One-dimensional Two-phase Flow Research Articles

Modeling non-monotonic variation of plume angle with superheat index of flash boiling spray

There is an urgent need for modeling angles and widths of liquid jet with internal phase change, but existing semi-empirical models rely strongly on coefficient fitting and lack a thorough understanding of the additional phase-change physics. In the present work, we proposed a theoretical model to predict the non-monotonic variation of plume angle with the defined superheat index of flash boiling spray. Assuming that the plume angle is determined by the trajectories of tiny droplets in the perimeter of the spray, this model identifies the angle with the inverse tangent of the ratio of the streamwise and crosswise velocities of the tiny droplets. The streamwise velocity is determined by solving a one-dimensional two-phase flow within the channel, and the crosswise velocity is determined by modeling the burst of an equivalent bubble at the exit of the nozzle. Compared with the existing semi-empirical models, this model is free of fitting parameters, and it agrees well with the experimental data from a rectangular microchannel with discrepancies being sufficiently discussed. This model has the potential of being applied to modeling the plume angle of flash boiling sprays with different nozzle geometries in various atomization practices.

A two-phase flow model for sedimentation and consolidation

Sedimentation and consolidation, a multi-physical phenomenon of great significance in aquatic environments, usually involves dynamic pore pressure, inertial effects, fluid-particle interphase interaction and solid stress. However, simplified models for sedimentation and consolidation typically assume hydrostatic mixture pressure and neglect inertial effects without proper justifications. Here, a one-dimensional three-equation two-phase flow model (TTP) is proposed for sedimentation and consolidation, which directly resolves dynamic fluid pressure and inertial terms. The present TTP model is benchmarked against a series of experimental cases and two existing four-equation two-phase flow (FTP) models. It features encouraging performance as compared to measured data and computed results of the existing FTP model. Furthermore, the present TTP model shows superior computing efficiency over the FTP models. To investigate the influences of inertial effects and non-hydrostatic mixture pressure, two simplified versions of the TTP model are constructed and compared with the TTP model. It is shown that incorporating inertial effects and non-hydrostatic fluid pressure are important for accurately predicting the sedimentation-consolidation process. The present study facilitates a promising framework for modelling sedimentation and consolidation, thereby supporting effective sediment management.

Symmetry and scaling in one-dimensional compressible two-phase flow

Investigations of shock compression of heterogeneous materials often focus on the shock front width and overall profile. The number of experiments required to fully characterize the dynamic response of a material often belie the structure–property relationships governing these aspects of a shock wave. Recent observations measured a pronounced shock-front width on the order of 10 s of ns in particulate composites. Here, we focus on particulate composites with disparate densities and investigate whether the mechanical interactions between the phases are adequate to describe this emergent behavior. The analysis proceeds with a general Mie–Grüneisen equation of state for the matrix material, a general drag force law with general power-law scaling for the particle-matrix coupling of the phases, and a volume fraction-dependent viscosity. Lie group analysis is applied to one-dimensional hydrodynamic flow equations for the self-consistent interaction of particles embedded in a matrix material. The particle phase is characterized by a particle size and volume fraction. The Lie group analysis results in self-similar solutions reflecting the symmetries of the flow. The symmetries lead to well-defined scaling laws, which may be used to characterize the propagation of shock waves in particle composites. An example of the derived scaling laws for shock attenuation and rise time is shown for experimental data on shock-driven tungsten-loaded polymers. A key result of the Lie analysis is that there is a relationship between the exponents characterizing the form of the drag force and the exponent characterizing the shock velocity and its attenuation in a particulate composite. Comparison to recent experiments results in a single exponent that corresponds to a conventional drag force.

New Analytical Expressions of Concentrations in Packed Bed Immobilized-Cell Electrochemical Photobioreactor

An electrochemical photobioreactor with a packed bed containing transparent gel granules and immobilized photosynthetic bacterial cells is shown with a one-dimensional two-phase flow and transport model. We consider the biological/chemical events in the electrochemical photobioreactor, the intrinsically connected two-phase flow and mass transport, and other factors. This model is based on a system of nonlinear equations. This paper applies Akbari-Ganji’s and Taylor series methods to find analytical solutions to nonlinear differential equations that arise in an immobilized-cell electrochemical photobioreactor. Approximate analytical expressions of the concentration of glucose and hydrogen are obtained in liquid and gas phases for different parameter values. Numerical simulations are presented to validate the theoretical investigations.

Identifying the enhancement mechanism of Al/MoO3 reactive multilayered films on the ignition ability of semiconductor bridge using a one-dimensional gas-solid two-phase flow model

Energetic Semiconductor bridge (ESCB) based on reactive multilayered films (RMFs) has a promising application in the miniature and intelligence of initiator and pyrotechnics device. Understanding the ignition enhancement mechanism of RMFs on semiconductor bridge (SCB) during the ignition process is crucial for the engineering and practical application of advanced initiator and pyrotechnics devices. In this study, a one-dimensional (1D) gas-solid two-phase flow ignition model was established to study the ignition process of ESCB to charge particles based on the reactivity of Al/MoO3 RMFs. In order to fully consider the coupled exothermic between the RMFs and the SCB plasma during the ignition process, the heat release of chemical reaction in RMFs was used as an internal heat source in this model. It is found that the exothermal reaction in RMFs improved the ignition performance of SCB. In the process of plasma rapid condensation with heat release, the product of RMFs enhanced the heat transfer process between the gas phase and the solid charge particle, which accelerated the expansion of hot plasma, and heated the solid charge particle as well as gas phase region with low temperature. In addition, it made up for pressure loss in the gas phase. During the plasma dissipation process, the exothermal chemical reaction in RMFs acted as the main heating source to heat the charge particle, making the surface temperature of the charge particle, gas pressure, and gas temperature rise continuously. This result may yield significant advantages in providing a universal ignition model for miniaturized ignition devices.

Dynamics of gas-driven eruption on Ceres as a probe to its interior

The mineralogy of localized bright deposits on Ceres observed by the DAWN mission suggests their brine-enriched cryovolcanic origin. Based on the morphological observations of these deposits, explosive and effusive styles have been proposed for their eruption. Because volcanic eruption style and velocity are controlled by the extent of gas expansion inside the conduit, constraints on the internal aqueous environment, such as gas concentration and temperature, could be placed based on the observations of localized deposits on Ceres. However, the way these properties control the eruption style and velocity is complex. Cryomagma ascending from a subsurface reservoir gains buoyancy due to both boiling of water and exsolution of dissolved gas, owing to decompression to the extremely low pressure near the Ceres surface. Gas–melt segregation should also affect the dynamics. Thus, it is not yet fully understood how the internal environment of Ceres affects the ascent dynamics of cryovolcanism and subsequently controls the styles (explosive versus effusive) and velocities of eruptions. To address this problem, we developed a one-dimensional steady-state two-phase flow model for the ascent dynamics of gas-driven cryomagma under the conditions of Ceres taking both water boiling and gas exsolution into account. We found that the velocity and explosivity of an eruption are strongly controlled by the following three parameters, which characterize the cryomagmatic environment of Ceres's interior: (a) conduit conductivity (CC; rc2/μ, where rc is the conduit radius and μ is the magma viscosity), (b) dissolved gas concentration c0, and (c) magma reservoir temperature T0. Our model results reveal that low CC always leads to effusive or low-explosivity eruptions. Higher CC allows explosive eruption when either c0 or T0 is sufficiently high. These dependences can be summarized as four modes of eruption under the following CC-c0-T0 conditions. (1) Exsolution-driven explosive eruptions (X1 type) occur with volatile-rich magma (CC ≳ 10−3 m2/(Pa·s) and c0 ≳ 0.1 wt% of CO2). (2) Boiling-driven explosive eruptions (X2 type) occur with warm magma (CC ≳ 10−3 m2/(Pa·s), c0 ≪ 0.1 wt% of CO2, and high T0). (3) Viscosity-induced effusive eruptions (F1 type) occur with a narrow conduit and/or high-viscosity magma (CC ≲ 10−3 m2/(Pa·s)). (4) Low-gas-production-induced effusive eruptions (F2 type) occur with low-temperature and low-volatile magma (CC ≳ 10−3 m2/(Pa·s), c0 ≪ 0.1 wt% of CO2, and low T0). Our model predicts that either c0 ≳ 0.5 wt% of CO2 or T0 ≳−5°C is required for explosive eruptions to achieve eruption velocities ≳30 m/s, which has been proposed based on the size of some large faculae on Ceres. Such gas-rich or warm magma condition is unlikely to be achieved by equilibrium within the shallow crust. Thus, our results suggest that magma needs to be supplied from a deeper subsurface. In contrast, low-velocity effusion of brines has also been proposed based on morphometric analyses of evaporites on Ceres. Our results show that magma of such brine effusions is viscous and transported to the surface through a narrow conduit or they are sourced from reservoirs equilibrated to the ambient material within the shallow crust. Because the effusive eruption origin of faculae in the Occator crater is consistent with small conduits, the effusive nature may not necessarily rule out relatively high-volatile or warm magma inside Ceres in the recent past. These results show that the morphometric properties of facula deposits can place important constraints on the internal conditions of Ceres when the relevant eruption style/velocity is known. Our modeling results indicate that detailed observations (e.g., vesicularity, cooling history, and inclusion of eroded conduit material) of deposits and the possible vent structure in faculae by landing missions allow us to further probe the interior conditions of Ceres (e.g., magma temperature, gas concentration, viscosity, and conduit size).

Singular surface for non-ideal two-phase modified Chaplygin flow consisting of source term

In this manuscript, a system of partial differential equations (PDEs) outlining one-dimensional isentropic two-phase flow model consisting of a non-constant source term with non-ideal modified Chaplygin gas is derived. The model is reduced to an equivalent system of ordinary differential equations (ODEs) via Lie group scheme. The transport equation for the singular surface is derived using the compatibility conditions and solved numerically by coupling with the system of ODEs. Further, the effects of inclination of the flow and non-idealness on the amplitude of steepened wave (or singular surface) are investigated.

Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity

The exact Riemann solutions are constructed in completely explicit forms for the drift-flux equations of the one-dimensional inviscid, compressible and isentropic liquid-gas two-phase flow model in an inclined pipeline under gravity. It is found that the curved delta shock wave and vacuum state are involved in the Riemann solutions for the pressureless situation with the adiabatic exponent being one. It is proved rigorously that this curved delta shock wave solution satisfies the pressureless drift-flux equations in the sense of distributions. Finally, the asymptotic limits of Riemann solutions are investigated in detail when the adiabatic exponent tends to one, in which the concentration phenomenon can be observed when the non-self-similar Riemann solution consisting of curved 1-shock wave, 2-contact discontinuity and 3-shock wave converges to this curved delta shock wave solution. In addition, the cavitation phenomenon can also be inspected that all the states in the two rarefaction wave fans become the vacuum states in the limiting situation.

Numerical simulation research of inner ballistic overload of guided projectile based on coated mixed charge

In order to study the numerical variation law of the internal ballistic overload of the guided projectile under different coated mixed charge structures, and to provide a basis for the development of a new type of high muzzle velocity and low overload propellant charge design, taking a large-caliber suppressed artillery as the simulation object, the layered combustion model of the coated propellant was established by using the one-dimensional two-phase flow theory, and the lace 37-hole nitroguanidine propellant was used as the main charge (MC) and lace 19-hole nitroguanidine coated propellant as auxiliary charge (B). The effects of mixed charges with different charge mass, different mixing ratios and different coating layer thicknesses on the internal ballistic overload value were studied by simulation calculation. The research results show that the increase of the total charge mass will increase the overload impact of the guided projectile and the muzzle velocity of the projectile ; with the increase of the thickness of the coating layer and the proportion of the coated propellant in the mixed charge ratios, the longitudinal overload and the muzzle velocity of the projectile in the chamber of the guided projectile will be decreased to a certain extent and the time point when the maximum overload occurs will be delayed; under the structure of the coated mixed charge, the influence of the proportion of coated propellant in different mixed charge ratios and the coating layer thickness of coated propellant on the launch overload of the guided projectile is greater than the muzzle velocity of the projectile, and the effect of reducing the firing overload in the chamber by increasing the proportion of coated propellant in different mixed charge ratios is the most significant.

On convergence of explicit finite volume scheme for one-dimensional three-component two-phase flow model in porous media

Abstract In this work, we develop and analyze an explicit finite volume scheme for a one-dimensional nonlinear, degenerate, convection–diffusion equation having application in petroleum reservoir. The main difficulty is that the solution typically lacks regularity due to the degenerate nonlinear diffusion term. We analyze a numerical scheme corresponding to explicit discretization of the diffusion term and a Godunov scheme for the advection term. L ∞ {L}^{\infty } stability under appropriate CFL conditions and BV {\rm{BV}} estimates are obtained. It is shown that the scheme satisfies a discrete maximum principle. Then we prove convergence of the approximate solution to the weak solution of the problem, and we mount convergence results to a weak solution of the problem in L 1 {L}^{1} . Results of numerical experiments are presented to validate the theoretical analysis.

Application of different Krylov subspace methods in subcooled flow boiling simulation

In this work, a two-phase flow and heat transfer code was developed using the one-dimensional single-pressure six-equation two-phase flow model and the semi-implicit method. The developed code was validated with the Bartolomei’s subcooled flow boiling experiment and the numerical results indicated that the developed code has the capability for the simulation of subcooled flow boiling behavior. After that, the accuracy and efficiency performance of six Krylov subspace methods (CGS, BICG, BICGSTAB, GMRES, QMR and TFQMR) were evaluated. The results indicated that these six Krylov subspace methods have the capability for the accurate simulation of subcooled flow boiling behavior, and the TFQMR and CGS have better computational efficiency performance compared to other four Krylov subspace methods. This work could provide the benefit for the further development of nuclear reactor system analysis code.

Study on Micro Recoil Mechanism of the Weapon with a Nozzle and Two Chambers Separated by a Partition

In order to improve the recoil reduction ability of the weapon without reducing the projectile velocity, the weapon with a nozzle and two chambers separated by a partition is proposed. Taking the 35 mm caliber grenade launcher as the research object, the physical model of its launching process is proposed, and the one-dimensional two-phase flow interior ballistic model is established. MacCormack difference scheme is used to calculate the coupling of multiple physical fields formed by front and rear chambers and nozzles. Compared with the calculation results obtained by using the classical interior ballistic model, the correctness of the two-phase flow interior ballistic model is verified. The effects of the charge amount in the rear chamber and the size of the air guide hole in the barrel on the internal ballistic performance of the weapon with a nozzle and two chambers separated by a partition. The calculation results show that compared with conventional weapons, the recoil impulse can be reduced with maintaining muzzle velocity, and the recoil reduction efficiency can reach 72.27%, which is of great significance for improving weapon performance.

Mathematical Modelling and Simulation for One Dimensional - Two-Phase Flow Equation in Petroleum Reservoir: A Matlab Algorithm Approach

The reservoir behaviors described by a set of differential equation those results from combining Darcy’s law and the law of mass conservation for each phase in the system. The one-dimensional two-phase flow equation is implicit in the pressure and saturation and explicit in relative permeability. A mathematical model of a physical system is a set of partial differential equations together with an appropriate set of boundary conditions, which describes the significant physical processes taking place in that system. The processes occurring in petroleum reservoirs are fluid flow and mass transfer. Two immiscible phases (water& oil) flow simultaneously while mass transfer may take place among the phases. Gravity, capillary, and viscous forces play a role in the fluid-flow process. The model equations must account for all these forces and should also take into account an arbitrary reservoir description with respect to heterogeneity and geometry. Finally, one-dimensional two-phase flow equation through porous media is formulated by considering above reservoir parameters and forces. A numerical method based on finite difference scheme is implemented to get the solutions of one-dimensional two-phase flow equation. A MATLAB algorithm is used to solve the equation with mathematical analysis resulting in upper and lower bounds for the ratio of time step to mesh. The MATLAB algorithm is modified as per the model with appropriate initial and boundary conditions. The algorithm is applied to two-phase water flooding problems in laboratory size cores, and resulting saturation and pressure distribution are presented graphically. The saturation and pressure distribution of two-phase flow model is in agreement with the prediction of the Buckley Leveret theory. The numerical solution is used as a base for evaluating the numerical methods with respect to machine time requirement and allowable tie step for fixed mesh spacing.

Numerical simulation of two-phase flow in a side spray gun considering piston reset motion

In order to study the effect of the piston reset motion on the flow of propellant gas in a piston-controlled side spray gun, the propulsion process of the gun was modeled and simulated based on the one-dimensional two-phase flow interior ballistic theory. First, by considering the reciprocating motion of the piston-spring system that controls the opening and closing of the rear spray channel, a mathematical model of the gun propulsion process was established. It combines the gas-solid two-phase flow in the barrel, the fluid-solid coupling between the piston and the gas in the piston cavity, and the transient gas flow in the exhaust pipe. The flow field coupling between the barrel and the piston cavity, and the flow field coupling between the piston cavity and the exhaust pipe were modeled, respectively, and the solution procedure was displayed. The MacCormack scheme and the Runge-Kutta method were used in the simulations, and the accuracy of the numerical method was validated by the published data. Next, the propagation law of the rarefaction wave in the barrel during the firing cycle was gained. The projectile velocity and the pressure at the projectile base and the breech were presented. Then, the distributions of the pressure, the gas velocity, and the solid velocity in the barrel of the piston-controlled side spray gun were compared with those in the traditional gun. Finally, the effects of the piston reset motion on the propellant gas flow and the recoil reduction efficiency were analyzed. The results show that compared with the situation ignoring the piston reset motion, when the muzzle velocity is reduced by 1.52%, the recoil reduction efficiency of the case considering the reset motion drops from 38.86% to 32.88% because the piston closes the rear spray channel during the reset process. Therefore, the reset motion of the piston cannot be ignored in the numerical simulation on the gun firing process.

A suitability analysis of transient one-dimensional two-fluid numerical models for simulating two-phase gas-liquid flows based on benchmark problems

Gas-liquid two-phase flows in pipes are present in a variety of engineering applications. These applications require transient one-dimensional mathematical models coupled with robust numerical methods to simulate the flow behavior in time and space. As there exist several possible combinations of models and numerical methods, questions arise as to the suitability of these numerical models to best accommodate the problem features. Aiming to partially answer this question, we present in this work numerical simulations of two well-known gas-liquid benchmarks, the water faucet, and the shock tube problems, carried out with two two-fluid models – 4E1P (four equations and one pressure) and 5E2P (five equations and two pressures) – in association with three numerical methods – FCT (Flux-Corrected Transport method), FORCE (First-Order Centered Scheme) and ModFORCE. The numerical methods used herein are written in a general form and do not require the solution of the associated Riemann problem. The obtained results are sought to serve as a reference to choose the best approaches, among the ones studied, to tackle some transient one-dimensional two-phase flow problems, highlighting the advantages and disadvantages of each model and method combination regarding hyperbolicity, diffusive and dispersive effects. Overall, the combination of the 5E2P model with the ModFORCE numerical method provides the most accurate results compared to the analytical solutions available.

Thermal prediction of transient two-phase flow in cryogenic transportation based on drift-flux model

Accurate prediction as well as effective thermal management of transient cryogenic transportation is of great importance to the safe and high-efficiency utilization of cryogenic fluids. To predict the unstable cryogenic transportation process, a one-dimensional model coupling two-phase flow with transient heat conduction of solid tube is developed in this study. The transient two-phase flow is described by a drift-flux model, and a finite volume method (FVM) with staggered grid mesh is adopted for numerical calculation. Verified by a lot of experimental data, the proposed model shows its applicability in a wide range of conditions. Then, thermal performance and pressure surge phenomenon are investigated in detail. The intermittent chill-down strategy is recommended to take full use of the sensible energy of fluid from the perspective of energy saving. Besides, the pressure surge is verified as a special physical phenomenon in cryogenic fluids transportation process, which brings higher challenges to the storage, handling and transport of cryogenic fuels.

Recoil Reduction Method of Gun with Side to Rear Jet Controlled by Piston Motion

Excessive recoil severely restricts the loading of high-power traditional guns on modern vehicles. To reduce the recoil without breaking the continuous firing mode and reducing the projectile velocity, a recoil reduction method that controls the lateral ejecting of propellant gas by a piston was proposed. The recoil reduction device is symmetric about the barrel axis. First, a one-dimensional two-phase flow model of interior ballistic during the gun firing cycle was established. Next, the MacCormack scheme was used to simulate, and the piston motion was gained. Then the propagation of the rarefaction wave in the barrel was presented. Finally, the propulsion difference between the piston-controlled gun and the traditional gun was discussed. The results showed that the recoil momentum was reduced by 31.80%, and the muzzle velocity was decreased by just 1.30% under the reasonable matching of structural parameters.

Development and validation of a one-dimensional solver in a CFD platform for boiling flows in bubbly regimes

This paper presents a new one-dimensional solver for two-phase flow simulations where boiling is involved. The solver has been implemented within the OpenFOAM® platform. The basic formulation follows the Eulerian description of the Navier–Stokes equations. Different closure equations for one-dimensional simulations are also included, as well as a subcooled boiling model in order to perform accurate computations of the mass and heat transfer between phases. In addition to the fluid, a domain is included in order to represent the solid structure, so the solver is able to solve conjugate heat transfer problems. Two different test cases are presented in this work, first a single-phase test case in order to verify the conjugate heat transfer, and then a case based on the Bartolomej international benchmark, which consists of a vertical pipe where the fluid runs upwards while it is heated. Transient calculation were performed, and the results were compared to the TRACE system code, and to the experimental data in the corresponding case. With this calculations, the capability of this new solver to simulate one-dimensional single-phase and two-phase flows including boiling is demonstrated. This work is a first step of a final objective, which consists in allowing a 1D–3D coupling within the CFD platform, avoiding external links.

Appearance of the instability from the inhomogeneity in two-phase flow with gas-producing reaction in fractured porous medium

A homogenized model of incompressible two-phase flow accompanied by a gas-producing reaction in a double porosity medium with a chemically active skeleton is derived. The equations of the homogenized model contain non-local in time source terms corresponding to the contribution of the gas-producing chemical reaction in the matrix blocks. The time non-locality, which manifests itself as the appearance of a time delay between the change in reactant concentrations and the reaction rate, is shown to stimulate the instability of the one-dimensional two-phase flow initiated by injection of the acid solution into the double porosity medium with chemically active matrix blocks. The instability results in the development of the self-oscillating mode of the reaction wave propagation.

Simulation of Double One-dimensional Two-phase Flow of Single Coated Propellant Internal Ballistic

In this paper, based on the one-dimensional two-phase flow model, we established a model of a single coated propellant and wrote the corresponding software. Using software to simulate the internal ballistic process of a 105mm tank gun, the calculation results are compared with the experimental results of the actual coated propellant. The results show that the calculated values are in good agreement with the experimental values.