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Journal articles on the topic 'Polytropic coefficient'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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1

Zhang, Yahui, and Tielong Shen. "In-cylinder Pressure Pegging Algorithm Based on Cyclic Polytropic Coefficient Learning." International Journal of Automotive Engineering 8, no. 2 (2017): 79–86. http://dx.doi.org/10.20485/jsaeijae.8.2_79.

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2

Lin, Binbin, Nong Xiang, and Jing Ou. "The ion polytropic coefficient in a collisionless sheath containing hot ions." Physics of Plasmas 23, no. 8 (August 2016): 083508. http://dx.doi.org/10.1063/1.4960558.

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3

Liu, Dengming, and Changyu Liu. "Global Existence and Extinction Singularity for a Fast Diffusive Polytropic Filtration Equation with Variable Coefficient." Mathematical Problems in Engineering 2021 (April 28, 2021): 1–9. http://dx.doi.org/10.1155/2021/5577777.

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In this article, we deal with an inhomogeneous fast diffusive polytropic filtration equation. By using the energy estimate approach, Hardy–Littlewood–Sobolev inequality, and a series of ordinary differential inequalities, we prove the global existence result and obtain the conditions on the occurrence of the extinction phenomenon of the weak solution.
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4

Kim, Hyunseok, and Jihoon Lee. "The Incompressible Limits of Viscous Polytropic Fluids with Zero Thermal Conductivity Coefficient." Communications in Partial Differential Equations 30, no. 8 (July 2005): 1169–89. http://dx.doi.org/10.1080/03605300500257560.

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5

Zhan, Huashui, and Zhen Zhou. "The Well-Posedness of the Solutions Based on the L1 Initial Value Condition." Journal of Function Spaces 2018 (September 16, 2018): 1–12. http://dx.doi.org/10.1155/2018/6525637.

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The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.
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6

Lapuerta, Magı́n, Octavio Armas, and Santiago Molina. "Study of the compression cycle of a reciprocating engine through the polytropic coefficient." Applied Thermal Engineering 23, no. 3 (February 2003): 313–23. http://dx.doi.org/10.1016/s1359-4311(02)00193-x.

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7

Hoffman, Mark A., Robert G. Prucka, and Zoran S. Filipi. "Real time calculation of residual gas fraction utilising the polytropic coefficient of compression." International Journal of Powertrains 6, no. 4 (2017): 383. http://dx.doi.org/10.1504/ijpt.2017.088509.

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Filipi, Zoran S., Mark A. Hoffman, and Robert G. Prucka. "Real time calculation of residual gas fraction utilising the polytropic coefficient of compression." International Journal of Powertrains 6, no. 4 (2017): 383. http://dx.doi.org/10.1504/ijpt.2017.10009491.

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9

Luo, Qing-he, Bai-gang Sun, and Hua-yu Tian. "The characteristic of polytropic coefficient of compression stroke in hydrogen internal combustion engine." International Journal of Hydrogen Energy 39, no. 25 (August 2014): 13787–92. http://dx.doi.org/10.1016/j.ijhydene.2014.04.035.

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10

Dewri, M. "A Magnetized Dark Energy Type R/W Model with Polytropic Equation of State in Brans-Dicke Theory." Journal of Scientific Research 12, no. 3 (May 1, 2020): 251–57. http://dx.doi.org/10.3329/jsr.v12i3.43313.

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In this paper, we study the spatially homogeneous Robertson-Walker cosmological models with magnetized isotropic dark energy like fluid in the scalar-tensor theory of gravitation proposed by Brans-Dicke. Variable cosmological constant ᴧ and Polytropic equation of state have been used to find exact solutions of the models with volumetric expansion and power-law relation. The Physical and dynamical behaviors of the models have been discussed using some physical quantities like energy density, pressure, and coefficient of bulk viscosity.
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11

Kuwabara, Takuhito, and Chung-Ming Ko. "Magneto-rotational instability with the effect of cosmic rays." Proceedings of the International Astronomical Union 11, A29B (August 2015): 744. http://dx.doi.org/10.1017/s1743921316006670.

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AbstractCosmic ray (CR) is an important component of the interstellar medium. It interacts with plasma via embedded magnetic irregularities. We study the magneto-rotational instability (MRI) in the presence of CRs. We analyse the effect of CRs including their diffusion using both linear stability analysis and MHD simulations. Two models are studied. (1) In the shearing box model, uniform initial state is adopted. Linear analysis shows that the growth rate of MRI is not sensitive to the value of CR diffusion coefficient. (2) In the differentially rotating cylinder model, the initial state is taken as a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both linear results are confirmed by MHD simulations.
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12

Brind, James, and Graham Pullan. "Modelling Turbine Acoustic Impedance." International Journal of Turbomachinery, Propulsion and Power 6, no. 2 (June 7, 2021): 18. http://dx.doi.org/10.3390/ijtpp6020018.

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We quantify the sensitivity of turbine acoustic impedance to aerodynamic design parameters. Impedance boundary conditions are an influential yet uncertain parameter in predicting the thermoacoustic stability of gas turbine combustors. We extend the semi-actuator disk model to cambered blades, using non-linear time-domain computations of turbine vane and stage cascades with acoustic forcing for validation data. Discretising cambered aerofoils into multiple disks improves reflection coefficient predictions, reducing error by up to an order of magnitude compared to a flat plate assumption. A parametric study of turbine stage designs using the analytical model shows acoustic impedance is a weak function of degree of reaction and polytropic efficiency. The design parameter with the strongest influence is flow coefficient, followed by axial velocity ratio and Mach number. We provide the combustion engineer with improved tools to predict impedance boundary conditions, and suggest thermoacoustic stability is most likely to be compromised by change in turbine flow coefficient.
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13

NOJIRI, Kunpei, Mizuki SAKAMOTO, Naomichi EZUMI, Satoshi TOGO, Takaaki IIJIMA, Seowon JANG, Akihiro TERAKADO, et al. "Effect of High Ion Temperature on the Polytropic Coefficient in the End Region of GAMMA 10/PDX." Plasma and Fusion Research 14 (June 3, 2019): 2401086. http://dx.doi.org/10.1585/pfr.14.2401086.

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14

Khan, Majid, S. S. Hussain, Z. Sheng, and M. Kamran. "Polytropic Coefficient Function for Tonks-Langmuir-Type Bounded Plasmas with Kappa-Distributed Electrons and Cold Ion Source." Brazilian Journal of Physics 49, no. 3 (April 8, 2019): 372–78. http://dx.doi.org/10.1007/s13538-019-00659-4.

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15

Martelli, F., S. Pazzi, and V. Michelassi. "Automatic computational fluid dynamics-based procedure for the optimization of a centrifugal impeller." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 219, no. 7 (November 1, 2005): 549–57. http://dx.doi.org/10.1243/095765005x31261.

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A typical centrifugal impeller characterized by a low flow coefficient and cylindrical blades is redesigned by means of an intelligent automatic search program. The procedure consists of a feasible sequential quadratic programming algorithm (Fletcher, R. Practical Methods of optimization, 2000 (Wiley)) coupled to a lazy learning (LL) interpolator 1 to speed-up the process. The program is able to handle geometric constraints to reduce the computational effort devoted to the analysis of non-physical configurations. The objective function evaluator is an in-house developed structured computational fluid dynamics (CFD) code. The LL approx-imator is called each time the stored database can provide a sufficiently accurate performance estimate for a given geometry, thus reducing the effective CFD computations. The impeller is represented by 25 geometric parameters describing the vane in the meridional and s-0 planes, the blade thickness, and the leading edge shape. The optimization is carried out on the impeller design point maximizing the polytropic efficiency with nearly constant flow coefficient and polytropic head. The optimization is accomplished by maintaining unaltered those geometrical parameters which have to be kept fixed in order to make the impeller fit the original stage. The optimization, carried out on a cluster of 16 PCs, is self-learning and leads to a geometry presenting an increased design point efficiency. The program is completely general and can be applied to any component which can be described by a finite number of geometrical parameters and computed by any numerical instrument to provide performance indices. The work presented in this paper was done under the METHOD EC funded project for the implementation of new technologies for optimization of centrifugal compressors.
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16

Khoramabadi, Mansour, and S. Farhad Masoudi. "The effects of the polytropic coefficient on plasma sheath in two cases isothermal and adiabatic ion thermal flow." Astrophysics and Space Science 341, no. 2 (April 21, 2012): 501–5. http://dx.doi.org/10.1007/s10509-012-1075-9.

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17

Kim, Kyoung Hoon, Dong Joo Kim, Kyoung Jin Kim, and Seong Wook Hong. "An Assessment of Wet Compression Process in Gas Turbine Systems with an Analytical Modeling." Applied Mechanics and Materials 234 (November 2012): 23–27. http://dx.doi.org/10.4028/www.scientific.net/amm.234.23.

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Recently humidified gas turbine systems in which water or steam is injected have attracted much attention, since they can offer a high efficiency and a high specific power with a relatively low cost compared to combined-cycle gas turbine systems, and therefore they have a potential for future power generation. In this study, performance analysis of the wet compression process is carried out with an analytical modeling which was developed from heat and mass transfer, and thermodynamic analyses based on droplet evaporation. Wet compression variables such as temperature-averaged polytropic coefficient, compressor outlet temperature, and compression work are estimated. Parametric studies show the effect of system parameters such as droplet size, water injection ratio or compression ratio on transient behavior.
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18

Kim, Kyoung Hoon, and Chul Ho Han. "Performance Analysis of Wet Compression Process under Critical Conditions of Water Injection." Applied Mechanics and Materials 229-231 (November 2012): 2541–45. http://dx.doi.org/10.4028/www.scientific.net/amm.229-231.2541.

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In wet compression process water is injected at an inlet of compressor and continuous cooling occurs due to evaporation of water droplets during the compression process of air, which can save the compression work and enhance the performance of gas turbine system. In this work, performance analysis of the wet compression process is carried out under the critical conditions of water injection which are defined as the maximum water injection which can be evaporated completely inside the compressor. For various ambient conditions the important variables of wet compression process such as water injection ratio, temperature-averaged polytropic coefficient, compressor outlet temperature, and compression work are estimated under the critical injection conditions. Parametric studies show that compression work decreases with ambient temperature, however, the reduction ratio of compression work relative to dry increases with ambient temperature.
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19

Wang, Tao, and Huijiang Zhao. "One-dimensional compressible heat-conducting gas with temperature-dependent viscosity." Mathematical Models and Methods in Applied Sciences 26, no. 12 (October 25, 2016): 2237–75. http://dx.doi.org/10.1142/s0218202516500524.

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We consider the one-dimensional compressible Navier–Stokes system for a viscous and heat-conducting ideal polytropic gas when the viscosity [Formula: see text] and the heat conductivity [Formula: see text] depend on the specific volume [Formula: see text] and the temperature [Formula: see text] and are both proportional to [Formula: see text] for certain non-degenerate smooth function [Formula: see text]. We prove the existence and uniqueness of a global-in-time non-vacuum solution to its Cauchy problem under certain assumptions on the parameter [Formula: see text] and initial data, which imply that the initial data can be large if [Formula: see text] is sufficiently small. Such a result appears to be the first global existence result for general adiabatic exponent and large initial data when the viscosity coefficient depends on both the density and the temperature.
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20

Farrugia, C. J., V. A. Osherovich, and L. F. Burlaga. "The non-linear evolution of magnetic flux ropes: 3. effects of dissipation." Annales Geophysicae 15, no. 2 (February 28, 1997): 152–64. http://dx.doi.org/10.1007/s00585-997-0152-9.

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Abstract. We study the evolution (expansion or oscillation) of cylindrically symmetric magnetic flux ropes when the energy dissipation is due to a drag force proportional to the product of the plasma density and the radial speed of expansion. The problem is reduced to a single, second-order, ordinary differential equation for a damped, non-linear oscillator. Motivated by recent work on the interplanetary medium and the solar corona, we consider polytropes whose index, γ, may be less than unity. Numerical analysis shows that, in contrast to the small-amplitude case, large-amplitude oscillations are quasi-periodic with frequencies substantially higher than those of undamped oscillators. The asymptotic behaviour described by the momentum equation is determined by a balance between the drag force and the gradient of the gas pressure, leading to a velocity of expansion of the flux rope which may be expressed as (1/2γ)r/t, where r is the radial coordinate and t is the time. In the absence of a drag force, we found in earlier work that the evolution depends both on the polytropic index and on a dimensionless parameter, κ. Parameter κ was found to have a critical value above which oscillations are impossible, and below which they can exist only for energies less than a certain energy threshold. In the presence of a drag force, the concept of a critical κ remains valid, and when κ is above critical, the oscillatory mode disappears altogether. Furthermore, critical κ remains dependent only on γ and is, in particular, independent of the normalized drag coefficient, ν*. Below critical κ, however, the energy required for the flux rope to escape to infinity depends not only on κ (as in the conservative force case) but also on ν*. This work indicates how under certain conditions a small change in the viscous drag coefficient or the initial energy may alter the evolution drastically. It is thus important to determine ν* and κ from observations.
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21

Lucas, Radika, Andy Jones, Wesley Ford, and Matt Doyle. "The effective use of data analytics in an advanced compressor performance and degradation monitoring system." APPEA Journal 58, no. 2 (2018): 723. http://dx.doi.org/10.1071/aj17086.

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Origin is the upstream operator and joint venture partner in Australia Pacific LNG. Origin’s integrated gas operations require reliable, sustainable delivery of gas to the downstream LNG facility on Curtis Island. This scale of operation requires establishing a ‘single source of truth’ regarding compressor condition and performance while achieving maximum and reliable compression capacities. Therefore, capability of monitoring performance of centrifugal compressors across the fleet is considered an essential component of production surveillance. Xodus leveraged Origin’s OSIsoft PI AF (PI Historian Asset Framework) tool. This system was used to build a compressor performance and degradation monitoring tool to accurately identify early indications of degradation in a multi-stage centrifugal compression train. The tool utilises live data from the PI historian to calculate key performance indicators which define compressor and driver operation. Dimensionless parameter analysis allows Origin to accurately quantify performance degradation regardless of variations in plant inlet conditions at each gas processing facility. Deviation from baseline performance in dimensionless parameters such as polytropic efficiency, work input number and polytropic head coefficient is used to quantify capacity losses, additional power consumption and increase in suction pressure. The tool provided the ability to use performance indicators to confidently determine the mode and extent of compressor degradation and prevent accelerated fouling which can lead to premature bundle changes. Also, this information helps streamline and has led to a major step change for the decision-making process concerning maximum production from rotating equipment. Additionally, this allowed operations to be confident on the condition of the compressor bundle, continue operation with higher capacities during high demand periods and ensure compressor bundle changeout is optimised for availability and economic aspects.
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22

CHALONS, C., and F. COQUEL. "THE RIEMANN PROBLEM FOR THE MULTI-PRESSURE EULER SYSTEM." Journal of Hyperbolic Differential Equations 02, no. 03 (September 2005): 745–82. http://dx.doi.org/10.1142/s0219891605000610.

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We prove the existence and uniqueness of the Riemann solutions to the Euler equations closed by N independent constitutive pressure laws. This model stands as a natural asymptotic system for the multi-pressure Navier–Stokes equations in the regime of infinite Reynolds number. Due to the inherent lack of conservation form in the viscous regularization, the limit system exhibits measure-valued source terms concentrated on shock discontinuities. These non-positive bounded measures, called kinetic relations, are known to provide a suitable tool to encode the small-scale sensitivity in the singular limit. Considering N independent polytropic pressure laws, we show that these kinetic relations can be derived by solving a simple algebraic problem which governs the endpoints of the underlying viscous shock profiles, for any given but prescribed ratio of viscosity coefficient in the viscous perturbation. The analysis based on traveling wave solutions allows us to introduce the asymptotic Euler system in the setting of piecewise Lipschitz continuous functions and to study the Riemann problem.
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23

Mrazík, Lukáš, and Pavel Kříž. "Porous Medium Equation in Graphene Oxide Membrane: Nonlinear Dependence of Permeability on Pressure Gradient Explained." Membranes 11, no. 9 (August 29, 2021): 665. http://dx.doi.org/10.3390/membranes11090665.

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Membrane performance in gas separation is quantified by its selectivity, determined as a ratio of measured gas permeabilities of given gases at fixed pressure difference. In this manuscript a nonlinear dependence of gas permeability on pressure difference observed in the measurements of gas permeability of graphene oxide membrane on a manometric integral permeameter is reported. We show that after reasoned assumptions and simplifications in the mathematical description of the experiment, only static properties of any proposed governing equation can be studied, in order to analyze the permeation rate for different pressure differences. Porous Medium Equation is proposed as a suitable governing equation for the gas permeation, as it manages to predict a nonlinear behavior which is consistent with the measured data. A coefficient responsible for the nonlinearity, the polytropic exponent, is determined to be gas-specific—implications on selectivity are discussed, alongside possible hints to a deeper physical interpretation of its actual value.
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24

Rakitskii, Valery N., E. G. Chkhvirkiya, and T. M. Epishina. "The toxicity of the technical product, derived triazolinones." Health Care of the Russian Federation 64, no. 2 (April 20, 2020): 83–87. http://dx.doi.org/10.46563/0044-197x-2020-64-2-83-87.

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Introduction. Technical products that are part of pesticides recommended for use in agriculture must undergo a comprehensive sanitary and Toxicological examination, which is the basis for preventing the adverse effects of pesticides on the health of workers and the population, as well as on the sanitary state of the environment. Purpose of research - the study of the biological effect of the technical product derived triazolinthionov, with its repeated oral intake in mammals (rats), justification of the permissible daily dose (DSD) for humans. Material and methods. Chronic (12 months) experiment was conducted on male rats with a body weight of 200-210 g tested doses: 5.0; 50.0 and 500.0 mg/kg body weight (1 control and 3 experimental groups and 20 individuals each). In the dynamics of the experiment, we observed the condition and behavior of animals, water and food consumption, fixed the timing of death, recorded changes in body weight, physiological, biochemical and hematological parameters. Results. It was found that the dose of 5.0 mg/kg body weight does not cause significant changes in all studied parameters, doses of 50.0 and 500.0 mg/kg body weight had a polytropic effect on the body of experimental animals. Discussion. The studied technical product at repeated intake in doses of 50,0 and 500,0 mg/kg of body weight causes changes in the state of the Central nervous system of animals (statistically significant changes in SPP, total activity, path length, rest time), as well as changes in carbohydrate, lipid, and lipoprotein metabolism in the body, as evidenced by statistically significant changes in biochemical and hematological indicators. Consequently, doses of 50,0 and 500,0 mg/kg of body weight have a polytropic effect on the body of male rats and are effective. The dose of 5.0 mg/kg of body weight, when administered in animals of the experimental group in comparison with animals of the control group, there are no changes in all the studied parameters throughout the experiment, is accepted as invalid. On the basis of an inactive dose of 5.0 mg/kg of body weight and a reserve factor of 100, we have scientifically justified DSD for humans at the level of 0.05 mg/kg. Conclusion. Studies have shown that long-term repeated oral administration of the studied product into the body of animals (male rats) at a dose of 5.0 mg per 1 kg of body weight does not cause statistically significant changes in all the studied parameters, so the indicated dose is invalid. Doses of 50,0 and 500,0 mg/kg MT have a polytropic effect on the body of male rats and are effective. DSD for humans at the level of 0.05 mg/kg is justified based on the inactive dose at the level of 5.0 mg per 1 kg of body weight, established in a 12-month chronic experiment conducted on male rats, and the reserve coefficient of 100 (taking into account the unexpressed specific and long-term effects).
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25

Anco, Stephen C., and Amanullah Dar. "Conservation laws of inviscid non-isentropic compressible fluid flow in n > 1 spatial dimensions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2121 (March 24, 2010): 2605–32. http://dx.doi.org/10.1098/rspa.2009.0579.

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Recent work giving a classification of kinematic and vorticity conservation laws of compressible fluid flow with barotropic equations of state (where pressure is a function only of the fluid density) in n >1 spatial dimensions is extended to general non-isentropic equations of state in which the pressure is also a function of the dynamical entropy (per unit mass) of the fluid. Two main results are obtained. First, we find that, apart from the familiar conserved integrals for mass, momentum, energy, angular momentum, Galilean momentum and volumetric entropy, additional kinematic conserved integrals arise only for non-isentropic equations of state given by a generalized form of the well-known polytropic equation of state with dimension-dependent exponent γ =1+2/ n , such that the proportionality coefficient is an arbitrary function of the entropy (per unit mass). Second, we show that the only vorticity conserved integrals consist of a circulatory entropy (which vanishes precisely when the fluid flow is irrotational) in all even dimensions. In particular, the vorticity integrals for helicity in odd dimensions and enstrophy in even dimensions are found to be no longer conserved for any non-isentropic equation of state.
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26

Quintana, Sebastián H., Edisson S. Castaño-Mesa, and Iván D. Bedoya. "Experimental Study of the Polytropic Coefficient for an Air-Cooled, High-Compression-Ratio, Spark-Ignition Engine Fueled with Natural Gas, Biogas, and a Propane–Syngas Blend." Energy & Fuels 32, no. 2 (January 10, 2018): 2376–84. http://dx.doi.org/10.1021/acs.energyfuels.7b03063.

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27

Viana, Felipe A. C., Valder Steffen Jr., Marcelo A. X. Zanini, Sandro A. Magalhães, and Luiz C. S. Góes. "Identification of a Non-Linear Landing Gear Model Using Nature-Inspired Optimization." Shock and Vibration 15, no. 3-4 (2008): 257–72. http://dx.doi.org/10.1155/2008/246271.

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This work deals with the application of a nature-inspired optimization technique to solve an inverse problem represented by the identification of an aircraft landing gear model. The model is described in terms of the landing gear geometry, internal volumes and areas, shock absorber travel, tire type, and gas and oil characteristics of the shock absorber. The solution to this inverse problem can be obtained by using classical gradient-based optimization methods. However, this is a difficult task due to the existence of local minima in the design space and the requirement of an initial guess. These aspects have motivated the authors to explore a nature-inspired approach using a method known as LifeCycle Model. In the present formulation two nature-based methods, namely the Genetic Algorithms and the Particle Swarm Optimization were used. An optimization problem is formulated in which the objective function represents the difference between the measured characteristics of the system and its model counterpart. The polytropic coefficient of the gas and the damping parameter of the shock absorber are assumed as being unknown: they are considered as design variables. As an illustration, experimental drop test data, obtained under zero horizontal speed, were used in the non-linear landing gear model updating of a small aircraft.
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28

Golovin, Dmitrii Vital`Evich. "Simulation of Infrasound Pistonphone." Proceedings of the Institute for System Programming of the RAS 32, no. 5 (2020): 181–98. http://dx.doi.org/10.15514/ispras-2020-32(5)-14.

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There are presented the results of numerical simulation of an applied acoustic problem – modeling of gas processes occurring in the measuring chamber of the infrasound pistonphone 3202 at different frequencies of piston oscillation (0.1 – 1000 Hz) and characterized by extremely small Mach numbers (9.1·10-7÷9.1·10-3). The simulation was performed using quasi-gas-dynamic (QGD) and quasi-hydrodynamic (QHD) equations of a viscous compressible heat-conducting gas with the use of a time-explicit difference scheme, all spatial derivatives was approximated by central differences. It is shown that QGD and QHD models can be used for a simulation of applied acoustics and, in particular, to the simulation of infrasonic pistonphone: the stability limits of the QGD and QHD algorithms in this problem were determined, the dependence of sound pressure on the tuning parameter α is investigated and it is shown that this dependence is quite small. The spectra of sound pressure at the control point calculated by QGD and QHD are given, their dependence on the tuning parameter α is shown, both models equally predict the value of the sound pressure amplitude at the fundamental frequency oscillations. At the end of the article, the sound pressure at the control point at the fundamental frequency oscillations obtained by using QGD and QHD is compared with the values calculated by using semi-empirical formula of sound pressure at closed volume for a case of small oscillations using the polytropic index obtained by Henry Gerber instead of the adiabatic coefficient.
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29

Zhu, Shengguo. "Existence results for viscous polytropic fluids with degenerate viscosity coefficients and vacuum." Journal of Differential Equations 259, no. 1 (July 2015): 84–119. http://dx.doi.org/10.1016/j.jde.2015.01.048.

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30

Li, Yachun, and Zhaoyang Shang. "Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients." Journal of Hyperbolic Differential Equations 16, no. 03 (September 2019): 443–93. http://dx.doi.org/10.1142/s0219891619500164.

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We consider the planar compressible magnetohydrodynamics (MHD) system for a viscous and heat-conducting ideal polytropic gas, when the viscosity, magnetic diffusion and heat conductivity depend on the specific volume [Formula: see text] and the temperature [Formula: see text]. For technical reasons, the viscosity coefficients, magnetic diffusion and heat conductivity are assumed to be proportional to [Formula: see text] where [Formula: see text] is a non-degenerate and smooth function satisfying some natural conditions. We prove the existence and uniqueness of the global-in-time classical solution to the initial-boundary value problem when general large initial data are prescribed and the exponent [Formula: see text] is sufficiently small. A similar result is also established for planar Hall-MHD equations.
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31

Van Hoolst, T. "Quadratic and Cubic Couplings of Oscillation Modes of Stars." International Astronomical Union Colloquium 155 (1995): 287–88. http://dx.doi.org/10.1017/s0252921100037131.

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The strength of nonlinear interactions of oscillation modes of stars is determined by the amplitudes as well as by the eigenfunctions of the oscillation modes. The intrinsic couplings of modes through their eigenfunctions can be described by coupling coefficients. Here, we concentrate on quadratic and cubic coupling coefficients that describe the nonlinear coupling of modes with itself and are called self-coupling coefficients.We considered radial and nonradial oscillation modes of polytropic models with degrees of central condensation that correspond to central condensations of main sequence stars to highly condensed evolved stars. We study the influence of the radial order and the degree of the oscillation mode on the self- coupling coefficients.
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32

Murphy, J. O., and R. Fiedler. "Physical Structure of a Sequence of Two Zone Polytropic Stellar Models." Publications of the Astronomical Society of Australia 6, no. 2 (1985): 219–22. http://dx.doi.org/10.1017/s1323358000018154.

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AbstractExpressions for the physical structure of a sequence of two zone polytropic stellar models, based on composite analytical solutions of the Lane-Emden equation with indices n = 1 and n = 5, hâve been determined. The coefficients of vibrational stability for radial oscillations of this sequence of models have also been calculated and it is found that increasing the extent of the n = 5 outer zone has a stabilizing effect.
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33

Pu, Hong Bin, Yun Ping Zheng, Yu Chun Wang, Bai Song Cai, and Qi Liu. "Research on Modeling of Compressor Characteristics for Sichuan-East Gas Transmission Pipeline Project." Advanced Materials Research 468-471 (February 2012): 2393–98. http://dx.doi.org/10.4028/www.scientific.net/amr.468-471.2393.

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Optimized operation of compressor stations is of great importance for energy saving of Sichuan-East transmission pipeline at high flow rate. However, it is difficult to build an accurate mathematical model to describe the performance curves of centrifugal compressor due to the wide range of rotary speed. The achievements of this thesis are shown as follows. Firstly, the mathematic models for performance curves of the Euramerican centrifugal compressors were established. The optimized regression coefficients were solved rapidly and accurately by Zhan Chong-xi method. Secondly, the compressor ratio, polytropic efficiency, shaft power, outlet pressure, polytropic head and outlet temperature of centrifugal compressors at different flow rates and rotating speeds were calculated accurately. These results provides excellent modeling methods and reliable mathematics models of operating and managing compressor of Sichuan-East gas transmission pipeline. It was found that the lowest correlative index of six optimized models was 0.9772, and the maximum error is 4.2869%.
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34

Dunn, Patrick F., Flint O. Thomas, James B. Leighton, and Dayu Lv. "Determination of Henry’s law constant and the diffusion and polytropic coefficients of air in aviation fuel." Fuel 90, no. 3 (March 2011): 1257–63. http://dx.doi.org/10.1016/j.fuel.2010.11.039.

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35

Borovkov, Aleksey, Igor Voinov, Yuri Galerkin, Aleksandr Nikiforov, Maksim Nikitin, Olga Solovyeva, and Kirill Kabalyk. "Issues of gas dynamic characteristics modeling: a study on a centrifugal compressor model stage." E3S Web of Conferences 140 (2019): 06003. http://dx.doi.org/10.1051/e3sconf/201914006003.

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The paper presents the results of CFD-calculations of a centrifugal compressor stage with a high-pressure 3D impeller and a vaneless diffuser. The stage was designed by Prof. A. M. Simonov in the Problem Laboratory of Compressor LPI according to the following design parameters: flow rate coefficient 0.080, loading factor 0.74, and the relative Mach number 0.78. Two design grids were used: 2.4 and 4.4 million cells for the sector with one blade. The entire stage was calculated with a sparser grid. Special “Stage” interface conditions are used to interface the gas-dynamic parameters at the boundary regions. The SST turbulence model was used in the calculations. The results of efficiency characteristics and work coefficient comparison showed the following: in design flow rate all three variants of the calculation overstate the loading factor by 14.3%; the calculated characteristics of polytrophic work coefficient in the staging of 360 degrees are closest to the experimental characteristics, but the absolute value is greater than 12% at a flow rate coefficient of 0.085; the maximum calculated efficiency of a stage (the circle of 360 degrees) is almost equal to the measured maximum efficiency.
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36

Huang, Bingkang, and Yongkai Liao. "Global stability of combination of viscous contact wave with rarefaction wave for compressible Navier–Stokes equations with temperature-dependent viscosity." Mathematical Models and Methods in Applied Sciences 27, no. 12 (September 20, 2017): 2321–79. http://dx.doi.org/10.1142/s0218202517500464.

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We study the nonlinear stability of a composite wave pattern, which is a combination of a viscous contact wave with a rarefaction wave, to the Cauchy problem of one-dimensional compressible Navier–Stokes equations for a viscous and heat conducting ideal polytropic gas with large initial perturbation when the transport coefficients depend on both temperature and density. Our main idea is to use the “smallness mechanism” induced by the structures of the equations under consideration and the smallness of the strengths of the two elementary waves to control the possible growth of the solutions caused by the nonlinearities of the equations, the interactions between the solutions themselves and the wave pattern, and the interactions of waves between different families. The main ingredient in the analysis is to derive the uniform positive lower and upper bounds on the specific volume and the temperature.
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37

Mikułowski, Grzegorz, and Rafał Wiszowaty. "Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification." Mathematical Problems in Engineering 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7074206.

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Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA), which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.
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38

Perri, Barbara, Allan Sacha Brun, Antoine Strugarek, and Victor Réville. "Impact of solar magnetic field amplitude and geometry on cosmic rays diffusion coefficients in the inner heliosphere." Journal of Space Weather and Space Climate 10 (2020): 55. http://dx.doi.org/10.1051/swsc/2020057.

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Cosmic rays are remarkable tracers of solar events when they are associated with solar flares, but also galactic events such as supernova remnants when they come from outside our solar system. Solar Energetic Particles (SEPs) are correlated with the 11-year solar cycle while Galactic Cosmic Rays (GCRs) are anti-correlated due to their interaction with the heliospheric magnetic field and the solar wind. Our aim is to quantify separately the impact of the amplitude and the geometry of the magnetic field, both evolving during the solar cycle, on the propagation of cosmic rays of various energies in the inner heliosphere (within Earth orbit). We focus especially on the diffusion caused by the magnetic field along and across the field lines. To do so, we use the results of 3D magnetohydrodynamics (MHD) wind simulations running from the lower corona up to 1 AU. This gives us the structure of the wind and the corresponding magnetic field. The wind is modeled using a polytropic approximation, and fits and power laws are used to account for the turbulence. Using these results, we compute the parallel and perpendicular diffusion coefficients of the Parker cosmic ray transport equation, yielding 3D maps of the diffusion of cosmic rays in the inner heliosphere. By varying the amplitude of the magnetic field, we change the amplitude of the diffusion by the same factor, and the radial gradients by changing the spread of the current sheet. By varying the geometry of the magnetic field, we change the latitudinal gradients of diffusion by changing the position of the current sheets. By varying the energy, we show that the distribution of values for SEPs is more peaked than GCRs. For realistic solar configurations, we show that diffusion is highly non-axisymmetric due to the configuration of the current sheets, and that the distribution varies a lot with the distance to the Sun with a drift of the peak value. This study shows that numerical simulations, combined with theory, can help quantify better the influence of the various magnetic field parameters on the propagation of cosmic rays. This study is a first step towards the resolution of the complete Parker transport equation to generate synthetic cosmic rays rates from numerical simulations.
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39

Nakariakov, Valery M., and Dmitrii Y. Kolotkov. "Magnetohydrodynamic Waves in the Solar Corona." Annual Review of Astronomy and Astrophysics 58, no. 1 (August 18, 2020): 441–81. http://dx.doi.org/10.1146/annurev-astro-032320-042940.

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The corona of the Sun is a unique environment in which magnetohydrodynamic (MHD) waves, one of the fundamental processes of plasma astrophysics, are open to a direct study. There is striking progress in both observational and theoretical research of MHD wave processes in the corona, with the main recent achievements summarized as follows: ▪ Both periods and wavelengths of the principal MHD modes of coronal plasma structures, such as kink, slow and sausage modes, are confidently resolved. ▪ Scalings of various parameters of detected waves and waveguiding plasma structures allow for the validation of theoretical models. In particular, kink oscillation period scales linearly with the length of the oscillating coronal loop, clearly indicating that they are eigenmodes of the loop. Damping of decaying kink and standing slow oscillations depends on the oscillation amplitudes, demonstrating the importance of nonlinear damping. ▪ The dominant excitation mechanism for decaying kink oscillations is associated with magnetized plasma eruptions. Propagating slow waves are caused by the leakage of chromospheric oscillations. Fast wave trains could be formed by waveguide dispersion. ▪ The knowledge gained in the study of coronal MHD waves provides ground for seismological probing of coronal plasma parameters, such as the Alfvén speed, the magnetic field and its topology, stratification, temperature, fine structuring, polytropic index, and transport coefficients.
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40

Дерябин, Сергей Львович, and Анна Сергеевна Кирьянова. "Construction of two-dimensional flows in physical space arising after the decay of a special discontinuity." Вычислительные технологии, no. 4(25) (September 16, 2020): 4–19. http://dx.doi.org/10.25743/ict.2020.25.4.002.

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Рассмотрены двумерные изэнтропические течения политропного газа, возникающие в начальный момент времени после мгновенного разрушения непроницаемой стенки, отделяющей неоднородный покоящийся газ от вакуума. В качестве математической модели используется система уравнений газовой динамики с учетом действия силы тяжести. В системе уравнений газовой динамики вводится автомодельная особенность в переменную x и для полученной системы ставится задача Коши с данными на звуковой характеристике. Решение начально-краевой задачи строится в виде степенного ряда. Коэффициенты ряда находятся при интегрировании обыкновенных дифференциальных уравнений. Для доказательства сходимости этого ряда ставится начально-краевая задача в пространстве других независимых переменных, а решение строится в виде своего сходящегося степенного ряда, и доказывается эквивалентность решений первой и второй начально-краевых задач The aim of this study is to construct a solution to the problem of the decay of a special discontinuity in physical space, i.e., two-dimensional isentropic flows of polytropic gas, arising after the instantaneous destruction of an impenetrable wall that separates an inhomogeneous resting gas from a vacuum. The study takes into account the effect of gravity. Research Methods. A variable, which governs the evolution of the self-similar singularity from the initial interface is introduced into the system of equations of gas dynamics. For the resulting system, the Cauchy problem is posed with prescribed values on the sound characteristic. The solution to this problem is constructed in the form of power series. The coefficients of the series are determined by solving algebraic and ordinary differential equations. Further, to prove the convergence of this series, an initial-boundary-value problem is posed in a special functional space. The solution to this initial-boundary value problem is constructed in the form of its convergent power series and the equivalence of solutions for the first and second initial-boundary value problems is proved. Solutions of the problem for the decay of a special discontinuity are constructed in the form of convergent power series. The equivalence of solutions in the physical and special functional space is proved. Conclusions. The solution constructed in physical space determines the initial conditions for the difference scheme for the numerical simulation of the given characteristic Cauchy problem, while the one, built in a special functional space, allows setting boundary conditions for this scheme
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41

Qi, Gong W., and X. Hong Zhang. "Effect of a volute on the unsteady flow in the vane diffuser of a centrifugal compressor." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 230, no. 8 (October 17, 2016): 773–91. http://dx.doi.org/10.1177/0957650916673935.

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A volute is the only circumferential asymmetric component in a centrifugal compressor, and thus, it should account for the circumferential asymmetry of the flow in a vane diffuser. This study performs a transient numerical analysis to investigate the effect of a volute on the flow in the vane diffuser of a centrifugal compressor under three operating conditions (near-stall, middle, and high mass flow). We compare numerical and experimental performance of the compressor, including polytropic efficiency, total pressure ratio, and unsteady pressure on a diffuser vane. The numerical scheme is proven valid owing to the fact that the numerical and experimental results considerably agree well with each other. Under middle and high mass flow conditions, the time-averaged static pressure recovery and the total pressure loss coefficients for all the diffuser passages indicate that the performance of the passages near and upstream of the volute tongue is affected negatively by the volute, whereas that of the passages downstream of the volute tongue is less affected. Under near-stall condition, the performance of all the passages is disturbed, and the diffuser passage marked as DP 3 demonstrates the worst performance. Investigation on the time-averaged aerodynamic forces, loading, and pressure on the vanes yields results that are consistent with those of the investigation on the performance of the passages. The harmonics with 0.5 fb and fb, which are included in the unsteady loading and pressure on the pressure and suction sides of the vanes, are dominant, where fb is the impeller main and splitter blades passing frequency. Their amplitude values increase as mass flow deviates from the middle mass flow condition. Under middle and high mass flow conditions, the harmonic with 0.5 fb is affected more negatively because of the larger amplitude on the vanes near and upstream of the volute tongue than those downstream, whereas the harmonic with fb is less affected by the volute. Under the near-stall condition, the transient vorticity fields along with the harmonics of 0.5 fb and fb are investigated to evaluate the performance of the diffuser passages. DP 3, which is located at approximately 90° downstream of the volute tongue, suffers the strongest flow deterioration and is inferred to stall first. Further researches for designing more matching diffuser/volute combination will be performed by referring this study.
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42

Ferrari, Alessandro, Oscar Vento, and Tantan Zhang. "The Polytropic Approach in Modeling Compressible Flows Through Constant Cross-Section Pipes." Journal of Fluids Engineering 143, no. 9 (May 27, 2021). http://dx.doi.org/10.1115/1.4050801.

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Abstract A compressible flow with wall friction has been predicted in a constant cross section duct by means of a barotropic modeling approach, and new analytical formulas have been proposed that also allow any possible heat transfer to the walls to be taken into account. A comparison between the distributions of the steady-state flow properties, pertaining to the new formulas, and those of a classic Fanno analysis has been performed. In order to better understand the limits of the polytropic approach in nearly chocked flow applications, a numerical code, which adopts a variable polytropic coefficient along the duct, has been developed. The steady-state numerical distributions along the pipe, obtained for either a viscous adiabatic or an inviscid diabatic flow by means of this approach, coincide with those of the Fanno and Rayleigh models for Mach numbers up to 1. A constant polytropic exponent can be adopted for a Fanno flow that is far from choking conditions, while it cannot be adopted for the simulation of a Rayleigh flow, even when the flow is not close to choking conditions. Finally, under the assumption of diabatic flows with wall friction, the polytropic approach, with a constant polytropic exponent, is shown to be able to accurately approximate cases in which no local maximum is present for the temperature along the duct. The Mach number value at the location where the local maximum temperature possibly occurs has been obtained by means of a new analytical formula.
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43

Hazby, Hamid, Michael Casey, and Luboš Březina. "Effect of Leakage Flows on the Performance of a Family of Inline Centrifugal Compressors." Journal of Turbomachinery 141, no. 9 (June 3, 2019). http://dx.doi.org/10.1115/1.4043786.

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The impact of the hub and shroud leakage flows on the compressor efficiency has been investigated for four compressor stages with flow coefficients of 0.017, 0.0265, 0.063, and 0.118 belonging to a family of centrifugal compressor stages, designed for process compressor applications. A very good agreement was observed between the measured and predicted performance when the detailed geometrical features were included in the calculations. The computational fluid dynamics (CFD) calculations indicated that addition of leakage cavities and leakage flows resulted in about 3% drop in stage polytropic efficiency for the highest flow coefficient stage. The detrimental effect of leakages increased to about 8% for the lowest flow coefficient stage investigated here. The increase in the compressor work input due to the disc windage and the leakage recirculation was estimated from the CFD calculations and compared with values obtained using 1D methods, showing a very good agreement between the two. The impact of parasitic losses on compressor efficiency has been investigated and the contribution of various loss sources to the stage efficiency is discussed.
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44

Oleynik, Yuriy Anatolyevich, Sergey Alekseyevich Saprykin, and Svetlana Naumenko. "Analyzing the Methods of Computation of the Polytropic Coefficient of Efficiency of the Centrifugal Super-charger." NTU "KhPI" Bulletin: Power and heat engineering processes and equipment, no. 11 (July 14, 2018). http://dx.doi.org/10.20998/2078-774x.2018.11.11.

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45

Hanschke, Benjamin, Arnold Kühhorn, Sven Schrape, and Thomas Giersch. "Consequences of Borescope Blending Repairs on Modern High Pressure Compressor Blisk Aeroelasticity." Journal of Turbomachinery 141, no. 2 (January 16, 2019). http://dx.doi.org/10.1115/1.4041672.

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Objective of this paper is to analyze the consequences of borescope blending repairs on the aeroelastic behavior of a modern high pressure compressor (HPC) blisk. To investigate the blending consequences in terms of aerodynamic damping and forcing changes, a generic blending of a rotor blade is modeled. Steady-state flow parameters like total pressure ratio, polytropic efficiency, and the loss coefficient are compared. Furthermore, aerodynamic damping is computed utilizing the aerodynamic influence coefficient (AIC) approach for both geometries. Results are confirmed by single passage flutter (SPF) simulations for specific interblade phase angles (IBPA) of interest. Finally, a unidirectional forced response analysis for the nominal and the blended rotor is conducted to determine the aerodynamic force exciting the blade motion. The frequency content as well as the forcing amplitudes is obtained from Fourier transformation of the forcing signal. As a result of the present analysis, the change of the blade vibration amplitude is computed.
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46

Wolfe, Tristan, Yu-Tai Lee, and Michael E. Slipper. "A Performance Prediction Model for Low-Speed Centrifugal Fans." Journal of Fluids Engineering 137, no. 5 (May 1, 2015). http://dx.doi.org/10.1115/1.4029397.

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A generalized model for mapping the trend of the performance characteristics of a double-discharge centrifugal fan is developed based on the work by Casey and Robinson (C&R), which formulated compressor performance maps for tip-speed Mach numbers ranging from 0.4 to 2 using test data obtained from turbochargers with vaneless diffusers. The current paper focuses on low-speed applications for Mach number below 0.4. The C&R model uses four nondimensional parameters at the design condition including the flow coefficient, the work input coefficient, the tip-speed Mach number, and the polytropic efficiency, in developing a prediction model that requires limited geometrical knowledge of the centrifugal turbomachine. For the low-speed fan case, the C&R formulas are further extended to a low-speed, incompressible analysis. The effort described in this paper begins by comparing generalized results using efficiency data obtained from a series of fan measurements to that using the C&R model. For the efficiency map, the C&R model is found to heavily depend on the ratio of the flow coefficient at peak efficiency to that at the choke flow condition. Since choke flow is generally not applicable in the low-speed centrifugal fan operational environment, an alternate, but accurate estimation method based on fan free delivery derived from the fan test data is presented. Using this new estimation procedure, the modified C&R model predicts reasonably well using the double-discharge centrifugal fan data for high-flow coefficients, but fails to correlate with the data for low-flow coefficients. To address this undesirable characteristic, additional modifications to the C&R model are also presented for the fan application at low flow conditions. A Reynolds number correction is implemented in the work input prediction of the C&R model to account for low-speed test conditions. The new model provides reasonable prediction with the current fan data in both work input and pressure rise coefficients. Along with the developments for the efficiency and work input coefficient maps, the use of fan shut-off and free delivery conditions are also discussed for low-speed applications.
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47

Qian, Yu, and David Z. Zhu. "Pressure oscillation of an air pocket beneath a water column in a vertical riser." Water Science and Technology, November 27, 2020. http://dx.doi.org/10.2166/wst.2020.560.

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Abstract Storm geysers have received significant attention lately due to its more frequent occurrences and the induced severe local flooding and infrastructure damages. Previous studies suggested that the air pocket pressure oscillated during geyser events especially in rapid filling process, but only the peak values were studied and the oscillation period was not discussed in detail. In this paper, a theoretical model was developed focusing on the period of the pressure oscillation induced by the expansion/compression of the air pocket below a water column in a vertical riser with film flow. It was found that the oscillation period was a function of the initial air pocket volume, initial air pocket pressure head, the riser diameter, and the initial water column length. The oscillation period increased with the air pocket pressure head and the air pocket volume, but decreased with the riser diameter and the polytropic coefficient. The oscillation period increased then decreased with an increasing water column length. Further, when considering the film flow along the riser, the oscillation period decreased slightly from the analytical solution. It was also found that the inflow rate change did not significantly influence the oscillation period.
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48

McGlumphy, Jonathan, Wing-Fai Ng, Steven R. Wellborn, and Severin Kempf. "3D Numerical Investigation of Tandem Airfoils for a Core Compressor Rotor." Journal of Turbomachinery 132, no. 3 (March 25, 2010). http://dx.doi.org/10.1115/1.3149283.

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The tandem airfoil has potential to do more work as a compressor blade than a single airfoil without incurring higher losses. The goal of this work is to evaluate the fluid mechanics of a tandem rotor in the rear stages of a core compressor. As such, the results are constrained to shock-free fully turbulent flow with thick endwall boundary layers at the inlet. A high hub-to-tip ratio 3D blade geometry was developed based on the best-case tandem airfoil configuration from a previous 2D study. The 3D tandem rotor was simulated in isolation, in order to scrutinize the fluid mechanisms of the rotor, which had not been previously well documented. A geometrically similar single blade rotor was also simulated under the same conditions for a baseline comparison. The tandem rotor was found to outperform its single blade counterpart by attaining a higher work coefficient, polytropic efficiency, and numerical stall margin. An examination of the tandem rotor fluid mechanics revealed that the forward blade acts in a similar manner to a conventional rotor. The aft blade is strongly dependent on the flow it receives from the forward blade, and tends to be more three-dimensional and nonuniform than the forward blade.
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49

Verheest, Frank. "Critical densities for Korteweg–de Vries-like acoustic solitons in multi-ion plasmas." Journal of Plasma Physics 81, no. 6 (November 20, 2015). http://dx.doi.org/10.1017/s0022377815001282.

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A generic proof has been given that, for the acoustic mode with the highest velocity in a plasma comprising a number of fluid species and one kind of inertialess electrons, even though there can be critical densities (making the coefficient of the quadratic nonlinearity in a Korteweg–de Vries equation vanish), no supercritical densities exist (requiring the simultaneous annulment of both the quadratic and cubic nonlinearities in a reductive perturbation treatment). Similar conclusions hold upon expansion of the corresponding Sagdeev pseudopotential treatment. When there is only one (hot) electron species, the highest-velocity mode is an ion-acoustic one, but if there is an additional cool electron species, with its inertia taken into account, the highest-velocity mode is an electron-acoustic mode in a two-temperature plasma. The cool fluid species can have various polytropic pressure–density relations, including adiabatic and/or isothermal variations, whereas the hot inertialess electrons are modelled by extensions of the usual Boltzmann description that include non-thermal effects through Cairns, kappa or Tsallis distributions. Together, in this way quite a number of plasma models are covered. Unfortunately, there seems to be no equivalent generic statement for the slow modes, so that these have to be studied on a case-by-case basis, which for models with more than three species is far from straightforward, given the parameter ranges to be discussed.
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50

Wang, Ting, and Jobaidur R. Khan. "Overspray and Interstage Fog Cooling in Gas Turbine Compressor Using Stage-Stacking Scheme—Part II: Case Study." Journal of Thermal Science and Engineering Applications 2, no. 3 (September 1, 2010). http://dx.doi.org/10.1115/1.4002755.

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A stage-by-stage wet compression theory and algorithm have been developed for overspray and interstage fogging in the compressor. These theory and algorithm are used to calculate the performance of an eight-stage compressor under both dry and wet compressions. A 2D compressor airfoil geometry and stage setting at the mean radius are employed. Six different cases with and without overspray are investigated and compared. The stage pressure ratio enhances during all fogging cases as does the overall pressure ratio, with saturated fogging (no overspray) achieving the highest pressure ratio. Saturated fogging reduces specific compressor work, but increases the total compressor power due to increased mass flow rate. The results of overspray and interstage spray unexpectedly show that both the specific and overall compressor power do not reduce but actually increase. Analysis shows that this increased power is contributed by the increased pressure ratio and, for interstage overspray, “recompression” contributes to more power consumption. Also it is unexpected to see that air density actually decreases, instead of increases, inside the compressor with overspray. Analysis shows that overspray induces an excessive reduction in temperature that leads to an appreciable reduction in pressure, so the increment of density due to reduced temperature is less than the decrement of air density affected by reduced pressure as air follows the polytropic relationship. In contrast, saturated fogging results in increased density as expected. After the interstage spray, the local blade loading immediately showed a significant increase. Fogging increases axial velocity, flow coefficient, blade inlet velocity, incidence angle, and tangential component of velocity. The analysis also assesses the use of an average shape factor in the generalized compressor stage performance curve when the compressor stage information and performance map are not available. The result indicates that using a constant shape factor might not be adequate because the compressor performance map may have changed with wet compression. The results of nonstage-stacking simulation are shown to underpredict the compressor power by about 6% and the net gas turbine output by about 2% in the studied cases.
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