scholarly journals Analysis of the application of ideal gas equation of state

2021 ◽  
Vol 252 ◽  
pp. 03019
Author(s):  
Yarong Wang ◽  
Peirong Wang
Keyword(s):  
Equation Of State ◽  
Molecular Motion ◽  
Interaction Force ◽  
Ideal Gas ◽  
Real Gas ◽  
Mathematical Relation

In nature, the molecules of real gas have a certain volume and have interaction force with each other. It is difficult to find the molecular motion law of real gas because of its complex properties. An ideal gas is an imaginary substance that does not exist in reality. Its molecules are elastic, non volume particles, and there is no interaction among them. This kind of gas is simple in nature and easy to be analyzed and calculated by simple mathematical relation. The introduction of the concept of ideal gas greatly simplifies the analysis of some thermodynamic problems.

Simple Predictions for the Sonic Conditions in a Real Gas

1977 ◽  
Vol 99 (1) ◽  
pp. 217-225 ◽  
Author(s):  
P. A. Thompson ◽  
D. A. Sullivan
Keyword(s):  
Equation Of State ◽  
Closed Form ◽  
Thermodynamic Parameters ◽  
Ideal Gas ◽  
Accurate Prediction ◽  
Bernoulli Equation ◽  
Real Gas ◽  
Similarity Principle ◽  
Isentropic Flow ◽  
The Ideal

The steady isentropic flow of a fluid which satisfies an arbitrary equation of state is treated, with emphasis on the prediction of pressure, density, velocity, and massflow at the sonic state. The isentrope P(v) is described by a limited number of thermodynamic parameters, the most important ones being the soundspeed c and fundamental derivative Γ. Using this description, an application of the Bernoulli equation and appropriate thermodynamic relations yields simple closed-form predictions for the sonic state. These predictions are recognizable as generalizations of well-known ideal gas formulas, but are applicable to fluids very far removed from the ideal gas state, even including liquids. Comparisons in several cases for which precise independent solutions are available suggest that the methods found here are accurate. A derived similarity principle allows the accurate prediction of sonic properties from any single given sonic property.

scholarly journals Compressible flow at high pressure with linear equation of state

2018 ◽  
Vol 843 ◽  
pp. 244-292 ◽  
Author(s):  
William A. Sirignano
Keyword(s):  
Equation Of State ◽  
Compressible Flow ◽  
Sound Speed ◽  
Ideal Gas ◽  
Real Gas ◽  
Cubic Equation Of State ◽  
Cubic Equation ◽  
Wide Range ◽  
Real Gas Effects ◽  
Flow Configurations

Compressible flow varies from ideal-gas behaviour at high pressures where molecular interactions become important. It is widely accepted that density is well described through a cubic equation of state while enthalpy and sound speed are functions of both temperature and pressure, based on two parameters, $A$ and $B$, related to intermolecular attraction and repulsion, respectively. Assuming small variations from ideal-gas behaviour, a closed-form approximate solution is obtained that is valid over a wide range of conditions. An expansion in these molecular interaction parameters simplifies relations for flow variables, elucidating the role of molecular repulsion and attraction in variations from ideal-gas behaviour. Real-gas modifications in density, enthalpy and sound speed for a given pressure and temperature lead to variations in many basic compressible-flow configurations. Sometimes, the variations can be substantial in quantitative or qualitative terms. The new approach is applied to choked-nozzle flow, isentropic flow, nonlinear wave propagation and flow across a shock wave, all for a real gas. Modifications are obtained for allowable mass flow through a choked nozzle, nozzle thrust, sonic wave speed, Riemann invariants, Prandtl’s shock relation and the Rankine–Hugoniot relations. Forced acoustic oscillations can show substantial augmentation of pressure amplitudes when real-gas effects are taken into account. Shocks at higher temperatures and pressures can have larger pressure jumps with real-gas effects. Weak shocks decay to zero strength at sonic speed. The proposed framework can rely on any cubic equation of state and can be applied to multicomponent flows or to more complex flow configurations.

Numerical Approach for Real Gas Simulations: Part I — Tabular Fluid Properties for Real Gas Analysis

2017 ◽  
Author(s):  
Francisco Moraga ◽  
Doug Hofer ◽  
Swati Saxena ◽  
Ramakrishna Mallina
Keyword(s):  
Equation Of State ◽  
Error Analysis ◽  
Critical Point ◽  
Ideal Gas ◽  
Phase Region ◽  
System Level ◽  
Component Level ◽  
Power Cycles ◽  
Real Gas ◽  
Fluid Properties

Recently there has been increased interest in the use of carbon dioxide (CO2) in closed loop power cycles. As these power cycles capitalize on the non-ideal gas behavior of CO2, their analysis both at the system level and at the detailed component level requires an advanced equation of state. Commonly used analytical equations of state as BWRS (BenedictWebbRubin equation of State) or Peng-Robinson are known to have high errors near the critical point and are thus unsuitable for the analysis of cycles or components where the flow conditions approach the critical point. An accurate equation of state is required at all phases of the development process from high level cycle calculations to the detailed component CFD. The NIST RefProp software package provides accurate CO2 fluid properties across the thermodynamic space but suffers from high computational over-head. This study is presented in two parts. Part I (this part) of this paper describes an approach to creating a tabular representation of the equation of state that is applicable to any fluid. This approach is applied to generating an accurate, fast and robust tabular representation of the RefProp CO2 properties and an error analysis is performed to meet the accuracy requirements. The paper also discusses two approaches used to define speed of sound in the two-phase region and their sensitivity analysis on the 3D compressor flow. Part II of the paper details the numerical simulations of a supercritical CO2 centrifugal compressor using the tabular approach. This paper shows that table resolution can be tailored to match the accuracy requirements while minimizing the time used to evaluate the tabulated thermo-physical functions. Error analysis are shown to demonstrate the level of accuracy possible with this approach.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

Pneumatic Mechanism of Gas Cooled or Heated Through a Throttle Orifice

2011 ◽  
Vol 141 ◽  
pp. 408-412 ◽  
Author(s):  
Yao Bao Yin ◽  
Ling Li
Keyword(s):  
Equation Of State ◽  
Total Energy ◽  
Negative Energy ◽  
Experimental Results ◽  
Attractive Force ◽  
Positive Energy ◽  
Real Gas ◽  
Thomson Coefficient ◽  
Theoretical Results ◽  
Conversion Temperature

The mechanism of gas cooled or heated through a pneumatic throttle orifice is analyzed. Supposing the total energy of the gas is constant, if the force between the molecules does positive energy, it makes gas heated; if it does negative energy, it makes gas cooled. The conversion temperature of gas is an evaluation parameter for repulsive or attractive force. It has utilized Joule-Thomson coefficient and real gas equation of state to obtain the characteristics of conversion temperature, and the relationships between the molecules distance and the phenomenon of gas cooled or heated after throttle at normal temperature by the conversion characteristics are achieved. The experimental results agreed well with the theoretical results.

The Structure of Laminar Premixed H2-Air Flames at Elevated Pressures

2000 ◽  
Vol 214 (4) ◽  
Author(s):  
M. El-Gamal ◽  
E. Gutheil ◽  
J. Warnatz
Keyword(s):  
Laminar Flame ◽  
Flame Structure ◽  
Ideal Gas ◽  
Fortran Program ◽  
Laminar Flame Speed ◽  
Real Gas ◽  
One Dimensional ◽  
Rocket Propulsion ◽  
Elevated Pressures ◽  
Engine Combustion

In high-pressure flames that occur in many practical combustion devices such as industrial furnaces, rocket propulsion and internal engine combustion, the assumption of an ideal gas is not appropriate. The present paper presents a model that includes modifications of the equation of state, transport and thermodynamic properties. The model is implemented into a Fortran program that was developed to simulate numerically one-dimensional planar premixed flames. The influence of the modifications for the real gas behavior on the laminar flame speed and on flame structure is illustrated for stoichiometric H

scholarly journals Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State

2021 ◽  
Vol 17 (1) ◽  
pp. 119-138
Author(s):  
M. R. Koroleva ◽  
◽  
O. V. Mishchenkova ◽  
V. A. Tenenev ◽  
T. Raeder ◽  
...  
Keyword(s):  
Equation Of State ◽  
Critical State ◽  
Stokes Equations ◽  
Safety Valve ◽  
Van Der Waals ◽  
Local Approximation ◽  
Critical Conditions ◽  
Nonlinear Processes ◽  
Real Gas ◽  
Van Der Waals Equation

The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions.

Thermoelasticity

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Equation Of State ◽  
Elastic Deformation ◽  
Additional Assumption ◽  
Polymer Network ◽  
Ideal Gas ◽  
Absolute Temperature ◽  
Constant Volume ◽  
Conformational Energy ◽  
Network Chain ◽  
Constant Deformation

The important postulate that intermolecular interactions are independent of extent of deformation leads directly to the conclusion that such interactions cannot contribute to an energy of elastic deformation ΔEel at constant volume. In the earliest theories of rubberlike elasticity, it was additionally assumed that, intramolecular contributions to ΔEel were likewise nil. In this idealization that the total ΔEel is zero, the elastic retractive force exhibited by a deformed polymer network would be entirely entropic in origin. At the molecular level, this would correspond, of course, to assuming all configurations of a network chain to be of exactly the same conformational energy and thus the average configuration to be independent of temperature. Under these circumstances, the dependence of stress on temperature is strikingly simple, as shown, for example, by the equation . . . f* = υkT/V (〈r2〉i/〈r2〉0)(α – α-2) . . . . . . (9.1) . . . that characterizes a polymer network in elongation where, it should be recalled, 〈r2〉i3/2 is proportional to the volume of the network. This additional assumption that 〈r2〉0 is independent of temperature would lead to the prediction that the elastic stress determined at constant volume and elongation α is directly proportional to the absolute temperature. Such network chains would be akin to the particles of an ideal gas, which would obey the equation of state p = nRT(1/V) and thus exhibit a pressure at constant deformation (1/V) likewise directly proportional to the temperature.

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

Water ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 530 ◽  
Author(s):  
Weixiang Ni ◽  
Jian Zhang ◽  
Lin Shi ◽  
Tengyue Wang ◽  
Xiaoying Zhang ◽  
...  
Keyword(s):  
Water Depth ◽  
Small Volume ◽  
Pressure Oscillation ◽  
State Equation ◽  
Ideal Gas ◽  
Pipeline System ◽  
Real Gas ◽  
Polytropic Equation ◽  
Real Gas Equations ◽  
Ideal Gas Model

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.

The performance of spiral groove dry gas seal under choked flow condition considering the real gas effect

2019 ◽  
Vol 234 (4) ◽  
pp. 554-566
Author(s):  
Hengjie Xu ◽  
Pengyun Song ◽  
Wenyuan Mao ◽  
Qiangguo Deng
Keyword(s):  
Carbon Dioxide ◽  
Flow Condition ◽  
Ideal Gas ◽  
Leakage Rate ◽  
Spiral Groove ◽  
Real Gas ◽  
Dry Gas Seal ◽  
Choked Flow ◽  
Real Gas Effect ◽  
Gas Effect

By taking carbon dioxide and hydrogen as lubricating gas, respectively, this paper presents an analysis on the pressure characteristics and temperature distribution of spiral groove dry gas seal which influenced by real gas effect under choked flow condition. Numerical results show that the deviation between real gas and ideal gas, which expressed by the deviation degree between compressibility factor Z and 1, is the main reason for real gas effect affecting sealing performance. Compared with ideal gas model, real gas effect raises exit pressure, opening force, leakage rate, Mach number in dam region, and temperature for carbon dioxide ( Z < 1), while it decreases those characteristics for hydrogen ( Z > 1) under the same operating conditions. In addition, choked flow effect increases opening force and reduces leakage rate and temperature-drop between entrance and exit of sealing clearance. Meanwhile, it may cause an unstable behavior for the seal.

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