We propose high-resolution numerical schemes for two-phase compressible flow simulations to reproduce dynamically created gas/vapor-liquid interfaces with phase change. In the Godunov-type finite ...volume framework, suppressing numerical dissipation errors in numerical schemes is crucial for capturing the discontinuous solutions. The MUSCL scheme has second-order accuracy for smooth solutions and non-oscillatory behavior near discontinuous solutions. However, the MUSCL scheme introduces excessive numerical dissipation and diffuses the discontinuities nonphysically, leading to difficulties in distinguishing gas/vapor and liquid phases, and thus causing a blur in the interfaces during the multi-phase flow simulations.
The hybrid-type boundary variation diminishing (BVD) scheme in this paper combines the MUSCL scheme and the THINC scheme to reduce the numerical dissipation errors near the discontinuities. The MUSCL-THINC-BVD scheme applies the MUSCL scheme for smooth solutions and the THINC scheme for discontinuous solutions, resulting in the successful capture of the discontinuities including the dynamically created gas/vapor-liquid interfaces. The Adaptive THINC-BVD scheme, which switches two types of THINC schemes with different values of gradient parameter, also captures the discontinuities clearly. The numerical results of the benchmark tests show that the proposed BVD schemes can lucidly reproduce the vapor-liquid interfaces newly created during the dynamical process of phase change.
•Hybrid BVD schemes are presented to compute gas/vapor interfaces in 6-equation model for multi-phase flows.•Interfaces newly generated between liquid and vapor during the evaporation process are well-reproduced for the first time.•Basic benchmark validations are conducted for two-phase flows associated with phase changes.•The numerical methods presented are well-suited for simulating multi-phase flows involving phase changes.
The present work is motivated by the engineering need to simulate the multiphase flows in the course of the start-up of a long-distance crude oil pipeline. We propose a model for compressible ...multiphase flows with heat and mass transfer and diffusion processes in elastic pipelines. The model is derived with two approaches, i.e., (a) the spatial averaging procedure of a single phase model and (b) the Arbitrary Lagrangian Eulerian (ALE) formulation of the Baer-Nunziato model with quasi-1D approximation. The diffusion processes include the viscous dissipation, wall friction, heat conduction, and heat exchange with external environment. In particular, the wall friction consists of steady friction term calculated by Darcy-Weisbach formula, and the unsteady friction determined by the instantaneous-acceleration-based (IAB) model. The unsteady friction modifies the characteristic structure of the hyperbolic part of the model. For the solution of the hyperbolic part, we propose a three-wave approximate Riemann solver incorporating the unsteady friction term. Mass and heat transfer are realized via instantaneous relaxations of the chemical potential and temperature, respectively. Efficient iterative relaxation procedures for N-phase flows have been proposed. We have validated the proposed model and numerical methods against some benchmark multiphase problems and applied the model to calculate the start-up of a realistic liquid pipeline with intermediate pump station boundary condition.
•The derivation of the quasi-1D BN-type model with diffusion physics and its reduction.•The development of a HLLC Riemann solver taking into consideration the unsteady wall friction term.•Efficient pressure and temperature relaxation methods for N-phases.•The application in simulating realistic pipe-startup problem.
Underwater explosion (UNDEX) events involve complex physical phenomena and can be categorized into three stages: initial shock wave propagation, cavitation, and bubble pulsation. This study focuses ...on double UNDEX bubbles, elucidating their highly nonlinear interactions across these stages. Both synchronous and asynchronous explosion cases are examined, with a particular emphasis on assessing the influence of phase change. Employing the 3-D high-fidelity computational framework that incorporates the physics-based cavitation model and non-ideal equations of state for water and explosion gas properties, we conduct validations with field experimental data on single bubbles and extend our analysis to double bubbles. Our principal finding is the interaction between the cavity created by the shock wave and the bubble pulsations. Notably, we discern a significant phase change effect in asynchronous explosion, wherein the vapor cavity region delays the contraction of the previously-generated bubble. This delay is attributed to the low-density region created by the phase change, allowing the bubble to remain expanded for an extended period, thereby enhancing agreement with experimental data. To our knowledge, this study represents the pioneering effort to explore the critical role of phase change in accurately simulating the intricate interactions within double UNDEX scenarios.
•Computational investigations on double UNDEX scenarios with thermodynamic cavitation process and non-ideal EOS.•Interactions between the cavity caused by the shock wave and the bubble pulsations are captured.•Phase change effect is more pronounced in asynchronous explosion.•Low-density cavity region delays the previously-generated bubble’s contraction.•3-D effect induced by the misalignment of gravity and bubble contraction direction.
•Pressure-based compressible multiphase flow formulation for interfacial and mixture flows.•Flashing in nozzles and valves.•Identified inconsistencies and key assumptions in cavitation model for ...compressible flow.•Thermodynamic effects in flashing such as variable latent heat was shown to be important for high pressure conditions.
A recently published pressure-based compressible multiphase flow model Labois and Narayanan (2017) is validated for applications relevant to safety of pressurized systems, such as flashing of high-pressure water through valves and nozzles. The pressure-based compressible multiphase flow solver is based on non-conservative discretization of the mixture continuity equation and has the advantage of being applicable to interface tracking and n-phase mixture formulations. For simulation of flashing, two well-known cavitation models Singhal et al.(2002), Yuan et al.(2001) have been implemented along with thermodynamic effects such as latent heat of phase change, variable saturation pressure, and heat capacities. The limitations of the well-established cavitation models in terms of their applicability to compressible flows have been clarified. The model was applied to the Super Moby Dick experiment Rousseau (1987). Good flow rates, and pressure and void fraction variations were obtained for three chosen conditions by tuning the cavitation model under incompressible conditions. It was found that the void fraction stops increasing beyond the throat due to thermodynamic effects where the latent heat and heat capacity are functions of pressure and temperature. The reduction of latent heat and rapid changes in liquid and vapour heat capacities close to the saturation line at high pressures was shown to be important. The accuracy, robustness, and efficiency of the pressure-based method has been proven for flashing under strong depressurization conditions. The cavitation model predictions are strongly sensitive to model parameters such as the nucleate density making the models not general enough to be applied to different problems without calibration. It was shown that there is significant room for development of improved cavitation models especially focussing on the constant number density constraint due to the strong sensitivity of the current models to this input parameter. The assumption of incompressibility and homogeneity of the phasic velocities is also identified as serious limitations requiring further study.
•Compressible gas flow model of the interaction between the liquid and the gas in injection molded gas dynamic virtual nozzle.•Assessment of the various geometric parameters on the micro-jet ...stability, shape and velocity.•Guidelines for optimum micro-nozzle design.
In this paper we present a numerical study investigating the effects of nozzle geometry on stability, shape and flow characteristics of micron-sized liquid jets, produced by injection molded gas dynamic virtual nozzles (GDVNs) operating in vacuum. The jet characteristics are described as a function of (i) capillary-to-orifice distance, (ii) nozzle outlet orifice diameter, and (iii) liquid feeding capillary angle. An experimentally verified numerical model of GDVN with laminar two-phase Newtonian compressible flow, based on finite volume method and volume of fluid interface tracking, is used to assess the changes. The study is performed for two sets of liquid flow rates while keeping the gas flow rate constant. It is observed that for each value of capillary-to-orifice distance and nozzle outlet diameter there is a minimum liquid flow rate below which the jet is unstable. We find that the nozzle outlet diameter has the biggest influence on the jet diameter, length and velocity, while liquid capillary angle has no observable effect on jet characteristic. Varying capillary-to-orifice distance does not affect the flow field around micro-jet. It is found that the liquid and the gas interaction near the meniscus primarily affect the jet stability and shape.
•Pressure-based compressible multiphase flow formulation for interfacial and mixture flows.•Non-conservative formation avoid spurious pressure oscillations across material fronts.•Thermodynamic and ...mechanical non-equilibrium and their impact on pressure wave propagation is possible.•Both isentropic and isothermal pressure wave propagation including the effect of mass-transfer on sound propagation can be captured.
A pressure-based compressible multiphase flow solver has been developed based on non-conservative discretization of the mixture continuity equation. The formulation is an extension of the single phase incompressible pressure-correction approach, such that it can be applied to both two-phase flows using interface resolving methods and general n-phase ensemble-averaged mixture flows. The formulation is currently presented with the single pressure and single temperature assumption, but extension to multiple temperatures is straightforward. A robust treatment of phase change allows the method to model conditions with rapid phase change such as expansion through nozzles and valves. The method has been validated thoroughly using canonical single phase problems such as the shock tube, tank filling and sudden valve closure problems. Multiphase flow validation has been carried out for sound propagation in mixtures using the ensemble-averaged model and pressure wave transmission and reflection across an air-water interface, using the level set interface tracking method. The method has been used to study sound propagation in saturated steam-water systems under thermodynamic non-equilibrium, where the expected drastic reduction in the speed of sound is reproduced. Finally the method is applied to the problem of critical (choked) flow in a nozzle for a saturated steam-water system.
Injector-type sandblasters are commonly sold with cylindrical of convergent-divergent Laval nozzles. While Laval nozzles are advertised to be more efficient, very little research on this topic has ...been published yet. Therefore, the advantages of Laval blasting nozzles in combination with injector-type abrasive blasting units were evaluated within this paper. Numerical simulations on basis of different solvers have been utilized to calculate the compressible multiphase-flow and also to identify the ideal numerical model in terms of stability and computational effort. By comparing flow and particle velocity distributions of cylindrical nozzles against the results of Laval-type nozzles, it has been found that using the latter type offers an increased productivity and a more uniform particle velocity distribution at the same air and particle flow rates. Further, it was concluded that the air flow rate and therefore the pressure and compressor energy demand can be reduced significantly without losing productivity in abrasive blasting.
•An injector-type sand blaster was investigated via numerical methods.•Conventional cylindrical and Laval-type nozzles were evaluated.•Several disadvantages of cylindrical nozzles were identified.•Laval nozzles offer a potential reduction of compressor power by 40 %.•Pressure-based coupled and density-based solver algorithms were evaluated.
During cavitation bubble pulsations, a phase change intensively occurs near the collapsing moment due to high pressure and temperature inside bubbles, accompanying distinctive flow features: the rate ...of evaporation and condensation significantly changes according to the phase change regime. To account for this non-isothermal effect, the high-fidelity computational framework incorporating the physics-based cavitation model and a new fluid property model based on artificial neural network is proposed. The key finding of this study is the interplay between the thermal and inertial effects during multiple pulsations. At the early stages of bubble contraction, the phase change is primarily driven by fluid inertia. However, as the bubble continues to compress, the thermal effect becomes dominant and controls the entire phase change region at each moment of collapse. It is observed that the isothermal model relying on the inertial bubble growth rate only, does not capture this transition of dominance and eventually fails to predict multiple pulsations. The physics-based cavitation model successfully captures the bubble pulsation beyond the second collapse. These findings highlight that explicit consideration of the non-isothermal effect is essential for problems with varying phase change regimes, and a phase change model reflecting this effect is vital for accurate computations.
•High-fidelity multi-phase computational framework ACTFlow_MP is proposed.•New fluid property model based on artificial neural network is constructed for water.•The thermal effect turns out to be dominant at the moment of each bubble collapse.•The physics-based model successfully captured bubble pulsations beyond 2nd period.
Thin-walled hollow ceramic pressure hulls on deep-sea underwater vehicles are at risk for highly destructive chain-reaction implosions. A numerical method of simulating the chain-reaction implosions ...of multiple ceramic pressure hulls in deep-sea environment was developed. The fluid solver used for this method adopted the compressible multiphase flow model and adaptive mesh refinement, combining the finite element method and the failure criteria of brittle materials to determine the conditions that trigger an implosion. An implosion experiment was conducted for a single ceramic pressure hull, and the experimental results verified the accuracy of the fluid solver based on compressible multiphase flow theory. The chain-reaction implosions of two ceramic pressure hulls were also computed. The computation results showed that the air cavity in a spherical pressure hull diffused the expansion wave during the compression stage. The pressure drop in the flow field initiated by the expansion wave caused the ceramic spherical shell to reach its ultimate strength, thus triggering chain-reaction implosions. The two implosion shockwaves were superimposed during the diffusion process. The peak pressure at the superposition position of the two shockwaves is related to the spacing between the two pressure hulls.
•A numerical simulation is developed to predict chain-reaction implosions of multi-spherical hollow ceramic pressure hulls.•An experiment and a numerical simulation of a single ceramic pressure hull implosion are carried out and compared.•The influence of the distance between ceramic pressure hulls on the shockwaves of the chain-reaction implosions is analyzed.•This research is of guiding implications for the arrangement of the ceramic pressure hulls in deep-sea underwater vehicles.
A front-tracking/ghost-fluid method is introduced for simulations of fluid interfaces in compressible flows. The new method captures fluid interfaces using explicit front-tracking and defines ...interface conditions with the ghost-fluid method. Several examples of multiphase flow simulations, including a shock–bubble interaction, the Richtmyer–Meshkov instability, the Rayleigh–Taylor instability, the collapse of an air bubble in water and the breakup of a water drop in air, using the Euler or the Navier–Stokes equations, are performed in order to demonstrate the accuracy and capability of the new method. The computational results are compared with experiments and earlier computational studies. The results show that the new method can simulate interface dynamics accurately, including the effect of surface tension. Results for compressible gas–water systems show that the new method can be used for simulations of fluid interface with large density differences.
