Ideal Gas Equation Of State Research Articles

Nemchinov–Dyson solutions of the two-dimensional axisymmetric inviscid compressible flow equations

We investigate the two-dimensional ($2$D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the $2$D velocity field is space-time separable and linearly variable in each corresponding spatial coordinate, we proceed to derive an infinite family of elliptic or hyperbolic, uniformly expanding or contracting ``gas cloud'' solutions. Construction of specific example solutions belonging to this family is dependent on the solution of a system of nonlinear, coupled, second-order ordinary differential equations, and the prescription of an additional physical process of interest (e.g., uniform temperature or uniform entropy flow). The physical and computational implications of these solutions as pertaining to quantitative code verification or model qualification studies are discussed in some detail.

Analysis of real gas equation of state for CFD modelling of twin screw expanders with R245fa, R290, R1336mzz(Z) and R1233zd(E)

Abstract Positive displacement expanders are widely investigated and theirs models commonly use the REFPROP database to evaluate fluid properties. However, estimating procedures in CFD models using REFPROP result in heavy use of CPU time. Therefore, a study has been carried out to determine if simpler methods for fluid property estimation are suitable. The ANSYS CFX solver used includes a number of cubic equations of state, namely, the Redlich Kwong, Soave Redlich Kwong, Aungier Redlich Kwong and Peng Robinson. To determine their suitability, performance simulations were carried out with each of them, on a twin screw expander with a 4/5 rotor configuration and an “N” rotor profile, operating with R245fa, R290, R1336mzz(Z) and R1233zd(E). For each considered equation, the expander's performance results deviation from those obtained using REFPROP is evaluated. These results show that the ideal gas equation of state gives predictions of flow and power that deviate significantly from those determined with REFPROP. The alternatively available cubic equations give far better agreement. Of these, the RK equation has the highest deviation, although it differs by only 2.2% maximum from the REFPROP values. The PR equation yields the closest agreement with a deviation of the order of only 0.8%, while the deviation with both SRK and ARK equations is less than 1.1% maximum, practically negligible. Apart from the good agreement obtained, the use of the real gas equations, in place of REFPROP, resulted in a saving of approximately 43% in CPU operating time to obtain same level of convergence of the solver.

Magnetic Fluid Infiltrated Microbottle Resonator Sensor With Axial Confined Mode

We report a magnetic field sensor based on an optofluidic microbottle resonator (OFMBR) with whispering gallery mode (WGM) strongly confined in the axial direction, with the hollow core inherently easy to infiltrate the magnetic fluid. The device is simply fabricated along a silica capillary through a fusing splicer. And the influence of number of discharges on the size of the device is analyzed according to the state equation of ideal gas, which is verified by experimental results. In the magnetic field range from the critical value (40 Gs) to the saturated value (300 Gs), the resonant wavelength shifts linearly with the increase of magnetic field strength, with a sensitivity of 8.45 pm/Gs demonstrated, based on the axial confined mode of OFMBR with a Q-factor of 1.28 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">6</sup> . This sensor possesses advantages of simple structure, easy fabrication process, and compact size for magnetic field sensing.

Mechanism and numerical model of bubble effect in oil-paper insulation based on microtubule model

In this paper, a numerical model of bubble evolution is established by studying the microstructure of pressboard and the physical process of bubble generation. In the model, the porous structure of fibers is equivalent to microtubules, the gases in the bubbles are classified into two categories, and the ideal gas state equation is used to describe the bubble state. Then the pressure conditions at the bubble boundary and the evaporation rate of water are taken as solution conditions to solve the physical quantities in the state equation. The numerical model provides a new way to calculate the initial temperature of bubble escape (ITBE). And the bubble evolution inside the pressboard is obtained which is hard to be observed in experiment. After that, the influences of moisture content of pressboard and cellulose aging on ITBE in the numerical model are discussed. The model results show that the expansion rate of bubble is not uniform. Bubble growth is slow in the early stage of temperature rise, when the temperature reaches a certain threshold the growth rate of bubble radius increases significantly, which is of great significance to the temperature limit on oil-immersed power transformers.

Modification of the Electron Entropy Production in a Plasma.

A modified expression of the electron entropy production in a plasma is deduced by means of the Kelly equations of state instead of the ideal gas equations of state. From the Debye–Hückel model which considers the interaction between the charges, such equations of state are derived for a plasma and the entropy is deduced. The technique to obtain the modified entropy production is based on usual developments but including the modified equations of state giving the regular result plus some extra terms. We derive an expression of the modified entropy production in terms of the tensorial Hermitian moments by means of the irreducible tensorial Hermite polynomials.

Thermodynamic class II Szekeres–Szafron solutions. Regular models

In a recent paper (Coll et al 2019 Class. Quantum Grav. 36 175004) we have studied a family of Szekeres–Szafron solutions of class II in local thermal equilibrium (singular models). In this paper we deal with a similar study for all other class II Szekeres–Szafron solutions without symmetries. These models in local thermal equilibrium (regular models) are analyzed and their associated thermodynamic schemes are obtained. In particular, we focus on the subfamily of solutions which are compatible with the generic ideal gas equation of state (), and we analyze in depth two notable interpretations that follow on from the choice of two specific thermodynamic schemes: firstly, as a generic ideal gas in local thermal equilibrium and, secondly, as a model having the homogeneous temperature of the FLRW limit. The models above are shown to fulfill the general necessary macroscopic requirements for physical reality (positivity of matter density, internal energy and temperature, energy conditions and compressibility conditions) in wide domains of the spacetime.

Real Gas Models in Coupled Algorithms Numerical Recipes and Thermophysical Relations

In the majority of compressible flow CFD simulations, the standard ideal gas state equation is accurate enough. However, there is a range of applications where the deviations from the ideal gas behaviour is significant enough that performance predictions are no longer valid and more accurate models are needed. While a considerable amount of the literature has been written about the application of real gas state equations in CFD simulations, there is much less information on the numerical issues involved in the actual implementation of such models. The aim of this article is to present a robust implementation of real gas flow physics in an in-house, coupled, pressure-based solver, and highlight the main difference that arises as compared to standard ideal gas model. The consistency of the developed iterative procedures is demonstrated by first comparing against results obtained with a framework using perfect gas simplifications. The generality of the developed framework is tested by using the parameters from two different real gas state equations, namely the IAPWS-97 and the cubic state equations state equations. The highly polynomial IAPWS-97 formulation for water is applied to a transonic nozzle case where steam is expanded at transonic conditions until phase transition occurs. The cubic state equations are applied to a two stage radial compressor setup. Results are compared in terms of accuracy with a commercial code and measurement data. Results are also compared against simulations using the ideal gas model, highlighting the limitations of the later model. Finally, the effects of the real gas formulations on computational time are compared with results obtained using the ideal gas model.

Research on the Accuracy Control Technology of Automated Peritoneal Dialysis

The automated peritoneal dialysis is accepted increasingly. The automated peritoneal dialysis makes use of a device called automated peritoneal dialysis cycler to realize the automated treatment. The liquid quantity of dialysis treatment is an important index of peritoneal dialysis. Thus the flow calculation accuracy of the automated peritoneal dialysis cycler is one of the most important performances. However, due to the complex usage situations, the cyclers based on different principles are extremely affected by touching, flow resistance fluctuating, etc., which causes inaccuracy and instability. This paper investigated an accurate calculation model and a control algorithm to address these issues. Based on the State Equation of Ideal Gas, a calculation model is established. By analyzing the influence factors of time-varying flow resistance, a control algorithm is designed. A prototype with our method is developed and tested by experiments. The results show that the flow calculation errors are reduced significantly and the accuracy and stability are improved obviously. It proves that our method can realize an accurate flow calculating and effectively reduce errors and keep accuracy stable.

Equivalence between first-order causal and stable hydrodynamics and Israel-Stewart theory for boost-invariant systems with a constant relaxation time

We show that the recently formulated causal and stable first-order hydrodynamics has the same dynamics as Israel-Stewart theory for boost-invariant, Bjorken expanding systems with an ideal gas equation of state and a regulating sector determined by a constant relaxation time. In this case, the general solution of the new first-order formulation can be determined analytically.

ЭВОЛЮЦИЯ НЕФТЕГАЗОВОЙ СТРУИ, ИСТЕКАЮЩЕЙ ЧЕРЕЗ РАЗРЫВ МАГИСТРАЛЬНОГО НЕФТЕПРОВОДА (ГАЗОПРОВОДА), РАСПОЛОЖЕННОГО НА ДНЕ ВОДОЕМА

Актуальность исследования связана с растущим интересом к добыче углеводородов на дне Мирового океана. При этом многократно увеличивается опасность аварийного разлива нефтепродуктов в воду. Разливы нефти на платформах Ixtoc-1 и Deepwater Horizon в Мексиканском заливе продемонстрировали неготовность современных методов к быстрой ликвидации аварийных утечек. В связи с этим существует необходимость в исследовании затопленных струй, состоящих из смеси углеводородов (нефти и газа). Кроме этого, при глубоководных разливах многофазной смеси нефти и попутных газов могут образовываться кристаллогидраты, которые могут влиять на динамику распространения этих выбросов. Поэтому изучение динамики распространения струи с учетом гидратообразования позволит сократить время ликвидации возможных утечек. В данной работе рассматривается математическая модель формирования затопленной многофазной струи с учетом гидратообразования при различных начальных условиях. Цель: исследовать формирование затопленной струи в зависимости от начальных условий. Объекты: многофазная струя углеводородов; компоненты струи: нефть, газ, вода; композитные пузырьки, покрытые гидратной оболочкой; характер распространения струйного течения, процесс гидратообразования. Методы. Для описания процесса распространения затопленной струи используется интегральный Лагранжевый метод контрольного объема, согласно которому струя представляется в виде последовательности элементарных объемов, каждый из которых характеризуется линейными размерами и теплофизическими характеристиками. Распространение затопленной струи рассматривается для глубоководных разливов на дне океана, что соответствует случаю, когда на поверхности пузырьков начинают образовываться гидратные оболочки и газовый пузырек превращается в гидратный. Для описания процесса гидратообразования в работе принята предельная схема, согласно которой гидратообразвание лимитируется диффузией газа через гидратную оболочку. Результаты. Дополнена математическая модель течения многофазной затопленной струи с учётом образования гидрата на поверхности пузырьков. Получены зависимости теплофизических характеристик затопленной струи от вертикальной координаты, траектория распространения струи. Для пузырьков метана, которые покрываются гидратной оболочкой, применено уравнение состояния для реальных газов. В результате расчетов получены зависимости радиусов газовой и гидратной составляющих композитного пузырька и его плотности от вертикальной координаты. Установлено, что радиус гидратной составляющей пузырька убывает для случая, когда поведение газа описывается уравнением состояния для идеального газа, и растет для случая применения уравнения состояния для реального газа.

Dispersion and behavior of hydrogen for the safety design of hydrogen production plant attached with nuclear power plant

Development of nuclear energy and hydrogen energy both as renewable energy open up a vast range of prospects. The scheme for hydrogen generation station in nuclear power plant has been carried out in china. However, Nuclear Energy is expected to encourage a safety culture that prevents serious accidents while dispersion of hydrogen from a container produces a risk of combustion. The dispersion and behavior of hydrogen production plant attached with nuclear power plant are still poorly understood. In this paper, a dispersion of hydrogen model is established and is calculated under two typical condition with corrected ideal gas state equation. The flammability of hydrogen after dispersion is studied. The range of flammability of dispersion of hydrogen production plant with different pressures, positions and temperatures is obtained. This work could contribute to the marginal hydrogen safety design for hydrogen production station and lay the foundation for the establishment of a safe distance standard that it's necessary to prevent hydrogen explosion.

Thermodynamic analysis of natural convection supercritical water flow past a stretching sheet using an equation of state approach

The present numerical study examines the free convection heat transfer characteristics of supercritical water flow past a stretching sheet. A suitable equation for the thermal expansion coefficient in a supercritical fluid region is derived based on the equation of state (EOS) approach in terms of compressibility factor, pressure, and temperature. In the present study, the Redlich–Kwong equation of state (RK-EOS) is used to calculate the thermal expansion coefficient in the supercritical region. The values of the thermal expansion coefficient calculated through RK-EOS lies close to the NIST data values when compared to the other equations of state like the Van der Waals equation of state and ideal gas EOS. Also, the behaviour of Nusselt number is studied to characterize the heat transfer characteristics of supercritical water. However, the equations governing the supercritical fluid flow past a stretching sheet are coupled and nonlinear in nature. Hence, the Runge–Kutta fourth-order integration scheme with shooting technique is used to solve these equations. Numerical computations are performed for supercritical water under the influence of various control parameters. Similarity solutions are obtained in terms of flow profiles in the supercritical fluid region. The present study reports that the normal velocity profile decreases and the temperature field increases for increasing values of reduced pressure and reduced temperature. Also, the axial velocity profile shows the dual behaviour for increasing values of unsteady parameter, reduced temperature, and reduced pressure in the supercritical boundary layer region. Furthermore, the component of the normal velocity profile decays for increasing values of the unsteady parameter in the supercritical fluid region. The calculated values of the thermal expansion coefficient using RK-EOS lies in the proximity of NIST data values when compared to Van der Waals and ideal gas equations of state. Also, the local skin-friction coefficient decreases for increasing values of reduced pressure and reduced temperature. Furthermore, the magnitude of local heat transfer rate increases with increasing values of unsteady parameter. The RK-EOS is the suitable EOS approach for predicting the free convection properties of water in a supercritical region.

Galaxy cluster hydrostatic masses using Tolman–Oppenheimer–Volkoff equation

Motivated by previous studies in literature about the potential importance of relativistic corrections to galaxy cluster hydrostatic masses, we calculate the masses of 12 relaxed clusters (with Chandra X-ray data) using the Tolman-Oppenheimer-Volkov (TOV) equation of hydrostatic equilibrium and the ideal gas equation of state. Analytical formulae for gas density and temperature profiles for these clusters, previously derived by Vikhlinin et al (astro-ph/0507092) were used to obtain these masses. We compare the TOV-based masses with those obtained using the corresponding Newtonian equation of hydrostatic equilibrium. We find that the fractional relative difference between the two masses are negligible, corresponding to $\sim \mathcal{O}(10^{-5})$.

Mathematical Model of Small-Volume Air Vessel Based on Real Gas Equation

The gas characteristics of an air vessel is one of the key parameters that determines the protective effect on water hammer pressure. Because of the limitation of the ideal gas state equation applied for a small-volume vessel, the Van der Waals (VDW) equation and Redlich–Kwong (R–K) equation are proposed to numerically simulate the pressure oscillation. The R–K polytropic equation is derived under the assumption that the volume occupied by the air molecules themselves could be ignored. The effects of cohesion pressure under real gas equations are analyzed by using the method of characteristics under different vessel diameters. The results show that cohesion pressure has a significant effect on the small volume vessel. During the first phase of the transient period, the minimum pressure and water depth calculated by a real gas model are obviously lower than that calculated by an ideal gas model. Because VDW cohesion pressure has a stronger influence on the air vessel pressure compared to R–K air cohesion pressure, the amplitude of head oscillation in the vessel calculated by the R–K equation becomes larger. The numerical results of real gas equations can provide a higher safe-depth margin of the water depth required in the small-volume vessel, resulting in the safe operation of the practical pumping pipeline system.

Numerical investigation on effects of fuel tube diameter and co-flow velocity in a methane/air non-premixed flame

In this paper, the effects of variations in the fuel tube diameter and co-flow velocity in the combustion chamber on the non-premixed laminar flame are investigated. Methane gas, as a fuel, and the dry air, as an oxidizer. The size of the combustion chamber is constant and, by changing the fuel tube diameter and co-flow velocity, changes in the numerical values of temperature, velocity, density, and concentration of the species of reactants and products in the combustion chamber are evaluated. A finite volume method (FVM) with staggered grids is used for numerical solution. Equations of continuity, momentum, energy, ideal gas state and kinetic equations with thermodynamic and thermochemical information of chemical species are solved using numerical method of SIMPLE. The convective terms are discretized using Power Law scheme (PLS).The calculations are carried out using Dryer and Glassman’s three-stage chemical kinetics. Variable under relaxation factor dependent on temperature has been used to handle the solving chemical kinetic equations. Initially, the results of calculations are compared with the experimental and numerical results of other researchers, which show an acceptable agreement.. The results show that increasing the diameter ratio reduces the length of the flame. With the large ratio of the diameters, location of the combustion’s maximum temperature is at the chamber entrance and for the small diameter ratios, its location moves to nearly outlet of the chamber. In addition, the reduction of the ratio of the diameters increases the flame lift-off. Also the results show that the optimal of diameters ratio is 0.6 in order to prevent the lift-off flame and return the flame to inlet opening of combustion chamber. Also increasing the fuel tube diameter, increases the amount of oxygen due to the return flow formation and decreases the volumes of water vapor and carbon dioxide in the centerline of the combustion chamber. The flame length attains the maximum possible value with respect to diameter ratio of 0.6 at inlet air velocity of 0.3 m/s. In addition, it is shown that increasing the air velocity increases the total flame lift-off and flame length until the air velocity reaches the value of around 0.3 m/s and by increasing the air velocity more than 0.3 m/s, the total flame lift-off and flame length decreases.

Development and testing of a mathematical model of the engine pre-start operation at low ambient temperatures

Starting a cold diesel engine, in the Arctic, with minimum temperatures below -60 ° C, presents significant difficulties due to: low temperature of the air charge; increased resistance to cranking the crankshaft and moving other kinematically related parts (pistons, parts of the gas distribution mechanism; etc.) due to the increased viscosity of the oil, deterioration of fuel atomization conditions, enhanced heat transfer to the cylinder wall, loss of part of the air charge. This article is devoted to solving the urgent problem associated with the development of a theoretical framework that provides comprehensive simulation of the starting mode of a diesel engine at low ambient temperatures when using start-up facilitators. The article proposes a mathematical model of a diesel engine, based on thermal mechanics (thermodynamics of open systems), which reflects the main features of an internal combustion engine (ICE) as a system that converts energy over time. The system of equations of the mathematical model is based on the laws of conservation of energy, mass, equations of motion of solid links and includes differential equations of the rate of change of temperature and density of the working fluid in the cylinder and in the engine crankcase, ideal gas equation of state, as well as differential equations of change of angular velocity and angle of rotation of engine shaft. The mathematical model is tested on the example of a 1CH9.5 / 8.0 diesel engine. The article presents graphs of changes in the angular velocity, pressure and temperature in the cylinder, as well as the results of calculating the engine pre-start operation at various low ambient temperatures in comparison with the results of full-scale experiments conducted in the refrigerating chamber.

Математическое моделирование процесса функционирования одноцилиндрового дизеля с воздушным охлаждением с учетом расхода картерных газов

At present, the most effective method for studying internal combustion engines (ICE) is mathe-matical modeling and computational experiment. The use of a computational experiment can signif-icantly reduce material and time costs in the research, design and refinement of the internal combus-tion engine. At the same time, despite the high level of the applied mathematical models, there are practically no studies aimed at establishing the regularities of the influence of the state of the cylin-der-piston group (CPG) on the crankcase gas consumption and other indicators of engine operation at steady-state and transient modes. This article is devoted to solving an urgent problem associated with the development of a theoretical base that provides a comprehensive simulation of steady-state and transient modes of diesel engine operation, taking into account the consumption of crankcase gases. The article presents a mathematical model of a diesel engine based on thermal mechanics, which reflects the main features of the engine as a system that converts energy in time. The system of equations of the mathematical model is based on the laws of conservation of energy, mass, equa-tions of motion of solid links and includes differential equations for the rates of change in the tem-perature and density of the working fluid in the cylinder and in the crankcase of the internal com-bustion engine, the ideal gas equation of state, as well as differential equations for the change in the angular speed and angle of motor shaft rotation. The mathematical model is tested on the example of a small-sized single-cylinder diesel engine 1Ch9.5 / 8.0 with air cooling. This type of engine is widely used for small-scale mechanization in agriculture, generator sets, etc. The article presents the results of calculations of a number of engine operating modes in comparison with the results of field tests carried out at the test bench.

Recitation program to improve students’ conceptual understanding of Thermodynamics

The purpose of this research was to analyze the improvement of students’ mastery of thermodynamics concepts after they learn three packages of recitation program that cover state equation of ideal gas, The First Law of Thermodynamic, and The Second Law of Thermodynamic. The subjects consisted of 21 undergraduate students enrolling in the fundamental physics course. The results showed that the recitation program improved students’ conceptual understanding of thermodynamic with the d-effect size of 2.51 and N-gain of 0.365. The program effectively helps the students in constructing P-V diagrams and understanding the relationship between the average particle’s kinetic energy and temperature of the gas. However, some contents need to be improved to help the students more fluent in determining total work and heat involved in any cyclic process.

Effect of CO2 diluent on the formation of pollutant NOx in the laminar non-premixed methane-air flame

In this paper, the effects of changes in the concentration of diluent CO2 in methane and air fuels are investigated. A finite volume method (FVM) with staggered grids is used for numerical solution. Equations of continuity, momentum, energy, ideal gas state and kinetic equations with thermodynamic and thermo-chemical information of chemical species are solved using the numerical method of SIMPLE. The convective terms are discretized using Power Law scheme (PLS). The under-relaxation factor dependent on temperature has been utilized to solve the chemical kinetic equations. In this research, by increasing the diluent mass fraction, the mass fraction of the fuel is diminished to the same extent. Therefore, the sum of the diluent and fuel mass fraction values remains constant. The results depicted that as the amount of CO2 diluent in the fuel increases, the total lift-off height and flame length decreases linearly, and the maximum temperature in the combustion chamber becomes smaller than that at the inlet of the chamber. When the concentration of CO2 increases in the fuel, the temperature changes become negligible at the inlet of the combustion chamber. By using the CO2 diluent, shorter combustion chambers can be used. While the diluent is used, the increase in the length of the combustion chamber will not have any effect on the NOx emissions reduction. Therefore, the more concentration of the diluent is used, the smaller the combustion chamber can be selected. Moreover, by increasing the diluent, NOx pollutant decreases in the combustion chamber.

Efficient calculation of the hydrodynamic coefficients and dynamic stiffness of an air-spring type vibration absorber

Integration of an air-spring device into an offshore platform can be an effective solution to modify the system properties, such as the restoring stiffness. In this study, the dynamic stiffness due to the linear vibration of the air and fluid entrapped inside an air-spring type vibration absorber is investigated. The device is modelled as a hollow column with a closed top and floats vertically in a water of constant depth. At the initial time, the free surfaces inside and outside the device are at the same level and there is an amount of air entrapped above the inner water surface. Within the device, the variation to the air pressure is assumed to occur adiabatically and the free-surface boundary condition is derived based on the ideal gas state equation. Energy dissipation is introduced into the region within the device by adding a resistance force on the inner free surface. The wave radiation due to the heave motion of the device is then concerned and an analytical model is developed to evaluate the associated hydrodynamic coefficients and the induced dynamic stiffness by using the method of separation of variables in conjunction with the matching technology. An alternative solution of the dynamic stiffness has also been developed based on a decomposition of the total velocity potential into two parts which depend purely on the oscillation of the device and the dynamic air pressure applied on the inner free surface, respectively. Based on the developed model, detailed numerical analysis is performed. The relative phases between the body motion and the dynamic stiffness are discussed for different wave conditions and geometric parameters.