Hydroshock theory in a two-phase gas-liquid mixture in a slug flow regime

A study is made of the intensity of a hydroshock in a two-phase gas-liquid mixture in a slug flow regime in the case when a pipeline is shut off by a liquid slug. The intensity is studied as a function of the length of the shut-off section of the liquid slug, the content of gas bubbles in the liquid slugs, and the pipeline shut-off law, and with allowance for the shock-wave character of the process [1, 2]. The calculated data using the shock-wave theory agree well with the experimental data of [3] and, unlike the results of the linear theory of [3], make it possible to determine the intensity of the hydroshock not only in the case of weak waves, but also in the case of waves of moderate intensity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 188–190, September–October, 1985.     

Nonequilibrium degassing of a single-component gas-liquid mixture

At the present time the calculation of the separation of gas-liquid mixtures is carried out according to methods based on the assumption of the existence of phase equilibrium between the liquid and separated gas [1, 2]. However, the validity of this assumption is violated with a decrease of the separation time. In the present work a model and a method of calculating non equilibrium degassing are proposed for the special case of a single-component gas-liquid mixture.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 110–117, September–October, 1976.     

Numerical solution of an inverse problem of nozzle theory for a two-phase gas-particle mixture

In the present paper gas flows with monodisperse and polydisperse particles in plane and axisymmetric nozzles are calculated by the inverse method [1, 2]. The gas velocity distribution is specified on the axis of symmetry of the nozzle, while the gas and particle parameters are specified in the entrance section. As a result of the numerical integration of a system of equations describing a flow of gas with condensate particles in it we determine the gas and particle parameters, the gas streamlines, and the particle trajectories with allowance for the mutual influence of the gas and particles. One of the gas streamlines is taken as the nozzle contour and the limiting trajectories and pure gas zone are found. A difference method is described which makes it possible to calculate the subsonic, transonic, and supersonic flow regions using a single algorithm, its features are noted, and the results of the calculation for monodisperse mixtures with particle diameters 1 and 5 m and fractions by weight 0.3 are given. A comparison is made with the results of calculations by other methods.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 106–114, July–August, 1986.The authors express their gratitude to N. B. Ponomarev and G. E. Dumnov for their useful discussions and help in carrying out the calculations.     

Statistical characteristics of two-phase gas-liquid flow in a vertical microchannel

This paper presents an experimental study of the structure of an upward gas-liquid flow in a vertical microchannel with a cross-sectional dimension of 0.67 × 2.00 mm and a length of 0.5 m. The tests were performed in the ranges of reduced rates of nitrogen 0.04–11.00 m/sec and water 0.07–0.41 m/sec. Using the method of two-beam laser scanning, we identified the main flow regimes (slug-bubble, slug, transient, emulsion, and annular) and determined the statistical characteristics of the two-phase flow. A map of flow regimes was constructed, the dependence of slug velocity on the reduced mixture velocity was obtained, and the friction factor for an upward gas-liquid flow in a microchannel was measured.     

A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials

In this paper, a two-phase mixture theory is presented which describes the deflagration-to-detonation transition (DDT) in reactive granular materials. The theory is based on the continuum theory of mixtures formulated to include the compressibility of all phases and the compaction behavior of the granular material. By requiring the model to satisfy an entropy inequality, specific expressions for the exchange of mass, momentum and energy are proposed which are consistent with known empirical models. The model is applied to describe the combustion processes associated with DDT in a pressed column of HMX. Numerical results, using the method-of-lines, are obtained for a representative column of length 10 cm packed to a 70% density with an average grain size of 100 μm. The results are found to predict the transition to detonation in run distances commensurate with experimental observations. Additional calculations have been carried out to demonstrate the effect of particle size and porosity and to study bed compaction by varying the compaction viscosity of the granular explosive.     

Thermal mechanism of wave damping in a gas-liquid mixture

The effect of interphase heat transfer on the process of propagation of a wave in a monodisperse gas-liquid mixture is investigated. A three-wave equation of the Boussinesq type is derived and formulas for the dependence of the thermal components of the dissipative coefficients on the thermophysical parameters of the mixture are obtained. The limits of applicability of the short-wave method are determined. The theoretical and experimental values of the phase wave velocity are compared and found to be in good agreement.Yerevan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 75–83, November–December, 1994.     

Drift-flux correlation for gas-liquid two-phase flow in a horizontal pipe

A drift-flux correlation has been often used to predict void fraction of gas-liquid two-phase flow in a horizontal channel due to its simplicity and practicality. The drift-flux correlation includes two important drift-flux parameters, namely, the distribution parameter and void-fraction-weighted-mean drift velocity. In this study, an extensive literature survey for horizontal two-phase flow is conducted to establish void fraction database and to acquire existing drift-flux correlations. A total of 566 data is collected from 12 data sources and 4 flow-regime-dependent and 1 flow-regime-independent drift-flux correlations are identified. The predictive capability of the existing drift-flux correlations is assessed using the collected data. It is pointed out that the drift velocity determined by a regression analysis may include a significant error due to a compensation error between distribution parameter and drift velocity. In this study, a simple flow-regime-independent drift-flux correlation is developed. In the modeling approach, the void-fraction-weighted mean drift velocity is approximated to be 0 m/s, whereas the distribution parameter is given as a simple function of the ratio of non-dimensional superficial gas velocity to non-dimensional mixture volumetric flux. The newly developed correlation shows an excellent predictive capability of void fraction for horizontal two-phase flow. Mean absolute error (or bias), standard deviation (random error), mean relative deviation and mean absolute relative deviation of the correlation are 0.0487, 0.0985, 0.0758 and 0.206, respectively. The prediction accuracy of the correlation is similar to the correlation of Chexal et al. (1991), which was formulated based on the drift-flux parameters by means of many cascading constitutive relationships with numerous empirical parameters.     

Propagation of modulated nonlinear waves in a relaxing gas-liquid mixture

The propagation of nonstationary weak shock waves in a chemically active medium is essentially dispersive and dissipative. The equations for short-wavelength waves for such media were obtained and investigated in [1–4]. It is of interest to study quasimonochromatic waves with slowly varying amplitude and phase. A general method for obtaining the equations for modulated oscillations in nonlinear dispersive media without dissipation was proposed in [5–8]. In the present paper, for a dispersive, weakly nonlinear and weakly dissipative medium we derive in the three-dimensional formulation equations for waves of short wavelength and a Schrödinger equation, which describes slow modulations of the amplitude and phase of an arbitrary wave. The coefficients of the equations are particularized for the considered gas-liquid mixture. Solutions are obtained for narrow beams in a given defocusing medium as well as linear and nonlinear solutions in the neighborhood of a diffraction beam. A solution near a caustic for quasimonochromatic waves was found in [9].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 133–143, January–February, 1980.     

Critical flow in a chemically reacting two-phase multicomponent mixture

A model that describes the critical flow of chemically reacting, two-phase, multicomponent mixtures in channels of constant cross section is discussed. As a consequence of an assumed interphase thermal and mechanical equilibrium the applicability of the model is restricted to situations where one phase is intimately mixed with the other, such that choking is determined by the sound speed in the homogeneous mixture. It is shown that under certain conditions the highly non-linear temperature dependency of the reaction rate promotes the possibility of a multiplicity of steady state solutions to the problem.     

Large scale structure in gas-liquid mixture flows

Relatively slow variation in mixture void fraction in gas-liquid mixture flows are indicated by low pass filter averaging. The slow void fluctuations are found to have a regular characteristic frequency or scale in the churn flow regime or near the boundary with the dispersed bubble flow regime. These regular disturbances develop inherently in a vertical pipe flow in strength and in size and are not due to the method of flow mixing. There was no evidence of distinctive gas slugs in the flow, and the structures were identified as large clouds of bubbles which moved faster than the average velocity, growing in size and strength as they moved with the flow. The magnitude of the voidage fluctuations in the churn flow regime was on average 57% of the value for a slug flow. The large scale bubble clouds convect coherently over relatively long distances at up to 1.45 times the mean mixture flow velocity at a gas volume flow fraction of 0.4. In the bubble flow regime, the slow voidage variations were more random in scale and were only approx. 10% of the slug flow (maximum possible) value. However, even in the bubble flow regime, the disturbances convected coherently over relatively long distances at a velocity of approx. 1.1 times the mean mixture velocity.     

Configurations of gas-liquid two-phase bubbles in immiscible liquid media

The configuration of a “two-phase bubble” constituted of a gas phase and a liquid phase in an immiscible liquid medium is classified into three types: complete engulfing of a gas bubble inside a liquid shell, partial coalescence of a gas bubble and a liquid drop forming a three-phase contact line, and non-coalescence whereby a gas bubble and a liquid drop remain separated. Simple criteria have been presented by which the favorable type of configuration in a given system is predicted from the values of the spreading coefficients characterizing the system. Experiments using some combinations of liquids as well as air suggest the general validity of the criteria.     

An analysis of holdup in horizontal two-phase gas-liquid flow

The Butterworth form of correlation for holdup in two-phase gas-liquid flow is justified theoretically for certain conditions. In addition, a wide range of experimental data were used to show that holdup data may be broadly classified into three major groups based on the flow pattern, and different relationships were found to represent the data in each group. Thus for slug and plug flow, the holdup is given by the Armand type of equation; for stratified flow the holdup is given by the theoretical equations which are derived while annular flow data are satisfactorily represented by a semi-empirical correlation.     

Distribution of spherical shock waves in a two-phase fuel mixture

A study has been made of the distribution of spherical shock waves in a two-phase fuel mixture. It is shown that interaction with the liquid fuel droplets increases the wave intensity. Conditions for spherical shock wave amplification in a two-phase fuel mixture are marked out.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 112–117, September–October, 1973.The authors wish to thank V. V. Adushkin for a useful discussion of the results obtained in this work.     

A two-phase, two-component model for vertical upward gas-liquid annular flow

In this paper, a new two-fluid two-component computational fluid dynamics (CFD) model is developed to simulate vertical upward two-phase annular flow. The two-phase VOF scheme is utilized to model the roll wave flow, and the gas core is described by a two-component phase consisting of liquid droplets and gas phase. The entrainment and deposition processes are taken into account by source terms of the governing equations. Unlike the previous models, the newly developed model includes the effect of liquid roll waves directly determined from the CFD code, which is able to provide more detailed and, the most important, more self-standing information for both the gas core flow and the film flow as well as their interactions. Predicted results are compared with experimental data, and a good agreement is achieved.     

Theory of regular and mach reflection of shock waves in a two-phase gas-liquid medium

An equilibrium model of a two-phase gas-liquid medium, with allowance for the proportion, density, and compressibility of the components, and with a difference from [1] in that the adiabatic velocity of sound is introduced, has been used in order to study the regular and Mach (elementary theory) reflection of a shock wave of moderate intensity from a solid wall throughout the whole range of gas proportions. A complicated nonmonotonic variation has been found for the pressure on the wall behind the reflected wave, the angle of reflection, and the angle of departure of the triple point as functions of the gas proportion, the angle of incidence, and the intensity of the incident wave. In particular, it is shown that oblique reflection for moderate and low gas contents leads to the formation of a stronger reflected shock wave than does normal reflection. The effect of the gas proportion on the position of the boundary between the regions of regular and Mach reflection has already been studied in [2]. The results are described of serial calculations of the parameters of reflection for an air-water mixture, and these results agree fairly well for normal reflection with the known experimental data [3] for low and moderate gas contents. In the limiting case, the results agree with the known results for single-phase media [4, 5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 188–190, March–April, 1985.     

On the nonequilibrium segregation state of a two-phase mixture in a porous column

The problem of segregation of a two-phase multicomponent mixture under the action of thermal gradient, gravity and capillary forces is studied with respect to component distribution in a thick oil-gas-condensate reservoir. Governing equations are derived on the basis of nonequilibrium thermodynamics. A steady state of the two-phase mixture with nonzero diffusion fluxes and exchange between phases is described. In the case of binary mixtures analytical formulae for saturation, component distribution and flow in the two-phase zone are obtained.     

Flow structure and distribution effects in gas-liquid mixture flows

Air-water mixtures which are assumed to flow homogeneously in a pipe are usually described by a one-dimensional momentum balance. This allows definition of a friction factor in a manner similar to single phase flows. By defining a momentum flux distribution parameter, the momentum balance has been modified to correctly include the etfects of phase and velocity distributions and the effect of these on calculated friction factors has been investigated. Resistivity probes were used to measure void fraction and gas phase velocity distributions for selected vertical and horizontal flow conditions, and these were combined with static pressure measurements to calculate friction factors. For bubbly flows, the inclusion of these distribution effects did not substantially alter friction factor estimates which are approximately 10% above single phase values (for Reynolds numbers based on liquid viscosity).

Friction factor values are shown to be related to flow development with higher values associated with deveioping flows. In particular, high friction factors are associated with the need to break-up bubbles to an “equilibrium” size. In order to experimentally simulate fully developed vertical flows, the highly turbulent nozzle mixer is most suitable while the less turbulent wall-injection type seems appropriate for horizontal flows.