Propagation of pressure waves in two-phase flow

We deal with a pressure wave of finite amplitude propagating in a gas and liquid medium or in the fluid in an elastic tube. We study the effects of pipe elasticity on the propagation velocity of the pressure wave. Pressure waves of finite amplitude progressing in the two-phase flow are treated considering the void fraction change due to pressure rise. The propagation velocity of the two-phase shock wave is also investigated, and the behavior of the reflection of the pressure wave at the rigid wall is analyzed and compared to that in a pure gas or liquid. The results are compared to experimental data of a pressure wave propagating in the two-phase flow in a vertical shock tube.     

Macro-mechanical modeling of blast-wave mitigation in foams. Part III: verification of the models

Three different approaches to macro-mechanical modeling of blast-wave mitigation in foam namely: the single-phase effective gas flow model, the two-phase mixture model and the single bubble/shock wave interaction model are critically reviewed. The nature and extent of the approximations inherent in the formulation of the first two models were examined in Part I of this study. In this part, the applicability of the aforementioned approaches is verified based on a comparison of experimental pressure records obtained in shock tube tests with the results of numerical predictions that used the models under consideration. Deficiencies and inconsistencies that are found during this comparison are clarified and possible improvements are suggested. It is emphasized that both the single-phase and the two-phase approaches predict well the refraction of the incident shock at the air/foam interface while they do not uniquely determine the relaxation process and the shape of the transmitted shock wave front. Various flexibilities that are exploited to better describe the inter-phase interactions do not improve the results significantly. The single bubble model is examined with particular attention paid to the manner in which it predicts the shape of the shock wave front. Connections between the flow viscosity and the transient dynamics of the bubble compression that occur at scales of the shock wave front thickness are explored.     

A semi-empirical model of two-phase flow of refrigerant-134a through short tube orifices

Measurements were conducted on Refrigerant-134a flowing through short tube orifices with length-to-diameter (L/D) ratios ranging from 5 to 20. Both two-phase and subcooled liquid flow conditions entering the short tube were examined for upstream pressures ranging from 896 to 1448 kPa and for qualities as high as 10% and subcoolings as high as 13.9°C. Data were analyzed as a function of the main operating variables and tube geometry. Semi-empirical models for both single- and two-phase flow at the inlet of the short tubes were developed to predict the mass flow of Refrigerant-134a through short tube orifices.

Choked flow conditions for Refrigerant-134a were typically established when downstream pressures were reduced below the saturation pressure corresponding to the inlet temperature. The flow rate strongly depended on the upstream pressure and upstream subcooling/quality. The mass flow also depended on cross-sectional area and short tube length. The mass flow model utilized a modified orifice equation that formulated the mass flow as a function of normalized operating variables and short tube geometry. For a two-phase flow entering the short tube, the modified orifice equation was corrected using a theoretically derived expression that related the liquid portion of the mass flow under two-phase conditions to a flow that would occur if the flow were a single-phase liquid. It was found that for sharp-edged short tubes with single- and two-phase flow, approximately 95% of the measured data and model's prediction were within ±15% of each other.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

Separated two-phase flow in a nozzle

This work was performed to extend and further test the method of handling separated two-phase flow by studying each phase separately and, particularly, by placing emphasis on the study of the gas phase with interface transport expressions showing the influence of the liquid phase on it. A one-dimensional flow model for accelerating flows was used in conjunction with experimental data to obtain the pressure distribution and velocity distribution in a converging nozzle for several values of flow quality and nozzle inlet stagnation pressure. The results tend to support the use of the model (which includes the assumption that the gas is in critical flow when the two-phase mixture is in critical flow) and give some insight regarding the nature of the liquid distribution near the nozzle throat.     

Analytical pressure drop correlation for adiabatic vertical two-phase flow

A new correlation for two-phase wall friction is proposed derived from analytical considerations and based upon an annular flow model. In spite of this basis in annular flow the correlation is consistent for all flow patterns in vertical two-phase flow.The correlation yields a smooth transition from two-phase flow to single-phase liquid flow, mainly because it incorporates the friction factor of the Moody diagram [1] for single-phase flow.The correlation is checked against 236 measurements from various sources and has turned out to be most favourable in comparison with the correlations of Dukler (case 2) [2] and Lockhart-Martinelli [3]. The standard deviation of these 236 measurements is 27.8%, with 68% having a relative error of less than 28.2%.     

The prediction of stratified two-phase flow with a two-equation model of turbulence

A two-equation model is applied to a stratified two-phase flow system to predict turbulent transport mechanisms in both phases.In the present analysis, the effects of interfacial waves on the flow field are formulated in terms of boundary conditions for the gas-liquid interface. For the gas phase, the wavy interface has such flow separation effects as a rough surface in a single-phase flow. While for the liquid phase, the waves generate turbulant energy which is transported progressively toward a lower wall region. The analytical results are in good agreement with available data regarding pressure drop, holdup and velocity profiles.     

Frictional pressure drop during vapour–liquid flow in minichannels: Modelling and experimental evaluation

Condensation in minichannels is widely used in air-cooled condensers for the automotive and air-conditioning industry, in heat pipes and other applications for system thermal control. The knowledge of pressure drops in such small channels is important in order to optimize heat transfer surfaces. This paper presents a model for calculation of the frictional pressure gradient during condensation or adiabatic liquid–gas flow inside minichannels with different surface roughness. In order to account for the effects of surface roughness, new experimental frictional pressure gradient data associated to single-phase flow and adiabatic two-phase flow of R134a inside a single horizontal mini tube with rough wall has been used in the modelling. It is a Friedel (1979) [Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. In: Proceedings of the European Two-Phase Flow Group Meeting, Ispra, Paper E2] based model and it takes into account mass velocity, vapor quality, fluid properties, reduced pressure, tube diameter, entrainment ratio and surface roughness. With respect to the flow pattern prediction capability, it has been built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and mist flow are here predicted. However, the suggested procedure is extended to the intermittent flow in minichannels and it is also applied with success to horizontal macro tubes.     

An experimental study of drag on a single tube and on a tube in an array under two-phase cross flow

In this work, the drag coefficient and the void fraction around a tube subjected to two-phase cross flow were studied for a single tube and for a tube placed in an array. The drag coefficients were determined by measuring the pressure distribution around the perimeter of the tube. Single tube drag data were taken when the tube was held both rigidly and flexibly. The test tube was made of acrylic and was 2.2 cm in diameter and 20 cm in length. In the experiments, liquid Reynolds number ranged from 430 to 21,900 for the single tube and liquid gap Reynolds number ranged from 32,900 and 61,600 for the tube placed in a triangular array. Free stream void fraction was varied from 0 to 0.4. At low Reynolds numbers, the ratio of two-phase to single-phase drag coefficient is found to be a strong function of εGr/Re2. However, at high Reynolds numbers only void fraction is the important parameter. Empirical correlations have been developed for the ratio of two-phase drag on a single tube and on a tube placed in an array.     

Modeling Non-Darcian Single- and Two-Phase Flow in Transparent Replicas of Rough-Walled Rock Fractures

While it is generally assumed that in the viscous flow regime, the two-phase flow relative permeabilities in fractured and porous media depend uniquely on the phase saturations, several studies have shown that for non-Darcian flows (i.e., where the inertial forces are not negligible compared with the viscous forces), the relative permeabilities not only depend on phase saturations but also on the flow regime. Experimental results on inertial single- and two-phase flows in two transparent replicas of real rough fractures are presented and modeled combining a generalization of the single-phase flow Darcy’s law with the apparent permeability concept. The experimental setup was designed to measure injected fluid flow rates, pressure drop within the fracture, and fluid saturation by image processing. For both fractures, single-phase flow experiments were modeled by means of the full cubic inertial law which allowed the determination of the intrinsic hydrodynamic parameters. Using these parameters, the apparent permeability of each fracture was calculated as a function of the Reynolds number, leading to an elegant means to compare the two fractures in terms of hydraulic behavior versus flow regime. Also, a method for determining the experimental transition flow rate between the weak inertia and the strong inertia flow regimes is proposed. Two-phase flow experiments consisted in measuring the pressure drop and the fluid saturation within the fractures, for various constant values of the liquid flow rate and for increasing values of the gas flow rate. Regardless of the explored flow regime, two-phase flow relative permeabilities were calculated as the ratio of the single phase flow pressure drop per unit length divided by the two-phase flow pressure drop per unit length, and were plotted versus the measured fluid saturation. Results confirm the dependence of the relative permeabilities on the flow regime. Also the proposed generalization of Darcy’s law shows that the relative permeabilities versus fluid saturation follow physical meaningful trends for different liquid and gas flow rates. The presented model fits correctly the liquid and gas experimental relative permeabilities as well as the fluid saturation.     

Experimental study on the two-phase pressure drop in copper foams

Experiments were performed to study pressure drops in copper foams embedded in a rectangular copper channel. De-ionized water was used as the working fluid with mass fluxes of 30–200 kg/m² s, and inlet temperature of 40–80°C. The copper foam has the porosity of 0.88 and the pore densities of 30, 60 and 90 ppi (pores per inch). Both single-phase liquid flow and boiling two-phase flow are studied. Effects of mass fluxes, vapor mass qualities, and average pore diameters of metallic foams are investigated. It is found that friction factors for the single-phase liquid flow are mainly dependent on the Reynolds number and the average pore diameter of metallic foams. The friction factors are decreased with increases in the Reynolds numbers, and will approach 0.22 at high Reynolds numbers. For the boiling two-phase flow, two-phase pressure drops are increased with increases in the outlet vapor mass qualities, mass fluxes, and ppi values. The two-phase multiplier is increased with increases in the outlet vapor mass qualities and mass fluxes, and it is decreased with increases in the Martinelli parameter and will attain a constant value depending on the mass fluxes. The larger the mass fluxes, the larger the constant value is. An experimental correlation considering the effects of vapor mass qualities, mass fluxes, and average pore diameters of metallic foams is recommended, showing good accuracy to predict the two-phase pressure drops in metallic foams.     

Analysis of frictionless two-phase flow in tubes under centrifugal acceleration and minimum heating for choked flow

To determine the void fraction in a tube of a rotating heat exchanger, an analytical investigation was undertaken to model frictionless two-phase flow boiling. Steady, one-dimensional separated two-phase conservation equations in differential form, were first applied to a stationary system. The equations were integrated between the inlet and exit of the flow channel to yield three coupled algebraic equations. The algebraic equations were then modified to represent rotating systems. To obtain closure, the velocity ratio, mass quality and void fraction are defined as a function of pressure.

A numerical technique was used to solve the equations. Sample results are presented in a graph of mass quality versus void fraction. The graph demonstrates that a minimum heat input must be exceeded to change from a single-phase flow to saturated two-phase flow boiling. Also, the void fraction was found to increase for increasing heat input, decreasing mass flow rate, increasing inlet mass quality and decreasing pressure difference between the inlet and exit.     

Single-Phase (Brine) and Two-Phase (DNAPL–Brine) Flows in Induced Fractures

This study reports an investigation on the characteristics of single-phase (brine) and two-phase (DNAPL–brine) flows in induced fractures. The fracture aperture and fluid phase distributions were determined using X-ray computer tomography. In the single-phase flow tests, the pressure gradient across the induced fractures increases linearly with increasing flow rate. However, models based on the measured aperture do not yield a consistent match with the experimental data because the effect of pressure losses due to aperture variation and undulation are not taken into account. In the two-phase flow tests, the measured phase distributions reveal that the flow pattern is dominated by a dispersed or mixed flow in which either DNAPL or brine phase is discontinuous. The channel flow pattern, in which DNAPL and brine phases are continuous in the fracture and well represented by the widely used Romm’s relative permeability relationship was not observed in this study. In contrast, a Lockhart–Martinelli-type correlation developed for gas–liquid flow in pipes was found to match the pressure gradient and phase saturation results obtained from the laboratory tests.     

Interaction of a shock wave with a loose dusty bulk layer

The interaction of a planar shock wave with a loose dusty bulk layer has been investigated both experimentally and numerically. Experiments were conducted in a shock tube. The incident shock wave velocity and particle diameters were measured with the use of pressure transducers and a Malvern particle sizer, respectively. The flow fields, induced by shock waves, of both gas and granular phase were visualized by means of shadowgraphs and pulsed X-ray radiography with trace particles added. In addition, a two-phase model for granular flow presented by Gidaspow is introduced and is extended to describe such a complex phenomenon. Based on the kinetic theory, such a two-phase model has the advantage of being able to clarify many physical concepts, like particulate viscosity, granular conductivity and solid pressure, and deduce the correlative constitutive equations of the solid phase. The AUSM scheme was employed for the numerical calculation. The flow field behind the shock wave was displayed numerically and agrees well with our corresponding experimental results.      

Numerical simulation of a turbulent flow with droplets injection in annular heated air tube using the Reynolds stress model

This work presents computational fluid dynamics (CFD) simulations of single-phase and two-phase flow. The droplets are injected in annular heated air tube. The numerical simulation is performed by using a commercial CFD code witch uses the finite-volume method to discretize the equations of fluid flow. The Reynolds-averaged Navier–Stokes equations with Reynolds stress model were used in the computation. The governing equations are solved by using a SIMPLE algorithm to treat the pressure terms in the momentum equations. The results of prediction are compared with the experimental data.     

Two-phase pressure drop with twisted-tape swirl generators

An experimental study has been conducted to determine the effect of twisted-tape swirl generators on adiabatic and diabatic two-phase flow pressure drops in vertical straight tubes. Tape-twist ratios (length for 180° twist/inside tube diameter) of 3.94, 8.94, and 13.92 were tested with R-113 over a range of pressures, mass velocities, qualities, and heat fluxes. Empty tube refcrence data were successfully predicted with a correlation from the literature. The twisted tape data were successfully correlated by using the hydraulic diameter and a single-phase swirl flow friction factor in the empty tube correlation. Data from the literature also were predicted well with this correlation.     

The effect of magnetic field on two-phase liquid metal flow

In this paper, the basic equations of two-phase liquid metal flow in a magnetic field are derived, and specifically, two-phase liquid metal MHD flow in a rectangular channel is studied, and the expressions of velocity distribution of liquid and gas phases and the ratioK ₀ of the pressure drop in two-phase MHD flow to that in single-phase are derived. Results of calculation show that the ratioK ₀ is smaller than unity and decreases with increasing void fraction and Hartmann number because the effective electrical conductivity in the two-phase case decreases. The Project is supported by the National Natural Science Foundation of China.     

Stagnation region of a blunt body in two-phase hypersonic flow

The fluid-mechanics equations of a two-velocity, two-temperature medium are used to investigate flow near the stagnation point of a blunt body washed by a hypersonic stream of gas containing solid or liquid deformed particles. The effect of particles of the gasdynamic flow parameters is analyzed. A relaxation layer was found to occur near the body, with marked changes in the gas parameters. It is shown that the presence of particles in the flow reduces the shock stand-off distance. The results of computations on the dynamics and heating of particles in the shock layer are discussed. A solution in finite form is obtained in the limiting case of fine particles by the method of asymptotic expansions. The motion of solid or liquid particles in hypersonic shock layers has been the subject of several papers [1–6], in which particle dynamics was examined, assuming that the particles have a negligible influence on the gasdynamic flow parameters. The solutions obtained are therefore limited to the case of low mass particle concentration in the incident flow. A numerical solution not subject to this limitation was obtained in [7] for supersonic two-phase flow over a wedge.     

Vortex shedding and fluidelastic instability in a normal square tube array excited by two-phase cross-flow

Laboratory experiments were conducted to determine the flow-induced vibration (FIV) response and fluidelastic stability threshold of a model heat exchanger tube bundle subjected to a cross-flow of refrigerant 11. The tube bundle consisted of a normal square array of 12 tubes with outer tube diameters of 7.11 mm and a pitch over diameter ratio of 1.485. The experiments were conducted in a flow-loop that was capable of generating single- and two-phase cross-flows over a variety of mass fluxes and void fractions. The primary intent of the research was to improve our understanding of the FIVs of heat exchanger tube arrays subjected to two-phase cross-flow. Of particular concern was the effect of array pattern geometry on fluidelastic instability. The experimental results are analysed and compared with existing data from the literature using various methods of parameter definition. Comparison of tube vibration response in liquid flow with previous results shows a similar occurrence of symmetric vortex shedding that validates the scale model approach in single-phase flow. It was found that the introduction of a small amount of bubbles in the flow disrupted the vortex shedding and thereby caused a significant reduction in streamwise vibration amplitude. The fluidelastic stability thresholds for the present array agree well with results from previous studies. Furthermore, a good collapse of the stability data from various investigations is obtained when the fluid density is defined using the slip model of Feenstra et al. and when an effective two-phase flow velocity is defined using the interfacial velocity model of Nakamura et al.