Real Gas Flow Research Articles

Large time existence and asymptotic stability of the generalized solution to flow and thermal explosion model of reactive real micropolar gas

We study the long time behavior of the generalized solution of the flow and thermal explosion model of the reactive real micropolar gas. The dynamics of the chemical reaction involved and the usual laws of conservation of mass, momentum, angular momentum, and energy generate a complex governing system of partial differential equations. The fluid is nonideal and non‐Newtonian. In this work, we prove that the problem can be solved in an infinite time domain and establish the asymptotic properties of the solution. Namely, we conclude that for certain parameter values, the solution stabilizes exponentially to a steady‐state solution, while for others the stabilization occurs but at power decay rate. At the end, we conducted a few numerical tests whereby we experimentally confirmed theoretical findings about long‐term behavior of the solution.

Implementation and assessment of a low-dissipative OpenFOAM solver for compressible multi-species flows

An ever-increasing number of engineering problems regard the numerical simulation of fluid flows with high-density ratio, shock wave onset, and different chemical species. In such conditions, obtaining reliable results depends on the ability of the numerical algorithm to offer a stable and robust time and space discretization of the governing equations while simultaneously limiting the numerical diffusivity.This work presents the extension and the assessment of a low-dissipative Navier–Stokes solver for compressible, multi-specie flows. We first studied the Richtmyer–Meshkov instability to test the code on fluid flows involving shock waves and species interactions for ideal gas. Then, we simulated a benchmark case regarding a cryogenic coaxial injector often used in rocket engines to explore the solver’s capability in representing high-Reynolds-number supercritical flows of multi-species real gases with large density gradients. Finally, we studied the flow in complex geometries like a high-pressure gasoline injector for propulsion application. The results demonstrate the capability of the present approach in the cases investigated.

A compressible flow solver for turbomachinery of the real gases with strongly variable properties

Accurate prediction of real gas flows with strongly variable properties is an essential prerequisite for turbomachinery performance analysis. This paper presents a density-based solver for real gas flows in turbomachinery. The solver employs a third-order discretization scheme to improve computational accuracy. Real gas equations of state and look-up table are utilized in the solver to account for the strong nonlinear variations of thermophysical properties. The preconditioning method is adopted for simulations, including low-Mach flow regions, to address convergence difficulties. The implicit Time Consistent Preconditioned Gauss-Seidel Scheme (TCPGS) is employed for the time-stepping. The solver is validated by transonic compressor cascade wind tunnel experiments. Numerical test cases are adopted to evaluate the solver performance, including NASA Rotor 67, NASA Rotor 37, real gas flows in the Laval nozzle, and compressor seal. It has been proved that the numerical test results are consistent with published technical data. The advantages of this solver include numerical stability, computational efficiency, and physical accuracy, which indicate its applicability in the turbomachinery design process for real gases.

High-fidelity numerical investigation of a real gas annular cascade with experimental validation

This study aims at investigating real gas flow in the complex geometry of the Cambridge University annular turbine cascade using numerical simulations. The objectives include validating the numerical approach and understanding the loss mechanisms in this configuration. The numerical results are compared to experimental measurements obtained at various locations in the domain. Two turbulence modeling techniques, large Eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS), are employed to assess the influence of turbulence models and inlet turbulence levels. The results show good agreement between numerical simulations and experimental measurements in regions upstream of the trailing edge. However, discrepancies arise in the transition region of the suction side boundary layer, and RANS results are influenced by the choice of turbulence injection. In the wake of the blade, both RANS and LES accurately predict the stagnation pressure ratio, with some slight differences in shock positions and total pressure levels. The analysis reveals that large vortical structures at the hub contribute significantly to the overall losses in this annular configuration. The study quantifies losses due to boundary layers, the wake, and vortical structures using a loss coefficient, with RANS and LES producing slightly different results. These differences, while calling for further experimental measurements, also hint at the possible inaccuracy of the present turbulence models in the context of real gas flows for which a dedicated modeling effort is required.

Detonation in van der Waals Gas

Solving problems of detonation control is associated with obtaining detailed information about the gas dynamics accompanying the detonation process. This paper focuses on the dynamics of real gas flow through a plane detonation wave. The influence of real gas parameters on the Chapman–Jouguet detonation process has been studied. The process is described using the Rankine–Hugoniot system of equations. To model the thermodynamic properties of a real gas, the van der Waals equation of state is used. Equations are obtained to determine the ratio of speeds and pressures during the passage of a wave. The influence of van der Waals parameters on changes in the parameters of the detonation process was elucidated. An increase in parameter A slows down the increase in pressure in the detonation wave, and an increase in parameter B enhances it. Differences in the speed of combustion products for ideal and real gases are shown. For an ideal gas, combustion products flow from the detonation front at a critical (sonic) speed. For a van der Waals gas, the speed of combustion products may be greater than the critical one. Moreover, both factors, additional pressure (A) and additional volume (B), lead to acceleration of combustion products. Effects of heat release on the process parameters were elucidated.

A priori test of Large-Eddy Simulation models for the Sub-Grid Scale turbulent stress tensor in perfect and transcritical compressible real gas Homogeneous Isotropic Turbulence

In this study, the focus lies on the modeling of the subgrid-scale stress tensor in the context of real gas flows. By conducting tests on perfect and dense gas configurations using six different models, the research findings highlight the superiority of gradient models over eddy-viscosity models in capturing the structural behavior of the stress tensor. However, the models’ performance experiences a significant decline when considering the intricate thermodynamics of real gases. To address this challenge, dynamic models that take into account the characteristics of the flow are also tested, resulting in some improvements in the outcomes. Despite these advancements, the achieved results still fall short of being entirely satisfactory. In particular, the models fail to accurately predict the occurrence of large values of the subgrid-scale stress tensor in the real gas flow. The complex thermodynamic nature of real gases therefore significantly influences the subgrid-scale stress tensor and the outcomes of this study underscore the urgent need for continued research to advance our understanding and modeling capabilities of subgrid-scale terms in real gas flows, paving the way for statistically accurate Large-Eddy Simulations of industrial real gas flows using moderately refined grids.

Kinetic-energy- and pressure-equilibrium-preserving schemes for real-gas turbulence in the transcritical regime

Numerical simulations of compressible turbulent flows governed by real-gas equations of state, such as high-pressure transcritical flows, are strongly susceptible to instabilities. In addition to the inherent multi-scale nature of the flow, the presence of a pseudo-interface can generate spurious pressure oscillations when conventional schemes are utilized. This study proposes a general framework to derive and analyze discretization methods that are able to preserve kinetic energy by convection, and simultaneously maintain pressure equilibrium in discontinuity-free compressible real-gas flows. The formal analysis reveals that the discrete pressure-equilibrium condition can be fulfilled at most to second-order accuracy, as it requires the spatial differential operator to satisfy a discrete chain rule when total or internal energy are directly discretized. A novel class of schemes based on the solution of a pressure equation is thus proposed, which preserves mass, momentum, kinetic energy and pressure equilibrium, but not total energy. Extensive numerical tests of increasing complexity confirm the theoretical predictions, and show that the proposed scheme is capable of providing non-dissipative, stable and oscillation-free simulations, unlike existing methods tailored for the transcritical regime.

On the Development of an Implicit Discontinuous Galerkin Solver for Turbulent Real Gas Flows

The aim of this work is to describe an efficient implementation of cubic and multiparameter real gas models in an existing discontinuous Galerkin solver to extend its capabilities to the simulation of turbulent real gas flows. The adopted thermodynamic models are van der Waals, Peng–Robinson, and Span–Wagner, which differ from each other in terms of accuracy and computational cost. Convective numerical fluxes across elements interfaces are calculated with a thermodynamic consistent linearized Riemann solver, whereas for boundary conditions, a linearized expression of the generalized Riemann invariants is employed. Transport properties are treated as temperature- and density-dependent quantities through multiparameter correlations. An implicit time integration is adopted; Jacobian matrix and thermodynamic derivatives are obtained with the automatic differentiation tool Tapenade. The solver accuracy is assessed by computing both steady and unsteady real gas test cases available in the literature, and the effect of the mesh size and polynomial degree of approximation on the solution accuracy is investigated. A good agreement with experimental and numerical reference data is observed and specific non-classical phenomena are well reproduced by the solver.

A HiLo interior ballistic model based on the hypothesis of gases adiabatic transformation in the high pressure chamber

Weapons built on high-low pressure (HiLo) principle involve the existence of two chambers between which a gas flow occurs. The usual approach in the mathematical models developed for such systems is to consider that the gas flow is accompanied by an isothermal transformation of gas in the high pressure chamber. The present paper deals with the development of a lumped interior ballistic model built on more realistic assumptions like an adiabatic transformation of the gases in the high pressure chamber, an isentropic flow of real gases through the nozzles, a variable burning surface of the propellant grains and the occurrence of heat losses at the level of vent holes lateral surfaces. The experimental results obtained with a modified closed vessel were used in order to validate the proposed model. The pressure time variations in both chambers were accurately predicted by the proposed lumped model. The lumped model application on a 40 mm grenade launcher gives results consistent to the experimental measurements regarding the grenade muzzle velocity.

Study on Multiscale Fluid–Solid Coupling Theoretical Model and Productivity Analysis of Horizontal Well in Shale Gas Reservoirs

In order to study the productivity dynamic evolution laws of shale gas horizontal well, a multiscale seepage theoretical model considering the fluid–solid coupling effect is proposed first in this paper, which introduces an anisotropic matrix permeability model that comprehensively considers multiple flow regimes and an artificial hydraulic fracture conductivity model that considers proppant deformation and embedment. Then the reliability of the theoretical model is verified by the field production data obtained from the Marcellus shale. Based on the established productivity model, the evolution laws of pore pressure and permeability in different areas of the reservoir with different production periods are studied first, and then the shale gas production rate and cumulative production under different physical mechanisms, different shale gas flow regimes, and different reservoir parameters are quantified and analyzed. The simulation results show that the pore pressure in the hydraulic fracture area decreases rapidly at the initial stage of production, resulting in large deformation, and the fracture conductivity tends to be stable gradually at the later stage of production. The desorption effect will increase shale gas production, while the stress sensitivity is just the opposite. When only real gas flow is considered, the gas cumulative production is the highest. The fluid–solid coupling of hydraulic fractures has a great impact on the production, while the fluid–solid coupling in the matrix area has a small impact on the production, which can be ignored if appropriate. During the sensitivity analysis of reservoir parameters, it is observed that the influence of parameters of hydraulic fractures on production is much higher than that of matrix regional parameters. During the production process, these influencing factors can be adjusted according to the change of production data to achieve the optimization of shale gas production. In a word, the new model proposed in this paper provides a more accurate method to estimate the impact of multiple physical mechanisms, especially the fluid–solid coupling effect, on shale gas production compared with the existing model. The research results of this study can provide some reference and guidance for the dynamic prediction of shale gas production and optimization of production parameters.

Characterization of the Knudsen Number and Gas Transport in Shale Reservoirs: Coupling the Microfracture Network and Capillary Network

An accurate understanding of gas seepage mechanisms in shale reservoirs would have a positive impact on promoting shale gas development. Shale is a complex dual-porosity medium composed of a microfracture network and capillary network. However, most shale dual-porosity permeability models have usually ignored the influence of key mechanisms, such as effective stress and gas adsorption. In addition, the depiction and analysis of the Knudsen number has not been fully discussed in previous studies. In this study, the inner relationship between intrinsic permeability and porosity has been taken to be a bridge, with the fracture width including the pore radius being quantified, leading to a modification of the Knudsen number in the microfracture network and capillary network. Based on the modified Knudsen number, a dual-porosity permeability model has been developed for typical shale reservoirs that considered real gas effect, flow regimes, effective stress, and gas adsorption. The reliability of the new model has been validated by published experimental data under different conditions and through comparisons with the existing theoretical models. Finally, the evolution law relating to gas apparent permeability and the Knudsen number in the microfracture network and capillary network has been discussed, and the effects of different factors concerning apparent permeability and the Knudsen number have been quantified. Based on the results, the relationships between the coupled effects relating to the rock deformation field, the microfracture network seepage field, the capillary network seepage field, and the Knudsen number have been proposed. Moreover, the mechanisms relating to the internal swelling coefficient and gas rarefaction coefficient, including different pore network occupancies on total gas transport capacity, have been presented. The research results will provide a basis for the accurate numerical simulation for shale gas and will be of great significance to the economic development of shale gas in the future.

A Similarity-Based Solution for Nonlinear Gas Fractional Diffusivity Equation with Application to Rate Transient Analysis of Unconventional Heterogeneous Reservoirs

Summary Production characteristics of fractured wells in unconventional heterogeneous reservoirs have been shown to be effectively captured via anomalous diffusion model in which a partial differential equation (PDE) with fractional derivatives is solved. This paper presents a novel semianalytical solution of the nonlinear fractional diffusivity equation (FDE) applied to compressible fluid (gas) flow toward hydraulic fractures placed in heterogeneous and complex geological porous media. Self-similar theory and scaling transformation are used to solve the nonlinear PDE of fractional derivative written for real gas flow using density as the primary variable. The governing nonlinear partial gas FDE is transformed to ordinary nonlinear fractional differential equation after introducing similarity variables, which is later solved via shooting method coupled with Runge-Kutta integration. Pressure-dependent gas properties are captured straightforwardly in the solution without resorting to any further linearization via pseudopressure or pseudotime functions. The proposed similarity-based semianalytical solution is benchmarked against a Laplace transform-based analytical solution for linear, liquid FDE, and validated against a finely gridded numerical solution for the nonlinear, gas FDE. The proposed solution enables the diagnostic interpretation and characterization of production responses of unconventional gas wells exhibiting power-law behavior on the premise of anomalous diffusion during early transient period, which permits the estimation of important reservoir and fracture properties as shown in the case studies. Field and numerical examples are presented to showcase the capabilities of the proposed approach in the inverse, rate transient analysis.

Local existence theorem for micropolar viscous real gas flow with homogeneous boundary conditions

We consider the model for one‐dimensional micropolar, viscous, polytropic, and thermally conductive real gas flow with homogeneous boundary conditions, using the generalized equation of state for pressure. The generalization is shown by the fact that the pressure depends on the mass density as a power function. The governing system of partial differential equations is given in the Lagrangian description. Using the Faedo–Galerkin method and a priori estimates, we prove that the generalized solution exists locally in time.

Assessment of an algebraic equilibrium wall-function for supercritical flows

In this work the application of an algebraic equilibrium wall-function to real-gas flows is presented and analyzed. The aim is to assess capabilities of existing algebraic wall-functions in supercritical conditions. In particular a systematic analysis on the coupled wall-function of Cabrit and Nicoud is carried out a-priori on a wall-resolved Large Eddy Simulations (WR-LES) database, featuring cryogenic para-hydrogen flow in a heated pipe at supercritical pressure. The model is shown to overestimate the wall-temperature for increasing values of the imposed heat flux and to slightly underestimate the skin friction velocity. The causes of the failure are investigated. In particular the focus is on the equilibrium boundary layer hypothesis, on the validity of the Van Driest transformation for supercritical, stratified flows and on the ideal-gas assumption employed in the original derivation of the model. For the latter, a consistent thermodynamic correction is proposed in order to extend the applicability of the mentioned wall-function to any arbitrary Equation of State (EOS). The proposed extension is tested a-priori and is shown to provide improved temperature and skin friction velocity predictions at wall, although still presenting relevant deviations from the reference database solution. The discrepancies seem to be addressed to the equilibrium assumption and to the Van Driest transformation. The former in particular accounts for 5−20% of the reference value for the skin friction velocity, among all cases and 〈y+〉 examined, and for 1−20% in terms of wall-temperature depending on the considered heat flux. The latter is shown to fail on the mentioned database for increasing stratifications, with errors between 1−40% depending on the considered case. An additional analysis of more recently proposed transformations for variable property flows reveals the same limitations.

Real-Gas Effects for Shock/Shock Interaction in Earth and Mars Atmospheres

Shock/shock interactions of types IV, V, and VI are simulated for Earth and Mars conditions using perfect-gas, real-gas chemical nonequilibrium (real-gas CN), and real-gas thermochemical nonequilibrium (real-gas TCN) solvers for double-wedge configurations. In type IV interactions, the real-gas flow has normal shock closer to the second wedge as compared to the perfect-gas assumption. Similarly, for type V Mach reflection interaction, the Mach disk is noticed to shift downstream for the planet Earth conditions; whereas for the Martian case, transition to the type V regular reflection (RR) is observed. No noticeable change is evident in the type VI shock pattern for either atmospheric case. Increments in the freestream stagnation enthalpy, in both the planetary conditions, transforms the type IV interaction to type V (RR) and type V to a type VI when real-gas CN is assumed. Furthermore, the type VI interaction portrays a thinner shock layer. Although the shock structure is independent of stagnation enthalpy for a perfect-gas, simulations for high-enthalpy airflows using the real-gas TCN solver reveal resistance to shock transformations, unlike what is seen using the real-gas CN solver. But, the shock pattern is analogous for Martian conditions at simulated enthalpies for both of the real-gas models.

One-Dimensional Model and Numerical Solution to the Viscous and Heat-Conducting Reactive Micropolar Real Gas Flow and Thermal Explosion

One-Dimensional Model and Numerical Solution to the Viscous and Heat-Conducting Reactive Micropolar Real Gas Flow and Thermal Explosion

Dynamics of expanding gas from supercritical state in conical nozzle and cluster formation

A gas dynamic model of supersonic expansion of a real (supercritical) gas flow in nozzle based on the Redlich-Kwong equation of state has been developed. The proposed model can serve as a basis for describing the expansion of the main gas (carrier gas), against which processes of interest (formation of clusters, microcapsules, condensation) occur. Specific calculations were performed for clustering in Ar and Kr flow. Experimental verification of results of the model calculations of the sizes and densities of Ar and Kr clusters using the Rayleigh scattering method was performed. The proposed model for describing cluster jets has been tested in the experiments aimed at creating X-ray sources and accelerated electron beams in the process of relativistic laser action on a krypton cluster jet.

Plasma assisted CO2 dissociation in pure and gas mixture streams with a ferroelectric packed-bed reactor in ambient conditions

Carbon dioxide decomposition is a challenging target to combat climate change. Nonthermal plasmas are advantageous for this purpose because they operate at ambient conditions and can be easily scaled-up. In this study, we attempt the CO2 splitting into CO and O2 in a parallel plate packed-bed plasma reactor moderated with Lead Zirconate Titanate (PZT) as ferroelectric component, achieving conversion rates and energy efficiencies higher than those obtained with BaTiO3 in our experimental device. The analysis of the reaction mechanisms with optical emission spectroscopy under various operating conditions has shown a direct correlation between energy efficiency and intensity of CO* emission bands. These results and those obtained with a LiNbO3 plate placed onto the active electrode suggest that high temperature electrons contribute to the splitting of CO2 through an enhancement in the formation of CO2+ intermediate species. Results obtained for CO2 + O2 mixtures confirm this view and suggest that back recombination processes involving CO and O2 may reduce the overall splitting efficiency. The study of mixtures of CO2 and dry air has proved the capacity of ferroelectric packed-bed reactors to efficiently decompose CO2 with no formation of harmful NXOY subproducts in conditions close to those in real facilities. The found enhancement in energy efficiency with respect to that found for the pure gas decomposition supports that new reaction pathways involving nitrogen molecules are contributing to the dissociation reaction. We conclude that PZT moderated packed-bed plasma reactors is an optimum alternative for the decompositon of CO2 in real gas flows and ambient conditions.

Local existence for viscous reactive micropolar real gas flow and thermal explosion with homogeneous boundary conditions

In this paper, we prove that the one-dimensional model of reactive micropolar real gas flow and thermal explosion has a solution locally in time. We first define the notion of a generalized solution for the governing initial-boundary value problem. We prove the claim of local existence by deriving a sequence of approximate problems obtained by Faedo-Galerkin projections. A priori estimates allow us to choose small enough time interval of existence, and show that the sequence of approximations is bounded in certain functional spaces, and therefore has a convergent subsequence. In the end, we show that it is precisely this limit that is the solution to the observed problem.

One-dimensional model and numerical solution to the viscous and heat-conducting micropolar real gas flow with homogeneous boundary conditions

In this paper, we analyze the micropolar, viscous, polytropic, and heat-conducting real gas, whereby we assume the generalized form of pressure function in the sense that pressure is the affine function of temperature and power function of mass density. Using the stated thermodynamical and constitutive assumptions, we derive a one-dimensional model based on balance laws, first in the Eulerian and then in the Lagrangian description.The main result of this paper is the implementation of the Faedo–Galerkin method to obtain a numerical solution to a corresponding problem with homogeneous boundary conditions, where we analyze the performance of different ODE solvers. We also validated the method using some selected examples. The numerical results are also compared with the already known models, which are a special case of the model analyzed here.