Compressible Two-phase Flow Model Research Articles

Comparison of rotor hovering aerodynamic performance in free-surface and ground effects using numerical methods

The aerodynamic performance of the rotor hovering on the air–water free-surface, which is significant for cross-medium unmanned aerial vehicles, is merely studied. In this study, a compressible two-phase flow model is used to compare the aerodynamic performance in the free-surface effect (FSE) and the ground effect (GE) with various dimensionless distances, γ, between the rotor and the ground (or free-surface). According to the results, the vortex core in FSE moves further in both vertical and radial directions than in GE for the early stages. Additionally, the blade surface is separated into three parts. In zone I, the aerodynamic performance is mostly determined by proximity effects. For both FSE and GE, the downward induced velocity at the rotor disk rises with increasing γ, leading to a decrease in the sectional thrust coefficient CT,S. By the way, CT,S is larger in FSE. In zone III, the aerodynamic performance is mostly governed by the blade tip vortex. The trend of aerodynamic performance with γ is reversed compared with zone I. The above-mentioned two opposing tendencies result in a smaller rotor thrust in FSE than in GE within the range of 0.60≤γ≤3.00, but a higher rotor thrust in FSE within the range of γ≤0.60.

Numerical investigation on the interaction characteristics between the gaseous detonation wave and the water droplet

In this paper, the interaction characteristics between the gaseous detonation and the water droplet are numerically investigated, utilizing a modified compressible two-phase flow model coupling with detailed hydrogen-oxygen chemistry. Firstly, an analysis is conducted on the propagation behaviors of the cellular detonation obstructed by the droplet. It is found that the cellular detonation undergoes reflection, diffraction, local extinction, and re-ignition upon the obstruction, and these behaviors vary with the droplet relative positioning with multi-dimensional structures of the cellular detonation, particularly in terms of the extinction degree caused by the diffraction and the relative positioning of the re-ignition region. Further, the droplet deformation characteristics are detailly analyzed. It has been revealed that the deformation behavior of the shocked droplet under planar detonation is consistent with that under high-speed airflow. However, for the droplet shocked by the cellular detonation, several windward surface pits are induced due to impaction from transverse shocks and direct hitting of the triple-point. The emergence of these pits notably precedes the onset of surface instabilities caused by high-speed airflow erosion. Further investigation has revealed that post-detonation flow, through the entrainment effect of the central pit, progressively penetrates and segregates the droplet into upper and lower segments, and this penetrating effect heavily depends on the droplet relative positioning. Moreover, the side pit, whose presence is significantly determined by whether there is direct impaction of the triple-point on the droplet windward side, is crucial for the deformation around the droplet equator and the subsequent shedding of smaller droplets.

An enhanced compressible two-phase flow model with detailed chemistry under the adaptive mesh refinement frame

In the present study, an enhanced compressible two-phase flow model is advanced, considering the effect of chemical reactions within a detailed mechanism. In this model, two immiscible fluids (liquid and gaseous mixture) are accurately separated with the resolved interface. Unlike the classical five-equation two-phase flow model, the thermal properties of gases are no longer assumed to be constant but rather vary as functions of temperature. A modified mechanical relaxation procedure is proposed and employed at the gas-liquid interface to prevent the occurrence of nonphysical pressure oscillation. In the gaseous mixture, numerous gas components are included and resolved by their mass fraction among the gaseous mixture. In this model, the heat release effect is simulated by a detailed chemistry. Furthermore, the numerical results of several benchmark problems in one dimension and two dimensions demonstrate the efficacy of the proposed compressible multiphase flow model, such as the air shock tube, the gaseous detonation tube, the shock-droplet interaction, and especially the detonation-droplet interaction that has received little focused interest and investigations. Moreover, a self-developed adaptive mesh refinement strategy is performed for a high efficiency of numerical solving.

High-Order ADER Discontinuous Galerkin Schemes for a Symmetric Hyperbolic Model of Compressible Barotropic Two-Fluid Flows

This paper presents a high-order discontinuous Galerkin (DG) finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced by Romenski et al. in [59, 62], in multiple space dimensions. In the absence of algebraic source terms, the model is endowed with a curl constraint on the relative velocity field. In this paper, the hyperbolicity of the system is studied for the first time in the multidimensional case, showing that the original model is only weakly hyperbolic in multiple space dimensions. To restore the strong hyperbolicity, two different methodologies are used: (i) the explicit symmetrization of the system, which can be achieved by adding terms that contain linear combinations of the curl involution, similar to the Godunov-Powell terms in the MHD equations; (ii) the use of the hyperbolic generalized Lagrangian multiplier (GLM) curl-cleaning approach forwarded. The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model. To illustrate the performance of the method, several different test cases and benchmark problems have been run, showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.

Two approaches to compute unsteady compressible two-phase flow models with stiff relaxation terms

The paper deals with the numerical modeling of two-phase flows while using Baer–Nunziato type models. Focus is given here on the numerical treatment of source terms that involve three (or four) relaxation time scales. A new coupled approach relying on the continuous analysis of the system of ODEs is compared with a more widely used strategy grounded on the fractional step approach. Properties of schemes are given in both cases. Several numerical applications show that the coupled approach should be preferred for both stability and accuracy reasons.

Numerical study of dynamics of cavitation bubble collapse near oscillating walls

This paper presents a numerical study of the dynamics of an initially spherical bubble collapse near an oscillating rigid wall with a large amplitude; the wall oscillating amplitude is greater than 1% of the initial maximum bubble radius. Numerical simulations were conducted using a compressible two-phase flow model and the volume of fluid (VOF) interphase-sharpening technique on a general curvilinear moving grid. The numerical results for bubbles in the free field and near a wall were computed and compared with published experimental data. To study the effects of the oscillating wall on bubble collapse, a sinusoidal function was used for wall oscillation. The initial bubble conditions were set as a Rayleigh bubble located above the rigid wall at a dimensionless bubble-boundary distance with initial phases of 0° and 180°. During bubble collapse, the interface deformation, jetting behavior, bubble collapse time, and bubble migration were determined. Violent collapse of the bubble, jetting behavior, and shock propagation from the significant effects of the oscillating wall were observed in simulation cases with different wall motions. The effects of the non-dimensional amplitude scale and non-dimensional period timescale were considered with the initial phases in the problem. The trend lines of typical characteristics and critical points of bubble collapse were determined.

Homogenization of a two-phase flow accompanied by dissociation of a gas hydrate in a fractured porous medium

A homogenized model of non-isothermal compressible two-phase flow accompanied by dissociation of a gas hydrate in a fractured porous medium is derived. The equations of the homogenized model contain non-local in time source terms corresponding to the contribution of the gas hydrate in the matrix blocks. The model of phase behavior of a gas hydrate is used that admits coexistence of the hydrate and products of its decomposition in a finite region of the phase diagram. This possible behavior is a consequence of non-linearity of the skeleton potential dependence on the depth of phase transition.

Study of Thermodynamic Effect on the Mechanism of Flashing Flow Under Pressurized Hot Water by a Homogeneous Model

Abstract The flashing flow in a Moby_Dick converging-diverging nozzle under pressurized hot water from 460.5 to 483.5 K is simulated using a homogeneous compressible water-vapor two-phase flow model. The kinematic and thermodynamic mass transfer are accessed using the cavitation model based on the Hertz–Knudsen–Langmuir equation. Our simplified thermodynamic model is coupled with the governing equations to capture the phase-change heat transfer. This numerical method proved its reliability through a comparison with available experimental data of flow parameters inside the nozzle. Consequently, the present numerical method shows good potential for simulating the flashing flow under pressurized hot water conditions. The satisfying prediction of averaged flow parameters with a slight improvement compared to reference numerical data is reproduced. The results confirm a noticeable impact of the thermodynamic effect on the mechanism of flashing flow, resulting in a considerable decrease in the flow temperature and the saturated vapor pressure. The flashing nonequilibrium is significantly decreased, forcing the flashing flow to be classified as the usual cavitation behavior and better suited to homogeneous model. While the temperature drop is highly dependent on evaporation, the thermodynamic suppression is influenced by the condensation. The suppression effect, unobserved in water at a lower temperature in previous studies, is noticeable for the pressurized hot water flow characterized by the cavitation mechanism. The vapor void fraction decreased considerably in the radial and axial directions as the water temperature rose to 483.5 K in this study.

Numerical simulation of flash evaporation in the presence of secondary nucleation

Rapid depressurization of a stagnant liquid below its prevailing saturation brings it to a metastable superheated state. Thermodynamic equilibrium is regained through a rapid evaporation or flashing which starts in a thin layer at the free surface and continues to propagate downward by nucleation and evaporation in the subsequent layers of superheated liquid below it. Secondary nucleation (from spurious locations) in the bulk of the superheated liquid or from the wall of the container uniquely affects the propagation of the free surface evaporating front.We computationally simulate the propagation of evaporating front in the presence of secondary nucleations, adopting a one dimensional, compressible two-phase flow model with diffuse interface. For simulating secondary nucleation at pre-determined sites, vapour density is assumed at the location and active interface is imposed locally.Secondary nucleation is noted to slow down the propagation of the evaporating front while the effect is more prominent with the proximity of the site. The secondary phase change interface is observed to grow towards the primary one and has a higher velocity as has been reported in different experiments. Secondary nucleation also hinders the propagation of the wave reflected back from the end of the domain. We also discuss some limitations of the model.

The Riemann problem for a drift-flux model of compressible two-phase flow in a variable cross-section duct

The Riemann problem for isentropic drift-flux model of compressible two-phase flow in a variable cross-section duct is considered. First, the two-phase duct flow model is established based on the balance laws. Then, by averaging the equations of single phase flow, the drift-flux model in a variable cross-section duct is deduced. The model includes two parts: mass conservation and momentum conservation. The elementary waves that make up the Riemann solutions are analyzed subsequently. Besides, the global entropy condition is imposed to select the physical relevant solution when across the stationary wave. Furthermore, we discuss the uniqueness of Riemann solutions and conclude that the solutions are unique in an expanding duct while not unique in a contracting duct. The results may contribute to the design of numerical schemes in the future study.

Compressible Two-Phase Viscous Flow Investigations of Cavitation Dynamics for the ITTC Standard Cavitator

In this paper, the ITTC Standard Cavitator is numerically investigated in a cavitation tunnel. Simulations at different cavitation numbers are compared against experiments conducted in the cavitation tunnel of SVA Potsdam. The focus is placed on the numerical prediction of sheet-cavitation dynamics and the analysis of transient phenomena. A compressible two-phase flow model is used for the flow solution, and two turbulence closures are employed: a two-equation unsteady RANS model, and a hybrid RANS/LES model. A homogeneous mixture model is used for the two phases. Detailed analysis of the cavitation shedding mechanism confirms that the dynamics of the sheet cavitation are dictated by the re-entrant jet. The break-off cycle is relatively periodic in both investigated cases with approximately constant shedding frequency. The CFD predicted sheet-cavitation shedding frequencies can be observed also in the acoustic measurements. The Strouhal numbers lie within the usual ranges reported in the literature for sheet-cavitation shedding. We furthermore demonstrate that the vortical flow structures can in certain cases develop striking cavitating toroidal vortices, as well as pressure wave fronts associated with a cavity cloud collapse event. To our knowledge, our numerical analyses are the first reported for the ITTC standard cavitator.

Verification and Validation of openInjMoldSim, an Open-Source Solver to Model the Filling Stage of Thermoplastic Injection Molding

In the present study, the simulation of the three-dimensional (3D) non-isothermal, non-Newtonian fluid flow of polymer melts is investigated. In particular, the filling stage of thermoplastic injection molding is numerically studied with a solver implemented in the open-source computational library O p e n F O A M ® . The numerical method is based on a compressible two-phase flow model, developed following a cell-centered unstructured finite volume discretization scheme, combined with a volume-of-fluid (VOF) technique for the interface capturing. Additionally, the Cross-WLF (Williams–Landel–Ferry) model is used to characterize the rheological behavior of the polymer melts, and the modified Tait equation is used as the equation of state. To verify the numerical implementation, the code predictions are first compared with analytical solutions, for a Newtonian fluid flowing through a cylindrical channel. Subsequently, the melt filling process of a non-Newtonian fluid (Cross-WLF) in a rectangular cavity with a cylindrical insert and in a tensile test specimen are studied. The predicted melt flow front interface and fields (pressure, velocity, and temperature) contours are found to be in good agreement with the reference solutions, obtained with the proprietary software M o l d e x 3 D ® . Additionally, the computational effort, measured by the elapsed wall-time of the simulations, is analyzed for both the open-source and proprietary software, and both are found to be similar for the same level of accuracy, when the parallelization capabilities of O p e n F O A M ® are employed.

A compressible two-phase flow model for pressure oscillations in air entrapments following green water impact events on ships

A compressible two-phase flow model for pressure oscillations in air entrapments following green water impact events on ships

Real-fluid phase transition in cavitation modeling considering dissolved non-condensable gas

In this article, a fully compressible two-phase flow model combined with a multi-component real-fluid phase equilibrium solver is proposed for cavitation modeling. The model is able to simulate the dissolving process of non-condensable gas through resolving the real-fluid phase change equations. A three-dimensional cavitating nozzle test is considered to validate the suggested model. The achieved numerical results have been compared to the available x-ray experiments. The results have confirmed that the model can tackle the phase transition phenomena including gas dissolving and homogeneous nucleation processes. Thus, the cavitation inception has been modeled dynamically when the fluid crosses the phase boundary from the single-phase state to the two-phase state and vice versa. The effects of non-condensable gas on the cavitation inception, development, and unsteadiness have been particularly analyzed, based on the large eddy simulations and x-ray experiments. Finally, the encountered challenges are mentioned, aiming at providing recommendations for similar research studies.

Cavitation on Model- and Full-Scale Marine Propellers: Steady And Transient Viscous Flow Simulations At Different Reynolds Numbers

In this paper, we conducted numerical simulations to investigate single and two-phase flows around marine propellers in open-water conditions at different Reynolds number regimes. The simulations were carried out using a homogeneous compressible two-phase flow model with RANS and hybrid RANS/LES turbulence modeling approaches. Transition was accounted for in the model-scale simulations by employing an LCTM transition model. In model scale, also an anisotropic RANS model was utilized. We investigated two types of marine propellers: a conventional and a tip-loaded one. We compared the results of the simulations to experimental results in terms of global propeller performance and cavitation observations. The propeller cavitation, near-blade flow phenomena, and propeller wake flow characteristics were investigated in model- and full-scale conditions. A grid and time step sensitivity studies were carried out with respect to the propeller performance and cavitation characteristics. The model-scale propeller performance and the cavitation patterns were captured well with the numerical simulations, with little difference between the utilized turbulence models. The global propeller performance and the cavitation patterns were similar between the model- and full-scale simulations. A tendency of increased cavitation extent was observed as the Reynolds number increases. At the same time, greater dissipation of the cavitating tip vortex was noted in the full-scale conditions.

Positivity-preserving finite volume scheme for compressible two-phase flows in anisotropic porous media: The densities are depending on the physical pressures

We are concerned with the approximation of solutions to a compressible two-phase flow model in porous media thanks to an enhanced control volume finite element discretization. The originality of the methodology consists in treating the case where the densities are depending on their own pressures without any major restriction neither on the permeability tensor nor on the mesh. Contrary to the ideas of [23], the point of the current scheme relies on a phase-by-phase “sub”-unpwinding approach so that we can recover the coercivity-like property. It allows on a second place for the preservation of the physical bounds on the discrete saturation. The convergence of the numerical scheme is therefore performed using classical compactness arguments. Numerical experiments are presented to exhibit the efficiency and illustrate the qualitative behavior of the implemented method.

Real-fluid injection modeling and LES simulation of the ECN Spray A injector using a fully compressible two-phase flow approach

A fully compressible two-phase flow model consisting of four balance equations including two mass, one momentum, and one internal energy equation, formulated with the mechanical and thermal equilibrium assumptions is developed in this article. This model is closed with a real fluid equation of state (EoS) and has been applied to the simulation of different 1D academic cases, in addition to the 3D Large-Eddy Simulation (LES) of the Engine Combustion Network (ECN) Spray A injector including the needle to target part with and without the phase change (i.e. frozen) assumptions. The obtained numerical results from the model with phase change have proven to be able to accurately predict the liquid, vapor penetrations and rate of injection compared to experimental data. However, the frozen model has presented some uncertainties and deviations in predicting the penetration length as with different measure criterions, even though an excellent agreement can be achieved in the estimation of rate of injection, near-nozzle mass and velocity distribution. Several conclusions are drawn from the simulations: (1) the initial in-nozzle flow has a strong effect on the early jet development; (2) considering phase change is still essential in the high temperature, high pressure (HTHP) injection modeling since it strongly affects the temperature distribution, turbulence intensity and thereby the jet development; (3) significant variations of liquid compressibility factor and density, as well as the cooling effect through the nozzle are highlighted. Overall, the detailed analysis of the numerical results reported in this article may complement the Engine Combustion Network (ECN) experimental database.

Efficient exact solution procedure for quasi-one-dimensional nozzle flows with stiffened-gas equation of state

We propose an efficient and accurate exact solution procedure for the converging–diverging nozzle flows of compressible liquids governed by a stiffened-gas equation of state (SG-EOS). First, we elaborate on how to formulate a complete SG-EOS and suggest a new method to determine the parameters of SG-EOS. Next, we derive the relations for the quasi-one-dimensional nozzle flow of the SG-EOS liquids and propose an efficient solution procedure to obtain the exact solution at various boundary conditions. The proposed solution procedure can accurately calculate the position of the shock wave regardless of the number of computational grid points. We then verify the solution procedure against the previous results for the air and water nozzle flows. We also investigate the influence of the SG-EOS parameters on the nozzle flow of liquid water containing a shock wave. The proposed solution procedure can be used for the basic design of a compressible liquid nozzle and the validation of compressible two-phase flow model.

Positive control volume finite element scheme for a degenerate compressible two-phase flow in anisotropic porous media

In this paper, we are concerned with the convergence analysis of a positive control volume finite element scheme (CVFE) for a degenerate compressible two-phase flow model in anisotropic porous media. For this, we consider the global pressure saturation formulation. We next use an implicit Euler scheme in time and a CVFE discretization in space. This approach rests on a particular choice of the mean value of the gas density on the interfaces, a centered scheme of the total mobility, and the upwind approximation of fractional fluxes according to the total velocity. Thus, the maximum principle is fulfilled without any constraint on the stiffness coefficients. Moreover, uniform estimates on the discrete gradient of the global pressure and the dissipative term are derived. As the mesh size is sent to zero, we establish that the sequence of approximate solutions converges to a weak solution of the continuous problem. Numerical tests are presented in two dimensions to exhibit the behavior of the gas pressure and the water saturation through the medium.

An improved homogenization result for immiscible compressible two-phase flow in porous media

The paper deals with a degenerate model of immiscible compressible two-phase flow in heterogeneous porous media. We consider liquid and gas phases (water and hydrogen) flow in a porous reservoir, modeling the hydrogen migration through engineered and geological barriers for a deep repository for radioactive waste. The gas phase is supposed compressible and obeying the ideal gas law. The flow is then described by the conservation of the mass for each phase. The model is written in terms of the phase formulation, i.e. the liquid saturation phase and the gas pressure phase are primary unknowns. This formulation leads to a coupled system consisting of a nonlinear degenerate parabolic equation for the gas pressure and a nonlinear degenerate parabolic diffusion-convection equation for the liquid saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. The aim of this paper is to extend our previous results to the case of an ideal gas. In this case a new degeneracy appears in the pressure equation. With the help of an appropriate regularization we show the existence of a weak solution to the studied system. We also consider the corresponding nonlinear homogenization problem and provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence.