Choking and shock phenomena in a single component two-phase flow including vibrational effects

An analytical and experimental investigation including vibratory effects of flashing flow in a tube with a sharp edged entrance is presented. A free streamline flow model is applied to predict choking in single-component two-phase flow. By identifying three separate regimes (i.e. jet flow, two-phase homogeneous flow, and single-phase liquid flow) in the flashing flow system, an expression is obtained for the prediction of the minimum stagnation pressure loss under choked flow conditions. A normal shock located between the flashing two-phase mixture and the single-phase liquid was experimentally observed. The location of the shock is predicted as a function of the stagnation pressure drop across the tube. The analytical predictions are verified by experimental data.     

The elimination of severe slugging-experiments and modeling

Severe slugging can occur in a pipeline-riser system operating at low liquid and gas rates. The flow of gas into the riser can be blocked by liquid accumulation at the base of the riser. This can cause formation of liquid slugs of a length equal to or longer than the height of the riser. A cyclic process results in which a period of no liquid production into the separator occurs, followed by a period of very high liquid production. This study is an experimental and theoretical investigation of two methods for eliminating this undesirable phenomenon, using choking and gas lift. Choking was found to effectively eliminate or reduce the severity of the slugging. However, the system pressure might increase to some extent. Gas lift can also eliminate severe slugging. While choking reduces the velocities in the riser, gas lift increases the velocities, approaching annular flow. It was found that a relatively large amount of gas was needed before gas injection would completely stabilize the flow through the riser. However, gas injection reduces the slug length and cycle time, causing a more continuous production and a lower system pressure. Theoretical models for the elimination of severe slugging by gas lift and choking have been developed. The models enable the prediction of the flow behavior in the riser. One model is capable of predicting the unstable flow conditions for severe slugging based on a static force balance. The second method is a simplified transient model based on the assumption of a quasi-equilibrium force balance. This model can be used to estimate the characteristics of the flow, such as slug length and cycle time. The models were tested against new severe slugging data acquired in this study. An excellent agreement between the experimental data and the theoretical models was found.     

An analytical theory of heated duct flows in supersonic combustors

One-dimensional analytical theory is developed for supersonic duct flow with variation of cross section, wall friction, heat addition, and relations between the inlet and outlet flow parameters are obtained. By introducing a selfsimilar parameter, effects of heat releasing, wall friction, and change in cross section area on the flow can be normalized and a self-similar solution of the flow equations can be found. Based on the result of self-similar solution, the sufficient and necessary condition for the occurrence of thermal choking is derived. A relation of the maximum heat addition leading to thermal choking of the duct flow is derived as functions of area ratio, wall friction, and mass addition, which is an extension of the classic Rayleigh flow theory, where the effects of wall friction and mass addition are not considered. The present work is expected to provide fundamentals for developing an integral analytical theory for ramjets and scramjets.     

The effects of rate of expansion and injection of water droplets on the entropy generation of nucleating steam flow in a Laval nozzle

The entropy generation due to irreversible heat transfer between vapor and liquid phases in a nucleating steam flow in a Laval nozzle is studied. To calculate the entropy generation due to self-condensation in transonic steam flow, a thermodynamic model is presented. The calculations of nucleating steam flow and the predictions of entropy generation rely on one-dimensional two-phase model. This model shows that the most of the thermodynamic losses take place during the nucleation phenomena. The effect of rate of expansion on the exergy losses is considered by decreasing the divergent angle of nozzle. Also micro-sized pure water droplets is injected theoretically to supercooled steam right after the nozzle throat at the onset of divergent section and the effects of injected droplets on thermodynamic losses and nucleation phenomena are investigated. The results indicate that decreasing the divergent angle and also injection of droplets diminishes the pressure rise in transonic steam flow and decreases the thermal entropy generation due to nucleation.     

The expansion of wet steam through a compressible confined vortex in a fluidic vortex diode

The pressure-flow characteristics of a Zobel-type vortex diode have been measured using a working fluid of compressible wet steam. Tests using superheated steam with inlet/outlet pressure ratios across the diode of up to 30 have shown clearly the effects of compressibility and choking on the diode characteristics. Repeating the tests using wet steam, with known dryness fractions, has shown separately the effects of wetness on the diode performance.

When the diode was installed into the pipwork in the high-resistance direction, excessive steam wetness (quality <0.93) led to a build-up of water and when this was eventually swept through to the diode the resistance was seen to fall substantially as the strong internal vortex was destroyed.     

Stability of severe slugging

For a constant flow rate of liquid and gas in a pipe one expects the conditions along the pipe to be of a steady state nature. However, for a pipe in a hilly terrain or in an offshore pipeline-riser system, a steady state operation is often not possible, and conditions of severe or terrain slugging develop. This causes the system to operate in an undesired cyclic fashion in which alternate long liquid slugs are followed by the production of high gas flow rate. The present work deals with the condition under which steady state operation is possible. It shows theoretically that it is possible to stablize the flow by increasing the back pressure of the separator or by employing a controlled choking at the pipe exit.     

Variation of velocity profile of jet and its effect on interfacial stability

IntroductionSincenineteencentury ,thestabilityofgas_liquidtwo_phasejethasattractedalotofpeoplefortheoreticalstudybecauseofitswideapplicationsinindustry .Thestabilitybehavioriscloselyrelatedtotheshapeofbasicvelocityprofile,andthevelocityprofilesmeasuredfromexperimentsarenotaccurateenough ,itisworthwhiletostudythevelocitymodelinthenumericalsimulation .Insimplermodels,top_hatprofile[1,2 ]issuggestedasbasicflowfortheinviscidandincompressibleliquidandgas.Tocompareitwithrealisticflow ,Suetal.[3]ass…     

Types of choking in vertical pneumatic systems

Choking is examined in terms of its definitions. Three choking initiation mechanisms are identified: type A (accumulative) choking occurs when solids start to accumulate at the bottom of the conveyor as the saturation gas carrying capacity is reached; type B (blower-/standpipe-induced) choking results from instabilities due to gas blower-conveyor or solids feeder-conveyor interactions where there is insufficient pressure or too limited solids feed capacity to provide the needed solids flow; and type C (classical) choking corresponds to a transition to severe slugging. Approaches for predicting the onset of each of these type of choking are recommended. Implications for regime transitions in fast fluidization are also identified.     

Numerical and experimental evidence of the Fabri-choking in a supersonic ejector

The purpose of a supersonic ejector consists in the mixing of two fluids with different stagnation pressures in order to obtain a fluid at an intermediate stagnation pressure at the discharge. Depending on the geometry of the ejector and on the operating conditions, the entrained secondary stream may reach sonic/supersonic velocities within the ejector, leading to the capping of the entrained mass flow rate for fixed reservoir conditions. Although the associated limitation of the entrainment ratio (due to choking) is a well known phenomenon, there is still a lack of understanding of the complex flow phenomena at play within supersonic ejectors, and further detailed knowledge and modeling of the choking process is necessary. This paper presents a detailed analysis of the choking phenomenon through advanced post-processing of CFD calculations which are validated with experimental results both at the global and the local scales. This in-depth investigation of the choking phenomenon within the ejector is proposed both qualitatively and quantitatively for given reservoir conditions. The complex flow signature highlighted by means of the numerical results is then investigated and corroborated through experimental shadowgraphy. Studies combining experimental results (including visualizations) with numerical simulations are rather scarce in the open literature and to the knowledge of the authors, this study is the first one that proposes such a detailed analysis. For the present ejector geometry and operating conditions, the choking phenomenology of the secondary stream is found to closely correspond to the model of the Fabri-choking early postulated in Fabri and Siestrunck (1958).     

Transport of salts and micron-sized particles entrained from a boiling water pool

The entrainment of soluble (KI, CsI) and non-soluble (Al₂O₃) substances through droplets, which are produced by disintegrating steam bubbles at the surface of a boiling water pool, is determined in a pilot-scale facility. Integral measurements are conducted at steady-state conditions in an atmosphere of either pure steam or an air–steam mixture. The ratio of the entrained liquid mass flow and the gas mass flow through the pool, the entrainment factor, is determined for air–steam ratios between 0 and 0.47 kg/kg in the gas atmosphere and at constant total pressures between 2 and 6 bar. The influence of the vertical temperature profile in the gas atmosphere on the convective velocity field is demonstrated by phase Doppler anemometry and particle image velocimetry measurements at a location 2.1 m above the pool surface. The influences of nucleation and natural convection are demonstrated during slow de-pressurization of the facility at rates below 420 Pa/s.     

Effect of wall friction and vortex generation on the radial distribution of different phases

Arguments are presented to prove the existence of rolling vortices in single-phase and two-phase flow. In the liquid phase, they appear in a boundary layer near a wall while in the continuous vapor phase they occur near the interface with a liquid film. The intensity and size of these vortices depend on the local velocity gradients normal to the wall. The interaction between the rotational field associated with such vortices and bubbles in liquid flow or droplets in vapor flow is discussed. This interaction may be called the wall-vortex effect. It appears that several, apparently unrelated, phenomena observed in two-phase flow systems may be interpreted in terms of this mechanism. Among these are: (i) radial void peaking near the walls (ii) vapor velocities less than liquid velocity observed also in vertical upward flow (iii) reduced droplet diffusion near the liquid film and (iv) reduced vapor mixing between subchannels at low steam qualities. The cause of secondary flows in non-circular channels may also be explained in terms of rolling vortices near the walls. Finally, a comparison is made with the well known Magnus effect.     

Explosive discharge of a gas-saturated liquid from channels and tanks

A mathematical model for the discharge of a gas-saturated liquid from cylindrical channels is developed. Two limiting cases of linear and quadratic, relations between the flow friction force and the flow velocity are considered. It is established that the process of evacuation, from a semi-infinite channel consists of two stages. In the initial stage, the flow drag can be ignored, and the process of discharge is described by a Riemann wave solution. For the next stage, in which inertia is insignificant, nonlinear equations are obtained and self-similar solutions are constructed for them. The problem of flow through a slot in a tank of finite volume is solved. It is shown that the discharge proceeds either in a gas-dynamic choking regime or in a subsonic regime, depending on the conditions inside the tank and at the outlet. Examples of numerical calculations are given. Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000 Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 64–73, January–February, 1999.     

Numerical study of condensing a small concentration of vapour inside a vertical tube

The purpose of this study is to analyse the combined heat and mass transfer of liquid film condensation from a small steam–air mixtures flowing downward along a vertical tube. Both liquid and gas stream are approached by two coupled laminar boundary layer. An implicit finite difference method is employed to solve the coupled governing equations for liquid film and gas flow together with the interfacial matching conditions. The effects of a wide range of changes of three independent variables (inlet pressure, inlet Reynolds number and wall temperature) on the concentration at exit tube, local Nusselt and Sherwood numbers, film thickness, accumulated condensate rate and temperature are carefully examined. The numerical results indicate that in the case of condensing a small concentration of vapours from a mixture, the resistance to heat and mass transfer by non-condensable gas becomes very intense. The comparisons of average Nusselt number and local condensate heat transfer coefficient with the literature results are in good agreement.     

An analytical approach to estimate local liquid heights in horizontal diabatic slug flow

As the intermittent (slug) flow pattern was recently shown to be, along with the stratified flow regime, responsible for circumferential anisothermality of horizontal steam generating tubes operating at moderate steam qualities, the ability to estimate the local liquid levels in such tubes and to compare them with the position of the circumferentially maximum value of the externally applied heat loading appears to be of great practical importance for boiler designers. While the procedure of the estimation of minimum liquid heights (h_L) in horizontal stratified flows was suggested in previous papers, this study presents an analytical approach for engineering evaluations of h_L in the horizontal, diabatic slug flow pattern. It is, importantly, shown that the use of the stratified flow-based approach to evaluate h_L in slug flows results in the overestimation of actual liquid heights which may be detrimental for boiler tubes, especially under circumferentially nonuniform heat loading.     

Effects of the gas phase molecular weight and bubble size on effervescent atomization

The effervescent atomization from an industrial Coker feed nozzle is compared for two different gas densities (air and mixed gas of 81.4 vol.% helium/18.6 vol.% nitrogen) at equivalent operating temperatures. The application is to observe the similarity of lab tests using air at 20 °C to the industrial process using steam at 300-400 °C. The effects of operating conditions, such as gas to liquid mass ratio, mixing pressure and void fraction on the flow regime, bubble size, and droplet size distribution were also examined in this study. The experiments were performed using mixtures of water with air or mixed gas, which resulted in gas to liquid mass ratios ranging from 1% to 4%.Stroboscopic back scattered imagery (SBSI) indicates that the average bubble size inside the nozzle conduit is similar when air and water are used as the process fluids, when compared to the case when mixed gas and water are used as the process fluids. Under similar conditions, the Phase Doppler Particle Anemometer (PDPA) data indicate that the droplet size in the spray is similar when using either mixed gas or air as the atomization gas.Experimental results obtained by high-speed video shadowgraphy (HSVS) indicate that the flow pattern inside the nozzle feeding conduit was slug flow with a tendency to attain annular flow with increased air to liquid mass ratios. Thus, from the experimental results it is evident that the smaller molecular weight of the mixed gas versus air (8.4 versus 29) does not significantly reduce the bubble (<±10% difference) and droplet size (<±1.5% difference), indicating a weak dependence of the gas phase density on two-phase atomization. This confirms that laboratory experiments on effervescent nozzles using air have reliable similarity to systems that use high temperature steam for the gas phase.     

The flow of thin liquid films around corners

Situations arise where it is required to strip a moving liquid film from a boundary wall. The need to sample wet steam isokinetically is one such situation. Equally it is sometimes desirable for a film not to separate from a boundary wall as in, for example, liquid separators. A theoretical analysis is developed to examine the radial stress distribution within a uniformly thin liquid film flowing around a sharp bend of fixed radius. The results of the analysis are discussed in the light of experimental observations. The controlling parameters in the film flow are identified and are evaluated for a given situation.     

Hydrodynamic and Thermal Fields in a Porous Medium with Injection of Superheated Steam

The plane one-dimensional and radially symmetric problems of injection of superheated steam into a porous medium saturated with gas are considered. Self-similar solutions are constructed on the assumption that in this case four zones are formed in the porous medium, namely, a gas flow zone, superheated and wet steam zones, and a water slug zone formed due to steam condensation. On the basis of the solution obtained, both the effects of the boundary pressure, mass flow rate, and temperature of the injected superheated steam and the effect of the initial state of the porous medium on the propagation of the hydrodynamic and thermal fields in the porous medium are studied.     

Three-dimensional modelling of steam flush for DNAPL site remediation

Numerical simulation of steam flush for clean-up of non-aqueous phase liquid (NAPL) contaminated groundwater sites involves solution of the multiphase, multicomponent subsurface flow equations. This paper describes techniques for discretizing problems with horizontal wells in a three-dimensiontetrahedral mesh. The effectiveness of non-linear flux limiters for reducing numerical dispersion is discussed. Primary variable selection and thermodynamic state transition rules will also be compared. Some example results for several steam flush scenarios will be presented.     

The characteristics of gas/liquid flow in large risers at high pressures

Although most of the work reported on two-phase flows are limited to small pipe diameters, two-phase flow in large risers are increasingly being encountered in the petroleum and nuclear industries. In the present work, a wire mesh sensor was employed to obtain void fraction and bubble size distribution data and visualizations of steam/water flow in a large vertical pipe (194 mm in diameter) at 46 bar. For comparison purposes, measurements were made at similar phase velocities and physical properties to a dataset for nitrogen/naphtha flow in a similar-sized riser. There exist significant differences between both sets of data. Churn-turbulent flow is observed in the present work instead of slug flow, and this differs from the intermittent and semi-annular flow patterns reported for nitrogen/naphtha data. The mean void fraction of the nitrogen/naphtha data is higher than that of the present steam/water data due to the differences in purity in the liquid phases. Furthermore, core peak distributions are observed for the present work in contrast to the flatter profiles deduced for the nitrogen/naphtha using a power law relationship.