Ideal Gas Model Research Articles

Determination of the applicability limits of the ideal gas model for the calculation of moist air properties

The submitted paper deals with the finding of such moist air states in which the components of moist air and hence the humid air itself can be described by the ideal gas model while maintaining a predefined accuracy. Both components of moist air (dry air and water vapor) can be described by a model of ideal gas at sufficiently low pressures and sufficiently high temperatures. In the paper, we are looking for such combinations of pressures and temperatures for both components, where the relative deviation in the density calculation using the ideal gas model does not exceed the desired value. In addition, on the basis of the mixture theory, such moist air conditions (characterized by pressure, temperature and specific humidity) are searched, on which the accuracy of the calculation meets the required conditions. Subsequently, diagrams are constructed that can be used to help identify the interface between a moist air area that can be described by a simple ideal gas model, and areas where it is necessary to use a more accurate model for one of the components.

Thermal performance difference of ideal gas model and van der Waals gas model in gas-loaded accumulator

Real gas that considering intermolecular force and molecular volume shows difference compared with the assumption as ideal. While designing accumulator or quantitatively evaluating working state of accumulator in hydraulic circuit, charged in gas-loaded accumulator, the gas properties involves pressure, temperature and stored energy are assumed by the first law of thermodynamics and gas equation of state. The discrepancy of thermodynamic behaviours of real gas from ideal gas should be highlighted. In this paper, the well-known van der Waals equation was employed as real gas model to compare with ideal gas model. The gas behaviours have shown different trends during compression and expansion by mathematically analysis and being confirmed in both isothermal and adiabatic operations. A detailed pressure deviation between ideal gas model and van der Waals model was displayed.

Thermal performance difference of ideal gas model and van der Waals gas model in gas-loaded accumulator

Real gas that considering intermolecular force and molecular volume shows difference compared with the assumption as ideal. While designing accumulator or quantitatively evaluating working state of accumulator in hydraulic circuit, charged in gas-loaded accumulator, the gas properties involves pressure, temperature and stored energy are assumed by the first law of thermodynamics and gas equation of state. The discrepancy of thermodynamic behaviours of real gas from ideal gas should be highlighted. In this paper, the well-known van der Waals equation was employed as real gas model to compare with ideal gas model. The gas behaviours have shown different trends during compression and expansion by mathematically analysis and being confirmed in both isothermal and adiabatic operations. A detailed pressure deviation between ideal gas model and van der Waals model was displayed.

Relaxation to equilibrium in relativistic heavy ion collisions

Relaxation to equilibrium of hot and dense matter produced in central area of relativistic heavy ion collisions at energies ranging from several AGeV to hundreds AGeV is studied within two Monte Carlo transport models. The analysis was performed for three different areas: (i) fixed cubic cell with volume V = 125 fm3, (ii) fixed asymmetric cell with volume V = 4 x 4 x 1 = 16 fm3, and (iii) expanding cell. In the last case the cell volume follows the growth of the area with uniformly distributed energy. To check whether or not the system is equilibrated, its hadron yields and their energy spectra are compared with those of the statistical model of ideal hadron gas. For all cells and for all collision energies it was found that the matter in the cell was approaching the equilibrium state. The higher the collision energy, the shorter the time of equilibration. The equilibration phase lasts about 10 - 20 fm/c, after that the matter becomes very dilute and the thermal contact between hadrons is lost. Equation of state is well fitted to linear dependence P/ɛ = a = c2s , where the square of the sonic velocity c2s increases from 0.12 at Elab = 11.6AGeV to 0.145 at Elab = 160AGeV. The characteristic kinks observed in the T - μB phase diagrams are linked to inelastic freeze-out in the expanding fireball.

Relaxation to equilibrium and EOS in ultra-relativistic heavy-ion collisions

We study relaxation to equilibrium of hot and dense hadron-string matter produced in the central zone of central heavy-ion collisions at energies 11:6AGeV ≤ Elab ≤ 160AGeV. Two microscopic transport models, UrQMD and QGSM, are employed. The analysis is performed for the central cubic cell with volume V = 125 fm3. To check how close the system is to the equilibrium, its hadron yields and hadron energy spectra are compared with those of the statistical model of ideal hadron gas. For all collision energies it was found that the matter in the cell was approaching the equilibrium state, which lasted about 10 - 20 fm/c. After that the matter became very dilute and the thermal contact between the hadrons was lost. Equation of state is well fitted to linear dependence P/ε = a = c2s, where the square of the sonic velocity c2s increases from 0.12 at Elab = 11:6AGeV to 0.145 at Elab = 160AGeV. These results are valid also for very early times of the system evolution when the matter is still out of equilibrium. Together with the isentropic expansion, the linear dependence of P on ε supports the application of hydrodynamic description to early stages of heavy-ion collisions.

On a computing test of an ideal non-interacting gas model

On a computing test of an ideal non-interacting gas model

Van der Waals Interactions and Hadron Resonance Gas: Role of resonance widths modeling on conserved charges fluctuations

The quantum van der Waals (QvdW) extension of the ideal hadron resonance gas (HRG) model which includes the attractive and repulsive interactions between baryons – the QvdW-HRG model – is applied to study the behavior of the baryon number related susceptibilities in the crossover temperature region. Inclusion of the QvdW interactions leads to a qualitatively different behavior of susceptibilities, in many cases resembling lattice QCD simulations. It is shown that for some observables, in particular for χBQ11/χB2, effects of the QvdW interactions essentially cancel out. It is found that the inclusion of the finite resonance widths leads to an improved description of χB2, but it also leads to a worse description of χBQ11/χB2, as compared to the lattice data. On the other hand, inclusion of the extra, unconfirmed baryons into the hadron list leads to a simultaneous improvement in the description of both observables.

Development of Modified Incompressible Ideal Gas Model for Natural Draft Cooling Tower Flow Simulation

The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.

Flow characteristic of a multistage radial turbine for supercritical compressed air energy storage system

Compressed air in supercritical compressed air energy storage system expand from supercritical to atmospheric conditions at lower inlet temperature (<500 K) to generate MW scale power. Therefore, a new multistage radial turbine is adopted and the flow characteristic is investigated by numerical simulation. Effects of ideal gas model and tip clearance on the performance and flow field of the multistage turbine are revealed. Results show that ideal gas model can reveal flow pattern under supercritical condition correctly while leading to obvious deviation of isentropic enthalpy drop, entropy, and inlet-to-exit total temperature ratio. Relative differences for mass flow and efficiency are less than 2%, while the relative differences for output power reaches to 9.36%. For shrouded rotor, mixing of working fluid near hub, blade suction surface, and shroud is the main influencing factor of the flow loss in the rotor. For unshrouded rotor, leakage vortex promote mixture of the fluid deriving from the hub, shroud, and suction surface, and causes much higher flow loss in the channel of rotor. The rotors, which have higher blade height variation rate, present higher efficiency reduction when the tip clearance height is increased, which is because the proportion of tip clearance in blade inlet height increases with the increase of average aspect ratio, resulting in the increase of leakage flow at the leading edge of rotor blade. The pressure fluctuation near the tip clearance and efficiency reduction is also increased. The present study provides a reference for further design and optimization of the multistage radial turbines in compressed air energy storage.

Computer simulation of effective potentials for generalized Boltzmann-Gibbs statistics

We consider a previously proposed non-extensive Statistical Mechanics approach based on an entropy expression that does not depend on any parameter and it is only given in terms of the probability distribution, as in the Boltzmann-Gibbs (BG) case. The theory reproduces the BG theory in a well defined limit. In this article we demonstrate that the theory is consistent with the existence of a generalized H-theorem. The corresponding H function is given in terms of the Maxwellian state, and a generalized version of the ideal gas model can be derived. For denser systems, we present predictions obtained by Monte Carlo computer simulations for fluids whose particles interact via square-well (SW) or Lennard-Jones (LJ) potentials. Results allow us to obtain a well-defined mapping between the BG and non-extensive Statistical Mechanics theories through the introduction of an effective potential of mean force. Using this effective potential, effective Boltzmann factors can be defined in order to obtain non-extensive thermodynamic properties within the BG framework. We discuss how this mapping resemblances an analogy with the definition of Slater sums in Quantum Statistical Mechanics.

Extinction Analysis of a Methane-Oxygen Counterflow Flame at High Pressure

ABSTRACTA numerical study on a high-pressure laminar counterflow diffusion flame is presented. Extinction limits are studied at pressures up to 100 atm for two cases: one with pure methane and the other for a diluted mixture of methane with 40% water vapor mass fraction. The fuel stream flows against pure oxygen on both cases. Solutions for the 1D ideal-gas model and for a real-gas model are provided with both detailed and reduced chemical kinetics, and are compared against real-gas results from the literature. Previous studies increased the strain rate by rising the inflowing velocities of the opposing streams, yielding very high speeds near extinction. Here, strain rate is increased mainly by moving the nozzles closer to each other and also by small increases in the inflow velocities until extinction occurs. When no water is present, there is good agreement in the extinction strain rate between all the cases. However, substantial differences appear in extinction temperature, which features a local minimum between 70 atm and 90 atm, which was not previously reported in the literature. Furthermore, when water vapor is mixed with the fuel, both extinction strain rate and extinction temperature behave differently with increasing pressure. Extinction strain rate increases with pressure and reaches an asymptotic value at about 50 atm, while extinction flame temperature increases from 1 atm to 20 atm, and then decreases almost linearly.

On the RH relations across weak and strong shocks in van der Waals gases

The Rankine–Hugoniot (RH) jump relations for normal shock waves in van der Waals fluids have been studied in order to improve a theoretical understanding of those shock related phenomena as observed in a real atmosphere which cannot be accounted for by the ideal gas model. The RH jump relations for the pressure, density, particle velocity, temperature, speed of sound, adiabatic compressibility and change-in-entropy across the shock front have been analysed in terms of the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas. Further, as the strength of shock waves may range from weak to strong, the convenient forms of RH jump relations for weak and strong shock waves have been discussed, simultaneously. Finally, the effects on the flow-field behind the shock front have been explored due to the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas.

Performance Predictions of Dry and Wet Vapors Ejectors Over Entire Operational Range

If a traditional ideal-gas ejector model is used to evaluate the performance of a wet vapor ejector, large deviations from the experimental results will be unavoidable. Moreover, the model usually fails to assess the ejector performance at subcritical mode. In this paper, we proposed a novel model to evaluate the performance of both dry and wet vapors ejectors over the entire operational range at critical or subcritical modes. The model was obtained by integrating the linear characteristic equations of ejector with critical and breakdown points models, which were developed based on the assumptions of constant-pressure mixing and constant-pressure disturbing. In the models, the equations of the two-phase speed of sound and the property of real gas were introduced and ejector component efficiencies were optimized to improve the accuracy of evaluation. It was validated that the proposed model for the entire operational range can achieve a better performance than those existing for R134a, R141b and R245fa. The critical and breakdown points models were further used to investigate the effect of operational parameters on the performance of an ejector refrigeration system (ERS). The theoretical results indicated that decreasing the saturated generating temperature when the actual condensing temperature decreases, and/or increasing the saturated evaporating temperature can improve the performance of ERS significantly. Moreover, superheating the primary flow before it enters the ejector can further improve the performance of an ERS using R134a as a working fluid.

Numerical estimation of ultrasonic production of hydrogen: Effect of ideal and real gas based models

Based on two different assumptions regarding the equation describing the state of the gases within an acoustic cavitation bubble, this paper studies the sonochemical production of hydrogen, through two numerical models treating the evolution of a chemical mechanism within a single bubble saturated with oxygen during an oscillation cycle in water. The first approach is built on an ideal gas model, while the second one is founded on Van der Waals equation, and the main objective was to analyze the effect of the considered state equation on the ultrasonic hydrogen production retrieved by simulation under various operating conditions. The obtained results show that even when the second approach gives higher values of temperature, pressure and total free radicals production, yield of hydrogen does not follow the same trend. When comparing the results released by both models regarding hydrogen production, it was noticed that the ratio of the molar amount of hydrogen is frequency and acoustic amplitude dependent. The use of Van der Waals equation leads to higher quantities of hydrogen under low acoustic amplitude and high frequencies, while employing ideal gas law based model gains the upper hand regarding hydrogen production at low frequencies and high acoustic amplitudes.

State-of-the-Art Calculations of Sublimation Enthalpies for Selected Molecular Crystals and Their Computational Uncertainty.

A computational methodology for calculation of sublimation enthalpies of molecular crystals from first principles is developed and validated by comparison to critically evaluated literature experimental data. Temperature-dependent sublimation enthalpies for a set of selected 22 molecular crystals in their low-temperature phases are calculated. The computational methodology consists of several building blocks based on high-level electronic structure methods of quantum chemistry and statistical thermodynamics. Ab initio methods up to the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction with an estimated complete basis set description [CCSD(T)/CBS] are used to calculate the cohesive energies of crystalline phases within a fragment-based additive scheme. Density functional theory (DFT) calculations with periodic boundary conditions (PBC) coupled with the quasi-harmonic approximation are used to evaluate the thermal contributions to the enthalpy of the solid phase. The properties of the vapor phase are calculated within the ideal-gas model using the rigid-rotor harmonic-oscillator model with correction for internal rotation using a one-dimensional hindered rotor approximation and a proper treatment of the molecular rotational degrees of freedom in the vicinity of 0 K. All individual terms contributing to the sublimation enthalpy as a function of temperature are discussed and their uncertainties estimated by comparison to critically evaluated experimental data.

Van der Waals Interactions in Hadron Resonance Gas: From Nuclear Matter to Lattice QCD.

An extension of the ideal hadron resonance gas (HRG) model is constructed which includes the attractive and repulsive van der Waals (VDW) interactions between baryons. This VDW-HRG model yields the nuclear liquid-gas transition at low temperatures and high baryon densities. The VDW parameters a and b are fixed by the ground state properties of nuclear matter, and the temperature dependence of various thermodynamic observables at zero chemical potential are calculated within the VDW-HRG model. Compared to the ideal HRG model, the inclusion of VDW interactions between baryons leads to a qualitatively different behavior of second and higher moments of fluctuations of conserved charges, in particular in the so-called crossover region T∼140-190 MeV. For many observables this behavior resembles closely the results obtained from lattice QCD simulations. This hadronic model also predicts nontrivial behavior of net-baryon fluctuations in the region of phase diagram probed by heavy-ion collision experiments. These results imply that VDW interactions play a crucial role in the thermodynamics of hadron gas. Thus, the commonly performed comparisons of the ideal HRG model with the lattice and heavy-ion data may lead to misconceptions and misleading conclusions.

Compensation of pressure enthalpy effects on temperature fields for throttling of high-pressure real gas

For the pressure enthalpy of high pressure pneumatics, the computational fluid dynamics (CFD) simulation based on ideal gas assumption fails to obtain the real temperature information. Therefore, we propose a method to compensate the pressure enthalpy of throttling for CFD simulation based on ideal gas assumption. Firstly, the pressure enthalpy is calculated for the pressure range of 0.101 to 30 MPa and the temperature range of 190 to 298 K based on Soave-Redlich-Kwong (S-R-K) equation. Then, a polynomial fitting equation is applied to practical application in the above mentioned range. The basic idea of the compensation method is to convert the pressure enthalpy difference between inlet air and nodes into the compensation temperature. In the above temperature and pressure range, the compensated temperature is close to the real one, and the relative temperature drop error is below 10%. This error is mainly caused by the velocity difference of the orifice between the real and ideal gas models. Finally, this compensation method performs an icing analysis for practical high pressure slide pilot valve.

Computational study of state equation effect on single acoustic cavitation bubble’s phenomenon

Many models have been established to study the evolution of the bubble dynamics and chemical kinetics within a single acoustic cavitation bubble during its oscillation. The content of the bubble is a gas medium that generates the evolution of a chemical mechanism governed by the internal bubble conditions. These gases are described by a state equation, linking the pressure to the volume, temperature and species amounts, and influencing simultaneously the dynamical, the thermal and the mass variation in the cavitation bubble. The choice of the state equation to apply has then a non-neglected effect on the obtained results. In this paper, a comparative study was conducted through two numerical models based on the same assumptions and the same scheme of chemical reactions, except that the first one uses the ideal gas equation to describe the state of the species, while the second one uses the Van der Waals equation. It was found that though the dynamic of the bubble is not widely affected, the pressure and temperature range are significantly increased when passing from an ideal gas model to a real one. The amounts of chemical products are consequently raised to approximately the double. This observation was more significant for temperature and pressure at low frequency and high acoustic amplitude, while it is noticed that passing from ideal gas based approach to the Van der Waals one increases the free radicals amount mainly under high frequencies. When taking the results of the second model as reference, the relative difference between both results reaches about 60% for maximum attained temperature and 100% for both pressure and free radicals production.

CFD analysis of thermally induced thermodynamic losses in the reciprocating compression and expansion of real gases

The efficiency of expanders is of prime importance in determining the overall performance of a variety of thermodynamic power systems, with reciprocating-piston expanders favoured at intermediate-scales of application (typically 10–100 kW). Once the mechanical losses in reciprocating machines are minimized (e.g. through careful valve design and operation), losses due to the unsteady thermal-energy exchange between the working fluid and the solid walls of the containing device can become the dominant loss mechanism. In this work, gas-spring devices are investigated numerically in order to focus explicitly on the thermodynamic losses that arise due to this unsteady heat transfer. The specific aim of the study is to investigate the behaviour of real gases in gas springs and to compare this to that of ideal gases in order to attain a better understanding of the impact of real-gas effects on the thermally induced losses in reciprocating expanders and compressors. A CFD-model of a gas spring is developed in OpenFOAM. Three different fluid models are compared: (1) an ideal-gas model with constant thermodynamic and transport properties; (2) an ideal-gas model with temperature-dependent properties; and (3) a real-gas model using the Peng-Robinson equation-of-state with temperature and pressure-dependent properties. Results indicate that, for simple, mono- and diatomic gases, like helium or nitrogen, there is a negligible difference in the pressure and temperature oscillations over a cycle between the ideal and real-gas models. However, when considering heavier (organic) molecules, such as propane, the ideal-gas model tends to overestimate the pressure compared to the real-gas model, especially if the temperature and pressure dependency of the thermodynamic properties is not taken into account. In fact, the ideal-gas model predicts higher pressures by as much as 25% (compared to the real-gas model). Additionally, both ideal-gas models underestimate the thermally induced loss compared to the real-gas model for heavier gases. This discrepancy is most pronounced at rotational speeds where the losses are highest. The real-gas model predicts a peak loss of 8.9% of the compression work, while the ideal-gas model predicts a peak loss of 5.7%. These differences in the work loss are due to the fact that the gas behaves less ideally during expansion than during compression, with the compressibility factor being lower during compression. This behaviour cannot be captured with the ideal-gas law. It is concluded that real-gas effects must be taken into account in order to predict accurately the thermally induced loss mechanism when using heavy fluid molecules in such devices.

Heat Engines running upon a Non-Ideal Fluid Model with Higher Efficiencies than upon the Ideal Gas Model

We consider both Otto and Diesel heat engine cycles running upon the working substances modeled by the van der Waals fluid as a simple non-ideal gas model. We extensively perform the efficiency study in these model engines. Then we find that this “real” engine model can go beyond its ideal-gas counterpart in efficiency, whereas as well-known, the maximum Carnot efficiency is the same for both ideal and non-ideal gas engines. In fact, the higher the density of non-ideality is, the higher efficiency tends to be found, especially in the low-temperature regime, but with more shrinkage in the range of physically allowed compression ratio determined by the Carnot upper bound, namely, the Second Law of thermodynamics. Our findings imply that in addition to the engine architectures and bath temperatures, the properties of working substances should also be taken into consideration in the performance study of heat engines, the theoretical model aspects of which have not sufficiently been discussed so far. It is straightforward that our methodology may also apply for other non-ideal fluid models.