116 research outputs found
General solution of drop evaporation modelling in non-viscous steady-state gaseous environment
No full textThe problem of steady-state mass transport from a spherical mono-component droplet immersed in gaseous environment is addressed to find a solution for the expected vaporisation rate under general ambient conditions. The continuity, momentum and energy equations are written on a radial coordinate system. The effect of thermal gradient in the vapour phase is taken into account, while the viscous and dissipation terms in the momentum and energy equations are neglected. The model yields a non-linear second order ODE that is numerically and analytically solved to calculate the steady-state vaporisation rate. The description in terms of non-dimensional variables introduces some new parameters that are expected to influence the vaporisation rate. The model is then compared to the existing simplified Maxwell equation and the well-known Stefan-Fuchs model. Quantitative comparisons are presented and discussed and an application to water droplets floating in hot gas environment, under the operating conditions typical of fire protection spray scenarios, is presented.</jats:p
The Influence of Curvature on the Modelling of Droplet Evaporation at Different Scales
No full textThe evaporation of liquid drops in stagnant gaseous environment is modelled, accounting for the effect of drop curvature and size at the macro- and microscopic scales. At the macro-scale level, the validity of the conjectured dependence of the local fluxes on the drop surface curvature is analysed. Analytical solutions to the gas-phase conservation equations for five drop shapes (sphere, oblate and prolate spheroids and inverse oblate and prolate spheroids), under uniform Dirichlet boundary conditions, are used to calculate the local vapour and heat fluxes. The analysis shows that in general non-dimensional fluxes do not solely depend on local curvature, but possibly the effect of the whole drop shape must be taken into account. At the micro-scale level, the equilibrium vapour pressure at a convex curved surface is higher than that at a flat surface, thus leading to a considerable enhancement of the evaporation rate for nanometre sized droplets. To model the increase in equilibrium vapour pressure, we consider the Kelvin correction. Our analysis shows that the Kelvin correction is strictly required for droplet radii below 20 Å, as typically encountered for modelling the growth of critical clusters in phase transition processes initiated by homogeneous nucleation. At these conditions, it is mandatory to consider also the repartition of molecules in the different phases, in order to prevent a significant overestimation of the equilibrium vapour pressure
On the Measurement of Velocity Field Within Wall-Film During Droplet Impact on It Using High-Speed Micro-PIV
No full textThe relationship between ‘microscopic’ velocity field and ‘macroscopic’ outcomes of liquid droplet impact on wall-films is not yet fully understood. This article reports a preliminary experimental investigation to measure the velocity field within wall-film when a droplet impacts on it, using micro-Particle Image Velocimetry (μ-PIV). The challenges associated with measuring the velocity field within the wall-film are outlined. In this context, the limitations of the traditional μ-PIV technique are discussed, leading to the adoption of high-speed μ-PIV as the suitable technique for measuring the spatio-temporal evolution of velocity within wall-film. The salient features of the high-speed μ-PIV set-up are discussed. Further, results from preliminary experimental investigations on water droplet impacting on water wall-film at moderate impact velocities are presented. It is seen that the current high-speed μ-PIV set-up can be used to obtain reliable measurements of in-plane radial velocity, V, at ‘intermediate’ values of radial, r, and temporal, t, coordinates. Within the measurement range of the current set-up, it is observed that V scales with r and t as V ∝ r/t, which is similar to that reported in literature based on analytical considerations. The limitations of the current set-up, and the requirements for further experiments and validation are highlighted
Heat and mass transfer modelling of water droplets in non-viscous steady-state gaseous environment
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"Sono è vero, tolerati ... gli Ottolini et i Cossali". Affermazione economica e accettazione sociale dei Cossali a Verona
No full textIl contributo si sofferma sull'affermazione economica e sociale della famiglia Cossali di Verona nel corso del XVI e del XVII secolo. Di essa sono analizzati l'insediamento in riva all'Adige e gli acquisti agrari; l'attività mercantile; le residenze di città e di campagna; la nobilitazione
Orthogonal Curvilinear Coordinate Systems
No full textOrthogonal curvilinear coordinates occupy a special place among general coordinate systems, due to their special properties. There exists a number of such coordinate systems where the Laplace or Helmholtz equations may be separable, thus yielding a powerful tool to solve them. Operations like gradients, divergence, Laplacian take on much simpler forms in orthogonal coordinates. In this chapter the summation convention will not be used
Introduction to Constitutive Equations
No full textWhen the conservation equations for mass, chemical species, momentum and energy were derived in the previous chapter, it became soon evident that the number of unknown functions was far larger than that of the equations. To allow the closure of the problem some quantities need to be related to others and to the properties of matter, and these are the diffusive mass fluxes, j(p), the deviatoric stress tensor, τjk, the internal energy per unity of mass, u^ (or the specific enthalpy, h^ ) and the heat flux, q. The laws that describe these quantities are known as constitutive equations, and in thermo-fluids they are inherently empirical, although they must satisfy some requirement based upon first principles, like the condition of material objectivity (material properties must be independent of observer), the symmetry properties of a material body and the law of thermodynamics (particularly, the entropy inequality)
Introduction to Tensor Analysis
No full textTensor theory provides a remarkably concise mathematical framework for the formalisation of problems in many branches of physics and engineering
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