Multicomponent Vaporization Modeling of Petroleum-Biofuel Mixture at High-Pressure Conditions

Numerical simulation of the vaporization of multi-component liquid fuels under high-pressure conditions is conducted in this study. A high-pressure drop vaporization model is developed by considering the high-pressure phase equilibrium which equates the fugacity of each component in both liquid and vapor phases. Peng-Robinson equation of state is used for the calculation of fugacity. To model the vaporization of diesel fuel under high-pressure conditions, continuous thermodynamics based on a gamma distribution is coupled with phase equilibrium by correlating the parameters of the equation of state with the molecular weights of the continuous components. The highpressure vaporization model is validated using the experimental data of n-heptane drops under different ambient pressures and temperatures. Good levels of agreement are obtained in drop size history. Predicted results of the vaporization of diesel fuel drops show that increasing ambient pressure leads to a shorter drop lifetime under high temperature conditions (e.g., 900 K). The model was further applied to biodiesel and its blends with diesel fuel. The fuel blend is modeled based on a method that continuous thermodynamics is used to model diesel fuel and biodiesel is modeled as a mixture of its five representative components. Results of single drop vaporization history show that drop lifetime increases as the volume fraction of biodiesel in the fuel blend increases. It is also observed that the volume fraction of biodiesel in the fuel blend increases during vaporization and its vapor concentrates near the tip of the liquid spray while diesel fuel vapor is around the entire liquid spray. Introduction* Liquid drop vaporization modeling in multidimensional engine simulation is of great importance due to its impact on the accuracy of spray combustion prediction. Since the compositions of practical engine fuels are very complicated, an important means to improve vaporization modeling is to replace the singlecomponent assumption with a multi-component approach. Multi-component approach based on continuous thermodynamics can be used to model complex fuels such as gasoline and diesel fuel, which are usually composed of hundreds of components [1]. Using this approach, fuel is assumed to be composed of an infinite number of continuously distributed components, and a probability distribution function (PDF) is used to model the distribution of the molecular weights of the components in the fuel. In addition to the composition of multi-component fuels, vaporization modeling also needs to consider the effects of high pressure since liquid fuel drops frequently experience such conditions in practical combustion devices such as diesel engines and gas turbines. Traditionally, for computational efficiency, drop vaporization models are mostly based on the Raoult’s law which is a low-pressure simplification of the general vaporliquid phase equilibrium. The phase equilibrium calculation based on the Raoult’s law involves the assumptions of ideal gas law and no gas dissolving in the liquid phase. Since such assumptions are not entirely true un* Corresponding author der high-pressure conditions, errors will be generated in the prediction of drop vaporization rate and vapor distribution at high-pressure conditions. To improve the accuracy of multi-dimensional computational fluid dynamics simulation, general phase equilibrium relations, which are characterized by the equality of fugacities of both phases, need to be used to replace the Raoult’s law in drop vaporization simulation. Since petroleum fuels are questionable in availability in the future, biorenewable fuels are being used in many kinds of combustion devices. Especially in diesel engines, since biodiesel is close to diesel fuel in terms of physical and chemical properties, it can be used without significant modifications to the engine. Due to the high miscibility, biodiesel is usually blended with regular diesel fuel in practical applications. Successful applications of biodiesel in diesel engines rely on the detailed knowledge of its spray and combustion behaviors. Research has shown that most of biodiesel derived from vegetable oils are mainly composed of five C16 to C18 fatty acids [2, 3]. The vaporization of biodiesel and its blends with diesel fuel at various ambient temperatures was simulated under atmospheric pressure by Zhang and Kong [4], who assumed biodiesel as a mixture of five components and applied a mixing rule to obtain the properties of biodiesel. The purpose of present study is to predict the vaporization behaviors of diesel fuel, biodiesel, and the blend of both fuels under engine operating conditions which are characterized by high pressures and temperatures. A multi-component drop vaporization model for high-pressure conditions based on continuous thermodynamics is developed. The model is first validated using the high-pressure vaporization experiments of single-component fuel (i.e. n-heptane). Both the drop vaporization history and the vapor distribution of liquid spray using biodiesel and its blends with diesel fuel under high-pressure conditions will also be shown. MODEL FORMULATION In this section, the phase equilibrium in a vaporliquid system, which is composed of fuel components and the species of the surrounding gases at the surface of the liquid drop, will be discussed. Such an equilibrium provides boundary conditions for the governing equations of both phases. In solving the onedimensional governing equations in the gas phase, the pseudo-steady assumption will be applied. The methods for calculating the physical properties of the fuels at high-pressure conditions will also be presented. Gas and fuel species in both phases at the phase interface can be regarded as a system in thermodynamic equilibrium at a specific pressure and temperature. Such an equilibrium requires the minimum of the total Gibbs free energy, namely, 0 dG = [5]. It can be shown that this requirement will lead to the equality of fugacity , , ˆ ˆ i l i v f f = . (1) Subscripts l and v denote the liquid and vapor phases, respectively. fi indicates the fugacity of component i, and ^ denotes the property of a component in a mixture. In practice, the fugacity coefficient is more frequently used in describing phase equilibrium replacing fugacity in the above equation and is defined by