Gas Equation Research Articles

Numerical and Theoretical Analysis of Model Equations for Multicomponent Rarefied Gas

Model equations approximating the system of Boltzmann equations for a multicomponent gas are investigated. Methods for determining parameters in relaxation terms corresponding to cross-collision integrals are analyzed. Numerical solutions based on three model systems and the Boltzmann equations are compared as applied to the following problems: relaxation of a mixture to equilibrium, shock wave structure, and the dynamics of a vapor-gas cloud generated by pulsed laser irradiation of a target. It is shown that the parameters in the relaxation operators influence the degree of difference in the solutions produced by the various models.

Combining wall interactions, fluid momentum balances and the Maxwell-Stefan equations for gas transport in porous media: An alternative approach

This paper presents a modelling framework for incorporating wall interactions into the Maxwell-Stefan equations for ideal gases in porous media. In contrast to already existing models in literature, such as the Dusty Gas, Binary Friction and Modified Binary Friction models, the framework makes use of N−1 (with N being the number of gas species) independent mass balances for the gas species in combination with a total fluid momentum balance. This approach has the advantage that already existing numerical schemes for fluid momentum balances, such as Darcy’s law or the Brinkman equations, can be used with only minor modifications. It also allows for separate initialisation of the velocity and pressure fields, something that is often beneficial when solving convection–diffusion equations numerically. The derived model is validated against both stationary and time-dependent experimental data from literature for binary Ar-He systems in porous media, using Knudsen diffusivities to define the wall friction terms.

Full-band modeling of AM and FM interband cascade laser frequency combs

A numerical model for the simulation of frequency combs in interband cascade lasers is developed. The approach is based on slowly varying amplitude approximation for electromagnetic field and semiconductor Bloch equations for the electron gas. The electron gas nonequilibrium distribution function is computed explicitly. Effects of both radiative and nonradiative recombination are considered. The model is applied to both amplitude modulated and frequency modulated combs.

Numerical and Theoretical Analysis of Model Equations for Multicomponent Rarefied Gas

Numerical and Theoretical Analysis of Model Equations for Multicomponent Rarefied Gas

The application of differential constraint method for the solution of non-homogeneous generalized Riemann problem

This paper reports the solution to the Non-homogeneous Riemann problem by applying the approach of differential constraint for the one-dimensional (1 − D) generalized Chaplygin gas equations with non-constant initial data. Here we take source term as a Coulomb type constant frictional term. We reduced the governing non-homogeneous model into a homogeneous one by introducing a new velocity variable. By virtue of this advantage of frictional type source term, we would easily determine the solution of reformulated homogeneous governing model. We have computed the differential constraint and its consistency conditions for the specified model. Moreover, we have derived here the compatibility condition between the governing model and the differential constraints. The solutions to generalized Riemann problem for the 1 − D Euler’s equation of governing gas model are obtained as well as for the smooth and non-constant initial conditions the comprehensive overview of the solutions is studied.

A semi-analytical method for the static stability analysis of air cushion supported floating platforms

Air cushion-supported floating platforms (ACSFPs) have a simple structure and low construction cost, yet they possess excellent stability and hydrodynamic performance, making them suitable for deep-sea wind or wave energy exploitation. However, efficient methods for evaluating the stability of ACSFPs are lacking. In this paper, a semi-analytical stability analysis method was developed for ACSFPs, which analytically calculates the displacement of ACSFPs and air cushion volume. It numerically solves the nonlinear equations that consist of the conservation of ACSFP displacement and the ideal gas equations for air cushions to obtain the stability lever. The semi-analytical method not only allows for the quick evaluation of the initial stability of ACSFPs but also efficiently assesses larger angles, including extreme conditions such as air leakage from cushions and submergence of the wetted surface. The effectiveness of the semi-analytical method was demonstrated by using it to calculate the stability of a circular ACSFP, and its results were verified using the CAD method.

Correspondence of the Symmetry of Thermodynamic Properties of Matter with the Symmetry of Equations of State.

Thermodynamics contains rich symmetries. These symmetries are usually considered independent of the structure of matter or the thermodynamic state where matter is located and, thus, highly universal. As Callen stated, the connection between the symmetry of fundamental laws and the macroscopic properties of matter is not trivially evident. However, this view is now being challenged. Recently, with symmetry to the ideal gas equation of state (EOS), an ideal dense matter EOS has been proposed, which has been verified to be in good agreement with the thermodynamic properties of high-density substances. This indicates that there is a certain symmetry between the thermodynamic properties of substances in their high- and low-density limits. This paper focuses on the distinctive features and the significance of this symmetry. It is a new class of symmetry that is dependent on the thermodynamic state of matter and can be incorporated into the existing symmetrical theoretical system of thermodynamics. A potential path for developing the EOS theory arising from this symmetry is discussed. EOS at high densities could be developed by correcting or extrapolating the ideal dense matter EOS based on this symmetry, which might fundamentally solve the difficulty of constructing EOS at high densities.

Numerical simulation study on the leakage and diffusion characteristics of high-pressure hydrogen gas in different spatial scenes

This paper presents a computational fluid dynamics (CFD) model for simulating high-pressure hydrogen leakage and diffusion. The model incorporates heat exchange during hydrogen leakage diffusion and the real gas equation of state in high-pressure conditions. The CFD model can provide superior predictions of pressure, temperature, hydrogen density, and mass flow rate within the hydrogen storage cylinder changes during high-pressure hydrogen leakage compared to existing models. Moreover, the model validated by experimental data enables simulation of the spatiotemporal evolution law of hydrogen concentration and the change of the combustible region in space following a high-pressure hydrogen storage cylinder leak in various spatial scenarios. It can also determine the safe distance after the hydrogen leakage and simulate the impact of the hydrogen leakage on the surrounding environment in terms of temperature, pressure and other physical factors. Furthermore, the model is applicable for simulating the leakage and diffusion behavior of high-pressure hydrogen in various leakage conditions. This capability helps researchers understand the characteristics of high-pressure hydrogen leakage and diffusion, and further study the phenomenological evolution law of hydrogen safety accidents, so as to formulate emergency response strategies.

Bubbles and bed expansion in low pressure fluidization

Fluidization at low pressure has significant benefits over traditional fluidized beds for the fine chemical industry. Yet there is a lack of knowledge of bubbling and bed behaviour under the slip flow regime (low pressure), and this presents a hindrance to the optimization of this process. In this work, the fundamental aspects of gas bubbles and bed expansion are investigated for a wider range of operating pressure, flow rates and bed aspect ratio. Typically, rising individual bubbles undergo a series of breakups and coalesce as they rise in the bed. The lowering of pressure below 14,884 Pa was found to inhibit this behaviour indicating a qualitative indication of the impact of pressure on the bubble dynamics. The bubbles formed at low pressure were larger in average size, greater in number at the inlet and have a higher aspect ratio. All these factors were directly related to the expansion of gas due to the lowering of operating pressure. Under a controlled environment with single rising bubbles, the gas expansion was predictable using the ideal gas equation. However, where the pressure is low enough (≤ 24,231 Pa) the inhomogeneous fluidization impacted the predictability and trend of the bubbling zone and bed expansion. Despite this, the overall consumption of fluidizing mass was magnitudes lower to generate similar sizes of bubbles at atmospheric pressure. This has a direct impact on the usage of fluidizing gas while maintaining similar gas-solid mixing behaviour. Overall, the benefits of low pressure can be obtained at moderate pressure between 49,130 pa and 24,231 Pa at AR 3 with homogeneous fluidization.

On a doubly reduced model for dynamics of heterogeneous mixtures of stiffened gases, its regularizations and their implementations.

We deal with the reduced four-equation model for the dynamics of heterogeneous compressible binary mixtures with the stiffened gas equations of state. We study its further reduced form, with the excluded volume concentrations, and with a quadratic equation for the common pressure of the components; this form can be called a quasi-homogeneous form. We prove new properties of the equation, derive simple formulas for the squared speed of sound, and present an alternative proof for a formula that relates it to the squared Wood speed of sound; also, a short derivation of the pressure balance equation is given. For the first time, we introduce regularizations of the heterogeneous model (in the quasi-homogeneous form). Previously, regularizations of such types were developed only for the homogeneous mixtures of perfect polytropic gases, and it was unclear how to cover the case considered here. In the 1D case, based on these regularizations, we construct new explicit two-level in time and symmetric three-point in space finite-difference schemes without limiters and provide numerical results for various flows with shock waves.

Multidimensional numerical simulation of thermodynamic and oscillating gas flow processes of a Gifford-McMahon cryocooler

Abstract The Gifford-McMahon cryocoolers are considered to be prominent candidates for the cooling of high-temperature superconducting magnets, liquefaction of permanent gases, helium recondensation in magnetic resonance imaging machines, cooling of superconducting quantum interference device, etc. In this paper, multi-dimensional numerical simulation is performed to visualize the oscillating heat and fluid flow processes that happen in a mechanically driven GM cryocooler. Influence of the ideal gas equation and real gas equation of states on the cooling behaviour is explained. The minimum achievable refrigeration temperature of a uniform mesh regenerator is compared with a multi-mesh regenerator. It is noticed that a multi-mesh regenerator produces a lower refrigeration temperature as compared to a uniform mesh regenerator. In addition to this, a one-dimensional simulation is conducted and results are compared with multi-dimensional numerical simulation. The no-load temperature value calculated by the one-dimensional model and multi-dimensional model with ideal gas is lower than that of real gas equations. Additionally, the refrigerating capacity calculated by the one-dimensional model and multi-dimensional model with the ideal gas equation is higher than those of the real gas equation of state.

The partial null conditions and global smooth solutions of the nonlinear wave equations on [formula omitted] with d = 2,3

In this paper, we investigate the fully nonlinear wave equations on the product space R3×T with quadratic nonlinearities and on R2×T with cubic nonlinearities, respectively. It is shown that for the small initial data satisfying some space-decay rates at infinity, these nonlinear equations admit global smooth solutions when the corresponding partial null conditions hold and while have almost global smooth solutions when the partial null conditions are violated. Our proof relies on the Fourier mode decomposition of the solutions with respect to the periodic direction, the efficient combinations of time-decay estimates for the solutions to the linear wave equations and the linear Klein-Gordon equations, and the global weighted energy estimates. In addition, an interesting auxiliary energy is introduced. As a byproduct, our results can be applied to the 4D irrotational compressible Euler equations of polytropic gases or Chaplygin gases on R3×T, the 3D relativistic membrane equation and the 3D nonlinear membrane equation on R2×T.

Approximated decompositions for computational continuum mechanics

Solid and fluid mechanics problems often involve the computation of eigenvalues and eigenvectors. One has short algebraic expressions for the Euler equations and the perfect gas equation of state. However, algebraic expressions for solid mechanics models can become substantial. Computing the eigenvalues and eigenvectors algebraically for different models can become cumbersome. Also, larger formulae may result in increased overall computational time. Internal energy plays a significant role in modeling the medium, and thermodynamic consistency is indispensable. The models should correctly capture heat transfer, mechanical response, and fluid flow, e.g., in mechanocaloric and bone remodeling (BR) problems. In mechanocaloric problems, temperature variation occurs because of load and unload stresses. In BR problems, several mathematical models were developed for modeling its behavior. Flexibility for testing different models is an essential requirement. Hence, our goal is to propose and test approximated eigensystem and singular value (SVD) decompositions for continuum mechanics problems. We tested the resolution and accuracy of our propositions in benchmarking CFD problems. For the solid mechanics, we solved a few classical problems, verified the accuracy, and solved mechanocaloric tests and bar under tension. Although more expensive, the approximated eigensystem decomposition is more flexible. It is high-order and high-resolution, can capture heat transfer, fluid flow, discontinuities, and mechanical response, and can model real-world applications. The SVD is a viable possibility and can be used to adjust the computational time of severe situations, but it needs to be improved.

Numerical simulation and experiment of double chamber brake based on CFD

The artillery firing process will instantly produce high-temperature and high-pressure gunpowder gas, this process will produce shock waves. The gunpowder gas has a limited effect on the projectile during the firing and ballistic after-effects period, however, it has a very obvious effect on the stability of the gun body, and the reduction of the stability of the gun body directly affects the firing accuracy and the safety of the firing personnel. Based on the method of Computational Fluid Dynamics (CFD), numerical simulation is carried out, and the structure and flow parameters of the muzzle flow field are obtained by using three-dimensional Euler's control equation, gas equation of state, and k-epsilon model, as well as dynamic mesh technology. By comparing the flow parameters of the brake before and after optimization, and analyzing the results obtained from the 8-round firing experiments, the efficiency of the optimized brake is increased by 8.2%, and the deviation between the experimental data and the simulation results is only 10.5%, which not only verifies the accuracy of the numerical simulation calculations but also verifies the optimized brake's good retracting effect. The results of the study can provide a reference for the optimization and design of the double-chamber brake.

Numerical study for the combustion analysis of wood volatiles in porous radiant burner for the application of biomass cooking stove

This article presents a computational study of wood volatiles combustion in a two-layer porous radiant burner (PRB) at different power inputs (1–3 kW) and porosity ranges from 0.7 to 0.9 respectively. A 2-D computational model is designed to numerically solve the combustion of wood-volatiles and air. A finite volume technique is utilized to solve governing equations including; continuity equation, momentum equation, species transport equation, radiative transport equation, and gas and solid phases energy equations. The utilized model is validated with previous literature for a two-layer porous radiant burner and the deviation of comparison is found within the acceptable range. The results reveal that the higher temperature was found in the central part of the burner and the minimum at the circumference. The longitudinal temperature distribution along the central line ruled out the occurrence of flashbacks. Moreover, the transport species contours reveal that the maximum combustion reactions occur in the upper layer of the porous zone. Further, the radiation efficiency decreases with input power and increases with porosity. The maximum value of radiation efficiency is found 36% at 1 kW and porosity of 0.9. while the minimum is 26% found at 3 kW and porosity of 0.7. The overall assessment showed that the PRB-based cooking stove is capable for providing a desired temperature range and efficient radiation efficiency in the range of 1–3 kW of power input.

Modeling of the Gas Dynamic Processes with Different Equations of State

The work is devoted to the study of the features of gas-dynamic processes at the high pressures. The flows of air, hydrogen and water vapor are considered. The results obtained using the ideal gas equation and two real gas equations - van der Waals and Soave-Redlich-Kwong are analyzed. The comparison has been done on the numerical simulation results for the safety valve operation problem. The problem was solved in a three-dimensional non-stationary formulation using the finite volume method. Numerical solution method was built on the basis of the Godunov’s method. The results of a comparison of isotherms for each media are presented. Those are obtained using the considered equations of state in the regions when the gases thermodynamic parameters are changed. The influence of the gas model on the processes in the safety valve has been studied in detailsfor hydrogen. A detailed comparison of the local distributions of pressure, temperature, density, and flow velocity has been made. The complex impact of the flow parameters was studied using the integral characteristics - the gas-dynamic force acting on the disk and the gas flow rate. It has been found the gas-dynamic forces obtained within the framework of ideal gas model and the Soave-Redlich-Kwong gas are close to each other in magnitude and exceed the force for the van-der-Waals gas. However, the flow rate of ideal gas significantly exceeded that for both real gases. It is due to a twofold increase in density, which is not compensated by a decrease in the flow velocity. Thus, to obtain accurate data on the dynamic and velocity effects of gas flows on technical devices at high pressures it is necessary to use the real gas equations of state.

Applicability Evaluation of Natural Gas State Equations at Low Temperatures

The paper analyzes the possibility of operating range expanding of natural gas state equations for low temperatures. The state equations of natural gas and methods of estimating the compressibility factor, entrenched in modern national and international standards, were analyzed. It has been shown that the range of their applicability is limited to a temperature value of 250 K, however, these temperature limitations is not restricted bystate equations directly butstipulated by the lack of reliable data about natural gas compressibility factor values at temperatures below 250 K and methods for complementary errorcalculation that may arise. The results of comparison of values of natural gas compressibility factor as a function of temperature at pressure of 1.3 and 6 MPa calculated by means of the most widely used state equations are presented. It was found that the results of the calculation according to the considered methods have satisfactory convergence within the range of 220 K, that generally confirms the applicability of modern state equations for low temperatures. In its turn, the effect of assumptions applied nowadays to definegas volume flow rateon flow metering error showed that application of substitutive compressibility values may result in significant complementary systematic error. This indicates the practicability of expanding the database of compressibility factor values for natural gas for low temperatures, as well as developmentof a standard to assess the value of the corresponding complementary error.

System of Model Kinetic Equations for a Multicomponent Gas

System of Model Kinetic Equations for a Multicomponent Gas

Using dark solitons from a Bose–Einstein condensate necklace to imprint soliton states in the spectral memory of a free boson gas

A possible use of matter-wave dark-soliton crystal produced by a Bose–Einstein condensate (BEC) with ring geometry, to store soliton states in the quantum memory of a free boson gas, is explored. A self-defocusing nonlinearity combined with dispersion and the finite size of the BEC, favor the creation of dark-soliton crystals that imprint quantum states with Jacobi elliptic-type soliton wavefunctions in the spectrum of the free boson gas. The problem is formulated by considering the Gross–Pitaevskii equation with a positive scattering length, coupled to a linear Schrödinger equation for the free boson gas. With the help of the matter-wave dark soliton-crystal solution, the spectrum of bound states created in the free boson gas is shown to be determined by the Lamé eigenvalue problem. This spectrum consists of quantum states whose wave functions and energy eigenvalues can be unambiguously identified. Among these eigenstates some have their wave functions that are replicas of the generating dark soliton crystal.

Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas

We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formulation of linearly degenerate systems governing delta-functional reductions of the kinetic equation for dense soliton gas is established (for KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases).