Phase and velocity distributions in vertically upward high-viscosity two-phase flow

The two-phase pressure drop in vertical industrial pipes is mainly determined by gravitation and acceleration of the fluid, which means that the void fraction is key an important parameter in any model to predict pressure drops. Typically, these models are applied in industry to size pumps and, e.g., emergency relief systems. There is a shortage of void fraction data in the literature for liquids with a dynamic viscosity above 1000 mPa s. Adiabatic experiments have been performed of mixtures of nitrogen and solutions of polyvinylpyrrolidone (Luviskol^®) in water with dynamic viscosities in the range 900–7000 mPa s. Inner tube diameter was 54.5 mm. Mass flux and quality were varied in a wide range: 8–3500 kg/m²/s and 0–82%, respectively. The corresponding superficial velocities were 0.005–3.4 m/s for the liquid and 0–30 m/s for the nitrogen. For comparison, reference measurements were taken of mixtures of nitrogen with water (1 mPa s). Care has been taken to measure only well-developed flows.     

Experiments on the effect of acceleration on the drag of tapwater bubbles

Three-dimensional (3D) trajectories of spherical air bubbles passing through a converging part of a rectangular channel have been measured. Bubble diameters, d _b, were less than 1 mm and the Reynolds numbers, Re _b, for stagnant tapwater and for mean liquid velocity vˉ _L=0.25 m/s were in about same range. Received: 15 January 2001 / Accepted: 12 June 2001     

A Way to Reduce Pressure Drop in Once-through Micro-Evaporators

This investigation explores the possibilities to reduce the pressure drop of a single-channel micro-evaporator. The availability of micro-technology to create three-dimensional structures at a micro-meter scale opens opportunities to better control process conditions in once-through boilers. However, process miniaturization possesses some inherent drawbacks as well. Among others, the relatively large pressure drop in a micro-system makes it rather unsuitable for low-pressure applications. Especially in phase-change processes, the pressure drop may become large due to the expansion in small-sized channels. To address this drawback, flow boiling relations for small diameter tubes are first studied. These relations show a general form of the empirical correlations. Using this formulation, reduction factors could be deduced for the momentum pressure drop and friction pressure drop in case of a conical channel. These theoretically derived reduction factors show that the total pressure drop can be reduced significantly. The momentum pressure drop completely vanishes for outflow/inlet diameter ratios of 6.3 in the case of water. The friction pressure drop is reduced by a factor of ten at an outflow/inlet diameter ratio larger than four. An experimental comparison using a five-times diameter increase shows that the estimated reduction factor approaches the theoretically derived value for higher water supplies.     

Effects of contact angle on condensate topology, drainage and efficiency of a condenser with minichannels

Epoxy coatings with good adhesion characteristics have been developed that are suitable for large-scale manufacturing and application in compact heat exchangers. Two of them, with a static contact angle for water of 105° and 79° have been tested in a finned-tube condenser comparing flat plate minichannels on the gas-side. Contrary to the expectation, the thermal efficiency of the 105° condenser is slightly less than that of the 79° one. This is due to a reduction of condensate drop size at detachment, resulting in relatively small dry paths after drainage. In the present study, geometry and coating thickness of the two coated exchangers used have not been optimized, since emphasis has been on the effect of contact angle. The finned-tube geometry is shown to be less favourable, for a condenser, than the compact cross-flow plate geometry with minichannels on both the gas- and coolant side that was tested previously.     

Temperature fields induced by direct contact condensation of steam in a cross-flow in a channel

The temperature fields in the center plane of a channel with a square cross-section have been measured. Steam injected at relatively low mass fluxes through a small hole in one of the walls of the channel condensed intermittently in a small area close to the inlet. The upstream temperature of the liquid cross-flow, T _L , the momentum ratio, J, and the Prandtl number proved to be important for the single-phase temperature field induced in the jet further away from the steam inlet. Jet centerlines of velocity and temperature are measured and positions are compared. Different locations for J < 100 and low T _L are explained from dependencies on Reynolds and Prandtl numbers. Next to the jet centerline a second high-temperature zone was found to occur, close to the wall and downstream of the steam inlet. The importance of capillary forces is investigated with the aid of 3D CFD computations.     

Experimental Determination of Lagrangian Velocity Statistics in Turbulent Pipe Flow

The calculation of Lagrangian statistics out of experimentally determined data from homogeneously seeded inhomogeneous turbulent flows is far from straightforward since statistical properties are position-dependent, necessitating local sampling. Two solutions for the preferential sampling of faster particles at a certain position in the flow are proposed. The performance of both methods was tested using DNS calculations for turbulent pipe flow. Both methods show a good performance for various statistical properties, thus providing two reliable ways to analyze experimental data from inhomogeneous turbulent flows.     

Mass flow rate measurements in gas–liquid flows by means of a venturi or orifice plate coupled to a void fraction sensor

Two-phase flow measurements were carried out using a resistive void fraction meter coupled to a venturi or orifice plate. The measurement system used to estimate the liquid and gas mass flow rates was evaluated using an air–water experimental facility. Experiments included upward vertical and horizontal flow, annular, bubbly, churn and slug patterns, void fraction ranging from 2% to 85%, water flow rate up to 4000 kg/h, air flow rate up to 50 kg/h, and quality up to almost 10%. The fractional root mean square (RMS) deviation of the two-phase mass flow rate in upward vertical flow through a venturi plate is 6.8% using the correlation of Chisholm (D. Chisholm, Pressure gradients during the flow of incompressible two-phase mixtures through pipes, venturis and orifice plates, British Chemical Engineering 12 (9) (1967) 454–457). For the orifice plate, the RMS deviation of the vertical flow is 5.5% using the correlation of Zhang et al. (H.J. Zhang, W.T. Yue, Z.Y. Huang, Investigation of oil–air two-phase mass flow rate measurement using venturi and void fraction sensor, Journal of Zhejiang University Science 6A (6) (2005) 601–606). The results show that the flow direction has no significant influence on the meters in relation to the pressure drop in the experimental operation range. Quality and slip ratio analyses were also performed. The results show a mean slip ratio lower than 1.1, when bubbly and slug flow patterns are encountered for mean void fractions lower than 70%.     

A diffuse-interface approach to two-phase isothermal flow of a Van der Waals fluid near the critical point

A novel numerical method for simulations of isothermal, compressible two-phase flows of one fluid component near the critical point is presented on the basis of a diffuse-interface model and a Van der Waals equation of state. Because of the non-convexity of the latter, the nature of the set of governing equations is mixed hyperbolic–elliptic. This prevents the application of standard numerical methods for compressible flow. Moreover, the Korteweg capillary stress tensor, characteristic for the diffuse-interface approach, introduces third-order spatial derivatives of mass density in the Navier–Stokes equation, resulting in a dispersive behavior of the solution. Our computational method relies on a transformation of the conserved variables, which controls dispersion, stabilizes the numerical simulation and enables the use of coarser grids. A one-dimensional simulation shows that this method provides better stability and accuracy than without transformation of variables. Two- and three-dimensional simulations for isothermal liquid–vapor flows, in particular the retraction of a liquid non-spherical drop in vapor and the binary droplet collision in vapor, show the applicability of the method. The surface tension calculated from the numerical results is in good agreement with its theoretical value if the computational grid is sufficiently fine.     

The mean condensate heat resistance of dropwise condensation with flowing,inert gases

The quantification of the condensate heat resistance is studied for dropwise condensation from flowing air-steam mixtures. Flows are essentially laminar and stable with gas Reynolds numbers around 900 and 2000. The condensate shaping up as hemispheres on a plastic plane wall and the presence of inert gases make it possible that thermocapillary convection occurs making the resistance less than the mean condensate thickness (ca. 0.185 mm) divided by the heat conduction coefficient. The analysis of experiments shows that the effective mean condensate resistance might indeed be less, by a factor of 0.8±0.2. The analysis takes account of the sensible heat transfer which may be as large as 35% of the total heat transfer if inlet vapor concentration,c _in, is low (ca. 0.07). A method is presented to determine the gas-condensate interface temperature,t _i , that is needed in the analysis of the heat resistance. The highest temperature differences(t _i –t _w ),t _w being the mean temperature of the condenser plate at the gas side, have been found to occur for relatively high values ofc _in (ca. 0.3).Es wird der thermische Kondensationswiderstand bei Tropfenkondensation aus einem strömenden Luft-Dampf-Gemisch untersucht. Die Strömung ist laminar und stationär mit Gas Reynolds-Zahlen zwischen 900 und 2000. In Anwesenheit von Intertgas kann thermokapillare Konvektion am halbkugelförmigen Kondensattropfen auftreten, wobei der thermische Widerstand kleiner ist, als der Quotient aus der mittleren Kondensatdicke (ca. 0,185 mm) und dem Wärmeübergangskoeffizienten. Die Analyse der Experimente zeigt, daß der effektive mittlere Kondensatwiderstand tatsächlich um einen Faktor 0,8±0,2 kleiner sein kann. Der Energieanteil infolge Kondensatunterkühlung wird berücksichtigt, er kann bis zu 35% der gesamten Wärmeübertragung ausmachen, falls die Dampfkonzentrationc _in am Eintritt klein ist (ca. 0,07). Zur Bestimmung der in die Berechnung des thermischen Widerstandes eingehende Temperatur an der Grenzfläche zwischen Gas und Kondensatt _i , wird eine spezielle Methode entwickelt. Die größte Temperaturdifferenz (t _i –t _w ) ergibt sich bei relativ hohenc _in-Werten (ca. 0,3), wobeit _w die mittlere Temperatur der Kondensatorplatte auf der Gasseite ist.     

The dynamics of a boiling bubble before and after detachment

An overview is given of prediction methods for motion and deformation of a bubble that is created by boiling at a wall, at times before and after detachment, with a focus on added mass forces in the vicinity of the wall. The possibility to apply added mass coefficients derived in potential flows also to flows with vorticity is examined. An introduction to Lagrangian methods is given. Added mass tensors are derived for deforming bubbles at and away from a plane wall. Expressions for induced hydrodynamic lift forces are given, and validation experiments are briefly discussed.

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