Waves reflected by solid wall in the mixture of liquid with vapour bubbles

The liquid and gas mixtures are met in many natural and industrial processes. In the paper the results of investigation of waves reflected by solid wall of the stationary shock waves with moderate intensities or the transient pulses propagated in the mixture of liquid with vapour bubbles are presented. The effect of initial conditions, shock strength, size of the bubbles and volume fraction of vapour phase on the behaviour of the waves reflected by solid wall is studied.

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Shock Waves in Liquids With Bubbles Containing Evaporating Drops

10.1115/imece2000-1523 ◽

2000 ◽

Author(s):

Nail S. Khabeev ◽

Arnold F. Bertelsen ◽

Oleg R. Ganiev

Keyword(s):

Shock Waves ◽

Static Pressure ◽

Volume Fraction ◽

Initial Conditions ◽

Wave Structure ◽

Physical Parameters ◽

Volume Changes ◽

Wave Processes ◽

Steady Shock ◽

Evaporating Drops

Abstract An investigation of wave processes in liquids with bubbles containing evaporating drops is presented. A model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution inside and around the bubbles. An analysis of the microsopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The evolution of non-steady shock waves in liquids with bubbles containing evaporating drops is studied by numerical methods. The effect of the initial conditions, shock strength, volume fraction, dispersity of the vapor phase, initial static pressure and of the thermophysical properties of the phases on shock-wave structure and evolution is studied. The possible enhancement of disturbances in the region of their initiation is shown. The phenomenon of the nonlinear anomalous enhancement of waves reflected from a wall is established.

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Waves in liquids with vapour bubbles

Journal of Fluid Mechanics ◽

10.1017/s0022112088000059 ◽

1988 ◽

Vol 186 ◽

pp. 85-117 ◽

Cited By ~ 18

Author(s):

R. I. Nigmatulin ◽

N. S. Khabeev ◽

Zuong Ngok Hai

Keyword(s):

Mass Transfer ◽

Heat And Mass Transfer ◽

Volume Fraction ◽

Initial Conditions ◽

Wave Structure ◽

Original System ◽

Shock Adiabat ◽

Vapour Phase ◽

Physical Parameters ◽

Dissipative Effects

An investigation of wave processes in liquids with vapour bubbles with interphase heat and mass transfer is presented. A single-velocity two-pressure model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. An analysis of the microscopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The original system of differential equations of the model is modified to a form suitable for numerical integration. An elliptic equation is obtained to determine the field of the mixture average pressure at an arbitrary time through the known fields of the remaining quantities. The existence of the steady structure of shock waves, either monotonic or oscillatory, is proved. The effect of the initial conditions, shock strength, volume fraction, and dispersity of the vapour phase and of the thermophysical properties of the phases on shock-wave structure and relaxation time is studied. The influence of nonlinear, dispersion and dissipative effects on the wave evolution is also investigated. The shock adiabat for reflected waves is analysed. The results obtained have proved that the interphase heat and mass transfer determined by the thermal diffusivity of the liquid greatly influences the wave structure. The possible enhancement of disturbances in the region of their initiation is shown. The model has been tested for suitability and the results of calculations have been compared with experimental data.

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Dispersive shock waves in viscously deformable media

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.628 ◽

2013 ◽

Vol 718 ◽

pp. 524-557 ◽

Cited By ~ 35

Author(s):

Nicholas K. Lowman ◽

M. A. Hoefer

Keyword(s):

Shock Waves ◽

Volume Fraction ◽

Initial Conditions ◽

Leading Edge ◽

Wave Dispersion ◽

Cross Sectional ◽

Theoretical Predictions ◽

Number Dynamics ◽

Long Time ◽

Constitutive Parameters

AbstractThe viscously dominated, low-Reynolds-number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behaviour when viewed appropriately. In these systems, nonlinear self-steepening competes with wave dispersion, giving rise to dispersive shock waves (DSWs). Example systems considered here include magma migration through the mantle as well as the buoyant ascent of a low-density fluid through a viscously deformable conduit. These flows are modelled by a third-order, degenerate, dispersive, nonlinear wave equation for the porosity (magma volume fraction) or cross-sectional area, respectively. Whitham averaging theory for step initial conditions is used to compute analytical, closed-form predictions for the DSW speeds and the leading edge amplitude in terms of the constitutive parameters and initial jump height. Novel physical behaviours are identified including backflow and DSW implosion for initial jumps sufficient to cause gradient catastrophe in the Whitham modulation equations. Theoretical predictions are shown to be in excellent agreement with long-time numerical simulations for the case of small- to moderate-amplitude DSWs. Verifiable criteria identifying the breakdown of this modulation theory in the large jump regime, applicable to a wide class of DSW problems, are presented.

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Maximum intensity of rarefaction shock waves for dense gases

Journal of Fluid Mechanics ◽

10.1017/s0022112009991716 ◽

2009 ◽

Vol 642 ◽

pp. 127-146 ◽

Cited By ~ 23

Author(s):

ALBERTO GUARDONE ◽

CALIN ZAMFIRESCU ◽

PIERO COLONNA

Keyword(s):

Mach Number ◽

Shock Waves ◽

Equations Of State ◽

Vapour Phase ◽

Maximum Intensity ◽

Operating Conditions ◽

Maximum Pressure ◽

Pressure Jump ◽

Shock Strength ◽

Rarefaction Shock

Modern thermodynamic models indicate that fluids consisting of complex molecules may display non-classical gasdynamic phenomena such as rarefaction shock waves (RSWs) in the vapour phase. Since the thermodynamic region in which non-classical phenomena are physically admissible is finite in terms of pressure, density and temperature intervals, the intensity of RSWs is expected to exhibit a maximum for any given fluid. The identification of the operating conditions leading to the RSW with maximum intensity is of paramount importance for the experimental verification of the existence of non-classical phenomena in the vapour phase and for technical applications taking advantage of the peculiarities of the non-classical regime. This study investigates the conditions resulting in an RSW with maximum intensity in terms of pressure jump, wave Mach number and shock strength. The upstream state of the RSW with maximum pressure drop is found to be located along the double-sonic locus formed by the thermodynamic states associated with an RSW having both pre- and post-shock sonic conditions. Correspondingly, the maximum-Mach thermodynamic and maximum-strength loci locate the pre-shock states from which the RSW with the maximum wave Mach number and shock strength can originate. The qualitative results obtained with the simple van der Waals model are confirmed with the more complex Stryjek–Vera–Peng–Robinson, Martin–Hou and Span–Wagner equations of state for selected siloxane and perfluorocarbon fluids. Among siloxanes, which are arguably the best fluids for experiments aimed at the generation and measurement of an RSW, the state-of-the-art Span–Wagner multi-parameter equation of state predicts a maximum wave Mach number close to 1.026 for D6 (dodecamethylcyclohexasiloxane, [O-Si-(CH3)2]6). Such value is well within the capacity of the measurement system of a newly built experimental set-up aimed at the first-ever demonstration of the existence of RSWs in dense vapours.

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Simulation of MASPn Experiments in MISTRA Test Facility with COCOSYS Code

Science and Technology of Nuclear Installations ◽

10.1155/2008/896406 ◽

2008 ◽

Vol 2008 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Mantas Povilaitis ◽

Egidijus Urbonavičius

Keyword(s):

Boundary Conditions ◽

Nuclear Power ◽

Power Plants ◽

Volume Fraction ◽

Characteristic Length ◽

Initial Conditions ◽

Test Facility ◽

Work Package ◽

Acceptable Agreement

An issue of the stratified atmospheres in the containments of nuclear power plants is still unresolved; different experiments are performed in the test facilities like TOSQAN and MISTRA. MASPn experiments belong to the spray benchmark, initiated in the containment atmosphere mixing work package of the SARNET network. The benchmark consisted of MASP0, MASP1 and MASP2 experiments. Only the measured depressurisation rates during MASPn were available for the comparison with calculations. When the analysis was performed, the boundary conditions were not clearly defined therefore most of the attention was concentrated on MASP0 simulation in order to develop the nodalisation scheme and define the initial and boundary conditions. After achieving acceptable agreement with measured depressurisation rate, simulations of MASP1 and MASP2 experiments were performed to check the influence of sprays. The paper presents developed nodalisation scheme of MISTRA for the COCOSYS code and the results of analyses. In the performed analyses, several parameters were considered: initial conditions, loss coefficient of the junctions, initial gradients of temperature and steam volume fraction, and characteristic length of structures. Parametric analysis shows that in the simulation the heat losses through the external walls behind the lower condenser installed in the MISTRA facility determine the long-term depressurisation rate.

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Evolution of solitary waves in a two-pycnocline system

Journal of Fluid Mechanics ◽

10.1017/s0022112009991819 ◽

2009 ◽

Vol 642 ◽

pp. 235-277 ◽

Cited By ~ 11

Author(s):

M. NITSCHE ◽

P. D. WEIDMAN ◽

R. GRIMSHAW ◽

M. GHRIST ◽

B. FORNBERG

Keyword(s):

Solitary Waves ◽

Initial Conditions ◽

Oscillation Period ◽

Resonance Phenomenon ◽

Numerical Code ◽

Asymptotic Model ◽

Narrow Region ◽

Near Resonance ◽

Long Time ◽

The Waves

Over two decades ago, some numerical studies and laboratory experiments identified the phenomenon of leapfrogging internal solitary waves located on separated pycnoclines. We revisit this problem to explore the behaviour of the near resonance phenomenon. We have developed a numerical code to follow the long-time inviscid evolution of isolated mode-two disturbances on two separated pycnoclines in a three-layer stratified fluid bounded by rigid horizontal top and bottom walls. We study the dependence of the solution on input system parameters, namely the three fluid densities and the two interface thicknesses, for fixed initial conditions describing isolated mode-two disturbances on each pycnocline. For most parameter values, the initial disturbances separate immediately and evolve into solitary waves, each with a distinct speed. However, in a narrow region of parameter space, the waves pair up and oscillate for some time in leapfrog fashion with a nearly equal average speed. The motion is only quasi-periodic, as each wave loses energy into its respective dispersive tail, which causes the spatial oscillation magnitude and period to increase until the waves eventually separate. We record the separation time, oscillation period and magnitude, and the final amplitudes and celerity of the separated waves as a function of the input parameters, and give evidence that no perfect periodic solutions occur. A simple asymptotic model is developed to aid in interpretation of the numerical results.

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Shock-Induced Multiphase Instability in a High Volume Fraction Finite-Thickness Particle Layer

10.1115/fedsm2021-65446 ◽

2021 ◽

Author(s):

Bertrand Rollin ◽

Frederick Ouellet ◽

Bradford Durant ◽

Rahul Babu Koneru ◽

S. Balachandar

Keyword(s):

Shock Tube ◽

Volume Fraction ◽

Solid Phase ◽

Particle Volume Fraction ◽

Finite Thickness ◽

Spherical Particles ◽

Shock Strength ◽

Particle Volume ◽

Particle Cloud ◽

Particle Layer

Abstract We study the interaction of a planar air shock with a perturbed, monodispersed, particle curtain using point-particle simulations. In this Eulerian-Lagrangian approach, equations of motion are solved to track the position, momentum, and energy of the computational particles while the carrier fluid flow is computed in the Eulerian frame of reference. In contrast with many Shock-Driven Multiphase Instability (SDMI) studies, we investigate a configuration with an initially high particle volume fraction, which produces a strongly two-way coupled flow in the early moments following the shock-solid phase interaction. In the present study, the curtain is about 4 mm in thickness and has a peak volume fraction of about 26%. It is composed of spherical particles of d = 115μm in diameter and a density of 2500 kg.m−3, thus replicating glass particles commonly used in multiphase shock tube experiments or multiphase explosive experiments. We characterize both the evolution of the perturbed particle curtain and the gas initially trapped inside the particle curtain in our planar three-dimensional numerical shock tube. Control parameters such as the shock strength, the particle curtain perturbation wavelength and particle volume fraction peak-to-trough amplitude are varied to quantify their influence on the evolution of the particle cloud and the initially trapped gas. We also analyze the vortical motion in the flow field. Our results indicate that the shock strength is the primary contributor to the cloud particle width. Also, a classic Richtmyer-Meshkov instability mixes the gas initially trapped in the particle curtain and the surrounding gas. Finally, we observe that the particle cloud contribute to the formation of longitudinal vortices in the downstream flow.

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Isotherms of hydrogen, carbon monoxide and their mixtures

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1931.0210 ◽

1931 ◽

Vol 134 (824) ◽

pp. 502-512 ◽

Cited By ~ 19

Keyword(s):

Carbon Monoxide ◽

Pressure Range ◽

Close Agreement ◽

Gas Mixtures ◽

Industrial Processes ◽

Gaseous Mixtures ◽

Previous Communication ◽

New Apparatus ◽

Temperature Ranges

In a previous communication from these laboratories by G. A. Scott an account was given of the determination of the isotherms of hydrogen, carbon monoxide and mixtures of the two in the molecular proportion 2 : 1, 1 : 1 and 1 : 2 over a pressure range up to 170 atmospheres and at a temperature of 25° C. Since the completion of that investigation new apparatus has been installed so that the pressure and temperature ranges might be extended; and in this paper are embodied the results of further determinations carried out at both 0° C. and 25° C. and over a pressure range extending up to 600 atmospheres. In pursuing this investigation further it is our endeavour to furnish information in regard to the gaseous mixtures in question over the pressure and temperature ranges now commonly used in industrial processes. The Isotherms of the Single Gases . A repetition in our new apparatus of the determinations previously made by Scott both for the single gases and gas mixtures at 25° C. and at pressures up to 170 atmospheres showed his figures to be in close agreement with our own, the variations never exceeding 0·1 per cent.

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Über Energien von Drahtexplosionsstoßwellen / Energies of Shock Waves Produced bv Wire Explosions

Zeitschrift für Naturforschung A ◽

10.1515/zna-1973-0118 ◽

1973 ◽

Vol 28 (1) ◽

pp. 105-109 ◽

Cited By ~ 1

Author(s):

H. Jäger ◽

R. Schöfer

Keyword(s):

Shock Wave ◽

Shock Waves ◽

Energy Input ◽

Discharge Circuit ◽

Expansion Velocity ◽

Input Condition ◽

Wire Material ◽

Short Time ◽

The Waves ◽

Short Time Energy

For shock waves produced by special wire explosions the short time energy input condition of the theories of Lin, Sakurai and Vlases-Jones is fairly good fulfilled. In these cases the shock wave energies can be easily determined from the expansion velocity of the waves. Variation of the parameters of the discharge circuit show, how these parameters should be chosen in order to get a maximum transfer of energy either to the shock waves or to the wire material.

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