Maximum entropy method for biodiesel spray droplet distribution

Abstract

The efficiency of combustion process in diesel engine depends on the spray characteristics. The most important of them are droplet size and velocity distributions. There are four methods which are used for describing the droplet size distributions: empirical, maximum entropy formalism (MEF), discrete probability function (DPF) and stochastic method. The MEF assumes that spray formation is a random process that can be described using the principle of maximum entropy. DPF method is a combination of random and non-random processes when the drop-size distribution appears from fluctuations in the initial conditions. Under the DPF approach the spray formation is divided into following steps: liquid breakup, ligaments separation, breakup of ligaments into fragments, fragment breakup into droplets. The stochastic breakup model assumes that the probability of formation of daughter droplet breakup size is independent of its parent size (a fractal scaling of breakup has been identified). This paper presents an investigation into the application of MEF model for distribution of biodiesel droplets. We used the model approach with the constraints: normalization, mass conservation, momentum conservation and surface energy conservation. The resulting probability density function (PDF) for velocity and droplet size is obtained by maximizing the Shannon entropy. We also used the new numerical algorithm to improve the model accuracy. The PDF for droplets diameters with different Weber numbers were calculated for both diesel and biodiesel fuels. The MEF predictions were compared against the experimental data for diesel and biodiesel droplet distribution with different injection pressure. According to the maximum entropy method, the influence of fuel thermodynamic properties on the parameters of drop-size and velocity distribution function for fuel sprays has been analysed.

Experimental and Mathematical Tools to Predict Droplet Size and Velocity Distribution for a Two-Fluid Nozzle

“…This shortcoming makes this method less favorable for practical applications. Some of the recent applications of this method can be seen in [11][12][13].…”

Atomization of Bio-Fossil Fuel Blends

“…Figure 1 shows the drop-size probability density for diesel and biodiesel fuels when experimental data [42] are fitted by maximum entropy method [43].…”