Analytical solution for unsteady adiabatic and isothermal flows behind the shock wave in a rotational axisymmetric mixture of perfect gas and small solid particles

The approximate analytical solutions are obtained for adiabatic and isothermal flows behind a cylindrical shock wave in a dusty gas. A mixture of perfect gas and micro size small inert solid particles is taken as the dusty gas. The inert solid particles are distributed continuously in the mixture. It is considered that the equilibrium flow conditions are maintained. The flow variables are expanded in power series to obtain the solution of the problem. The analytical solutions are obtained for the first order approximation in both the adiabatic and isothermal cases. Also, the system of ordinary differential equations for second order approximations to the solution is obtained. The influence of an increase in the ratio of the density of the inert solid particles to the initial density of the perfect gas, the rotational parameter and the mass concentration of inert solid particles in the mixture are discussed on the flow variables for first approximation. Our first approximation to the solution corresponds to the Taylor’s solution for the creation of a blast wave by a strong explosion. A comparison is also made between the solutions for isothermal and adiabatic flows. It is investigated that the density and pressure near the line of symmetry in the case of isothermal flow become zero and hence a vacuum is formed at the axis of symmetry when the flow is isothermal. Also, it is found that an increase in the value of rotational parameter or the mass concentration of solid particles in the mixture has a decaying effect on shock wave. The present work may be used to verify the correctness of the solution obtained by self-similarity and numerical methods.

Compressor Map Corrections for Highly Non-Linear Fluid Properties

Turbomachinery systems are often subject to variations in ambient conditions and applied loads in operation. Standard maps (perhaps the most common being pressure ratio verses mass flow for compressors) are usually presented in terms of fixed inflow conditions. To account for changes in performance due to varying inlet conditions, compressors maps are often presented in standardized form where the mass flow and rotational speeds are normalized as a function of the reference condition total pressure and temperature. These methods are very widely used, particularly in the turbo charger industry. With these normalized maps, the actual performance of a compressor in a given environment can be deduced simply and easily with very reasonable accuracy in most cases. The underlaying assumption of this conventional normalization process is that the fluid behaves as a perfect gas. While this is usually sufficient for air compressors, the method is not viable where the fluid properties are not near perfect gas conditions, which is certainly the case for supercritical applications. The highly variable fluid properties near the critical point, and the challenges they present in design, have been well documented in the literature. The two most critical properties to consider in the design process are the density and the speed of sound. The density determines the volumetric flow for a given mass flow and this in turn determines the incidence angle, a primary driver of performance. The speed of sound directly affects the range of the compressor via choking. Choking range can be further complicated by the fact that under certain conditions, the choked state can be reached at Mach numbers less than one. While rare, this situation can occur when the inflow conditions are found close to the liquid side of the saturation dome. To account for these effects, a new method is proposed to generate normalized maps of performance that can be used to determine actual performance of a wide range of inlet conditions for highly non-linear thermodynamic properties. Although not as simple as the conventional perfect gas method that can be applied in a “back-of-the-envelope” style, the new method can be applied very rapidly using a spreadsheet-based method directly calling high fidelity NIST thermodynamic models. The end result of this tool is that a compressor map that has been painstakingly generated with testing or CFD can be applied to any inlet condition and the range and performance predicted very rapidly with high accuracy.

Critical and Choking Mach Numbers for Organic Vapor Flows Through Turbine Cascades

Results are presented of a theoretical and experimental study dealing with critical and choking Mach numbers of organic vapor flows through turbine cascades. A correlation was derived for predicting choking Mach numbers for organic vapor flows using an asymptotic series expansion valid for isentropic exponents close to unity. The theoretical prediction was tested employing a linear turbine cascade and a circular cylinder in a closed-loop organic vapor wind tunnel. The cascade was based on a classical transonic turbine airfoil for which perfect gas literature data were available. The cascade was manufactured by Selective Laser Melting (SLM), and a comparable low surface roughness level was established by subsequent surface finishing. Because the return of the closed-loop wind tunnel was equipped with an independent mass flow sensor and the test facility enabled stable long-term operation behavior, it was possible to obtain the choking Mach number with high accuracy. It was observed that non-perfect gas dynamics affect the critical Mach number locally, but the observed choking behavior of the turbine cascade was in good agreement with the asymptotic result for the considered dilute gas flow regime.

Starting and unstarting of hypersonic air inlets

This thesis concerns a technical hurdle that must be overcome in relation to air-breathing propulsion technologies for future space access vehicles--it discusses the flow starting process in supersonic and hypersonic air-inlets. A study is conducted, with the aid of numerical simulations, based on an inviscid model of a thermally perfect gas. Effects of boundary-imposed temporal and spatial gradients on the inlet starting phenomenon are documented for the first time. It is shown that purely accelerative starting is generally not possible, for inlets of any positive contraction, unless thousands of g 's of acceleration are imposed. It is proposed that removal of frangible structures, such as fast rupturing diaphragms, be used to impose sufficiently high spatial gradients, as necessary to permit starting beyond Kantrowitz' limit. It is shown that, for a perforated diffuser, starting takes place if a sonic line, at the leading edge of a slit, occurs at an area ratio equal to, or higher than, that corresponding to Kantrowitz' limit.

Starting and unstarting of hypersonic air inlets

This thesis concerns a technical hurdle that must be overcome in relation to air-breathing propulsion technologies for future space access vehicles--it discusses the flow starting process in supersonic and hypersonic air-inlets. A study is conducted, with the aid of numerical simulations, based on an inviscid model of a thermally perfect gas. Effects of boundary-imposed temporal and spatial gradients on the inlet starting phenomenon are documented for the first time. It is shown that purely accelerative starting is generally not possible, for inlets of any positive contraction, unless thousands of g 's of acceleration are imposed. It is proposed that removal of frangible structures, such as fast rupturing diaphragms, be used to impose sufficiently high spatial gradients, as necessary to permit starting beyond Kantrowitz' limit. It is shown that, for a perforated diffuser, starting takes place if a sonic line, at the leading edge of a slit, occurs at an area ratio equal to, or higher than, that corresponding to Kantrowitz' limit.

End-tidal to arterial PCO2 ratio: a bedside meter of the overall gas exchanger performance

Background The physiological dead space is a strong indicator of severity and outcome of acute respiratory distress syndrome (ARDS). The “ideal” alveolar PCO2, in equilibrium with pulmonary capillary PCO2, is a central concept in the physiological dead space measurement. As it cannot be measured, it is surrogated by arterial PCO2 which, unfortunately, may be far higher than ideal alveolar PCO2, when the right-to-left venous admixture is present. The “ideal” alveolar PCO2 equals the end-tidal PCO2 (PETCO2) only in absence of alveolar dead space. Therefore, in the perfect gas exchanger (alveolar dead space = 0, venous admixture = 0), the PETCO2/PaCO2 is 1, as PETCO2, PACO2 and PaCO2 are equal. Our aim is to investigate if and at which extent the PETCO2/PaCO2, a comprehensive meter of the “gas exchanger” performance, is related to the anatomo physiological characteristics in ARDS. Results We retrospectively studied 200 patients with ARDS. The source was a database in which we collected since 2003 all the patients enrolled in different CT scan studies. The PETCO2/PaCO2, measured at 5 cmH2O airway pressure, significantly decreased from mild to mild–moderate moderate–severe and severe ARDS. The overall populations was divided into four groups (~ 50 patients each) according to the quartiles of the PETCO2/PaCO2 (lowest ratio, the worst = group 1, highest ratio, the best = group 4). The progressive increase PETCO2/PaCO2 from quartile 1 to 4 (i.e., the progressive approach to the “perfect” gas exchanger value of 1.0) was associated with a significant decrease of non-aerated tissue, inohomogeneity index and increase of well-aerated tissue. The respiratory system elastance significantly improved from quartile 1 to 4, as well as the PaO2/FiO2 and PaCO2. The improvement of PETCO2/PaCO2 was also associated with a significant decrease of physiological dead space and venous admixture. When PEEP was increased from 5 to 15 cmH2O, the greatest improvement of non-aerated tissue, PaO2 and venous admixture were observed in quartile 1 of PETCO2/PaCO2 and the worst deterioration of dead space in quartile 4. Conclusion The ratio PETCO2/PaCO2 is highly correlated with CT scan, physiological and clinical variables. It appears as an excellent measure of the overall “gas exchanger” status.

AGB Stars and Their Circumstellar Envelopes. I. the VULCAN Code

The interplay between AGB interiors and their outermost layers, where molecules and dust form, is a problem of high complexity. As a consequence, physical processes like mass loss, which depend on the chemistry of the circumstellar envelope, are often oversimplified. The best candidates to drive mass-loss in AGB stars are dust grains, which trap the outgoing radiation and drag the surrounding gas. Grains build up, however, is far from being completely understood. Our aim is to model both the physics and the chemistry of the cool expanding layers around AGB stars in order to characterize the on-going chemistry, from atoms to dust grains. This has been our rationale to develop ab initio VULCAN, a FORTRAN hydro code able to follow the propagation of shocks in the circumstellar envelopes of AGB stars. The version presented in this paper adopts a perfect gas law and a very simplified treatment of the radiative transfer effects and dust nucleation. In this paper, we present preliminary results obtained with our code.