A 1D model for the description of mixing-controlled inert diesel sprays José V. Pastor, J. Javier López, José M. García * , José M. Pastor CMT – Motores Térmicos, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain article info Article history: Received 1 February 2008 Received in revised form 22 April 2008 Accepted 23 April 2008 Available online 21 May 2008 Keywords: Diesel sprays Mixing Evaporation abstract The paper reports an investigation focusing on the transient evolution of diesel sprays. In order to under- stand the relationship between fuel–air mixing and spray penetration, a one-dimensional spray model is developed, which is capable of predicting the spray behaviour under transient conditions. The main assumptions of the model are the mixing-controlled hypothesis and the validity of self-similarity for con- servative properties. Validation of such concepts is achieved by comparing model predictions with both CFD gas jet simulations and experimental diesel spray measurements. Results show that a reasonable estimation of the spray evolution can be obtained for both non-vaporising and vaporising conditions. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction The evolution of diesel engines in the last decades has been dri- ven by the stringent pollution legislation. In order to fulfill the reg- ulated limits, a detailed study of fuel–air mixing and combustion processes has been necessary. Such a research task has made it possible to optimise engine performance as well as to lower pollu- tant emissions. Understanding of diesel sprays is essential in this optimization process. Due to the engine working principle, fuel and air meet in- side the combustion chamber thanks to the spray momentum, which controls both fuel stream penetration inside the combustion chamber and the simultaneous mixing with air. Furthermore, such processes have a direct impact on the characteristics of the flame that forms after the onset of combustion reactions, both in terms of local temperatures and pollutant formation. Thus, momentum flux, spray tip penetration, mixture composition and temperature are closely linked. The previous relationship is implicit to the conservation equa- tions that are at the base of CFD models. However, the fact that such equations are solved at small cells hinders the identification of the link between macroscopic spray results and the boundary conditions of the problem (air density, injection velocity, ...). This limitation can be overcome with the use of one-dimensional (1D) spray models, which usually contain the necessary physics to solve the problem, but in a way that enables a straightforward identifi- cation of the influence of boundary parameters on the results. One-dimensional models have been successfully used in the past for the prediction of spray tip penetration [1]. They have been usually developed in the form of a more or less general correlation for this parameter [2]. In some cases, such models have also con- sidered some kind of mixture distribution within the spray. How- ever, they have been used mainly for inert conditions. Transient flame behaviour has not been so thoroughly investigated, and cor- responding 1D models have made use of corrections of air entrain- ment from gas jet experiments to account for heat release effects [3,4]. This paper reports an investigation that aims at understanding the existing relationship between the local fuel–air mixing process, the spray dynamic evolution and the transient tip penetration. For that purpose, a one-dimensional spray model is presented with a general formulation that enables the prediction of any type of spray flow, under both inert and reacting conditions. Furthermore, due to the mixing-controlled hypothesis upon which the model is based, it can be used for the description of both a gas jet and also a diesel spray working under real engine conditions. By making some assumptions derived from the theory of turbulent gas jets, the model enables the estimation of the distribution of properties within the spray (composition, temperature, density, ...), as well as the tip penetration. The work is presented as a series of two papers. This is the first one, which is devoted to the analysis of the spray under inert con- ditions. Even though this problem is largely analysed in the litera- ture, the approach presented here is original in the formulation of the conservation equations, which solves the on-axis variables by using cross-sectional integrals. A transient formulation makes it possible to use the model for both constant and also variable injec- tion rate shapes. The model is an improvement of a previous ver- sion reported in [5], which discretised the injected fuel mass in parcels that were tracked along the spray axis in a one-dimen- sional fashion. However, this approach could only be used under 0016-2361/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.fuel.2008.04.017 * Corresponding author. Tel.: +34 96 387 76 50; fax: +34 96 387 76 59. E-mail address: jgarciao@mot.upv.es (J.M. García). Fuel 87 (2008) 2871–2885 Contents lists available at ScienceDirect Fuel journal homepage: www.fuelfirst.com