Jean-Marc Delhaye

A slugh-churn flow model for small-diameter airlift pumps

Abstract In an airlift pumping process, air is injected into the pipe containing the fluid to be transferred. Small-diameter airlift pumps are in particular used for corrosive or radioactive liquids. Detailed experiments including differential pressure and void fraction measurements, are carried out on a 10 mm-diameter setup. Based on the results obtained, it is shown that existing models are not appropriate for small diameter airlifts, particularly because they overpredict the frictional pressure drop in slug flow. A new steady state airlift model is proposed. The pressure gradient in the riser is predicted by a combination of specific models describing slug and churn flow. These models are based on the available literature on two-phase flow. The particular structure of slug flow is accounted for by a cellular model. The model proposed represents an accurate analysis tool for the design of small diameter (up to 40 mm), tall (length-to-diameter ratio greater than 250) airlifts.

The local volumetric interfacial area transport equation: derivation and physical significance

Abstract In the two-fluid model, the closure relations for the mass, momentum and energy interfacial transfer terms involve the contact area between the phases per unit volume, namely the volumetric interfacial area. Ishii suggested that the local volumetric interfacial area should obey a transport equation. The main purpose of this paper is to derive this transport equation from geometrical considerations. No assumption on the interface configuration is needed so that the mathematical expression obtained for the transport velocity is valid for any two-phase flow regime. The physical significance of the transport velocity will be illustrated on some artificially generated bubbly flows with spherical bubbles. The link between the variables entering the transport equation and experimentally measurable quantities will be exemplified. The measurement of the local volumetric interfacial area and its transport velocity can be achieved by using four-sensor probes. As a preliminary study of real measurements, we have assessed the performance of some existing signal processing methods proposed for four-sensor probes on some artificially generated flows.

Interfacial area in bubbly flow: experimental data and correlations

Abstract Experimental data on volumetric interfacial area in air-water bubbly flow obtained by ultrasonic attenuation are presented and compared with existing correlations. In view of several shortcomings of these existing correlations, a new correlation is proposed that applies to upward bubbly flow in a vertical pipe with natural or forced circulation.

The second gradient theory: a tool for the direct numerical simulation of liquid–vapor flows with phase-change

Abstract In several numerical methods dedicated to the direct numerical simulation of two-phase flows, the concept of a continuous enlarged interfacial zone is used. In this communication, it is shown that for liquid–vapor systems, it is possible to use this concept in a thermodynamic coherent way. Indeed, if it is considered that the energy of the system depends on the density gradient, this theory being called the Van der Waals or Cahn–Hilliard or more generally the second gradient theory, then it is possible to derive the equations that characterize the fluid motion within a 3-D liquid–vapor interfacial zone. Modifying the thermodynamic behavior of the fluid, it is shown that it is possible to increase the thickness of an interface, so that it can be captured by a ‘standard’ mesh without changing the surface tension nor loosing the thermodynamic coherence of the model. Several examples of application show that this method can be applied to study various physical problems, including contact line phenomena.

Some issues related to the modeling of interfacial areas in gas–liquid flows I. The conceptual issues

Abstract Two-phase flow modeling has been under constant development for the past forty years. Actually there exists a hierarchy of models which extends from the homogeneous model valid for two-phase flows where the phases are strongly coupled to the two-fluid model valid for two-phase flows where the phases are a priori weakly coupled. However the latter model has been used extensively in computer codes because of its potential in handling many different physical situations. The two-fluid model is based on the balance equations for mass, momentum and energy, averaged in a certain sense and expressed for each phase and for the interface between the phases. The difficulty in using the two-fluid model stems from the closure relations needed to arrive at a complete set of partial differential equations describing the flow. These closure relations should supply the information lost during the averaging of the balance equations and should specify in particular the interactions of mass, momentum and energy between the phases. Another requirement for the interaction terms is that they should satisfy the interfacial balance equations. Some of these terms such as the added mass term or the lift force term do not depend on the interfacial area but some others do, such as the mass transfer term, the drag term or the heat flux term. It is then necessary to model the interfacial area in order to evaluate the corresponding fluxes. Another benefit resulting from the modeling of the interfacial area would be to replace the usual static flow pattern maps which specify the flow configuration by a dynamic follow-up of the flow pattern. All these reasons explain why so much effort has been put during the past twenty years on the modeling and measurement of the interfacial area in two-phase flows. This article contains two parts. The first one deals with the conceptual issues and has the following objectives: 1. to give precise definitions of the interfacial area concentrations; 2. to explain the origin of the interfacial area concentration transport equation suggested by M. Ishii in 1975; 3. to explain some paradoxical behaviors encountered when calculating the interfacial area concentration transport velocity.

Appendix 4: Report of study group on microphysics☆

Abstract This Report outlines scientific issues that involve microscopic phenomena in multiphase flows. A common theme is the need to understand the coupling between molecular scale phenomena and macroscopic phenomena. Phenomena to be discussed include boiling nucleation, contact line motion, flow regimes in microchannels, breakup and coalescence of fluid particles and jets, atomization and sprays, and the effects of surface-active molecules and drag-reducing polymers.

Some issues related to the modeling of interfacial areas in gas–liquid flows, II. Modeling the source terms for dispersed flows

Abstract The first part of this paper dealt with the conceptual issues encountered in the definition of the interfacial area and in the derivation of a transport equation. The second part has the following objectives: 1. to address the closure issues for the source terms appearing in the transport equation when dealing with a bubbly flow in a vertical pipe; 2. to provide a list of open questions to be answered before introducing a transport equation for the interfacial area concentration in a thermal–hydraulic computer code.

Two-phase flow modelling: the closure issue for a two-layer flow

Abstract The fully-developed, laminar flow of two fluid layers in a horizontal channel is studied by means of the height-averaged balance equations. The closure issue is addressed and the closure relations for the wall and interfacial shear stresses are given for some particular cases.

Stability of small diameter airlift pumps

Abstract In an airlift pumping process, air is injected into the pipe containing the fluid to be transferred. Small diameter airlift pumps are, in particular, used for corrosive or radioactive liquids. However, for certain combinations of the geometrical parameters and air flow rate, they may become unstable. In this case, the flow at the riser outlet pulsates strongly, which cannot be accepted for many applications. An airlift pump involves three different regions, e.g. a single phase liquid flow and a separate single phase gas flow upstream of the air injection device and a two-phase flow downstream. The instabilities are due to density wave oscillations in the two-phase flow. Depending on the liquid flow inertia, friction effects and gas flow compressibility, the density waves are sustained or not. The present study is based upon a detailed description of the steady state flow in a small diameter airlift pump. A linear stability analysis is performed and assessed against an extensive set of experimental data. Both the experimental and analytical results show that the influencing parameters have complex effects and strongly interact: the same variation of a parameter may have opposite effects, i.e. stabilizing or destabilizing, depending on the values of the other parameters. The effect of the compressibility of the gas flow between the regulating valve and the air-injection device is shown to be very important. The analysis presented leads to a numerical model that can be considered as a practical tool for airlift performance and stability analysis.

Drop-on-Demand: A Scale Analysis

An increasing number of applications deal with dispensing of micro-droplets. For several years the fluids used were mostly Newtonian with low viscosity but there is nowadays a tendency to use more complex fluids. Some recent applications are encountered in the pharmaceutical industry where there is a need of producing on-demand identical droplets of a given size that can be used for drug delivery and in bioengineering where droplets have to contain cells used for tissue manufacturing or organ printing. The objective of the paper is to show that scale analysis is an efficient tool to classify the physical phenomena contributing to the breakup of a jet or of a liquid filament of a complex fluid and to provide guidelines for controlling the droplet formation process.Copyright