Flow Of Ideal Gas Research Articles

Analysis of the ideal gas flow over body of basic geometrical shape

An approximate mathematical model of the heat transfer processes in the laminar and turbulent boundary layers, which occur near the surface of an aircraft moving at the hypersonic speed in the Earth’s atmosphere, is derived. This mathematical model makes it possible to calculate the convective heat transfer on the surface of typical structural elements of modern perspective aircrafts. 2D versions of the calculations of convective heat fluxes for bodies of simple geometric shapes are performed.

Aeroelasticity Analysis of Unsteady Rotor Blade Forces and Displacements in LP Last Stage Steam Turbine with Various Pressure Distributions the Stage Exit

Several high vibration amplitude problems have been reported regarding the slender last stage blading of commercial LP steam turbines. This paper analyses rotor blade unsteady forces and displacements in the last stage of a low pressure steam turbine with symmetrical and non-symmetrical (exhaust hood induced) pressure distributions behind the rotor blades. The FSI partially integrated method was used for the 3D ideal gas flow. 3D unsteady non-viscous flow was analysed using the Godunov-Kolgan method. Non-symmetrical pressure distributions in the stage exit were taken from 3D viscous CFX ANSYS calculations, using a CFD mesh of all the stator blades, all the rotor blades (rotating and not vibrating) and the exhaust hood. The non-uniform and uniform pressure distributions cause rotor blades to vibrate in different bending-torsion modes. Introducing blade vibration into the flow model causes the appearance of unsteady force and blade displacement harmonics that are not multiples of the rotation frequency. The unsteady rotor blade forces and blade displacements analysis shows the importance of including an exhaust hood in the CFD mesh.

Riemann problem and elementary wave interactions in dusty gas

The present paper concerns with the study of the Riemann problem for a quasi-linear hyperbolic system of partial differential equations governing the one dimensional isentropic dusty gas flow. The shock and rarefaction waves and their properties for the problem are investigated. We also examine how some of the properties of shock and rarefaction waves in a dusty gas flow differ from isentropic ideal gas flow. The solution of Riemann problem of dusty gas flow for different initial data is discussed. Under certain conditions, the uniqueness and existence of the solution of the Riemann problem has been analyzed. Finally, all possible interactions of elementary waves are discussed.

A one-dimensional model for compressible fluid flows through deformable microchannels

Fluid-structure interactions in low-Reynolds-number flows have received an increasing interest due to emerging bio-applications of deformable microfluidics. We utilize the lubrication theory and wide-beam framework to develop a one-dimensional coupled fluid-solid-mechanics model for the prediction of the characteristic behavior of compressible fluid flows through deformable microchannels. An explicit relationship is extracted for the mass flow rate as a function of pressure difference across a microchannel, undeformed channel dimensions, and properties of channel’s ceiling such as thickness, modulus of elasticity, and Poisson’s ratio. The resulting fifth-order algebraic equation is also solved numerically to obtain the pressure distribution within the microchannel. As a special case for compressible fluid flows, the characteristics of ideal gas flows are extracted from the general model. Rigid and deformable microchannels are fabricated, and the mass flow rates of air through the channels are measured under various pressure differences across the channels. The proposed model predicts the mass flow rate with an acceptable accuracy. Our experimental and theoretical results highlight the importance of fluid compressibility and microchannel deformability, demonstrating that neglecting either of them under sufficiently large pressure differences can lead to erroneous results. To the best of the authors’ knowledge, this is the first theoretical model simultaneously addressing both fluid compressibility and microchannel deformability for an equilibrium pressure-driven compressible fluid flow in microscale.

Aeroelastic Behaviour of a 3.5-Stage Aircraft Compressor Rotor Blades Following a Bird Strike

This paper analyses unsteady forces acting on rotor blades in a 3.5 stage compressor following a bird strike. The strike was modelled by partially blocking the engine inlet. An in-house code was used to calculate 3D unsteady non-viscous flow of ideal gas through a 3.5 stage compressor. The numerical analysis included blade vibrations. This paper has shown that partial admission causes low-frequency harmonics to affect not only the 1st and 2nd rotor blade stages, but also the 3rd stage, with only slightly smaller amplitude values. Partial admission at the inlet strongly influenced unsteady forces in all three stages, with the dominance of low frequency unsteady force components. In the case of full admission, only high frequency components appeared, due to the number of stator blades.

Unsteady Forces in Jet Engine 7.5 Compressor Stage

This paper analyzes unsteady forces acting on rotor blades in a 7.5-stage compressor with full admission. An in-house code was used to calculate 3D-unsteady non-viscous flow of ideal gas through a 7.5-stage compressor, using the Godunov–Kolgan method. The numerical analysis included blade vibrations and aerodynamic multistage coupling. All the stator blade rows in front of R1, R2, R3, R4, R5, R6, and R7 rotor blades as well as one stator row behind these rotor blades experienced excitation and multistage coupling occurred. This means that the first stator can influence not only the first rotor blades, but also other blades. For compressor rotor blade design, as previously only one stator cascade with high excitation frequencies was included in the equation of blade resonance margin: Hk = 〈0.9 b N1 n, 1.1 b N1 n〉, where N1 is the number of stator blades behind rotor blade row, b is the engine order excitation, and n is the rotation speed. We suggest applying several resonance mergions.

Rotating accretion flows in D dimensions: Sonic points, critical points, and photon spheres

We give the formulation and the general analysis of the rotational accretion problem on $D$-dimensional spherical spacetime and investigate sonic points and critical points. First, we construct the simple two-dimensional rotating accretion flow model in general $D$-dimensional static spherically symmetric spacetime and formulate the problem. The flow forms a two-dimensional disk lying on the equatorial plane and the disk is assumed to be geometrically thin and has uniform distribution in the polar angle directions. Analyzing the critical point of the problem, we give the conditions for the critical point and its classification explicitly and show the coincidence with the sonic point for generic equation of state (EOS). Next, adopting the EOS of ideal photon gas to the analysis, we reveal that there always exists a correspondence between the sonic points and the photon spheres of the spacetime. Our main result is that the sonic point of the rotating accretion flow of ideal photon gas must be on (one of) the unstable photon sphere(s) of the spacetime in arbitrary spacetime dimensions. This paper extends this correspondence for spherical flows shown in the authors' previous work to rotating accretion disks.

A numerical comparison between ideal and dense gas flow structures in the supersonic regime for a cascade of wedge-shaped straight plates

A real dense gas such as R245fa is mostly used in organic-Rankine-cycle turbine expanders. The dense gas effects should be taken into account, especially in the transonic and supersonic flow regimes. Oblique shock and the interaction of shock and separation on the turbine blades are phenomena that have little deviation between a real gas and an ideal gas. This research numerically simulated the flow passing through a cascade of simple straight blades with keen edges considered for an ideal gas (air) and dense R245fa gas in a supersonic flow regime. The blade geometry was selected so that the deviations between the dense and ideal gas flows would be clearer than that with actual blades. The AUSM density-based method and NIST real gas model were used to model the ideal and dense gas, respectively. A second-order scheme was used for discretization, and the shear stress transport (SST) model was for the turbulence. The results show that an oblique shock is created on the leading edge when the inlet Mach number is 2.18 in dense gas. In ideal gas, a bow shock is created at the front of the leading edge. Moreover, for a wall pressure coefficient distribution, the separation point in dense gas is posterior than that in ideal gas.

A unified description of oblique waves in ideal and non-ideal steady supersonic flows around compressive and rarefactive corners

According to classical gas dynamic theory, if a steady supersonic parallel flow encounters a sudden change in the wall slope, two very different phenomena may occur. If the flow expands around a sharp corner, the well-known isentropic Prandtl–Meyer fan is observed. Conversely, a shock wave occurs if the flow is compressed: for wedge angles smaller than the detachment value, which depends on the uniform upstream state, an oblique shock originates at the corner; at larger deviation angles, a detached shock is formed. A unified description of these flows is presented here to extend the validity of the common $$\beta $$ – $$\vartheta $$ (shock angle–deflection angle) diagram for shocked non-isentropic flows into the realm of isentropic expansions. The new graph allows for a straightforward identification of the wave angles for self-similar flow fields around compressive and rarefactive corners. Besides, it clarifies the relation between shock waves and rarefaction fans in the neighbourhood of the $${\vartheta =0}$$ axis, where shock waves are weak enough to be fairly well approximated by isentropic compressions. At $${\vartheta =0}$$ , indeed, shock and rarefaction curves are demonstrated to be first order continuous. This result is interpreted in view of the bisector rule for oblique shock waves. Exemplary diagrams are reported for both ideal-gas flows, dilute-gas flows and non-ideal flows of dense vapours in the close proximity of the liquid–vapour saturation curve and critical point. The application of the new diagram is illustrated for the textbook case of the supersonic flow past a diamond-shaped airfoil.

Расчет времени адиабатического истечения идеального газа из резервуара постоянного объема с использованием относительных параметров

Расчет времени адиабатического истечения идеального газа из резервуара постоянного объема с использованием относительных параметров

Solution of weakly compressible isothermal flow in landfill gas collection networks

Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy–Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein.

Estimating the Error Component Associated with the Selection of a Gas Flow Model in Critical Nozzles

A more accurate model has been developed for an ideal compressed gas flow in a critical nozzle used as a standard for volumetric flow rate. An error assessment is carried out for the inadequacy of the classical model of a critical nozzle that is applied to obtaining the actual value of the volumetric flow rate produced by a nozzle in operating conditions. It is shown that the error of model inadequacy must be considered to be in the upper bounds region of the effective measurement ranges of gas counters when calibrating them by means of volumetric flow rate standards on critical nozzles.

Global strong solution to compressible Navier–Stokes equations with density dependent viscosity and temperature dependent heat conductivity

We obtain existence and uniqueness of global strong solution to one-dimensional compressible Navier–Stokes equations for ideal polytropic gas flow, with density dependent viscosity and temperature dependent heat conductivity under stress-free and thermally insulated boundary conditions. Here we assume viscosity coefficient μ(ρ)=1+ρα and heat conductivity coefficient κ(θ)=θβ for all α∈[0,∞) and β∈(0,+∞).

On free boundary problem for compressible navier-stokes equations with temperature-dependent heat conductivity

We obtain the existence of global strong solution to the free boundary problem in 1D compressible Navier-Stokes system for the viscous and heat conducting ideal polytropic gas flow, when the heat conductivity depends on temperature in power law of Chapman-Enskog and the viscosity coefficient be a positive constant.

Turbulent temperature profile in the quasi-fully developed region of a micro-tube

Turbulent temperature profiles in the quasi-fully developed region of a micro-tube were obtained numerically by solving the energy equation including the substantial derivative of pressure and viscous dissipation terms for the case of constant wall temperature. The fluid was assumed to be an ideal gas with constant density over the cross-section. The turbulent velocity profile was approximated by the three-layer model of Von Karman. The temperature profiles were compared with the laminar flow and previous numerical solutions. The total temperature was higher than the wall temperature depending on the Mach number. The static temperature in the quasi-fully developed region agrees well with the temperature results for an ideal gas flow obtained by solving the Navier-Stokes and energy equations.

V-shaped wings with an opening angle exceeding π at super- and hypersonic flow velocities

The results of theoretical investigation of an ideal-gas asymmetrical flow around V-shaped wings with an opening angle exceeding π and having supersonic forward edges at all modes are presented.

Numerical Analysis of the Three-Dimensional Nonstationary Flow of Ideal Gas in the Last Stage of Turbine Machine Taking into Consideration the Nonaxisymmetric Exhaust Pipe Branch

A problem related to the forecast of the aeroelastic behavior and aeroelastic instability of blades (in particular self-oscillations, flutter, and resonance vibrations) becomes of great importance for the development of high-loaded compressor and vent rows and the last turbine stages whose long and flexible blades can be exposed to such phenomena. The solution of this problem requires the development of new models for the nonstationary three-dimensional flow, the use of contemporary numeric methods and the comparison of theoretical and experimental data. This scientific paper gives the data of numerical simulation of the 3-D flow of ideal gas passing through the last stage of turbine machine taking into account the flow nonuniformity caused by guide blades and nonuniform pressure distribution in the exhaust pipe branch and also nonstationary effects caused by blade vibrations. The numerical method is based on the solution of combined aeroelastic problem for the 3-D flow of ideal gas passing through the turbine stage and the nonaxisymmetric exhaust pipe branch including the annular diffuser. To solve the combined problem a partially integral method was used that includes integral equations of gas dynamics (Euler equations) and vibrating blade dynamics (modular approach) at each time step with the information exchange. The given method of the solution of combined aeroelastic problem allows us to predict the amplitude-frequency spectrum of blade vibrations in the three-dimensional flow of ideal gas including forced self-excited vibrations and self-vibrations to increase efficiency and reliability of the blade units of turbine machines.

Supersonic flow past a flat lattice of cylindrical rods

Two-dimensional supersonic laminar ideal gas flows past a regular flat lattice of identical circular cylinders lying in a plane perpendicular to the free-stream velocity are numerically simulated. The flows are computed by applying a multiblock numerical technique with local boundary-fitted curvilinear grids that have finite regions overlapping the global rectangular grid covering the entire computational domain. Viscous boundary layers are resolved on the local grids by applying the Navier–Stokes equations, while the aerodynamic interference of shock wave structures occurring between the lattice elements is described by the Euler equations. In the overlapping grid regions, the functions are interpolated to the grid interfaces. The regimes of supersonic lattice flow are classified. The parameter ranges in which the steady flow around the lattice is not unique are detected, and the mechanisms of hysteresis phenomena are examined.

The integral invariant of the equations of motion of a viscous gas

An expression for the velocity of motion of a simple vortex contour for which the circulation of the fluid velocity is preserved in it is obtained in the general three-dimensional case for the flow of a viscous gas or liquid. The velocity of motion of the contour at each point is calculated from the values of the flow parameters and their derivatives at the same point. This result extends Thomson's theorem, which is well known for an ideal barotropic fluid. A previously unknown conservation property is found, which consists of the fact that the circumferential circulation of the swirling axisymmetric flow in the potential field of mass forces is the first integral of the equations of unsteady flow of a non-barotropic ideal gas.

Analysis of Flow Evolution and Thermal Instabilities in the Near-Nozzle Region of a Free Plane Laminar Jet

This work focuses on the evolution of a free plane laminar jet in the near-nozzle region. The jet is buoyant because it is driven by a continuous addition of both buoyancy and momentum at the source. Buoyancy is given by a temperature difference between the jet and the environment. To study the jet evolution, numerical simulations were performed for two Richardson numbers: the one corresponding to a temperature difference slightly near the validity of the Boussinesq approximation and the other one corresponding to a higher temperature difference. For this purpose, a time dependent numerical model is used to solve the fully dimensional Navier-Stokes equations. Density variations are given by the ideal gas law and flow properties as dynamic viscosity and thermal conductivity are considered nonconstant. Particular attention was paid to the implementation of the boundary conditions to ensure jet stability and flow rates control. The numerical simulations were also reproduced by using the Boussinesq approximation to find out more about its pertinence for this kind of flows. Finally, a stability diagram is also obtained to identify the onset of the unsteady state in the near-nozzle region by varying control parameters of momentum and buoyancy. It is found that, at the onset of the unsteady state, momentum effects decrease almost linearly when buoyancy effects increase.