J.L. Castillo

Bénard–Marangoni convection with a deformable interface and poorly conducting boundaries

Dispersion relations and threshold values for the onset of buoyancy–thermocapillary instability are given for the case of prescribed heat flux on the boundaries of a liquid layer heated from below when the upper boundary is a deformable surface open to the ambient air. The nonlinear evolution equations of this free surface under various circumstances are also provided (without and with buoyancy, for microgravity or standard ground conditions).

Thermal diffusion and the Marangoni-Benard instability of a two-component fluid layer heated from below

Abstract Predictions are given on stability conditions for experiments in standard and reduced-gravity conditions when the Soret effect is operating in a horizontal binary liquid layer heated from below and open to the ambient air.

A nonequilibrium theory of surface deposition from particle-laden, dilute condensible vapor-containing laminar boundary layers

Abstract The deposition rate of a condensible substance from, say, flowing combustion products to “cold” solid surfaces can be strongly influenced by the simultaneous presence of a particulate aerosol since the particles can: (a) “scavenge” vapor, thereby influencing the vapor deposition rate; and (b) thermophoretically drift to the cold surface, carrying their inventory of scavenged condensate. A rational, yet quite tractable thermophysical model of these nonequilibrium processes is developed here for high Reynolds number laminar stagnation region boundary layer flow, and implemented to the point of calculating and displaying the effects of mainstream particle loading, vapor loading and particle size on the deposition rate of condensible material at surface temperatures well below the vapor dew point. Despite the complexity of this multiphase flow situation, our theoretical model is quite general and is cast in terms of dimensionless parameters which dictate the importance of vapor-phase scavenging and particle thermophoresis, as well as the Kelvin (surface tension) effect in modifying the submicron particle (free-molecule) growth law. Illustrative numerical results are displayed for the deposition of alkali sulfate-like vapor from the combustion products of hydrocarbon fuel (or coal) with air, including the interesting “structurerd of such nonequilibrium multiphase boundary layers. As a useful by-product, our results reveal which combinations of particle-phase parameters cause (a) previous “uncoupled” vapor/particle deposition rates to be approximately valid as well as (b) recent local vapor/condensate equilibrium limit results to be sufficiently accurate. We conclude with an outline of straightforward extensions of the present theory to include such factors as: (i) a nonuniform (polydispersed) particle size mainstream aerosol; and (ii) size-dependent particle thermophoretic diffusivity; which are likely to be important in current or future engineering applications.

Theory of surface deposition from a unary dilute vapor-containing stream allowing for condensation within the laminar boundary layer

Abstract Deposition rates on targets cooled far below the dew point of undersaturated mainstreams have often been found to be surprisingly low and surface temperature dependent. A rational yet tractable theory to account for these observations is formulated and exploited in particular cases of current practical interest—e.g. the deposition of trace alkali sulfate vapors present in combustion products. The present physico-chemical model is based on the formation of a condensate aerosol near the deposition surface, with the resulting droplets (or particles) collected by the mechanism of thermophoresis [shown to be dominant, but previously neglected in related two-phase boundary layer (BL) analyses]. The vapor, assumed here to be in local equilibrium with the aerosol phase, is collected by the familiar mechanism of Fick (concentration) diffusion across the prevailing laminar BL(LBL), but the overly restrictive assumption D v ≌ α n (unity Lewis number) is not made. As by-products of the calculation of the total (aerosol + vapor) deposition rate the position of nucleation onset, as well as the structure of the LBL on either side of this “fog-locus”, are obtained. Encouraging agreement with limited available data on Na 2 SO 4 deposition is obtained by assuming that the thermophoretic diffusivity of the resulting aerosol phase is about one decade smaller than the momentum diffusivity of the host combustion products.

Mass transfer dominated by thermal diffusion in laminar boundary layers

The concentration distribution of massive dilute species (e.g. aerosols, heavy vapours, etc.) carried in a gas stream in non-isothermal boundary layers is studied in the large-Schmidt-number limit, Sc [Gt ]1, including the cross-mass-transport by thermal diffusion (Ludwig–Soret effect). In self-similar laminar boundary layers, the mass fraction distribution of the dilute species is governed by a second-order ordinary differential equation whose solution becomes a singular perturbation problem when Sc [Gt ]1. Depending on the sign of the temperature gradient, the solutions exhibit different qualitative behaviour. First, when the thermal diffusion transport is directed toward the wall, the boundary layer can be divided into two separated regions: an outer region characterized by the cooperation of advection and thermal diffusion and an inner region in the vicinity of the wall, where Brownian diffusion accommodates the mass fraction to the value required by the boundary condition at the wall. Secondly, when the thermal diffusion transport is directed away from the wall, thus competing with the advective transport, both effects balance each other at some intermediate value of the similarity variable and a thin intermediate diffusive layer separating two outer regions should be considered around this location. The character of the outer solutions changes sharply across this thin layer, which corresponds to a second-order regular turning point of the differential mass transport equation. In the outer zone from the inner layer down to the wall, exponentially small terms must be considered to account for the diffusive leakage of the massive species. In the inner zone, the equation is solved in terms of the Whittaker function and the whole mass fraction distribution is determined by matching with the outer solutions. The distinguished limit of Brownian diffusion with a weak thermal diffusion is also analysed and shown to match the two cases mentioned above.

Marangoni convection in liquid films with a deformable open surface

Abstract For a liquid film with an open deformable surface like a tear film, sufficient conditions are given for the onset of Marangoni convection when there is simultaneous heat and mass transport across the layer. It is shown that although temperature gradients in the film may not be responsible for convection they may, however, contribute to a drastic lowering of the solute (mucin) gradients needed for the instability. The convective threshold values are also given in terms of a capillary number, i.e., in terms of the deformation of the open surface. Our theoretical predictions are expected to be useful in fields ranging from dacriology to crystal growth and metal-semiconductor physical chemistry.

Photophoretic modification of the transport of absorbing particles across combustion gas boundary layers

Abstract Since radiation energy fluxes can be comparable to or even dominate ‘convective’ (Fourier) fluxes in large fossil-fuel-fired power stations and furnaces, we examine particle drift (‘phoresis’) induced by the nonuniform photon-produced heating of particles in a ‘host’ gas. Our analysis of the resulting photophoretic particle velocity shows that photophoresis is a significant transport mechanism for micronsized absorbing particles in high radiative transfer combustion environments, with equivalent photophoretic diffusivity ratios (dimensionless photophoretic velocities) being as large as 10% of the better-known thermophoretic diffusivity. Since previous experimental results demonstrated that thermophoresis causes over a 3-decade increase in small particle deposition rates by convective diffusion, clearly, for small, absorbing particles, photophoresis will also be an important contributor to observed deposition rates. Accordingly, we present predicted dimensionless mass transfer coefficients for particle transport across non-isothermal laminar gaseous boundary layers, including the simultaneous effects of both particle thermophoresis and photophoresis. It is also shown that our earlier ‘additive suction velocity’ prediction/correlation scheme successfully anticipates the present numerical (large Schmidt number, laminar boundary layer) results for radiative/conductive flux ratios encountered in practice.

A nonlinear evolution equation for Bénard-Marangoni convection with deformable boundary

Abstract For the case of small Biot number, i.e. small heat transfer, a nonlinear evolution equation is derived for the deformable upper surface in a liquid layer heated from below and open to the ambient air (Benard-Marangoni convection). As a byproduct of our analysis, threshold values and other relevant findings are obtained for the onset of convection.

Comparison of Experimental and Numerical Air Temperature Distributions Behind a Cylindrical Volumetric Solar Absorber Module

The current trend in volumetric solar receiver technology is to build modular receivers cooled by air (Hitrec I and II, Solair 200 kW and 3 MW) in order to facilitate the replacement of broken absorber modules (cups) and to simplify the upscaling of the receiver. In addition, the modular designs include an air return circuit to cool down the structure supporting the cups. Usually, the air outlet temperature from each module is characterized by measurements taken from a single thermocouple. However, the air temperature distribution behind the volumetric absorber module is not homogeneous, as it can be seen in some specific tests where several thermocouples were added behind different absorber modules. The radial distribution of outlet air temperatures shows very high temperature gradients. The goal of this work is to explain the inhomogeneous thermal maps behind the metallic absorbers by comparing some experimental results with numerical simulations performed using the computational fluid dynamics FLUENT code. The results show the wind influence over the air recirculation flow and its effects on the outlet air temperature radial distribution. Thus, the simulations suggest different ways to reduce the temperature gradients behind each cup.

Unsteady Effects in Droplet Vaporization Lifetimes at Subcritical and Supercritical Conditions

Abstract The heating and vaporization of a pure cold fluid package in a hot environment of the same fluid has been analyzed. The model applies to subcritical as well as supercritical fluid conditions and relics on the assumption of constant pressure and quasisteady conditions in the gas phase (in a reference system receding with the cold front). An asymptotic analysis is performed using the ratio of the hot fluid density to the density of the cold fluid package as the smallness parameter. Then, a transcendental equation is obtained which provides the evolution of the cold package radius. For longer times when isothermal conditions are achieved in the cold region, the d2 law is obtained. Some deviations from this law. due to the unsteadiness of the heating process in the cold region, are evaluated and discussed.