van der Cwm Cees Geld

Forces on bubbles growing and detaching in flow along a vertical wall

Abstract Experiments are performed on bubble detachment from an artificial cavity in a plane wall of a vertical rectangular channel. Mean upward velocity is varied. Steam bubbles are generated by local heating of the cavity, nitrogen bubbles of about the same size by injection. The experiments show a difference in take off direction between vapor and nitrogen bubbles. Steam bubbles take off into the liquid, while nitrogen bubbles more or less slide parallel to the wall. The bubble detachment radius decreases for increasing bulk liquid velocity, in a way that merely depends on the detachment radius without convection. Nitrogen bubbles, coming from a capillary with approximately the same radius are larger than water vapor bubbles. A force coefficient fit is performed on force components perpendicular to the wall. By analyzing flow- and non-flow experiments separately, some of the forces are quantified. By combining the results of nitrogen bubble and steam bubble experiments, a force due to the temperature difference at the bubble foot is studied. Such a force could explain the observed differences between steam and nitrogen bubbles. It is found that either a vorticity lift force of the type found by Auton [The dynamics of bubbles, drops and particles in motion in liquids, Ph.D. thesis, University of Cambridge (1983)] is negligible, or this temperature difference force may be important. A commonly used criterion to predict detachment radii is found not to be satisfactory.

Prediction of drop size distributions in sprays using the maximum entropy formalism : the effect of satellite formation

The droplet size distribution function for sprays is derived using the maximum entropy formalism (MEF) to link the end stage of the atomization process to an intermediate state, characterized by unstable liquid cylinders. The probability density function, PDF, for droplet diameter, δ, is mainly governed by conservation of mass and the energy equation. Many of the small droplets are supposedly created together with a much larger droplet, i.e. are supposed to be satellites. A dual PDF, f1(δ,δ∗), represents the number of satellites of diameter δ corresponding to a central or primary drop with diameter δ∗. The representation space is extended with the primary droplet diameter δ∗ and the MEF is applied to derive the function f1. The physical constraints are first related to parts of the liquid cylinders only, and some higher moments of the primary size distribution function, f0(δ∗), have to be known in order to be able to apply the MEF. Some problems inherent in the application of this formalism are examined. Without invoking fitting parameters or ad-hoc constraints the predicted PDFs are close to measured ones.

Determination of the coefficients of Langevin models for inhomogeneous turbulent flows by three-dimensional particle tracking velocimetry and direct numerical simulation

A promising and, in terms of computer power, low-cost way of describing flow properties such as turbulent diffusion is by Langevin models. The development of such models requires knowledge of Lagrangian statistics of turbulent flows. Our aim is to determine Lagrangian statistics of inhomogeneous flows, as most turbulent flows found in practical applications are inhomogeneous. The present paper describes how a Lagrangian measurement technique, three-dimensional particle tracking velocimetry, has been developed and applied to the most common example of inhomogeneous flows: turbulent pipe flow. A new direct numerical simulation (DNS) code has been developed and experimental results have been compared with results of this DNS code. The results concern Eulerian and Lagrangian velocity statistics at two Reynolds numbers. Based on these, coefficients of the Langevin model have been determined and physical consequences for Langevin modeling and turbulent dispersion have been explained.

Numerical simulation of the drying of inkjet-printed droplets

In this paper we study the behavior of an inkjet-printed droplet of a solute dissolved in a solvent on a solid horizontal surface by numerical simulation. An extended model for drying of a droplet and the final distribution of the solute on an impermeable substrate is proposed. The model extends the work by Deegan, Fischer and Kuerten by taking into account convection, diffusion and adsorption of the solute in order to describe more accurately the surface coverage on the substrate. A spherically shaped droplet is considered such that the model can be formulated as an axially symmetric problem. The droplet dynamics is driven by the combined action of surface tension and evaporation. The fluid flow in the droplet is modeled by the Navier-Stokes equation and the continuity equation, where the lubrication approximation is applied. The rate of evaporation is determined by the distribution of vapor pressure in the air surrounding the droplet. Numerical results are compared with experimental results for droplets of various sizes.

Marangoni convection in binary drops in air cooled from below

Marangoni convection in binary drops resting on a plate in quiescent air is studied. Water is used with low molar fractions of 2-butanol or ethanol. The droplets are homogeneously cooled from below with an initial temperature difference of 3.5 K. In the presence of air, the thermocapillary and concentration-gradients induced motions are mutually reinforcing. The latter motions last much longer than the time it takes for interfacial temperature gradients to become negligible. The Marangoni convection time increases with increasing concentration of alcohol if the volume concentration is less than 10 vol.%, levels off at higher concentrations and is higher for 2-butanol than for ethanol. The consequences for dropwise condensation in practical compact heat exchangers are investigated by measuring differences in temperature gradient histories during actual condensation processes.

Axisymmetric dynamics of a bubble near a plane wall

Explicit expressions for the added mass tensor of a bubble in strongly nonlinear deformation and motion near a plane wall are presented. Time evolutions and interconnections of added mass components are derived analytically and analysed. Interface dynamics have been predicted with two methods, assuming that the flow is irrotational, that the fluid is perfect and with the neglect of gravity. The assumptions that gravity and viscosity are negligible are verified by investigating their effects and by quantifying their impact in some cases of strong deformation, and criteria are presented to specify the conditions of their validity. The two methods are an analytical one and the boundary element method, and good agreement is found. It is explained why a strongly deforming bubble is decelerated. The classical Rayleigh– Plesset equation is extended with terms to account for arbitrary, axisymmetric deformation and to account for the proximity of a wall. An expression for the corresponding cycle frequency that is valid in the vicinity of the wall is derived. An equation similar to the Rayleigh–Plesset equation is presented for the most important anisotropic deformation mode. Well-known expressions for the angular frequencies of some periodic solutions without a wall follow easily from the equations presented. A periodically deforming bubble without initial velocity of the centroid and without a dominating isotropic deformation component is eventually always driven towards the wall. A simplified equation of motion of the centre of a deforming bubble is presented. If desired, full deformation computations can be speeded up by selecting an artificially low value of the polytropic constant Cp/Cv.

Temperatures and the condensate heat resistance in dropwise condensation of multicomponent mixtures with inert gases

The temperature variations occurring in dropwise condensation at condenser plates of a compact, polymer heat exchanger are studied using instantaneous infrared temperature field recordings. An averaging procedure in time and an assessment of extreme values is proposed and carried out. With the results, the heat resistance of the condensate is quantified. It is found that mixing and convection in the condensate, caused by coalescence and drainage of drops, reduces the condensate heat resistance by a factor 4 as compared with purely conductive heat transfer. This reduction is comparable, both in nature and in magnitude, to the effect of enhanced mixing due to turbulence in the liquid film of filmwise condensation. A second condensable species has been added to the gas mixture in order to study the contribution of Marangoni convection due to concentration gradients to the condensate heat transfer resistance. No contribution is found.

The shape factor of conduction in a multiple channel slab and the effect of non-uniform temperatures

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Forces on a boiling bubble in a developing boundary layer, in microgravity with g-jitter and in terrestrial conditions

Terrestrial and microgravity flow boiling experiments were carried out with the same test rig, comprising a locally heated artificial cavity in the center of a channel near the frontal edge of an intrusive glass bubble generator. Bubble shapes were in microgravity generally not far from those of truncated spheres, which permitted the computation of inertial lift and drag from potential flow theory for truncated spheres approximating the actual shape. For these bubbles, inertial lift is counteracted by drag and both forces are of the same order of magnitude as g-jitter. A generalization of the Laplace equation is found which applies to a deforming bubble attached to a plane wall and yields the pressure difference between the hydrostatic pressures in the bubble and at the wall, Δp. A fully independent way to determine the overpressure Δp is given by a second Euler-Lagrange equation. Relative differences have been found to be about 5% for both terrestrial and microgravity bubbles. A way is found to determine...

Geometry adaptations to improve the performance of compact, polymer condensers

Practical, relatively simple methods are presented to enhance heat transfer with condensation in a compact, polymer plate heat exchanger. Tilting the exchanger, while adapting the spacers, increases the condensate and heat fluxes by 6–8%, as a function of the inlet mass fraction of the moist air at ambient conditions. Polymer inserts increase convective heat transfer and yield a total heat flux improvement of 20%, at the cost of increased pressure drop.