Search Results (25)

The inlet operating conditions of centrifugal compressors in natural gas storage reservoirs, as well as the natural gas composition, continuously vary over time, significantly impacting compressor performance. To analyze the influence of these factors on centrifugal compressors, a method for converting the performance curves of centrifugal compressors under actual operating conditions has been established. This performance conversion process is implemented through a custom-developed program, which incorporates the polytropic index and exhaust temperature calculations. Verification results show that the conversion error of this method is within 2%. Based on the proposed performance prediction method for non-similar operating conditions, the effects of varying inlet temperatures, pressures, and natural gas compositions on compressor performance are investigated. It is observed that an increase in inlet temperature results in a decrease in compressor power and pressure ratio; an increase in inlet pressure leads to higher power consumption, while the pressure ratio varies with the flow rate at the operating point; and as the average molar mass of natural gas decreases, both the pressure ratio and power exhibit a certain degree of reduction. Full article

Supersonic vacuum generators, or ejectors, operate pneumatically to extract air from tanks in industrial applications. A key performance metric for ejectors is the Total Evacuation Time (TET), which measures the time required to reach minimum pressure. This research predicts TET using empirical models that rely on two key metrics: the characteristic curve, which relates absorbed flow rate to the working pressure, and the polytropic curve, which describes the evolution of the polytropic coefficient across working pressures. Accurately capturing both curves for subsequent fitting to polynomial curves is crucial for forecasting TET. Several experimental setups were employed to capture the curves, each of which refined the data and improved the quality of the polynomial fits and coefficients. Multiple setups were necessary to pinpoint the breakpoint, from supersonic to subsonic operation mode, which is a critical factor that affects the characteristic curve and the TET. Furthermore, the research shows an improvement in the TET forecasts for each setup, with deviations between experimental and predicted TET ranging from 7.6% (14.5 s) to a 1.4% (2.6 s) in the most precise setup. Once the models were validated, an optimized ejector design, extracted from an author’s previous article, was tested. It revealed a 4% improvement (8 s) in the TET. These results highlight the importance of the mathematical models developed, which can be used in the future to compare ejectors and reduce the need for experimental data. Full article

In this paper, we consider the unsteady flow of a compressible micropolar fluid between two moving, thermally isolated parallel plates. The fluid is characterized as viscous and thermally conductive, with polytropic thermodynamic properties. Although the mathematical model is inherently three-dimensional, we assume that the variables depend on only a single spatial dimension, reducing the problem to a one-dimensional formulation. The non-homogeneous boundary conditions representing the movement of the plates lead to moving domain boundaries. The model is formulated in mass Lagrangian coordinates, which leads to a time-invariant domain. This work focuses on numerical simulations of the fluid flow for different configurations. Two computational approaches are used and compared. The first is based on the finite difference method and the second is based on the Faedo–Galerkin method. To apply the Faedo–Galerkin method, the boundary conditions must first be homogenized and the model equations reformulated. On the other hand, in the finite difference method, the non-homogeneous boundary conditions are implemented directly, which reduces the computational complexity of the numerical scheme. In the performed numerical experiments, it was observed that, for the same accuracy, the Faedo–Galerkin method was approximately 40 times more computationally expensive compared to the finite difference method. However, on a dense numerical grid, the finite difference method required a very small time step, which could lead to an accumulation of round-off errors. On the other hand, the Faedo–Galerkin method showed the convergence of the solutions as the number of expansion terms increased, despite the higher computational cost. Comparisons of the obtained results show good agreement between the two approaches, which confirms the consistency and validity of the numerical solutions. Full article

In this work, we analyze a spherically symmetric 3D flow of a micropolar, viscous, polytropic, and heat-conducting real gas. In particular, we take as a domain the subset of $R^3$ bounded by two concentric spheres that present solid thermoinsulated walls. Also, here, we consider the generalized equation of state for the pressure in the sense that the pressure depends, as a power function, on the mass density. The model is based on the conservation laws for mass, momentum, momentum moment, and energy, as well as the equation of state for a real gas, and it is derived first in the Eulerian and then in the Lagrangian description. Through the application of the Faedo–Galerkin method, a numerical solution to a corresponding problem is obtained, and numerical simulations are performed to demonstrate the behavior of the solutions under various parameters and initial conditions in order to validate the method. The results of the simulations are discussed in detail. Full article

This study focusses on the energy efficiency of compressed air storage tanks (CASTs), which are used as small-scale compressed air energy storage (CAES) and renewable energy sources (RES). The objectives of this study are to develop a mathematical model of the CAST system and its original numerical solutions using experimental parameters that consider polytropic charging and discharging processes, changes in the time of the temperature, flow parameters of the inlet and outlet valves under choked and subsonic conditions, and the characteristics of the air motor. This model is used to select CAST as an energy storage system for compressed air generated by compressors and recycling, as well as an energy source to drive DC generators and a pneumatic propulsion system (PPS). A measuring test rig is built to verify the polytropic pressure and temperature variations during CAST charging and discharging obtained from numerical solutions. The topic of discussion is the functional model of a high-pressure air system (HPAS) that contains a CAST connected to an air motor coupled to a mechanical drive for a DC generator or PPS. Such a system is used in small-scale CASTs, which currently respond to socio-economic demands. The presented CAST energy efficiency indicators are used to justify the storage of compressed air energy on a small scale. Small-scale compressed air storage in CASTs is currently important and relevant due to the balance between peak electricity demand and the development of wind energy, photovoltaics, and other renewable energy sources. Full article

This review examines compressed air receiver tanks (CARTs) for the improved energy efficiency of various pneumatic systems such as compressed air systems (CAS), compressed air energy storage systems (CAESs), pneumatic propulsion systems (PPSs), pneumatic drive systems (PDSs), pneumatic servo drives (PSDs), pneumatic brake systems (PBSs), and compressed air vehicles (CAVs). The basic formulas and energy efficiency indicators used in a CART calculation and selection are included. New scientific research by the authors on measurements based on tank methods, numerical solutions in the process of charging and discharging, the valve-to-tank-to-valve system and pneumatic propulsion system was presented. The numerical model of the valve-tank-valve system takes into account CART polytropic charging and discharging processes, the mass flow balance equation, and the sound (choked) and subsonic mass flow rate in the inlet and outlet valves. Future research directions to improve the energy efficiency of a CART charging and discharge are highlighted. The effective density of energy storage in CART was compared to that of other renewable energy sources and other fuels. Economic and environmental issues were also considered by adopting various energy performance indicators. The discussion also focused on the design concept and computational model of the hybrid tricycle bike (HTB) pneumatic propulsion system. Full article

Hydro-pneumatic suspension (HPS) systems are increasingly being implemented in commercial vehicles and various industrial equipment, which is mainly attributed to the integration of adaptable nonlinear pneumatic stiffness and hydraulic damping properties. The integrated HPS design with a shared gas-oil chamber, however, leads to gas-oil emulsion flow within the suspension chambers, which intricately affects the internal and external properties of the HPS, especially under variations in temperature and excitation frequency. This study experimentally and analytically investigated the temperature- and frequency-dependent properties of the hydro-pneumatic suspension with the gas-oil emulsion. Laboratory experiments were performed under three different near-constant temperatures (30, 40, and 50 °C) in the 0.5–8 Hz frequency range. An analytical model of the HPS was formulated considering the effects of temperature on internal fluid properties, gas-oil emulsion flow between the coupled chambers, the dynamic seal friction, and polytropic change in the gas state. The internal parameters, including the gas volume fraction, the discharge coefficient of the emulsion, and the dynamic friction components, as well as the external stiffness and damping characteristics, were determined. The relationships between these properties and the system temperature, velocity, and excitation frequency were further investigated. The simulated responses obtained under different excitations showed reasonably good agreement with the experimental results of the HPS. The results suggested that increased temperature yielded greater equivalent stiffness and comparable damping properties of the system. The gas volume fraction, discharge coefficient, and magnitude of seal friction generally tended to increase with increasing temperature. Increased excitation frequency led to greater hysteresis in hydraulic damping force and seal friction, and reduced seal friction magnitude and Stribeck effect. Full article

This study aims to optimize and assess the quality of the sorting process into homogeneous size classes of dried and chopped medicinal plants, by obtaining multivariate regression functions of polytropic and polynomial forms. Assessment of sorting quality was carried out by calculating the average coefficient of separation. The influence of several important factors (material feed rate on the sieve, sieve dimensions, sieve inclination angle, sieve oscillation frequencies) on the sorting process was followed. Research was carried out on dried nettle herb (Urtica dioica) using a plant sorter with plane sieves, which allowed for modifying some constructive and functional parameters, making it possible to obtain optimal values. The results showed that the dry nettle herb chopped in bulk at 4 mm, with a moisture of 11.45%, was optimally sorted (index of average separation coefficient, 0.922) if the following parameters were met: drive mechanism speed n = 1000 rpm; sieve inclination angle α = 12.08°; material-specific flow q = 4 kg/dm·h; recommended sieve length L = 1.4 m. It was observed that at high rates, the average coefficient of separation decreased with the decrease in the sieve drive mechanism speed, and when the inclination angle of the sieve decreased, the average coefficient of separation increased. The maximum average deviation of the average separation coefficient was 5.5% for the polytropic function. The new advanced processing technologies of medicinal plants involve the short-term production of quality-finished products, thus supporting the processors of medicinal plants and the consumers of phytotherapeutic products with beneficial effects for health. Full article

The present study is concerned with studying the dynamical behavior of two space-dimensional nonlinear time-fractional models governing the unsteady-flow of polytropic-gas (in brief, pGas) that occurred in cosmology and astronomy. For this purpose, two efficient hybrid methods so-called optimal homotopy analysis $\mathbb{J}$-transform method (${}_O$HA$\mathbb{J}$TM) and $\mathbb{J}$-variational iteration transform method ($\mathbb{J}$-VITM) have been adopted. The _OHA$\mathbb{J}$TM is the hybrid method, where optimal-homotopy analysis method (${}_O$HAM) is utilized after implementing the properties of $\mathbb{J}$-transform ($\mathbb{J}$T), and in $\mathbb{J}$-VITM is the $\mathbb{J}$-transform-based variational iteration method. Banach’s fixed point approach is adopted to analyze the convergence of these methods. It is demonstrated that $\mathbb{J}$-VITM is $\mathrm{T}$-stable, and the evaluated dynamics of pGas are described in terms of Mittag–Leffler functions. The proposed evaluation confirms that the implemented methods perform better for the referred model equation of pGas. In addition, for a given iteration, the proposed behavior via ${}_O$HA$\mathbb{J}$TM performs better in producing more accurate behavior in comparison to $\mathbb{J}$-VITM and the methods introduced recently. Full article

A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter–energy content is represented by a perfect fluid whose volume elements perform polytropic flows. When the (thermodynamic) energy of the associated internal motions is taken into account as an additional source of the universal gravitational field, it compensates the DE needed to compromise spatial flatness in an accelerating universe. The unified model which is driven by a polytropic fluid not only interprets the observations associated with universe expansion but successfully confronts all the current issues of cosmological significance, thus arising as a viable alternative to the $\Lambda$CDM model. Full article

We briefly review some recent advances in the field of nonlinear dynamics of atomic clouds in magneto-optical traps. A hydrodynamical model in a three-dimensional geometry is applied and analyzed using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple scattering effects are both relevant, where the confinement damping and harmonic potential are both included. For generality, a general polytropic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriate spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived. These equations are applied to compare cylindrical and spherical geometry approximations. The results are restricted to potential flows. Full article

In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems. Full article

The maximal kinematical invariance group of the Euler equations of fluid dynamics for the standard polytropic exponent is larger than the Galilei group. Specifically, the inversion transformation $(\Sigma :t\to -1/t,\overrightarrow{x}\to \overrightarrow{x}/t)$ leaves the Euler equation’s invariant. This duality has been used to explain the striking similarities observed in simulations of the supernova explosions and laboratory implosions induced in plasma by intense lasers. The inversion symmetry extends to discontinuous fluid flows as well. In this contribution, we provide a concise review of these ideas and discuss some applications. We also explicitly work out the implosion dual of the Sedov’s explosion solution. Full article

Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity. The construction of these schemes makes use of results of the group classification of MHD equations previously obtained by the authors. On the basis of the classical Samarskiy–Popov scheme, new schemes are constructed for the case of finite conductivity. These schemes admit all symmetries of the original differential model and have difference analogues of all of its local differential conservation laws. New, previously unknown, conservation laws are found using symmetries and direct calculations. In the case of infinite conductivity, conservative invariant schemes are constructed as well. For isentropic flows of a polytropic gas the proposed schemes possess the conservation law of energy and preserve entropy on two time layers. This is achieved by means of specially selected approximations for the equation of state of a polytropic gas. In addition, invariant difference schemes with additional conservation laws are proposed. A new scheme for the case of finite conductivity is tested numerically for various boundary conditions, which shows accurate preservation of difference conservation laws. Full article

To investigate the static characteristics of aerostatic journal bearings with porous bushing, the flow model—in which the compressibility of lubricating gas is considered—is established based on the Reynolds lubrication equation, Darcy equation for porous material, and continuity equation. With the finite difference method, difference schemes for non-uniform grids, relaxation method, and virtual node method, the numerical method for the governing equations of compressible flow in porous journal bearings is proposed. The effects of nominal clearance of bearings and compressibility of gas on the static characteristics are analyzed. Under the same minimum film thickness and the same gas compressibility, as the nominal clearance widens, the load capacity, mass flow rate, and power consumption increase. Under the same minimum film thickness and the same nominal clearance, with the increase in gas polytropic index, the load capacity strengthens, while the mass flow rate and power consumption decline. This study could provide a reference for the design of porous journal bearings. Full article