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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

An investigation of the multi-mode Richtmyer-Meshkov instability at a gas/HE interface using Pagosa

Here, in this work, we present a hydrocode Pagosa and explore the Richtmyer-Meshkov Instability (RMI) at an air/high explosive (HE) interface for the first time that is important but has not received much attention yet in the high explosive safety field. Thus, the presented Pagosa can be expected to predict the whole deflagration-to-detonation transition (DDT) process in future. In Pagosa, spatial discretization is implemented on cubic staggered grids by computing different variables at the vertex and the cell center, respectively, a special operator-splitting technique is employed to reduce the computational cost, and an artificial viscosity is added to handle the discontinuous shock waves in our simulations. To quantitatively evaluate the capability of Pagosa to solve these kinds of instabilities, the single mode Rayleigh-Taylor instability (RTI) and the multimode RMI at an air/SF 6 interface are first performed, respectively. The Pagosa results are compared with the related numerical solutions in the existing references and the experimental result. Moreover, a theoretical derivation of growth of RTI is also provided based on our numerical method. Subsequently, we explore the multi-mode RMI at an air/HE interface as well as the effects of several factors using Pagosa. Numerical results show that Pagosa is a powerful toolset to generate the right structures and the amplitude of RTI and RMI at an air/SF 6 interface. The solid HE can be penetrated by a strong shock wave and forms RMI deformations. The RMI at an air/HE interface behaves very different than at an air/SF 6 interface, periodic, decreased oscillation is observed due to material character, and is very sensitive to the initial simulation settings, that is, a tiny change in physical quantities will lead to a remarkable RMI structure, which is also observed in a shock bubble interaction. The findings in this work are significant, and will present a new insight for the high explosive field.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An MPMD approach coupling electromagnetic continuum mechanics approximations in ALEGRA

In this work, two complementary approximations for describing aspects of continuum electromagnetics in moving media are discussed: electroquasistatic and magnetoquasistatic. Each has been implemented in the finite element shock code ALEGRA for modeling dynamic electromechanical phenomena on typical engineering time scales, with fully integrated circuit coupling. The approximations can be obtained by consistent asymptotic balancing of Maxwell’s equations relative to timescales associated with magnetic diffusion, charge relaxation, and electromagnetic wave propagation. In ALEGRA, the electroquasistatic approximation is used for ferroelectric (FE) modeling, while the magnetoquasistatic approximation is used for magnetohydrodynamic (MHD) modeling. In this paper we introduce for the first time a detailed derivation of a useful quasi-steady “low-R m ” variant of the MHD approximation applicable for cases, such as with detonators, where the thermodynamic pressure arising from Joule heating dominates over magnetic forces. An additional purpose of this paper is to present a coupling mode using Multiple Program-Multiple Data (MPMD) message passing communication that allows the user to run 3D FE problems together with 2D and/or 3D MHD problems with the respective simulation domains coupled through a common circuit equation. The MPMD coupling capability is used here to model the dynamic coupling of a notional ferroelectric generator with an RP-87 exploding bridgewire detonator. The simulated bridgewire heats up and bursts under current generated by simulated depoling of the ferroelectric generator, as a demonstration of the MPMD capability.

42 ENGINEERING↗
DOE OSTI2021

Empirical Acoustic Source Model for Chemical Explosions in Air

Chemical explosions generate pressure disturbances in air that radiate as nonlinear shock waves near the source and transition into acoustic waves with distance. Because low-frequency acoustic waves generally travel large distances without significant loss of energy, they are often used for explosion monitoring and yield estimation. However, quantitative relationships between acoustic energy and explosion yields are required for accurate yield estimation. Here, we develop an empirical acoustic source model for chemical explosions from experimental data. The empirical model returns the acoustic pressure waveform for the detonation of 1 kg of trinitrotoluene, which is conventionally used to represent the explosive release of 4.184 MJ of explosion energy. The full-waveform model can be used to predict acoustic signals for an arbitrary yield of a high-explosive detonation based on the standard scaling law and to estimate acoustic energies in a specific frequency range. We evaluate the accuracy of the acoustic source model independently by estimating the yield of other explosive events that are not included in the model development. Finally, statistical characteristics of the model and their implications for the uncertainty quantification of estimated yields are discussed.

58 GEOSCIENCES↗
DOE OSTI2024

A multi-Physics Experiment for Low-Yield Nuclear Explosion Monitoring

A series of multi-physics experiments, referred to as Physics Experiment 1 (PE1) is underway at the United States’ Nevada National Security Site (NNSS). The PE1 series includes detonations of three underground chemical explosions in P-tunnel, with fully coupled (PE1 A), partially decoupled (PE1 D L ), and fully decoupled (PE1 B) emplacements. Canisters with gas tracers are imbedded in the explosives, and the tracers are released when the canister is destroyed by the detonation. A dedicated electromagnetic (EM) experiment (EMX) generates well-characterized EM signals at an underground location near the chemical explosive experiments. A series of atmospheric experiments (METEX, REACT, and METREX) release smoke and radioactive tracers around Aqueduct Mesa to test gas transport in complex topography. Each of the chemical explosive experiments includes a network of sensors to record seismic, acoustic, and electromagnetic waves, measurement of atmospheric conditions, and air sample collection for measurement of tracer concentration. EMX records EM signals underground and on the surface of Aqueduct Mesa. METEX, REACT, and METREX include measurement of atmospheric condition, as well as tracking smoke releases. REACT and METREX add low-level radioactive gas tracers to the atmospheric releases.

58 GEOSCIENCES↗
DOE OSTI2020

A crisis for the verification and validation of turbulence simulations

Three algorithms have been proposed for solution of the Rayleigh–Taylor turbulent mixing problem. They are based upon three different physical principles governing the Euler equations for fluid flow. The principles serve to select the physically relevant solution from among many nonunique solutions. The admissibility principle is in dispute. The three different algorithms, expressing the three physical admissibility principles can be formulated in terms of the three energy dissipation rates or the entropy production rates, as selected by the size of the sub grid scale coefficients. These have maximal values or less than maximal values. The resulting solutions are markedly different. We find strong validation evidence that supports the maximum rate principle, based on a review of prior results and on new results presented here. We review experimental data used for validation and sufficient to discriminate among the three. We present a new analysis of this data. We show that the hypothesized long wave length perturbations in the initial conditions are not significant, so that validation can be based on this data in a straight forward manner. One of the algorithms is labeled direct numerical simulation, but is not, and as a consequence, the two algorithms with less than maximal SGS coefficients are variants of one another. Finally recommendations for the numerical modeling of the deflagration to detonation transition in type Ia supernova are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spatio-temporal ablation dynamics and plasma chemistry of aluminum induced by temporally modulated ytterbium fiber laser

Here, in this work, we studied single-pulse ablation dynamics of a temporally modulated continuous wave laser-material interaction with Al using in situ multimodal time-resolved diagnostics that describe in detail the associated physical and chemical processes. Time-resolved scattering, emission imaging, and optical emission spectroscopy unveiled a sequence of events spread out across three distinct phases: (i) early phase ablation process, associated with particle generation and liquid Al column formation (<20 μs), (ii) secondary detonation when sufficient ejected material is accumulated over the surface (20-50 μs), and (iii) molten liquid Al pool oscillation on the surface, followed by large droplet ejection from the liquid pool (100-500 μs). Atomic Al and AlO were observed with optical emission spectroscopy at different ratios during the entire lifetime of the event, verifying the formation of oxidized Al vapor upon its interaction with air. Morphological and compositional characterization confirmed surface oxidation and material re-solidification in the form of protrusions produced during the irradiation process. This work provides insights into the complex physical and chemical mechanisms of single-pulse ablation in the sub-millisecond laser pulse regime, which are critically important for parameter optimization in a variety of laser processing, microfabrication, and deposition applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Performance Characterization of a Natural Gas–Air Rotating Detonation Engine

An experimental study of a rotating detonation engine (RDE) operating with natural gas and air at elevated chamber pressures and air preheat temperatures was conducted to quantify its performance at conditions representative of land-based power generation gas turbine engines. Here, the thrust produced by the combustor was measured to characterize its work output potential. High-frequency pressure transducers and broadband chemiluminescence measurements of the flame provided information about the wave structure and dynamics. Analysis of common performance metrics demonstrated the necessity of normalizing any RDE performance parameter by the driving system potential, typically the reactant manifold pressure. Application of a thermodynamic performance model to a generic RDE identified the area ratio between the RDE exhaust and injection throats as the primary parameter affecting delivered pressure gain. The model was further applied to draw comparison with experimental measurements of net pressure gain for identical flow conditions. Only one of the two tested injector configurations followed the predicted trends, suggesting that performance of the second was governed by physical processes other than the reactant thermodynamics. Although an absolute pressure gain was not demonstrated, it is promising that the natural gas–air RDE delivered up to 90% of the theoretical performance.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2024

Flow and Performance Characterization of Rotating Detonation Combustor Integrated with Various Convergent Nozzles

In this study, convergent nozzles of various area ratios (ARs) are used downstream of an annular rotating detonation combustor (RDC) to increase the operating pressure and approach sonic conditions at the nozzle throat. Reactant methane and oxygen-enriched air (67% [Formula: see text] and 33% [Formula: see text] by volume) are supplied in counterflow arrangement from two separate plenums located at the base of the RDC annulus. Based on experimentation, a total mass flow rate of [Formula: see text] was chosen to achieve stable, single-wave mode RDC operation for all test cases, allowing for one-to-one comparisons. The internal performance of the RDC was characterized by ion probes and pressure measurements (wall static and oscillating) in supply plenums and across different axial locations of the combustor. Particle image velocimetry (PIV) at 100 kHz was utilized to measure axial and circumferential velocity components within a two-dimensional region of interest located downstream of the converging nozzle exit. Results show higher internal performance of the RDC with increasing AR of the convergent nozzle. PIV measurement illustrated that the flow oscillation amplitudes decrease with an increasing AR of the converging nozzle. The exit flow contained significant nonuniformity and unsteadiness even with a converging nozzle of AR 2.0, indicating incomplete choking of the flow at the nozzle throat.

Engineering↗
DOE OSTI2023

Plasma-assisted deflagration to detonation transition in a microchannel with fast-frame imaging and hybrid fs/ps coherent anti-Stokes Raman scattering measurements

Our study examines kinetic enhancement by nanosecond dielectric barrier discharge (ns-DBD) plasma on fuellean dimethyl ether (DME), oxygen (O 2 ), and argon (Ar) premixtures during deflagration to detonation transition (DDT) experiments in a microchannel. Non-equilibrium plasma produces active species and radicals and creates fast and slow heating of a mixture to promote ignition due to electronic and vibrational excitation. Experiments have been conducted to examine the influence of the plasma discharge on the premixture and on the resultant deflagration to detonation transition (DDT) onset time and distance through the use of high speed imaging and one-dimensional, two-beam, femtosecond/picosecond, coherent anti-Stokes Raman scattering (CARS). A highspeed camera is used to trace the time histories of flame front position and velocity and to identify the dynamics and onset of DDT. The results show that plasma discharge can nonlinearly affect the onset time and distance of DDT. It is shown that a small number of plasma discharge pulses prior to ignition result in reduced DDT onset time and distance by 60% and 40%, respectively, when compared to the results without pre-excitation by ns discharges. The results also show that an increase of plasma discharge pulses results in an extended DDT onset time and distance of 224% and 94%, respectively. Time history of the deflagration wave speed of DME and the analysis of ignition timescale under the choking condition of the deflagration front suggest low temperature ignition may play a role for DME near the isobaric choking condition of the burned gas and the DDT. Plasmainduced conversion of the reactive mixture was assessed via the O 2 to CO 2 ratio as measured through fs/ps CARS during the DBD discharges. The present experiments demonstrate the ability of non-equilibrium plasma to alter the chemistry of DME/O 2 /Ar premixtures in order to control DDT for applications in advanced propulsion engines.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Flow Development in Radial Plane of Rotating Detonation Engine Integrated with Aerospike

In this study, axial and radial velocity components are measured downstream of a rotating detonation engine (RDE) integrated with an aerospike by using particle image velocimetry (PIV) at 100 kHz. The RDE is operated at high pressures obtained by restricting the RDE exit with a converging nozzle, which also directs the flow radially toward the aerospike. Reactants, methane fuel, and enriched air (67% oxygen and 33% nitrogen) are supplied from separate plenums at ambient temperature. PIV data are presented to investigate how pressure ratios within the RDE channel affect the flow evolution across the aerospike. The RDE is shown to operate stably and consistently in a single wave mode for all six test runs. The study highlights large temporal and spatial variations in both axial and radial flow velocities at the nozzle throat that persist downstream across the aerospike. Each point in the flowfield oscillates at the frequency recorded inside the RDE channel. Overall, the temporally and spatially varying aerospike flowfield is far from the ideal case of a uniform flow at its exit, and it points toward the need to condition the flow within the RDE channel to produce more uniform conditions at the nozzle throat.

Engineering↗
DOE OSTI2023

Technical Report on Waveform Fit Metrics for Global Models

The new WAVEFORMS Initiative in the Ground-based Nuclear Detonation Detection (GNDD) program includes an increased emphasis on the development of Earth models and methods to predict entire seismic and acoustic waveforms more accurately. In general, this increased emphasis is predicated on the need to better characterize seismic events and provide improved model-based discrimination between event types including earthquakes and explosions. More specifically, while current moment tensor inversion methods tend to work well for larger events (M>~4) using tuned 1-D Earth models, the development of state-of-the-art 3-D models and methods is required for the prediction of shorter period waves over large areas for discrimination of smaller events. There is no standard metric for model-based waveform prediction accuracy used in the waveform modeling/inversion community. However, there are several popular waveform misfit definitions; and minimizing the corresponding objective functions is the goal of waveform inversion. Some example misfit definitions employed for adjoint waveform tomography include measures of simple travel time differences (e.g. Tape et al., 2010), cross-correlation travel time differences (e.g. Luo and Schuster, 1991), multi-taper frequency dependent methods (e.g. Lei et al., 2020), time-frequency phase misfit functions (e.g. Fichtner 2010; Rodgers et al., 2022), normalized cross-correlation methods (e.g. Tao et al., 2018), and others. In some cases, these misfit definitions also involve complicated weighting schemes and summations over multiple frequency bands making it difficult to duplicate the misfit measurement with alternative models and datasets. Although each of the misfit definitions mentioned above are useful for developing waveform models, the actual misfit values are not usually meaningful outside of a given project, model, and/or dataset. Therefore, it is difficult to understand and communicate model performance for predicting waveforms and comparing to other models and/or new model iterations with a different dataset. Therefore, there is a need for a generalized method for evaluating overall model performance that is independent from the specific misfit chosen to develop the waveform models that is also intuitive and meaningful. In this report, we describe a new metric we refer to as ‘Percent of Correlated Signal’. The following sections describe and demonstrate the metric with a case study event and a more rigorous test using a random selection of globally distributed events. While the focus here is on global tomography models, the metric is meant to applicable to regional ‘wiggle-for-wiggle’ waveform models/studies as well.

58 GEOSCIENCES↗
DOE OSTI2020

Extreme measurements with Photonic Doppler Velocimetry (PDV)

Photonic Doppler Velocimetry (PDV) is a fiber-based diagnostic for the extreme conditions created by high-speed impact, explosive detonation, electrical pulsed power, and intense laser ablation. PDV is a conceptually simple application of the optical Doppler effect, but measurements above 1 km/s only became practical at the beginning of the twenty-first century. In this work, I discuss the evolution of PDV, its operational details, practical analysis, and outstanding challenges.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Rock Fracturing Using High-Pressure Ethylene/Nitrous Oxide Detonations

The present work investigates high initial pressure detonations of a stoichiometric mixture of ethylene and nitrous oxide (C2H4 + 6N2O) as a method of fracturing rock beneath the ground surface. These tests were conducted at a test site operated by the Energetic Materials Research and Testing Center (EMRTC), Socorro, New Mexico. The volume under the surface used for testing (called the Down Hole Assembly) consists of a 0.438 in. ID x 50 ft. long stainless-steel tube running down from the test site to a well bore which is 3 in. ID x 10 ft. long and the rock in the well bore is exposed to the propagating combustion wave. The testing carried out at Zucrow Laboratories in the smaller, alloy steel combustion vessel provided a scaling of pressures expected in the well bore. The combustion is initiated by energizing an EBW (Exploding Bridge Wire) above the ground surface. The experimental setup accommodates one high pressure (100,000 psia) transducer to measure the pressure peak and is placed approximately 5 ft. above the ground surface and 5 ft. downstream of the EBW. The focus of this series of experiments is to investigate the dependence of fracture to the rock beneath the surface on initial pressures of the mixture of ethylene and nitrous oxide. Experiments were carried out at initial pressures varying between 125 psia and 300 psi. The transducer recorded elevated pressures, which were 2.3 to 2.6 times in excess of the CJ values. The experimental results are discussed and explained in this report.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Preshot Report for Carbonara: Dynamics of a Boron Carbide Sandwich

The main purpose of the Carbonara experiment is to provide much-needed data to inform physics modeling of boron carbide (B 4 C) subjected to a sweeping high explosive (HE) detonation. The proposed experiment will include three separate shots, each employing a rectangular slab of HE (4” × 3” × 1”) sandwiched between two wedges of B 4 C, see Fig.1. In each case the top B 4 C wedge tapers from a height of 2.5 cm to 0.5 cm, while the bottom wedge tapers from 1.5 cm to 0.5 cm. The wedges are 4” in the direction of the proton beam, and 3” in the direction transverse to the beam. Three shots are currently planned, each one using a different HE: PBX 9501, PBX 9502, and PBX 9701. The HE will be initiated using a line wave generator (LWG) to preserve planar symmetry, in conjunction with a Comp. B booster to smooth out the profile for the initial condition on the main charge and to aid in initiation of the PBX 9502 shot. In each case the booster spans the entire length and height of the main HE slab and extends 0.5” in toward the LWG.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Investigating growth to detonation in vapor-deposited hexanitrostilbene and pentaerythritol tetranitrate films using high-throughput methods

In this work, a high-throughput experimental setup was used to characterize initiation threshold and growth to detonation in the explosives hexanitrostilbene (HNS) and pentaerythritol tetranitrate (PETN). The experiment sequentially launched an array of laser-driven flyers to shock samples arranged in a 96-well microplate geometry, with photonic Doppler velocimetry diagnostics to characterize flyer velocity and particle velocity at the explosive–substrate interface. Vapor-deposited films of HNS and PETN were used to provide numerous samples with various thicknesses, enabling characterization of the evolution of growth to detonation. One-dimensional hydrocode simulations were performed with reactions disabled to illustrate where the experimental data deviate from the predicted inert response. Prompt initiation was observed in 144 μm thick HNS films at flyer velocities near 3000 m/s and in 125 μm thick PETN films at flyer velocities near 2400 m/s. This experimental setup enables rapid quantification of the growth of reactions in explosive materials that can reach detonation at sub-millimeter length scales. These data can subsequently be used for parameterizing reactive burn models in hydrocode simulations, as discussed in Paper II [D. E. Kittell, R. Knepper, and A. S. Tappan, J. Appl. Phys. 131, 154902 (2022)].

36 MATERIALS SCIENCE↗
DOE OSTI2023

The influence of physical and algorithmic factors on simulated far-field waveforms and source–time functions of underground explosions using unsupervised machine learning

SUMMARY Characterizing explosion sources and differentiating between earthquake and underground explosions using distributed seismic networks becomes non-trivial when explosions are detonated in cavities or heterogeneous ground material. Moreover, there is little understanding of how changes in subsurface physical properties affect the far-field waveforms we record and use to infer information about the source. Simulations of underground explosions and the resultant ground motions can be a powerful tool to systematically explore how different subsurface properties affect far-field waveform features, but there are added variables that arise from how we choose to model the explosions that can confound interpretation. To assess how both subsurface properties and algorithmic choices affect the seismic wavefield and the estimated source functions, we ran a series of 2-D axisymmetric non-linear numerical explosion experiments and wave propagation simulations that explore a wide array of parameters. We then inverted the synthetic far-field waveform data using a linear inversion scheme to estimate source–time functions (STFs) for each simulation case. We applied principal component analysis (PCA), an unsupervised machine learning method, to both the far-field waveforms and STFs to identify the most important factors that control variance in the waveform data and differences between cases. For the far-field waveforms, the largest variance occurs in the shallower radial receiver channels in the 0–50 Hz frequency band. For the STFs, both peak amplitude and rise times across different frequencies contribute to the variance. We find that the ground equation of state (i.e. lithology and rheology) and the explosion emplacement conditions (i.e. tamped versus cavity) have the greatest effect on the variance of the far-field waveforms and STFs, with the ground yield strength and fracture pressure being secondary factors. Differences in the PCA results between the far-field waveforms and STFs could possibly be due to near-field non-linearities of the source that are not accounted for in the estimation of STFs and could be associated with yield strength, fracture pressure, cavity radius and cavity shape parameters. Other algorithmic parameters are found to be less important and cause less variance in both the far-field waveforms and STFs, meaning algorithmic choices in how we model explosions are less important, which is encouraging for the further use of explosion simulations to study how physical Earth properties affect seismic waveform features and estimated STFs.

58 GEOSCIENCES↗
DOE OSTI2024

An exploration of anomalous electrical noise in shocked cyclotrimethylenetrinitramine (RDX)-based explosives

Gas gun shock experiments on cyclotrimethylenetrinitramine (RDX)-based explosive compositions that employ embedded gauge particle velocity tracers have noted a significant amount of electrical noise when compared to other explosive formulations. This paper reexamines previously published embedded gauge data on Cyclotols (60–80 wt. % RDX) to quantify the electromagnetic behavior of these materials. The primary observation is a fourfold increase in the electrical noise when Cyclotols are shocked above 4.22 ± 0.08 GPa. Electromagnetic gauge noise is also observed within particle velocity traces in reactive growth and off-Hugoniot shocks, although at higher pressures than the direct shock case, suggesting a temperature- or kinetically dependent transition. In all cases, the electrical noise disappears upon detonation. By comparing with the static high-pressure phase diagram of RDX, we interpret this change in electromagnetic behavior to be a change in the RDX crystal structure to a piezoelectric phase, although it is uncertain whether the γ or ε phase is responsible for the observed behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A simple and effective five-equation two-phase numerical model for liquid-vapor phase transition in cavitating flows

Numerical difficulties, notably the non-monotonic behavior of the Wood speed of sound and the volume fraction positivity, associated with the reduced five-equation two-phase flow model of Kapila et al. (2001) [A.K. Kapila, R. Menikoff, J.B. Bdzil, S.F. Son, D.S. Stewart, 2001. Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations, Physics of Fluids 13(10), 3002–3024] have been resolved in the past through the introduction of a frozen speed of sound and an algebraic approach for mechanical relaxation afforded by a pressure non-equilibrium six-equation model proposed by [R. Saurel, F. Petitpas, R.A. Berry, 2009. Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixture, J. Comput. Phys. 228, 1678–1712]. By contrast, it is explored and demonstrated in this work that these difficulties can in fact still be resolved within the numerical scheme for solving the reduced five-equation model by numerically replacing the Wood speed of sound for the estimates of wave speeds in the approximate Riemann solver HLLC with the monotonic mixture speed of sound for a transport five-equation model. For shock interface (artificial mixture separating pure or nearly pure fluids) interaction problems, with the apparent advantage of monotonic behavior of the speed of sound in the interface, the effect of the numerical replacement is also confined to the interface. Differences other than the behavior of the speed of sound within the interface in the solutions due to the replacement diminish with increasing resolution when reasonable solution can be obtained with Wood speed of sound. For cavitating/expansion problems in physical fluid mixture, it is pointed out and explained why acoustics in the numerical solutions still propagate at the Wood speed of sound (therefore consistent with the reduced five-equation model) even though in some cases a much higher speed of sound like the numerical replacement above for solving the reduced five-equation model or the frozen speed of sound for solving a six-equation model is used for the estimates of wave speeds in the HLLC scheme. A variant of the five-equation two-phase flow model by Saurel et al. (2008) [R. Saurel, F. Petitpas, R. Abgrall, 2008. Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech. 607, 313–350] is then constructed for liquid-vapor phase transition in cavitating flows. The relaxation toward thermo-chemical equilibrium during phase transition is achieved by solving a simple system of algebraic equations for the equilibrium state variables for better efficiency, following Pelanti and Shyue (2014) [M. Pelanti, K.-M. Shyue, 2014. A mixture-energy-consistent six-equation two-phase numerical model for fluid with interfaces, cavitation and evaporation waves. J. Comput. Phys. 259, 331–357]. Therefore, the current model retains both the simplicity afforded by the five-equation model and the efficiency of the algebraic relaxation solver. An alternative algebraic approach for handling the non-conservative term (the so-called K∇ · u term) in the reduced five-equation model for mechanical equilibrium of a liquid-vapor mixture is also explored by enforcing the thermal equilibrium at the same time. Finally, numerical results of sample tests in both one and two dimensions in the literature as well as that in three dimensions demonstrate the effectiveness and ability of the proposed model to simulate cavitating flows. An interesting mechanism of shock generation by acoustics in water due to phase transition is then found by the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗