Flow Of Ideal Gas Research Articles

Physics of gases

The physical chemistry of gases is discussed with reference to applications in anaesthesia. Definitions and explanations of relevant phenomena are given. Topics discussed include molecular theory of gases, pressure, ideal gas laws, vaporization, solubility and gas flow.

Steady shocks around black holes produced by sub-Keplerian flows with negative energy

We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas on to a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since Keplerian discs have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-Keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. We give a simple procedure to obtain analytically the position of the shocks. The comparison of the analytical results with the data of one-dimensional (1D) and two-dimensional (2D) axisymmetric numerical simulations confirms that the shocks form and are stable.

Extension of Ovsyannikov's Analytical Solutions to Transonic Flows

The solution of the equation of the velocity potential of a steady axisymmetric ideal-gas flow in the neighborhood of a given point at the axis of symmetry in the form of a double series in powers of the distance to the axis of symmetry and its logarithm is considered. Recurrent chains of equations with arbitrariness in two analytical functions of the streamwise variable are obtained for coefficients of the series. Convergence of the constructed series is proved by the method of special majorants. The theorem of existence and uniqueness of the solution of the initial-boundary problem for this nonlinear differential equation in partial derivatives with a singularity at the axis of symmetry is obtained as an analog of Kovalevskaya's and Ovsyannikov's theorems.

Cost-effectiveness of Basal Flow Sevoflurane Anaesthesia Using the Komesaroff Vaporizer inside the Circle System

After ethics committee approval, 51 consenting ASA physical status 1 or 2 adult patients were given basal flow sevoflurane anaesthesia using fresh gas flows of 150 to 300 ml x min(-1) oxygen. A Komesaroff vaporizer was placed on the inspiratory limb of the circle system. Basal flows were introduced immediately following intravenous induction of anaesthesia. The vaporizer was set to deliver the maximum concentration until the inspired sevoflurane concentration (FSI) reached 3%. The dial was then adjusted to maintain the FSI at 3%. After every 60 minutes, the circuit was washed out with 100% oxygen at a flow rate of 10 l x min(-1) for one minute. The FSI reached 3% after an average of 8.5 (3.8) [mean (SD)] minutes. The trends in FSI and the expired sevoflurane concentrations were significantly different (P<0.05) between the mechanically ventilated patients (n=21) and the spontaneously ventilating patients (n =30) and demonstrated a more gradual build-up in the former group. The consumption of sevoflurane was found to be 9.2 (2.8) ml x h(-1). This represented a 52.5% cost saving over the clinical application of the Mapleson's ideal fresh gas flow sequence for low-flow anaesthesia.

Viscous Effects on Cooled Pitot Tubes in Hypersonic Low Reynolds Number Flows

The influence of low Reynolds number viscous effects on blunt-nose stagnation pressure is investigated analytically for near-continuum hypersonic ideal gas flows around cooled bodies. It is shown that normal stress within the boundary layer acts to increase stagnation pressure slightly but that the usually neglected pressure slip at the wall introduces a significant opposing effect when the wall is cooled. Closed-form relationships describing this behavior as a function of Reynolds number, wall temperature ratio, and gas type are developed

Two-dimensional compressible multimaterial flow calculations in a unified coordinate system

We extend the unified coordinate system method introduced in [J Comput Phys 153 (1999) 596, Comput Fluid Dyn J 8 (2000) 495] for single-fluid computations to multimaterial fluid computations by incorporating a γ-model scheme [P.L. Roe, A new approach to computing discontinuous flow of several ideal gases, Technical Report, (Cranfield Institute of Technology) 1984, J Comput Phys 169 (2001) 594], and propose therefore a γ-model unified coordinate system method, in which interfaces of multifluids are described by contact discontinuities of a conservation equation, i.e., the γ-model that is added into the Euler equations, forming the extended Euler equations (of a single fluid). The Godunov/MUSCL method is then used to solve the extended Euler equations numerically. Numerical examples validate the scheme in avoiding disadvantages of excessive numerical diffusion across interfaces in the Eulerian description and of severe mesh deformation in the Lagrangian description which may result in numerical inaccuracy and even break down computations.

The axisymmetric nose shape of minimum wave drag for given size and volume

Within the limits of Newton's formula, a solution of the problem of designing axisymmetric nose shapes that minimize wave drag for given volume and maximum admissible size is presented. The solution is obtained both in the slender-body approximation and in the complete formulation (without assuming a small angle between the axis of the body and the tangent to its contour). In both formulations, the optimum contours, besides a two-sided extremum segment, may contain a cylindrical generator — a boundary extremum segment with respect to the maximum admissible radial coordinate. In addition, in the complete formulation the optimum contours may include a leading or trailing flat end — a boundary extremum segment in the sense of both the longitudinal coordinate and the limit of applicability of Newton's formula. Determination of the drag coefficient of the nose shapes designed using numerical integration of the equations of the axisymmetric flow of an ideal gas confirmed the advantages of convex configurations. In the same approximation, the drag of optimum nose shapes (within the limits of Newton's formula) with concave segments may exceed the drag of equivalent cones. The formulation of the variational problem modified for such cases (in particular, with the fixed specification of the volume replaced by a lower bound) yields Newton's solution with a free volume.

Basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas

Self-similar function of one-dimensional nonsteady flow is extended to a general form. With total energy kept constant, basic differential equation of self-similar motion of one-dimensional nonsteady flow of ideal gas is derived using dimension theory in combination with the basic motion equations of hydromechanics. When a non-dimensional natural parameter L, which is the ratio of velocity of fluid (u) and self-similar surface (r·), serves as the independent variable, the theoretical model reveals that self-similar law of non-dimensional nonsteady flow of ideal gas has the simplest mathematical form. The model overcomes the difficulty of divergence at the origin of self-similar function of Taylor and thus has significant importance.

Perspectives

We discuss a special case of formation of axisymmetric shocks in the accretion flow of ideal gas onto a Schwarzschild black hole: when the total energy of the flow is negative. The result of our analysis enlarges the parameter space for which these steady shocks are exhibited in the accretion of gas rotating around relativistic stellar objects. Since keplerian disks have negative total energy, we guess that, in this energy range, the production of the shock phenomenon might be easier than in the case of positive energy. So our outcome reinforces the view that sub-keplerian flows of matter may significantly affect the physics of the high energy radiation emission from black hole candidates. We give a simple procedure to obtain analytically the position of the shocks. The comparison of the analytical results with the data of 1D and 2D axisymmetric numerical simulations confirms that the shocks form and are stable.

A model for the oxidation of carbon silicon carbide composite structures

A mathematical theory and an accompanying numerical scheme have been developed for predicting the oxidation behavior of carbon silicon carbide (C/SiC) composite structures. The theory is derived from the mechanics of the flow of ideal gases through a porous solid. The result of the theoretical formulation is a set of two coupled non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov–Galerkin weighted residual method, allowing for the solution of the differential equations numerically. The numerical method is demonstrated by utilizing the method to model the carbon oxidation and weight loss behavior of C/SiC specimens during thermogravimetric experiments. The numerical method is used to study the physics of carbon oxidation in carbon silicon carbide composites.

A new small drill hole minipermeameter probe for in situ permeability measurement: Fluid mechanics and geometrical factors

Considerable heterogeneity is evident when permeability measurements are made on small scales, either in the field or in the laboratory on field samples. Small‐scale permeability measurements have commonly been made by inducing multidimensional gas flow through a sample with various configurations of the conventional surface‐sealing gas minipermeameter. In order to reduce weathering and seal‐quality problems, a new minipermeameter probe was designed for field application within small diameter holes drilled into an outcrop. We briefly describe the small drill hole minipermeameter, while developing in detail the associated data analysis methodology for performing in situ permeability measurements with this new probe. Analysis of field data, which consists of gas injection pressure and mass flow rate, is based on a numerical solution in cylindrical coordinates of the ideal gas flow equation, assuming homogeneous and isotropic conditions over the averaging volume of the measurements. In the following development the semianalytical inverse solution for permeability will be derived for the new small drill hole minipermeameter probe, which varies from that of the conventional surface‐sealing minipermeameter probe only in the choice of the appropriate characteristic length and in the magnitude of the associated geometrical factor.

Similarity of ideal gas flow at different scales

The similarity of ideal gas flow at different scales is investigated analytically and numerically. With the compressible and rarefied effects considered, two dimensionless parameters, Mach number and Knudsen number, are proposed as the similarity criterions, because the Reynolds number can be expressed by the Mach number and the Knudsen number of ideal gases. A DSMC method is used to simulate flows at different scales with the same Ma and Kn, including subsonic channel flows and the supersonic flows over a hot plate. Comparisons between the results of different scales show that the normalized fields of macroscopic quantities are the same. This confirms the similarity. Especially, the results indicate that the micro flow are similar to the rarefied flow of ideal gas, which suggests that many transformations are available from the existing rarefied flow results to the micro flow.

A COUPLED FLUID–STRUCTURE ANALYSIS FOR 3-D INVISCID FLUTTER OF IV STANDARD CONFIGURATION

A three-dimensional non-linear time-marching method and numerical analysis for aeroelastic behaviour of an oscillating blade row is presented. The approach is based on the solution of the coupled fluid–structure problem in which the aerodynamic and structural equations are integrated simultaneously in time. In this formulation of a coupled problem, the interblade phase angle at which a stability (or instability) would occur is a part of the solution. The ideal gas flow through multiple interblade passage (with periodicity on the whole annulus) is described by the unsteady Euler equations in the form of conservative laws, which are integrated by use of the explicit monotonic second order accurate Godunov–Kolgan volume scheme and a moving hybrid H–H (or H–O) grid. The structure analysis uses the modal approach and 3-D finite element model of the blade. The blade motion is assumed to be a linear combination of modes shapes with the modal coefficients depending on time. The influence of the natural frequencies on the aerodynamic coefficient and aeroelastic coupled oscillations for the Fourth Standard Configuration is shown. The stability (instability) areas for the modes are obtained. It has been shown that interaction between modes plays an important role in the aeroelastic blade response. This interaction has an essentially non-linear character and leads to blade limit cycle oscillations.

Ideal-Gas Axisymmetric Flows and Their Interaction with Obstacles

The interaction of ideal-gas flows with obstacles is analyzed numerically. The study examines the effect of rotation of the supersonic jet on its structure and on the parameters of the normal modes that arise in collision with obstacles. The origin of rotation when the gas is ejected from an orifice in a cavity is also investigated.

The Compressible boundary layer and the Boltzmann equation

We consider the flow of ideal gas in half space described by the system of compressible Navier-Stokes equations. We apply the Prandtl scaling and we obtain the system of compressible Prandtl equations. In this article, a modification of the classical Chapman-Enskog method is proposed, which allows us to derive the system of compressible Prandtl equations directly from the Boltzmann equation without the use of the Knudsen-layer correction. Different types of boundary conditions are discussed.

Coupled aeroelastic oscillations of a turbine blade row in 3D transonic flow

This paper presents the mutual time - marching method to predict the aeroelastic stability of an oscillating blade row in 3D transonic flow. The ideal gas flow through a blade row is governed by the time dependent Euler equations in conservative form which are integrated by using the explicit monotonous second order accurate Godunov-Kolgan finite volume scheme and moving hybrid H-O grid. The structure analysis uses the modal approach and 3D finite element dynamic model of blade. The blade movement is assumed as a linear combination of the first modes of blade natural oscillations with the modal coefficients depending on time. To demonstrate the capability and correctness of the method, two experimentally investigated test cases have been selected, in which the blades had performed tuned harmonic bending or torsional vibrations (The 1st and 4th standard configurations of the “Workshop on Aeroelasticity in Turbomachines” by Bolcs and Fransson, 1986). The calculated results of aeroelastic behaviour of the blade row (4th standard configuration), are presented over a wide frequency range under different start regimes of interblade phase angle.

Explicit analytical wave solutions of unsteady 1D ideal gas flow with friction and heat transfer

Several families of algebraically explicit analytical wave solutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families of standing wave solutions and one standing wave solution. Among them, the former four solution families contain arbitrary functions, so actually there are infinite analytical wave solutions having been derived. Besides their very important theoretical meaning, such analytical wave solutions can guide the development of some new equipment, and can be the benchmark solutions to promote the development of computational fluid dynamics. For example, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve the numerical computation skills such as differential schemes, grid generation ways and so on.

Relations between the Discharge Coefficients of the Sonic Venturi Nozzle and a Kind of Gases.

The discharge coefficients of the sonic Venturi nozzle were measured for eleven gases on the Reynolds number range from 2×103 to 4×104. The results showed that the discharge coefficients strongly depend on gases. And it was also suggested that the discharge coefficients of most of the gases tested can be described by using two parameters theoretically determined on the assumption of isentropic flow of ideal gas, if they are on the conditions which are not so far from the ideal gas state. The differences between the theoretical and the experimental discharge coefficients were within 0.5 percent, except for CO2, SF6 and C3H8.

Instability of self-similar ideal gas flows with shock waves

The results of the numerical simulation of three problems of ideal gas flow with shock waves, which admit self-similar solutions, are presented. These problems are the double Mach-type reflection of a shock from a wedge, the breakdown of a combined discontinuity on a 90° sharp corner, and the outflow of a supersonic jet from an expanding slot. It is shown that for certain input data the self-similar solution may become unstable and is replaced by a fluctuating flow. The reasons for the generation of these fluctuations and their mechanism are discussed.

The choice of the system of geometric parameters of an optimized wing

A direct optimization method is used to determine the form of the wing which enables the aerodynamic performance to be improved for a given lift in the supersonic flow of ideal gas. The flow around the wing and its characteristics are calculated within the framework of a model based on Euler's equations. On the basis of a local analysis of the load distribution on the wing, a method is proposed for choosing the system of geometric parameters which ensures rapid convergence to the optimum. It is shown that one of the parameters of the system (the angle of rotation of the wing panel relative to the central chord) has a very slight influence on the aerodynamic characteristics of the wing.