Heat and mass transfer of combusting monodisperse droplets in a linear stream
Introduction
Computation of modern combustion chambers of aero-engines and automotive direct injection engines, where the fuel is injected as a liquid spray, requires a reliable description of the heat and mass transfer parameters. When a fuel droplet enters a high temperature environment like in a combustion chamber, the droplet is heated, evaporates and finally the fuel vapor burns, delivering the energy for propulsion. Evaporation and combustion models of isolated, stagnant or moving fuel droplets are widely available in the literature ([1], [2] and [3], [4]). Particularly, the effect of the thermal radiation on the evaporation rate of single droplets was analyzed by Elperin and Krasovitov [5].
Improving the knowledge of the heat and mass transfer phenomena between the liquid droplet and its hot surrounding gaseous phase is a key issue to understand the highly complex phenomena occurring in spray combustion. One of the main difficulties is related to the constant variation of the physical properties of the gaseous phase, due to the change in its composition and temperature. Another difficulty is that the droplet-to-droplet interactions are not well taken into account. These interaction phenomena are highly important near the fuel injection devices, where the droplet density is high. Sangiovanni and Labowsky [6] have shown, using a monodisperse droplet line injected in a combustion chamber, the influence of the inter-droplet distance on the ignition time as well as on the diameter regression law. Brzustowski et al. [7] analyzed the combustion of two stagnant interacting droplets by solving Laplace’s equation and using qualitative experiments. Both the burning rate of each droplet and the shape of the flame were investigated: the burning rate was found to be smaller than that of an isolated droplet of the same size. More theoretical work was performed by Labowsky [8] or Marberry et al. [9], who developed a generalized treatment for burning rates of motionless droplets in finite arrays containing up to eight symmetrically arranged monodisperse droplets using the point sources method. Particle interactions were shown to be a function of particle size, number density and geometry of the array. Correction factors from which multiple particle burning rates can be calculated from single particle burning rates were established.
Generally speaking, the increase of droplet density tends to decrease the droplet drag coefficient and the vaporization rate. The heat transfer by forced convection is also influenced and modified by the interaction phenomena. Chiang and Sirignano [10] have investigated numerically the case of two vaporizing droplets moving in tandem, by taking into account the forced convection of the gas phase, the transient deceleration due to the drag force, the surface regression, the respective motion between the two droplets, the liquid phase internal circulation, the transient heating of the liquid phase and variable physical properties. The dependencies of the transfer numbers (i.e. Nusselt and Sherwood numbers) on initial droplet Reynolds number, initial droplet spacing, initial droplet size ratio, physical properties were considered. An extension of this study to the system of three droplets in a linear stream is presented by the same authors [11]. More recently, experimental results were obtained by Castanet et al. [12] on a monodisperse ethanol droplet stream, injected in the thermal boundary layer of a vertical heated plate. The droplet size reduction was measured by a light scattering technique simultaneously with the droplet temperature determined using a two-color laser-induced fluorescence technique. The convective heat transfer coefficient as well as the Nusselt number was inferred from the overall energy budget of the droplet in its gaseous surroundings: the influence of the inter-droplet distance, characterizing the interaction regime, was clearly highlighted. However this study was not related to the case of combusting droplet. The development of correlations that are able to describe adequately heat and mass transfer phenomena in the presence of droplet-to-droplet interactions is fundamental. Experimental data must be collected in basic experiments, where the time evolutions of the different parameters (i.e. droplet size, temperature, velocity, droplet spacing) can be easily separated. In the present study, the case of combusting single-component (ethanol) droplets in linear stream is considered. The energy budget equation shows that the experimental characterization of the evolution of the droplet temperature and droplet mass as a function of time are the critical parameters. In this study, the droplet diameter evolution has been measured by an optimized phase Doppler technique and the temperature by the two-color laser-induced fluorescence technique [13], [14].
Both Sherwood and Nusselt numbers will be characterized as functions of the usual non-dimensional numbers (i.e. Reynolds, Schmidt, Prandtl, Spadling and Lewis) and the non-dimensional distance parameter characterizing the droplet to droplet interactions.
Section snippets
Combusting monodisperse droplet stream facilities
A linear monodisperse droplet stream is generated by Rayleigh disintegration of a liquid jet, using of a mechanical vibration of the liquid column obtained by a piezoceramic actuator. The applied voltage on the actuator determines the position of the break-up zone of the jet depending also on the fuel physical properties, which are in turn related to the injection temperature.
For certain frequencies, the liquid jet breaks up into equally spaced and monosized droplets at the frequency of the
Droplet mass variation measurement using PDA
The PDA (particle dynamic analyzer) is widely used in sprays, to obtain statistical properties related to the droplet size distribution. In the present study, the PDA was used to determine the diameter evolution of a droplet as a function of the distance from the ignition point (i.e. as a function of time). The measurement of the mass flowrate must be as accurate as possible, since the evaporation heat flux is the product of this parameter times the latent heat of vaporization, and is therefore
Energy budget in a combusting, monodisperse stream
The droplet enthalpy evolution is directed by the variation of the heat fluxes resulting from forced convection with the surrounding gaseous environment, vaporization and radiation. The radiation effects are often neglected in the budget ([20], [21]), since the droplets are supposed to behave as a transparent medium. The case of a moving evaporating droplet with a regressing surface will be considered. Assuming that the local heat flux exchanged at the droplet surface is homogeneous, the
Measurement process
A wide range of aerothermal conditions was tested. Two kinds of processes, depending on the desired distance parameter, were implemented.
The first one is used for distance parameters ranging typically from 2 to 4. The injection pressure, i.e. the fuel flowrate and subsequently the injection velocity is first fixed and the frequency of the piezoceramic is adjusted to obtain the monodisperse injection conditions. The initial distance parameter is given by:
The droplet diameter Di at the
Concluding remarks
The combination of two optical techniques (two-colors LIF and PDA) allowed simultaneous measurement of the size, temperature and velocity of linearly streaming and combusting droplets.
The temperature measurements showed the existence of two phases: a transient phase of heating of the droplets followed by an equilibrium phase during which the droplets evaporate at constant temperature. Simultaneous measurements of the droplet size and mean temperature evolution allowed evaluation of the temporal
Acknowledgements
This work is supported by the European Community in the framework of the MUSCLES contract, Growth project GRD1-2001-40198.
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