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This study investigates the effect of heat conduction through the support fiber on a droplet's evaporation in a weakly convective flow. Experimentally, a droplet of n-heptane or n-hexadecane with an initial diameter of 700 or 1000 μm was suspended at the tip of a horizontal or vertical quartz fiber (diameter 50, 150, or 300 μm) to evaporate in an upward hot gas flow (at 490 or 750 K). A simple one-dimensional model of transient conduction is formulated in combination with evaporation of the droplet. The calculations agree well with the experiments. In general, heat conduction through the fiber enhances evaporation, with a stronger effect for a lower gas temperature and a thicker fiber. However, the total heat inputs are attenuated when the fiber's diameter is 300 μm. Orientation of the fiber is unimportant. Also, the evaporation rate is enhanced in an oxygen-containing gas flow, due to the additional heating from oxidation around the droplet.

This study aims to solve the discrepancies between the theoretical and experimental results for droplet evaporation. In the literature, all the experiments for microgravity droplet evaporation have been conducted in a hot furnace with the droplet suspended by a fiber. We propose that the discrepancies result from the fact that current theoretical models ignored the conduction into the droplet through the fiber and the liquid-phase absorption of the radiation from the furnace wall. For verification, we formulate a comprehensive model with the effects of fiber conduction and liquid-phase radiative absorption accounted for. For the droplet size variation and evaporation rate constant, good agreement is found between our calculations and the experimental data of H. Nomura, Y. Ujiie, H.J. Rath, J. Sato, M. Kono [Proceedings of 26th Symposium (Int.) on Combustion, 1996, pp. 1267–1273]. Radiative absorption and fiber conduction enhance the evaporation rate significantly. At a low temperature of 470 K, the discrepancies are mainly due to the additional fiber conduction, while at a high temperature of 750 K, the liquid-phase radiative absorption becomes mainly responsible.

The ignition of free and suspended monocomponent (iso-octane) and bicomponent (mixtures of n-hexadecane with n-heptane, n-dodecane, or iso-octane) droplets was experimentally investigated in the postflame gases (gas temperature, T∞, between 1080 and 1300 K; flow velocity U∞ of 2.0–2.5 m/s) of a flat-flame burner. Initial droplet diameters, d0, ranged from 300 to 1500 μm and droplet Reynolds numbers from 3.5 to 22. Comparing iso-octane and n-heptane droplets, both fuels with similar volatilities, iso-octane droplets had longer ignition delay times, larger ignition distances, and slower upstream flame propagation speeds, due to the lower reactivity of iso-octane. With decreasing initial diameter, ignition delay times decreased and became reaction-controlled. The ignition delay times of iso-octane droplets as small as 300 μm were, interestingly, longer than those for hexadecane droplets, despite their higher volatility. For bicomponent C7/C16 droplets of different proportions, the variation of the ignition location with gas temperature was similar to monocomponent droplets. For T∞ < 1220 K, ignition was initiated far downstream as a dim blue premixed flame, followed by rapid upstream propagation to form an envelope flame. The ignition location was closer to the droplet for higher temperatures. For large droplets, when the ignition was evaporation-controlled, ignition delay times were strongly affected by the proportion of fuels having different volatilities. For C7/C16, i − C8/C16, and C12/C16, the ignition delay time was similar to that of a pure volatile fuel droplet when the volume fraction of the volatile component (rν) was larger than 20%–40%. If rν was smaller, the ignition delay time resembled that of a pure nonvolatile fuel droplet. For small bicomponent droplets, ignition was reaction-controlled. The ignition delay times of C7/C16 droplets were independent of rν due to the kinetic similarity of both components. However, those of i − C8/C16 droplets were longer for high iso-octane fractions, due to the lower reactivity of iso-octane.

The effect of anisotropy on transport phenomena in anisotropic porous media is studied in this paper. For convenience, a bank of circular cylinders which can be treated as an anisotropic porous medium is employed such that both Darcy-Forchheimer drag and effective thermal conductivity can be accurately determined. Two problems including a forced flow and a natural convection are illustrated to investigate the effect of anisotropy on fluid flow and heat transfer through a bank of circular cylinders. The solutions reveal that inclination of the cylinder bundle could give rise to an influence of more than 100% on the heat transfer rate for both forced convection and natural convection. Hence, the anisotropy of an anisotropic porous medium should not be ignored.

Based on the microscale temperature, the effective thermal conductivity in the principal direction of an anisotropic porous medium is evaluated. A correlation of the effective thermal conductivity then is employed to predict the volume-averaged temperature of a two-dimensional nonhomogeneous anisotropic porous medium. Through the example, the present model is found to possess an excellent performance even when the principal direction of the anisotropic medium is not parallel to the physical coordinates. The results also reveal that using the classic mixing rule could lead to a significant error when the thermal conductivity ratio of the solid and fluid is large. The present numerical procedure is believed to be able to determine the effective thermal conductivity for most porous media as long as their microstructure is regular and known.

In the present investigation, an incompressible fluid flow across a bank of circular cylinders is studied and modeled as a non-Darcy flow through a porous medium. The continuity equation and the momentum equation in pore scale are solved on a Cartesian grid system. To circumvent the numerical difficulties arising from the flow domain of irregular shape, the weighting function scheme along with the APPLE algorithm and the SIS solver is employed. The Darcy-Forchheimer drag is then determined from the resulting volumetric flow rate under a prescribed pressure drop. The result indicates that the permeability approaches zero at the particular porosity of 0.2146 when the fluid flow across the cylinders becomes impossible. In addition, the pressure drag (Forchheimer drag) is found to contribute a significant resistance at large porosities and/or large granule Reynolds numbers. A correlation of Darcy-Forchheimer drag is proposed for 0.2146 ⩽ e ⩽ 1 and 0 ⩽ Red ⩽ 50.

A simplified theoretical model has been developed for describing transient ignition far downstream of a droplet with forced convection. The downstream velocity field is approximated by an analytic form pertaining to isothermal far-wake flow. The transient heating and evaporation of the droplet are treated using film theory; their effects on gas-phase temperature and species distributions are accounted for with integral conservation. Transport and chemical reaction are described with differential equations for mass and energy, together with the approximate analytic velocity field. The position of ignition and the ignition delay time are determined as when thermal runaway is reached in the calculations. For n-hexadecane droplets, ignition delay times and ignition positions have been calculated as a function of free-stream gas temperature, droplet diameter, velocity of the gas relative to the droplet, and initial temperature of the droplet. Numerical results agree well with experiment. The mechanism of convective droplet ignition is also discussed.

This paper is concerned with designing an efficient algorithm for computing the intersection of two unstructured meshes. The algorithm uses a background quadtree from the first unstructured mesh and a self-avoiding walk (SAW) from the second unstructured mesh. Due to the relationships between neighboring consecutive triangles in the triangle sequence of a SAW, we can track the location of each triangle in the second unstructured mesh by means of a background quadtree. This allows us to design an approximately linear time algorithm for computing the mesh intersection. Experiments show that our efficient algorithm for computing the mesh intersection saves considerable execution time when compared to other algorithms. We also present two new SAWs. Using our first-in-first-out (FIFO) SAW saves an additional 5% in the execution time over other SAWs as our FIFO SAW employs better data locality, which is especially beneficial to hierarchical-memory computer architectures.