Non-ideal Gas Flow Research Articles

Comprehensive analysis of normal shock wave propagation in turbulent non-ideal gas flows with analytical and neural network methods

Shock wave propagation in gases through turbulent flow has wide-reaching implications for both theoretical research and practical applications, including aerospace engineering, propulsion systems, and industrial gas processes. The study of normal shock propagation in turbulent flow over non-ideal gas investigates the changes in pressure, density, and flow velocity across the shock wave. The Mach number is derived for the system and explored across various gas molecule quantities and turbulence intensities. This study analytically investigated the normal shock wave propagation in turbulent flow of adiabatic gases with modified Rankine–Hugoniot conditions. Artificial neural network (ANN) techniques are used to estimate the solutions for shock strength and Mach number training validation phases of back-propagated neural networks with the Levenberg–Marquardt algorithm. The results reveal that pressure ratio with density ratio increase for higher values of increase in the turbulence level as well as intermolecular forces. A reverse trend is observed in velocity coefficient after shock in the presence of adiabatic gas. The regression coefficient values obtained using the network model ranged from 0.999 99 to 1, indicating an almost perfect correlation. These findings demonstrate that the ANN can predict the Mach number with high accuracy.

Evolution of shock waves in dusty nonideal gas flow with magnetic field

Abstract This paper deals with the study of propagation of shock waves in 2-D steady supersonic magnetogasdynamics flow of nonideal dusty gas using wavefront analysis method. We derived the transport equation, which determines the condition for the shock formation. Our aim is to analyze the effect of interaction of dust particles with magnetic field in nonideal gas on the evolution of shock formation and to examine how the flow patterns of the disturbance vary with respect to the variations in the physical parameters of the medium. It is found that the presence of magnetic field plays an essential role in the wave propagation phenomena. The nature of the solution with respect to the Mach number is analyzed, and it is examined how the shock formation distance changes with an increase or decrease in the value of Mach number. Also, the combined effect of nonidealness, magnetic field, and dust particles on the shock formation distance is elucidated and examined how the formation of shocks is affected by the increase in the value of corresponding physical parameters.

Numerical Investigation of Transonic Non-ideal Gas Flows Around a Circular Cylinder at High Reynolds Number

Numerical Investigation of Transonic Non-ideal Gas Flows Around a Circular Cylinder at High Reynolds Number

Investigation of non-ideal gas flows around a circular cylinder

The aerodynamic performance of a cylinder Pitot probe for velocity measurements in compressible non-ideal gas flows, such as those encountered in Organic Rankine Cycle (ORC) turbines, is investigated by means of Computational Fluid Dynamics. Numerical simulations are performed at subsonic and transonic conditions, and freestream Reynolds numbers are in the cylinder critical regime. The working fluid is the organic vapor Novec™ 649. Air flow simulations at similar inlet conditions are reported for comparison. Steady and unsteady RANS solutions are computed with the Spalart–Allmaras turbulence model. The results are assessed against experimental measurements collected in a wind tunnel. URANS is in good agreement with experimental data for all considered conditions, and delivers reasonably accurate estimations of the cylinder back pressure. Using a dense gas leads to a lower minimum pressure coefficient compared to air, alongside a reduced maximum Mach number due to the non-ideal speed of sound behaviour. In the experimentally studied range of compressibility factors and Mach numbers, discrepancies observed with respect to air flow are mostly an effect of the different isentropic exponents. In the transonic regime, shock waves causing boundary layer separation are weakened in the dense gas, but back pressure is also decreased, contributing to rising form drag.

Investigation of shale gas flows under confinement using a self-consistent multiscale approach

This report summarises our recent findings on non-ideal gas flow characteristics in shale nanopores facilitated by our strongly-inhomogeneous kinetic model. As there are a significant portion of nano-scale pores in shale, gas molecule size is comparable to both the gas mean free path and the characteristic length of the flow domain, and various factors including fluid-solid and fluid-fluid interactions, pore confinement, surface roughness, and non-equilibrium effect need to be considered in a self-consistent manner. These factors are either considered in the governing equation according to the dense gas and mean-field theories, or through the boundary condition based on molecular dynamics simulations. Our kinetic model results are consistent with the molecular dynamics data at the molecular scale and converge to the continuum predictions when pores become large. This model serves as an accurate tool to investigate multiscale transport of shale gas and is helpful for upscaling from the microscopic to continuum levels with a firm theoretical basis. Cited as: Shan, B., Ju, L., Guo, Z., Zhang, Y. Investigation of shale gas flows under confinement using a self-consistent multiscale approach. Advances in Geo-Energy Research, 2022, 6(6): 537-538 . https://doi.org/10.46690/ager.2022.06.11

A user-friendly pitot probe data reduction routine for non-ideal gas flow applications

This contribution presents a user-friendly and robust data reduction routine for Pitot probes which can be realized using widely available software. The routine rests on the general balance equations and a database for calculating the thermodynamic properties of the involved fluids. In the present study, the proposed data reduction routine has been established as a calculation sheet using common office software and REFPROP by NIST. In the calculation sheet, the user can easily select the fluid and, manually or automatically, insert the recorded Pitot probe data and stagnation conditions. A robust algorithm directly calculates the freestream Mach number and other flow and thermodynamic quantities. The new Pitot probe data reduction routine's accuracy is assessed through several test cases, including the subsonic and supersonic flow of dry air, Novec 649, and Siloxane MM in the dilute and dense gas regime. For compressible non-ideal gas flows, it is found that the classical Rayleigh-Pitot equation is systematically in error even in the dilute gas regime where relative deviations of more than 10% are noticed. In the dense gas regime, the Rayleigh-Pitot equation fails dramatically in calculating the freestream Mach number, and errors larger than 60% can occur.

Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics

ABSTRACT Recently, there is an increased interest in supercritical CO2 and organic Rankine cycles (ORC) for their ability to achieve higher thermodynamic efficiency. However, the non-ideal gas thermodynamic in these cycles may affect the flow properties critically, necessitating the research of non-ideal compressible fluid dynamics (NICFD). Thus, simulation tools that can accurately predict fluid flows with NICFD are significant. This study presents a new approximation Riemann solver in OpenFOAM for NICFD. The new solver uses a real-gas (look-up table based) approximate Riemann flux calculator (modified from HLLC ALE flux calculator) through adding a new thermodynamic library tightly coupled with the OpenFOAM®. To validate the solver, three cases are presented, including a NASA transonic nozzle operating with air, to confirm the ability to correctly simulate the transonic flow phenomena and the shock waves; the VKI 2D cascade operated with MDM to assess the ability in simulating non-ideal gas flows typically to industrial applications; and the dense gas flow (MD4M) passing a backward ramp to illustrate the ability of the flux calculator and look-up table mechanism that can work well in the non-ideal region of fluid properties. This study can benefit future engineering applications of computational fluid mechanics of NICFD and the OpenFOAM community.

The formation of shock wave in a two-dimensional supersonic planar and axisymmetric non-ideal gas flow with magnetic field

The formation of shock wave in a two-dimensional supersonic planar and axisymmetric non-ideal gas flow with magnetic field

High-order numerical scheme for compressible multi-component real gas flows using an extension of the Roe approximate Riemann solver and specific Monotonicity-Preserving constraints

The purpose of this paper is to develop a high-order shock-capturing scheme capable of predicting flows where shock waves with high-temperature jumps interact with multi-component real gas mixtures, assuming a local thermodynamic equilibrium. We first propose a generalization of the Roe solver for distinct species with non-ideal thermodynamic properties that relies on the original method proposed by Vinokur & Montagné [1]. This method uses an approximation of compressibility factors to estimate a coherent value of the speed of sound at the Roe averaged state.This Roe averaged state is introduced in the One-Step Monotonicity-Preserving (OSMP) scheme, originally developed by Daru and Tenaud [2], to obtain an extension to the high-order with Lax-Wendroff procedure adequate for dealing with non-ideal gas flows. To avoid thermodynamic inconsistencies in the evolution of the Roe average state over a large stencil, we propose to reformulate the discrete total energy flux of the initial solver. This new formulation uses a combination of Riemann invariants related to the species mass fractions and avoids the influence of the independent values of the compressibility factors in the total energy flux computation. An additional M-P constraint on this new combination allows dealing with discontinuities. Based on the averaged speed of sound estimated by our proposed extension of the Vinokur & Montagné method, we demonstrate that this new formulation is equivalent to selecting a new combination of compressibility factors that completely fulfill the jump relationships of the Riemann problem.To properly capture discontinuities while optimizing the number of numerical cells, the new high-order OSMP scheme is combined with an Adaptive Multiresolution [3] procedure to automatically refine grid in regions where steep gradients occur and coarsen grid elsewhere. The order of the numerical method is evaluated on the convection of density and mass fraction waves. Its capability of capturing discontinuities is validated on a 1-D shock tube problem with a mixture of Nitrogen, Oxygen and dense refrigerant R22 gases. We show that smooth solutions, as well as discontinuities, are recovered with high accuracy. The 2-D interaction between a shock wave in Air with a cylindrical bubble initially filled with dense refrigerant R22 gas is also considered. Present results compare very well with both a recent fully resolved numerical solution of ideal gases and experimental results obtained with real gases. Compared to ideal gas solutions corresponding to calorically perfect gas, drastic changes are recorded on the predicted temperature and the bubble flow patterns that fully justify the use of relevant thermodynamics and the proposed numerical method to account for real gas properties.

Similarity solutions for strong shock waves in non-ideal magnetogasdynamics under the effect of monochromatic radiation

This manuscript aims to deal with the one-dimensional unsteady flow of non-ideal gas with monochromatic radiation under the influence of a magnetic field, where the invariance method of the Lie group of transformations is applied in a cylindrically symmetric motion. The density is assumed to be uniform in the undisturbed medium. The radiation flux is considered to move through the non-ideal gas. The self-similar solutions of the considered model are obtained for the power-law and the exponential-law shock paths. The effects of the adiabatic exponent, radiation parameter, ambient magnetic field, and the parameter of non-idealness on the flow variables are shown graphically. Numerical calculations are performed to obtain the self-similar solutions.

The exact Riemann solutions to an isentropic non-ideal dusty gas flow under a magnetic field

Abstract We analyse exact solutions to the Riemann problem for a one-dimensional isentropic and perfectly conducting non-ideal dusty gas flow in the presence of a transverse magnetic field. We give the expression of wave curves as well as the behaviors of these wave curves. A new technique is provided to get a complete list of analytical solutions with the corresponding criteria. Moreover, the numerical solutions to the Riemann problem are also given. It is shown that the analytical solutions match well with the corresponding numerical solutions.

The analytical solutions to one-dimensional non-ideal dusty gas flow

The analytical solutions to one-dimensional non-ideal dusty gas flow

Two semi-analytical approaches for solving condensation shocks in supersonic nozzle flows

The paper describes two methods for solving condensation shocks in steady-state quasi-one- dimensional flows. A single-fluid-model has been implemented by solving the algebraic form of compressible flow conservation equations, in conjunction with nucleation and droplet growth laws from gas-kinetic theory. The second method assumes the condensation shock problem as a flow discontinuity, the downstream state of the shock being defined as a weak-detonation, and determined from intersections on the Rayleigh and Hugoniot curves. Both approximations have been implemented with complex multi-parameter equations-of-state based on the Helmholtz free energy, taking into account the non-ideal gas flow behavior of steam and carbon dioxide. In order to reproduce operating conditions of engineering applications, where non-equilibrium condensation occurs such as steam turbines, injectors, supercritical carbon dioxide compressors and supersonic gas flow separators. Both gas-kinetic and flow discontinuity approaches have been tested for several nozzle geometries and results have been compared with low- and high-pressure experimental data of steam and carbon dioxide. The results show that both models are able to model properly the pressure recovery that occurs in supersonic condensing flows. It has been found a low deviation 4% from experimental data of steam, and deviations within 8 % were found for the carbon dioxide case. The average droplet radius size distribution obtained from the droplet growth model is in the same order of magnitude of that of reported by experimental data available in open literature. Finally both methods were implemented in a converging-diverging nozzle of a carbon dioxide ejector in order to explore the effects of the stagnation temperature and to determine conditions free of condensation.

Pore-scale study of non-ideal gas dynamics under tight confinement considering rarefaction, denseness and molecular interactions

Non-ideal gas flow behaviors are investigated by an Enskog-Vlasov type kinetic model considering the simultaneous effects of gas molecule size (volume exclusion) and long-range intermolecular attractions at the molecular level, which corresponds to the real gas equation of state at the macroscopic level. The Knudsen minimum is captured and a local Knudsen maximum may appear if gas molecule sizes or intermolecular attractive forces are considered. Although the Boltzmann equation is applicable to all the flow regimes in rarefied gas dynamics, it is invalid for a dense gas system, such as a tight or a shale gas reservoir. The Boltzmann-BGK model and the Enskog-BGK model overestimate and underestimate the mass flow rate of real gases, respectively, while Guo's model is more accurate to investigate real gas dynamics under tight confinements from a physical perspective. As the channel width increases or the solid fraction decreases, the impact of intermolecular interactions reduces. An anomalous slip regime occurs if both the volume exclusion and long-range intermolecular attraction are considered. Although the rarefaction effect is more prominent at larger Knudsen numbers, the flow at a smaller Knudsen number (a larger solid fraction or channel width) contributes to more practical gas production. The effect of long-range intermolecular attractions on gas dynamics decreases with temperature for real gases. This paper provides a novel insight into the real gas flow characteristics in a dense gas system, such as tight and shale gas reservoirs, from molecular natures of fluids.

Evolution of $$C^{1}$$-wave and its collision with the blast wave in one-dimensional non-ideal gas dynamics

The aim of the present paper is to analyze the collision of discontinuity wave with blast wave in non-ideal gas flow through Lie group approach. The particular solution of the system of quasilinear hyperbolic PDEs, governing one-dimensional unsteady cylindrically symmetric motion in non-ideal gas, is obtained. The equation governing the evolutionary process of weak discontinuity in non-ideal gas is derived which is utilized to discuss the growth and decay process of the weak discontinuity. Furthermore, the collision of discontinuity wave with the blast wave is examined inside the state described by the exact solution of the blast wave. Also, the existence and uniqueness properties of reflection and transmission coefficients of the waves along with the discontinuity in the shock acceleration are discussed.

The propagation of weak shock waves in non-ideal gas flow with radiation

In the present paper, the evolutionary behavior of weak shock waves propagating in an unsteady one-dimensional flow in non-ideal radiating gas is analyzed. The effect of thermal radiation under optically thin limit is included in the energy equation of the governing system. The method of asymptotic analysis is used to derive the transport equation describing the propagation of waves under the high-frequency conditions which is also used to determine the time of first wave-breaking conditions. The equation governing the propagation of acceleration waves is also obtained. Furthermore, the movement of disturbance in the shape of saw-tooth profile is discussed. The effect of parameter of non-idealness under the influence of radiative heat transfer, on the decay of sawtooth profile is analyzed.

Riemann problem for non-ideal polytropic magnetogasdynamic flow

The main motive of the present paper is to derive the analytical solution of the Riemann problem for magnetogasdynamic equations governing an inviscid unsteady one-dimensional flow of non-ideal polytropic gas subjected to the transverse magnetic field with infinite electrical conductivity. By using the Lax entropy condition and R–H conditions, we derive the elementary wave solutions i.e. shock wave, simple wave and contact discontinuities without any restriction on the magnitude of initial data states and discussed about their properties. Further, the density and velocity distribution in the flow field for the cases of compressive wave and rarefaction wave is discussed. Here we also compare/contrast the nature of solution in non-ideal magnetogasdynamic flow and ideal gas flow.

Exact Solution of the Weak Shock Wave in Non-ideal Gas

In the present paper the exact solution of quasilinear hyperbolic system of equations governing the propagation of weak shock waves in a one dimensional non-ideal adiabatic gas flow with generalized geometries is derived. Here the density ahead of the shock front is assumed to vary according to a power law of the distance. The effect of van der Waals parameter on the radius of weak shock wave is analyzed. An analytical expression for the total energy carried by weak shock wave in non-ideal gas is also derived.

Classification of the Riemann problem for compressible two-dimensional Euler system in non-ideal gas

This work is devoted to the study of two-dimensional Riemann problem modeled by compressible Euler system for the non-ideal gas. The initial constant data are divided in four quadrants in such a way that only one planar elementary wave connects two neighboring states. We classify the different combinations of planar elementary waves and subsequently discuss one by one using the method of generalized characteristic analysis. Attention is drawn to the changes in elementary waves, with regard to their shape, speed and strength, under the influence of the van der Waals parameter b. It has been shown that only sixteen (respectively, fifteen) distinct combinations of planar elementary waves exist for isentropic (respectively, non-isentropic) non-ideal gas flows.

Coupling of high Knudsen number and non-ideal gas effects in microporous media

High Knudsen number non-ideal gas flows in porous media are important and fundamental in various applications including shale gas exploitation and carbon dioxide sequestration. Because of the small pore size in tight rocks, the Knudsen number (Kn) may be high (i.e. much higher than 0.01) even though the gas is really dense. In fact, due to the high pressure and temperature underground, the gas usually manifests a strong non-ideal gas effect. Understanding the coupling mechanism of the high Kn effect and non-ideal gas effect is a premise to accurately model deep-seated underground gas exploitation or carbon dioxide sequestration. In this work, we theoretically analyse the high Kn non-ideal gas flows in microporous media. Based on the relative importance of the non-ideal gas effect and high Kn effect, the coupling is divided into four types. The analysis is subsequently validated by multiscale numerical simulations, in which the four types of coupling are clearly demonstrated. After applying the analysis to laboratory measurements, we propose a characteristic pressure model to calculate the gas permeability of tight rocks with better precision. The new model incorporates the non-ideal gas effect with the high Kn effect accurately and better bridges the laboratory measurements with the reservoir engineering.