

There presented numerical analysis for the aeroelastic behaviour of the oscillations blade row in axial turbomachine in 3D ideal gas flow with coupled problem of a aerodynamics and elastic blades oscillations. The numerical analysis of the associated blade oscillation aerodempfirovanie confirmed the interaction of the first six eigenmodes. Figs.: 7. Tabl.: 1. Refs.: 8 titles. Keywords: aeroelastic behaviour; blade row; ideal gas; blade oscillations.

Analysis of plug flow reactors with variable mass density

The design of plug flow reactors with variable mass density is examined. Equations which include a two‐term constitutive equation for the reaction rate are derived for the flow of liquids and for the flow of ideal gases in steady plug flow reactors. It is shown that the addition of the second term in the constitutive equation can have a significant effect on the calculation of the reactor volume needed to carry out a specific conversion of the reactant. Published experimental plug flow reactor data support the observation that a reaction rate constitutive equation with two terms can provide a good representation of the experimental data for variable mass density reactors. © 2014 American Institute of Chemical Engineers AIChE J 60: 4185–4189, 2014

Convergent finite differences for 1D viscous isentropic flow in Eulerian coordinates

We construct a new finite difference method for the flow of ideal viscous isentropic gas in one spatial dimension. For the continuity equation, the method is a standard upwind discretization. For the momentum equation, the method is an uncommon upwind discretization, where the moment and the velocity are solved on dual grids. Our main result is convergence of the method as discretization parameters go to zero. Convergence is proved by adapting the mathematical existence theory of Lions and Feireisl to the numerical setting.

A macroscopic model for slightly compressible gas slip-flow in homogeneous porous media

The study of gas slip-flow in porous media is relevant in many applications ranging from nanotechnology to enhanced oil recovery and in any situation involving low-pressure gas-transport through structures having sufficiently small pores. In this paper, we use the method of volume averaging for deriving effective-medium equations in the framework of a slightly compressible gas flow. The result of the upscaling process is an effective-medium model subjected to time- and length-scale constraints, which are clearly identified in our derivation. At the first order in the Knudsen number, the macroscopic momentum transport equation corresponds to a Darcy-like model involving the classical intrinsic permeability tensor and a slip-flow correction tensor that is also intrinsic. It generalizes the Darcy-Klinkenberg equation for ideal gas flow, and exhibits a more complex form for dense gas. The component values of the two intrinsic tensors were computed by solving the associated closure problems on two- and three-dimensional periodic unit cells. Furthermore, the dependence of the slip-flow correction with the porosity was also verified to agree with approximate analytical results. Our predictions show a power-law relationship between the permeability and the slip-flow correction that is consistent with other works. Nevertheless, the generalization of such a relationship to any configuration requires more analysis.

Large-amplitude acoustic streaming

AbstractA mechanism is proposed for the generation of large-amplitude acoustically-driven streaming flows in which time-mean flow speeds are comparable to the instantaneous speed of fluid particles in a high-frequency sound-wave field. Motivated by streaming observed in high-intensity discharge (HID) lamps, two-dimensional flow of a density-stratified ideal gas in a channel geometry is analysed in the asymptotic limit of high-frequency acoustic-wave forcing. Predictions of streaming flow magnitudes based on classical arguments invoking Reynolds stress divergences originating in viscous boundary layers are orders of magnitude too small to account for the observed mean flows. Moreover, classical ‘Rayleigh streaming’ theory cannot account for the direction of the cellular mean flows often observed in HID lamps. In contrast, the mechanism proposed here, which invokes fluctuating baroclinic torques away from viscous boundary layers and thus is largely independent of viscous effects, can account both for the magnitude and the orientation of the observed streaming flows.

Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows

We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.

Simulation of the compressible flow with mass transfer of semi-continuous mixtures using the direct quadrature method of moments

We developed a method for the solution of the compressible flow with mass transfer of semi-continuous mixtures and it is based on the quadrature method of moments (QMoM) for continuous thermodynamics. The method extends the adaptive characterization of the continuous mixture to field problems and solves the mass transport equation for the continuous component. The method is referred as direct QMoM, or DQMoM, for continuous thermodynamics. It was implemented in the OpenFOAM® as a compressible ideal gas flow solver. The DQMoM was applied to the mixing flow of two gas streams with different compositions of a mixture with 57 hydrocarbons diluted in nitrogen. We showed that 4 adaptive components reproduced the mixture properties within 3% accuracy. Furthermore, the DQMoM CFD solution was approximately two times faster than the solution using 58 discrete components.

An experimental investigation of convection heat transfer during filling of a composite-fibre pressure vessel at low Reynolds number

The heat transfer process during filling of an evacuated vessel at low Reynolds number was investigated experimentally using air as the flow medium. The data was analysed using a thermodynamic model similar to one currently in use for the design of systems using commercial carbon fibre reinforced plastic vessels for storage of compressed hydrogen gas. Model assumptions included perfectly-stirred conditions within the vessel, one-dimensional unsteady heat conduction through the composite vessel wall, ideal gas and frictional adiabatic flow conditions through the inlet tube. A transition phenomenon from laminar to turbulent flow was observed by decreasing the inlet diameter while maintaining a similar mass flow rate. Based on the measurements, a new empirical correlation for the Nusselt number under low Reynolds number flow conditions is proposed.

The flow of a supersonic ideal gas with “weak” and “strong” shocks over a wedge

The problem of the flow of a uniform supersonic ideal (inviscid and non-heat-conducting) gas over a wedge is considered. If the turning angle of the flow, which is equal to the angle of inclination of the generatrix of the wedge, is less than the maximum value, the problem has two solutions. In the solution with an oblique low-intensity (“weak”) shock, the uniform flow between the shock and the wedge is almost always supersonic. One exception is a small vicinity of the maximum turning angle. For an ideal gas this vicinity does not exceed a fraction of a degree at all Mach numbers. Behind a high-intensity (“strong”) shock, the flow of an ideal gas is always subsonic. “Weak” shocks are observed in all experiments with finite wedges. Some researchers attribute this preference to the “downstream” boundary conditions (“on the right at infinity” for a flow incident on the wedge from the left), and others attribute it to the instability (“Lyapunov” instability) of a flow with a strong shock when it flows over the wedge and to the stability of flow with a weak shock. The results presented below from calculations of the flows that occur for finite wedges within the two-dimensional unsteady Euler equations, when the parameters behind the strong shock are specified on the right-hand boundary, i.e., on the arc of a circle between the wedge and the shock, demonstrate the correctness of the conclusion of the first group of researchers and the incorrectness of the conclusion of the other group. In these calculations, after both small and fairly large perturbations, the flows investigated (which are, in fact, Lyapunov unstable!) return to the solution with a strong shock. In addition, the problem of steady flow over a wedge was regarded as the limit of the two-dimensional non-steady problems at infinite time. Simplification of one of them leads to the problem of the submerged over-expanded supersonic steady outflow. In the ideal gas model this problem is equivalent to flow over a wedge with both weak and strong shocks. All the solutions considered are stable.

A model of the gas flow in hollow fibres with permeable walls

A model of the isothermal flow of a viscous ideal gas in long tubes (hollow fibres) with permeable walls is constructed. Analytical relations are derived for the relative flow rate of the gas through the permeable walls of tubes made of porous and non-porous materials. It is established that, for a specified pressure drop, there is an optimum length of the tube when the gas flow rate through its walls reaches a maximum value. A formula is derived for calculating the characteristic fibre length for which the gas flow rate through the tube walls becomes predominant in the overall balance of the gas flow rate entering the input section of the fibre. A single universal dimensionless relation, describing the balance of the gas flow rates for fibres having different permeability mechanisms, is proposed.

Nonself-similar flow with a shock wave reflected from the center of symmetry and new self-similar solutions with two reflected shocks

In some problems concerning cylindrically and spherically symmetric unsteady ideal (inviscid and nonheat-conducting) gas flows at the axis and center of symmetry (hereafter, at the center of symmetry), the gas density vanishes and the speed of sound becomes infinite starting at some time. This situation occurs in the problem of a shock wave reflecting from the center of symmetry. For an ideal gas with constant heat capacities and their ratio ? (adiabatic exponent), the solution of this problem near the reflection point is self-similar with a self-similarity exponent determined in the course of the solution construction. Assuming that ? on the reflected shock wave decreases, if this decrease exceeds a threshold value, the flow changes substantially. Assuming that the type of the solution remains unchanged for such ?, self-similarity is preserved if a piston starts expanding from the center of symmetry at the reflection time preceded by a finite-intensity reflected shock wave propagating at the speed of sound. To answer some questions arising in this formulation, specifically, to find the solution in the absence of the piston, the evolution of a close-to-self-similar solution calculated by the method of characteristics is traced. The required modification of the method of characteristics and the results obtained with it are described. The numerical results reveal a number of unexpected features. As a result, new self-similar solutions are constructed in which two (rather than one) shock waves reflect from the center of symmetry in the absence of the piston.

A Unified View of Topological Invariants of Barotropic and Baroclinic Fluids and their Application to Formal Stability Analysis of Three-Dimensional Ideal Gas Flows

Noether's theorem associated with the particle relabeling symmetry group leads us to a unified view that all the topological invari- ants of a barotropic fluid are variants of the cross helicity. The same is shown to be true for a baroclinic fluid. A cross-helicity representation is given to the Casimir invariant, a class of integrals including an arbitrary function of the specific entropy and the potential vorticity. We then develop a new energy-Casimir convexity method for three-dimensional stability of equilibria of gen- eral rotating flows of an ideal baroclinic fluid, without appealing to the Boussinesq approximation. By fully exploiting the Casimir invariant, we have succeeded in ruling out a term including the gradient of a dependent variable from the energy-Casimir function and have established a sharp linear stability criterion, being an extension of the Richardson-number criterion.

An implicit upwind parabolized Navier-Stokes code for chemically nonequilibrium flows

The previously developed single-sweep parabolized Navier-Stokes (SSPNS) space marching code for ideal gas flows has been extended to compute chemically nonequilibrium flows. In the code, the strongly coupled set of gas dynamics, species conservation, and turbulence equations is integrated with the implicit lower-upper symmetric Gauss-Seidel (LU-SGS) method in the streamwise direction in a space marching manner. The AUSMPW+ scheme is used to calculate the inviscid fluxes in the crossflow direction, while the conventional central scheme for the viscous fluxes. The k-g two-equation turbulence model is used. The revised SSPNS code is validated by computing the Burrows-Kurkov non-premixed H2/air supersonic combustion flows, premixed H2/air hypersonic combustion flows in a three-dimensional duct with a 15° compression ramp, as well as the hypersonic laminar chemically nonequilibrium air flows around two 10° half-angle cones. The results of these calculations are in good agreement with those of experiments, NASA UPS or Prabhu’s PNS codes. It can be concluded that the SSPNS code is highly efficient for steady supersonic/hypersonic chemically reaction flows when there is no large streamwise separation.

Wind energy: an application of Bernoulli's theorem generalized to isentropic flow of ideal gases

By considering the extension of Bernoulli's theorem to the case of the isentropic flow of ideal gases we conceive a small-scale wind–energy system able to work in the presence of low wind velocities in any direction. The flow of air inside a hyperbolically shaped pipe is studied using elementary physics concepts. The results obtained show that wind velocity in the system increases for decreasing cross-sectional areas, allowing a lower cut-in wind speed and an increase in the annual energy production of the device.

Growth and decay of acceleration waves in non-ideal gas flow with radiative heat transfer

Abstract The present paper is concerned with the study of the propagation of acceleration waves along the characteristic path in a non-ideal gas flow with effect of radiative heat transfer. It is shown that a linear solution in the characteristic plane can exhibit non-linear behavior in the physical plane. It is also investigated as to how the radiative heat transfer under the optically thin limit will affect the formation of shock in planer, cylindrical and spherically symmetric flows. We conclude that there exists critical amplitude such that any compressive waves with initial amplitude greater than the critical one terminate into shock waves while an initial amplitude less than the critical one results in the decay of the disturbance. The critical time for shock formation has been computed. In this paper we also compare/contrast the nature of solution in ideal and non ideal gas flows.

CONSERVATIVE CASCADE OF KINETIC ENERGY IN COMPRESSIBLE TURBULENCE

The physical nature of compressible turbulence is of fundamental importance in a variety of astrophysical settings. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional "conversion" scale-range despite not being an invariant of the compressible flow dynamics. We use high-resolution three-dimensional simulations of compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe regimes of forced steady-state isothermal flows and of unforced decaying ideal gas flows. The key quantity we measure is pressure dilatation cospectrum, $E^{PD}(k)$, where we provide the first numerical evidence that it decays at a rate faster than $k^{-1}$ as a function of wavenumber. This is sufficient to imply that mean pressure dilatation acts primarily at large-scales and that kinetic and internal energy budgets statistically decouple beyond a transitional scale-range. Our results suggest that an extension of Kolmogorov's inertial-range theory to compressible turbulence is possible.

Real gas flow simulation in damaged distribution pipelines

The paper discusses chosen issues concerning damaged gas pipelines. Attention is paid to modelling the steady-state flow of natural gas in distribution pipelines, and the most commonly applied models of isothermal and adiabatic flow are evaluated for both the ideal and the real gas properties. A method of accounting for a leakage by means of a reference flow equation with a discharge coefficient is presented, and the dependency of the discharge coefficient on pressure is demonstrated both with literature data and the authors' experimental results. A relevant computational study of a pipeline failure is presented for a high- and a medium pressure pipeline. The importance of an appropriate choice of the flow model (isothermal or adiabatic flow of real or ideal gas) is demonstrated by the results of the study. It is shown that accounting for the variability of the discharge coefficient is required if medium pressure pipelines are analysed. However, it is eventually shown that the impact of the discharge coefficient on the predicted outflow rate is of lesser importance than that of the applied flow model.

Conical gas flows with shock waves and turbulent boundary layer separation

The results of a theoretical and experimental investigation of nonsymmetric flow around a V-wing with supersonic leading edges are presented. The range of the angles of attack and yaw, on which additional singular lines are formed on the windward cantilever of the wing, are experimentally determined using different techniques of flow diagnostics. These are one convergence line and two divergence lines in the transverse flow which were not previously observable in the calculations of ideal-gas flow around wings. It is established that the appearance of the three new alternating singular lines located between the central chord of the wing and a convergence line, exterior to them and occurring within the framework of the ideal gas model, is associated with the relation between the intensities of two contact discontinuities. One of these proceeds from the branching point of the bow shock above the leeward cantilever, while the second issues out of the triple point of a λ-shaped shock configuration accompanying developed turbulent-boundary-layer separation generated by an internal shock incident on the leeward cantilever surface. If the intensity of the contact discontinuity proceeding from the branching point of the bow shock is large as compared with that of the contact discontinuity of the λ-configuration, then the flow pattern realized on the windward cantilever is analogous to that obtained within the framework of the ideal gas model, that is, it includes one convergence line on the wing surface. Under these conditions, the results of the calculations within the framework of the ideal gas model are applicable for understanding the phenomena occurring in the wing shock layer in a considerable part of the control parameter range, including the regimes with intense internal shocks generating turbulent boundary layer separation from the leeward cantilever. Corrections should be made only for a carachteristic pressure distribution in the separation zone and, as a consequence of separation, for an elevated pressure level in the vicinity of the central chord which is the stagnation line of the transverse flow that has passed across the oblique and terminating shocks of the λ-configuration and possesses a higher stagnation pressure than the flow that has passed in an ideal gas across the internal shock incident normally on the leeward cantilever. This is possible only when the divergence line, at which the stream surface enclosing the turbulent boundary layer separation zone enters, does not go over from the leeward onto the windward cantilever.

Interaction of a weak discontinuity with elementary waves of Riemann problem

We study the interaction of a weak discontinuity wave with the elementary waves of the Riemann problem for the one-dimensional Euler equations governing the flow of ideal polytropic gases, and investigate the effects of initial states, and the shock strength on the jumps in shock acceleration and the reflected and transmitted waves.

Deterministic Prediction of the Entropy Increase in a Sudden Expansion

This paper presents the results of a study of the prediction of the entropy growth within an internal free shear layer of an ideal gas flow downstream of a sudden expansion of the flow area. The objective of the study is exploratory in nature by invoking concepts from information theory to connect the deterministic prediction of the spectral entropy growth within the shear layer to the experimentally inferred increase in entropy across the flow region. The deterministic prediction of the spectral entropy increase along the shear layer is brought into agreement with the experimentally inferred increase in entropy through the ad hoc inclusion of the activation spectral entropy. The values for this activation spectral entropy are directly related to the area ratios across the expansion region and have a specific numerical value for each area ratio.