Shock Waves in Liquids With Bubbles Containing Evaporating Drops

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.

Waves in liquids with vapour bubbles

1988 ◽  
Vol 186 ◽  
pp. 85-117 ◽  
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.

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

2002 ◽  
Vol 24 (3) ◽  
pp. 167-180
Author(s):  
Duong Ngoc Hai ◽  
Nguyen Van Tuan
Keyword(s):  
Shock Waves ◽  
Volume Fraction ◽  
Initial Conditions ◽  
Solid Wall ◽  
Vapour Phase ◽  
Gas Mixtures ◽  
Industrial Processes ◽  
Shock Strength ◽  
Stationary Shock ◽  
The Waves

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.

scholarly journals Dispersive shock waves in viscously deformable media

2013 ◽  
Vol 718 ◽  
pp. 524-557 ◽  
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.

scholarly journals Nematic Dispersive Shock Waves from Nonlocal to Local

2021 ◽  
Vol 11 (11) ◽  
pp. 4736
Author(s):  
Saleh Baqer ◽  
Dimitrios J. Frantzeskakis ◽  
Theodoros P. Horikis ◽  
Côme Houdeville ◽  
Timothy R. Marchant ◽  
...  
Keyword(s):  
Shock Wave ◽  
Liquid Crystals ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Wave Structure ◽  
Beam Power ◽  
Input Beam ◽  
Shock Wave Structure ◽  
Wave Solutions ◽  
Modulation Theory

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

scholarly journals Effect of the Gas Volume Fraction on the Pressure Load of the Multiphase Pump Blade

Processes ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 650
Author(s):  
Guangtai Shi ◽  
Dandan Yan ◽  
Xiaobing Liu ◽  
Yexiang Xiao ◽  
Zekui Shu
Keyword(s):  
Flow Rate ◽  
Static Pressure ◽  
Volume Fraction ◽  
Pump Impeller ◽  
Impeller Blade ◽  
Multiphase Pump ◽  
Pressure Load ◽  
Gas Volume Fraction ◽  
Power Capability ◽  
Gas Volume

The gas volume fraction (GVF) often changes from time to time in a multiphase pump, causing the power capability of the pump to be increasingly affected. In the purpose of revealing the pressure load characteristics of the multiphase pump impeller blade with the gas-liquid two-phase case, firstly, a numerical simulation which uses the SST k-ω turbulence model is verified with an experiment. Then, the computational fluid dynamics (CFD) software is employed to investigate the variation characteristics of static pressure and pressure load of the multiphase pump impeller blade under the diverse inlet gas volume fractions (IGVFs) and flow rates. The results show that the effect of IGVF on the head and hydraulic efficiency at a small flow rate is obviously less than that at design and large flow rates. The static pressure on the blade pressure side (PS) is scarcely affected by the IGVF. However, the IGVF has an evident effect on the static pressure on the impeller blade suction side (SS). Moreover, the pump power capability is descended by degrees as the IGVF increases, and it is also descended with the increase of the flow rate at the impeller inlet. Simultaneously, under the same IGVF, with the increase of the flow rate, the peak value of the pressure load begins to gradually move toward the outlet and its value from hub to shroud is increased. The research results have important theoretical significance for improving the power capability of the multiphase pump impeller.

scholarly journals Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah Bin Sakidin ◽  
Muhammad Jamil ◽  
...  
Keyword(s):  
Energy Equation ◽  
Volume Fraction ◽  
Mhd Flow ◽  
Integral Transforms ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fourier’S Law ◽  
Fractional Model ◽  
Laplace Transformations ◽  
Fourier's Law

AbstractThe present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

scholarly journals Simulation of MASPn Experiments in MISTRA Test Facility with COCOSYS Code

2008 ◽  
Vol 2008 ◽  
pp. 1-7 ◽  
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.

A Dynamic Model for the Design of Methanol to Hydrogen Steam Reformers for Transportation Applications

2004 ◽  
Vol 126 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Gregory L. Ohl ◽  
Jeffrey L. Stein ◽  
Gene E. Smith
Keyword(s):  
Response Time ◽  
Dynamic Model ◽  
First Principles ◽  
Initial Conditions ◽  
Design Parameters ◽  
Physical Parameters ◽  
Steam Reformer ◽  
Powerful Means ◽  
Steam Reformers ◽  
Transportation Applications

As an aid to improving the dynamic response of the steam reformer, a dynamic model is developed to provide preliminary characterizations of the major constraints that limit the ability of a reformer to respond to the varying output requirements occurring in vehicular applications. This model is a first principles model that identifies important physical parameters in the steam reformer. The model is then incorporated into a design optimization process, where minimum steam reformer response time is specified as the objective function. This tool is shown to have the potential to be a powerful means of determining the values of the steam reformer design parameters that yield the fastest response time to a step input in hydrogen demand for a given set of initial conditions. A more extensive application of this methodology, yielding steam reformer design recommendations, is contained in a related publication.

scholarly journals Computational Modeling of Flow Characteristics in Three Products Hydrocyclone Screen

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1295
Author(s):  
Anghong Yu ◽  
Chuanzhen Wang ◽  
Haizeng Liu ◽  
Md. Shakhaoath Khan
Keyword(s):  
Static Pressure ◽  
Cfd Simulation ◽  
Volume Fraction ◽  
Flow Characteristics ◽  
Pressure Profile ◽  
Reynolds Stress Model ◽  
Grid Scheme ◽  
Cylindrical Screen ◽  
The Right ◽  
Axial Depth

Three products hydrocyclone screen (TPHS) can be considered as the combination of a conventional hydrocyclone and a cylindrical screen. In this device, particles are separated based on size under the centrifugal classification coupling screening effect. The objective of this work is to explore the characteristics of fluid flow in TPHS using the computational fluid dynamics (CFD) simulation. The 2 million grid scheme, volume fraction model, and linear pressure–strain Reynolds stress model were utilized to generate the economical grid-independence solution. The pressure profile reveals that the distribution of static pressure was axisymmetric, and its value was reduced with the increasing axial depth. The maximum and minimum were located near the tangential inflection point of the feed inlet and the outlets, respectively. However, local asymmetry was created by the left tangential inlet and the right screen underflow outlet. Furthermore, at the same axial height, the static pressure gradually decreased along the wall to the center. Near the cylindrical screen, the pressure difference between the inside and the outside cylindrical screen dropped from positive to negative as the axial depth increased from −35 to −185 mm. Besides, TPHS shows similar distributions of turbulence intensity I, turbulence kinetic energy k, and turbulence dissipation rate ε; i.e., the values fell with the decrease in axial height. Meanwhile, from high to low, the pressure values are distributed in the feed chamber, the cylindrical screen, and conical vessel; the value inside the screen was higher than the outer value.

scholarly journals Melting Effect on Unsteady Hydromagnetic Flow of a Nanofluid Past a Stretching Sheet

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ali J. Chamkha ◽  
A.M. Rashad ◽  
Eisa Al-Meshaiei
Keyword(s):  
Stretching Sheet ◽  
Volume Fraction ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Time Histories ◽  
Nanoparticles Volume Fraction ◽  
Layer Flow ◽  
Stretching Plate ◽  
Melting Effect

This paper considers unsteady, laminar, boundary-layer flow with heat and mass transfer of a nanofluid along a horizontal stretching plate in the presence of a transverse magnetic field, melting and heat generation or absorption effects. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the steady-state velocity, temperature and nanoparticles volume fraction profiles as well as the time histories of the skin-friction coefficient, Nusselt number and the Sherwood number are presented graphically and discussed.

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