Dynamic fluid flow behaviour of a tank draining through a vertical tube

This paper describes the unsteady draining of a sealed tank partially filled with water. The water discharges via a vertical tube into an open tank at atmospheric conditions. The air inflow, compensating for the volume of the discharged liquid, enters the system in an oscillatory manner, much like the “gulping” seen in an upended beer bottle. A mathematical model, based closly on that derived by Dougall & Kathiresan [Chem. Engng Commun. 8, 289–304 (1981)], has been applied to predict the pressure fluctuations in the closed tank. The rate of water discharge from the tank has been predicted and gives a much closer agreement with experimental results than a prediction based on a steady counter-current flooding limitation approach. A drift flux model has been used to describe the two-phase flow effect in the tube and the Wallis flooding criterion has been modified for use in the slug flow regime to describe the boundary conditions at the bottom of the tube. The pressure fluctuations in the sealed tank have been measured and compared with results obtained from the mathematical prediction for a variety of tube diameters.     

Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup

Experimental data and correlations available in the literature for the liquid holdup ε_L and the pressure gradient ΔP_TP/L for gas-liquid pipe flow, generally, do not cover the domain 0 < ε_L < 0.06. Reliable pressure-drop correlations for this holdup range are important for calculating flow rates of natural gas, containing traces of condensate. In the present paper attention is focused on reliable measurements of ε_L and ΔP_TPIL values and on the development of a phenomenological model for the liquid-holdup range 0 < ε_L < 0.06. This model is called the “apparent rough surface” model and is referred to as the ARS model. The experimental results presented in this paper refer to air-water and air-water + ethyleneglycol systems with varying transport properties in horizontal straight smooth glass tubes under steady-state conditions. The holdup and pressure gradient values predicted with the ARS model agree satisfactorily with both our experimental results and data obtained from the literature referring to small liquid-holdup values 0 < ε_L < 0.06. Further, it has been shown that in the domain 38 < < 72 mPa m the interfacial tension of the gas-liquid system has no significant effect on the liquid holdup. The pressure gradient, however, increases slightly with decreasing surface tension values.     

Gas-particle two-phase turbulent flow in a vertical duct

Two-phase gas-phase turbulent flows at various loadings between the two vertical parallel plates are analyzed. A thermodynamically consistent turbulent two-phase flow model that accounts for the phase fluctuation energy transport and interaction is used. The governing equation of the gas-phase is upgraded to a two-equation low Reynolds number turbulence closure model that can be integrated directly to the wall. A no-slip boundary condition for the gas-phase and slip-boundary condition for the particulate phase are used. The computational model is first applied to dilute gas-particle turbulent flow between two parallel vertical walls. The predicted mean velocity and turbulence intensity profiles are compared with the experimental data of Tsuji et al. (1984) for vertical pipe flows, and good agreement is observed. Examples of additional flow properties such as the phasic fluctuation energy, phasic fluctuation energy production and dissipation, as well as interaction momentum and energy supply terms are also presented and discussed.

Applications to the relatively dense gas-particle turbulent flows in a vertical channel are also studied. The model predictions are compared with the experimental data of Miller & Gidaspow and reasonable agreement is observed. It is shown that flow behavior is strongly affected by the phasic fluctuation energy, and the momentum and energy transfer between the particulate and the fluid constituents.     

On the numerical study of bubbly flow created by ventilated cavity in vertical pipe

The dispersion of bubbles into a down-liquid flow in a vertical pipe is investigated. At low flow rates, the intended design of a swarm of discrete bubbles is achieved. At high flow rates, a ventilated cavity is nonetheless formed, which is attached close to the gas sparger. Behind this ventilated cavity, three different flow regimes characterize the complex bubbly flow field downstream of the down-liquid flow: vortex region with high void fraction, transitional region and pipe flow region. In this study, a numerical model that solved the entire development of the gas–liquid flow including the extended single-phase liquid region upstream to the wall-jet and recirculating-vortex zones in order to allow a more realistic determination of the boundary conditions of the down-liquid flow was adopted. Coupling with the Eulerian–Eulerian two-fluid model to solve the respective gas and liquid phases, a population balance model was also applied to predict the bubble size distribution in the wake right below the cavity base as well as further downstream in the transitional and fully-developed pipe flow regions. The numerical model was evaluated by comparing the numerical results against the data derived from theoretical, numerical and experimental approaches. Prediction of the Sauter mean bubble diameter distributions by the population balance approach at different axial locations confirmed the dominance of breakage due to the high turbulent intensity below the ventilated cavity which led to the generation of small gas bubbles at high void fraction. Further downstream, the coalescence effect dominated leading to merging of the small bubbles to form bigger bubbles.     

Transient gas liquid flow in hilly terrain pipelines

Two phase flow in a hilly terrain pipeline, composed of uphill and downhill sections, exhibits a complex transient behavior at low flow rates owing to the accumulation of liquid in the low elbows and gas in the top elbows. At low flow rates gravity has a dominant effect, while frictional losses can be neglected.In this work a simplified modeling approach is proposed that is able to predict the transient behavior of gas and liquid flowing in a complex terrain pipeline with multiple valleys. The condition that marks the boundary between severe slugging cyclic behavior and steady state flow is included.An experimental system which consists of three hilly sections was constructed. The experimental data were compared to the predicted results, yielding reasonable agreement in spite of the simplifying model assumptions.     

Counter-current gas–liquid flow in a vertical narrow channel—Liquid film characteristics and flooding phenomena

Results are reported of an experimental investigation of gas–liquid counter-current flow in a vertical rectangular channel with 10 mm gap, at rather short distances from liquid entry. Flooding experiments are carried out using air and various liquids (i.e., water, 1.5% and 2.5% aqueous butanol solutions) at liquid Reynolds numbers Re_L < 350. Visual observations and fast recordings suggest that the onset of flooding at low Re_L (<250) is associated with liquid entrainment from isolated waves, whereas “local bridging” is dominant at the higher Re_L examined in this study. Significant reduction of flooding velocities is observed with decreasing interfacial tension, as expected. Instantaneous film thickness measurements show that under conditions approaching flooding, a sharp increase of the mean film thickness, of mean wave amplitude and of the corresponding RMS values takes place. Film thickness power spectra provide evidence that by increasing gas flow the wave structure is significantly affected; e.g., the dominant wave frequency is drastically reduced. These data are complemented by similar statistical information from instantaneous wall shear stress measurements made with an electrochemical technique. Power spectra of film thickness and of shear stress display similarities indicative of the strong effect of waves on wall stress; additional evidence of the drastic changes in the liquid flow field near the wall due to the imposed gas flow, even at conditions below flooding, is provided by the RMS values of the wall stress. A simple model is presented for predicting the mean film thickness and mean wall shear stress under counter-current gas–liquid flow, below critical flooding velocities.     

A film model for the prediction of flooding and flow reversal for gas-liquid flow in vertical tubes

A model is presented which demonstrates that the process of flooding and flow reversal can be explained on the basis of a film mechanism. The model predicts well the gas flow rate at which flooding and flow reversal begins and ends for a given liquid flow rate and the presence of a hysteresis loop between flooding and flow reversal. The predictions of the theory are in satisfactory agreement with experimental flooding data.     

Flow regime transition criteria for two-phase flow at reduced gravity conditions

Flow regime transition criteria are of practical importance for two-phase flow analyses at reduced gravity conditions. Here, flow regime transition criteria which take the frictional pressure loss effect into account were studied in detail. Criteria at reduced gravity conditions were developed by extending an existing model from normal gravity to reduced gravity conditions. A comparison of the newly developed flow regime transition criteria model with various experimental datasets taken at microgravity conditions showed satisfactory agreement. Sample computations of the model were performed at various gravity conditions, such as 0.196, 1.62, 3.71 and 9.81 m/s² corresponding to micro-gravity and lunar, Martian and Earth surface gravity, respectively. It was found that the effect of gravity on bubbly–slug and slug–annular (churn) transitions in a two-phase flow system was more pronounced at low liquid flow conditions, whereas the gravity effect could be ignored at high mixture volumetric flux conditions. While for the annular flow transitions due to flow reversal and onset of droplet entrainment, higher superficial gas velocity was obtained at higher gravity level.     

Low and high head flooding for countercurrent flow in short horizontal tubes

Experiments have been carried out discharging water along a horizontal 50 mm bore tube against a countercurrent flow of air. With the water flowrate constant, the air flowrate was slowly increased until waves appeared, restricting the outflow of water. This defined the low head flooding condition which was found to be in good agreement with previous theory for low water discharge rates. A new treatment gives good agreement over the whole experimental range. Once the low head flooding set in, the water head built up up in the water supply tank connected to the horizontal tube and the air flowrate had to be reduced substantially below that required for the initiation of flooding before the water discharge rate was fully reinstated. This is the high head flooding condition and experimental results are in substantial agreement with those of others. Previous theory for high head flooding is derived in a simpler fashion and related to the Kelvin—Helmholtz instability criterion. The theory is shown to be a generalization of the criterion.     

Effect of liquid viscosity on the stratified-slug transition in horizontal pipe flow

The effect of liquid viscosity on the initiation of slug flow was studied in horizontal 2.52 and 9.53 cm pipelines. The results show the stabilizing effect of viscosity predicted by Lin & Hanratty, and are at variance with analyses which use a long-wavelength inviscid approximation. For very viscous liquids a stability analysis which recognizes that slugs originate from a train of small-wavelength sinusoidal waves seems consistent with the measurements.     

Experimental study on a two-phase critical flow with a non-condensable gas at high pressure conditions

An experimental study was performed on a two-phase critical flow with a non-condensable gas at high pressure conditions. Experimental data for the critical flow rates were generated by using sharp-edged stainless steel pipes with an inner diameter of 10.9 mm, a thickness of 3.2 mm, and a length of 1000 mm. The test conditions were varied by using the stagnation pressures of 4.0, 7.0, and 10.0 MPa, water subcoolings of 0.0, 20.0, and 50.0 °C, and nitrogen gas flow rates of 0.0–0.22 kg/s. The experimental results show that the critical mass flux decreases rapidly with an increase of the volumetric non-condensable gas fraction. Also the critical mass flux increases with an increase of the stagnation pressure and a decrease of the stagnation temperature. An empirical correlation of the non-dimensional critical mass flux, which is expressed as an exponential function of the non-condensable gas fraction of the volumetric flow, is obtained from the experimental data.     

Two-phase flow instabilities in a horizontal single boiling channel

A study of the stability of an electrically heated single channel, forced convection horizontal system was conducted by using Freon-11 as the test fluid. Two major modes of oscillations, namely, density-wave type (high frequency) and pressure-drop type (low frequency) oscillations have been observed. The steady-state operating characteristics and stable and unstable regions are determined as a function of heat flux, exit orifice diameter and mass flow rate. Different modes of oscillations and their characteristics have been investigated. The effect of the exit restriction on the system stability has also been studied.A mathematical model has been developed to predict the transient behavior of boiling two-phase systems. The model is based on homogenous flow assumption and thermodynamic equilibrium between the liquid and vapor phases. The transient characteristics of boiling two-phase flow horizontal system are obtained for various heat inputs, flow rates and exit orifice diameters by perturbing the governing equations around a steady state. Theoretical and experimental results have been compared.     

Experiments on the hydrodynamics of air-water countercurrent flow through vertical short multitube geometries

A series of experiments were performed to improve understanding of the hydrodynamic mechanisms relevant to the flooding phenomenon in gas-liquid countercurrent flow through vertical short multitube geometries. In addition to the conventional measurements of global hydrodynamic parameters such as phasic flow rates and two-phase pressure drops, the local time-varying thicknesses of the liquid films trickling down the individual tubes were measured by means of conductance probes mounted flush at different locations of the inner wall surfaces. A PC-based data acquisition and analysis system was developed to collect these highly fluctuating data and to make detailed statistical analyses. The experimental results and visual observations revealed two dominant hydrodynamic instability mechanisms that have not been well taken into account by the existing semiempirical models.     

Two-dimensional planar flow of a viscoelastic plastic medium

The present study is concerned with finite element simulation of the planar entry flow of a viscoelastic plastic medium exhibiting yield stress. The numerical scheme is based on the Galerkin formulation. Flow experiments are carried out on a carbon black filled rubber compound. Steady-state pressure drops are measured on two sets of contraction or expansion dies having different lengths and a constant contraction or expansion ratio of 4:1 with entrance angles of 90, 45 and 15 degrees. The predicted and measured pressure drops are compared. The predicted results indicate that expansion flow has always a higher pressure drop than contraction flow. This prediction is in agreement with experimental data only at low flow rates, but not at high flow rates. The latter disagreement is possibly an indication that the assumption of fully-developed flow in the upstream and downstream regions is not realistic at high flow rates, even for the large length-to-thickness ratio channels employed. The evolution of the velocity, shear stress, and normal stress fields in the contraction or expansion flow and the location of pseudo-yield surfaces are also calculated.     

Three-phase upward flow in a vertical pipe

In this paper we develop an approach to design a three-phase, gas–solid–liquid flow system that transports pneumatically scarified solid particles, including sticky ones, through a vertical pipe. The proposed system permits the introduction and maintenance of a liquid film that coats the pipe’s inner wall and acts as a lubricant that ensures sticky particles continue to move upward without permanently adhering to the pipe wall. The system’s operating conditions fall within the boundaries of the annular dispersed region on a typical flow pattern map of vertical flow of a gas–liquid mixture. High gas superficial velocities combined with low liquid superficial velocities characterize such a region. A combination of a modified one-dimensional, two-fluid annular dispersed flow model and a one-dimensional pneumatic conveying model is shown to describe this transport process satisfactorily. Solution of the combined models produces all the necessary design parameters including power requirements and superficial velocities of the two-fluid media needed to transport a given amount of solid particles. Results of model calculations are compared with rare three-phase flow data obtained prior to the development of the present model, by an independent experimental team that used the physical conditions of the present approach. Reasonable agreement justifies the use of the combined model for engineering design purposes.     

Superposed flow between two discs contrarotating at differential speeds

This paper describes a combined computational and experimental study of the flow between two contrarotating discs for −1 ≤ Γ ≤ 0 (where Γ is the ratio of the speed of the slower disc to that of the faster one) for the case where there is a superposed radial outflow of air. The computations were conducted using an elliptic solver and a low-Reynolds-number k-ε turbulence model, and velocity measurements were made using a laser-Doppler anenometry system. Two basic flow structures can occur: Batchelor-type flow, where there are separate boundary layers on each disc with a rotating core of fluid between, and Stewartson-type flow, where there is virtually no core rotation. The main effect of a superposed flow is to reduce the core rotation and to promote the transition from Batchelor-type flow to Stewartson-type flow. For most of the results, there is good agreement between the computed and measured velocities. Computed moment coefficients show that, for Γ = −1, superposed flow has little effect on C_m: an accepted correlation of C_m for a free disc should provide a useful estimate for design purposes.     

Transitions in Poiseuille flow of nematic liquid crystal

Recent experiments by Sengupta et al. (Phys. Rev. Lett. 2013) [9] revealed interesting transitions that can occur in flow of nematic liquid crystal under carefully controlled conditions within a long microfluidic channel of width much larger than height, and homeotropic anchoring at the walls. At low flow rates the director field of the nematic adopts a configuration that is dominated by the surface anchoring, being nearly parallel to the channel height direction over most of the cross-section; but at high flow rates there is a transition to a flow-dominated state, where the director configuration at the channel centerline is aligned with the flow (perpendicular to the channel height direction). We analyze simple channel-flow solutions to the Leslie–Ericksen model for nematics. We demonstrate that two solutions exist, at all flow rates, but that there is a transition between the elastic free energies of these solutions: the anchoring-dominated solution has the lowest energy at low flow rates, and the flow-dominated solution has lowest energy at high flow rates.     

Two-phase flow instabilities in a silicon microchannels heat sink

Two-phase flow instabilities are highly undesirable in microchannels-based heat sinks as they can lead to temperature oscillations with high amplitudes, premature critical heat flux and mechanical vibrations. This work is an experimental study of boiling instabilities in a microchannel silicon heat sink with 40 parallel rectangular microchannels, having a length of 15 mm and a hydraulic diameter of 194 μm. A series of experiments have been carried out to investigate pressure and temperature oscillations during the flow boiling instabilities under uniform heating, using water as a cooling liquid. Thin nickel film thermometers, integrated on the back side of a heat sink with microchannels, were used in order to obtain a better insight related to temperature fluctuations caused by two-phase flow instabilities. Flow regime maps are presented for two inlet water temperatures, showing stable and unstable flow regimes. It was observed that boiling leads to asymmetrical flow distribution within microchannels that result in high temperature non-uniformity and the simultaneously existence of different flow regimes along the transverse direction. Two types of two-phase flow instabilities with appreciable pressure and temperature fluctuations were observed, that depended on the heat to mass flux ratio and inlet water temperature. These were high amplitude/low frequency and low amplitude/high frequency instabilities. High speed camera imaging, performed simultaneously with pressure and temperature measurements, showed that inlet/outlet pressure and the temperature fluctuations existed due to alternation between liquid/two-phase/vapour flows. It was also determined that the inlet water subcooling condition affects the magnitudes of the temperature oscillations in two-phase flow instabilities and flow distribution within the microchannels.     

Gas—liquid annular flow under microgravity conditions: a temporal linear stability study

A temporal linear stability study was performed for a gas—liquid annular flow configuration under microgravity conditions. Data used to validate the modeling includes that generated by Texas A&M as well as all the other known data in two-phase flow under reduced gravity conditions. Following a discussion of theoretical considerations on the growth rates of different instabilities, it is shown that given the fluid properties, pipe diameter and phasic flow rates, one can predict with a high level of confidence the flow regime in the pipe. Acceptable confidence levels (80%) are achieved when one differentiates between slug, slug—annular, and annular flow. Higher confidence levels (90%) are found when one differentiates between slug and annular flow by merging the annular and slug—annular categories.