Conditional Moment Closure Modelling for Spark Ignition in a Turbulent N-heptane Spray

Ignition and flame stabilisation have been simulated in a turbulent, bluff body stabilised spray flame. A complete first order Conditional Moment Closure (CMC) model for spray combustion is presented, as well as CMC modelling for spark ignition. The new elements of the two phase model formalism and the spark ignition models are illustrated using a one dimensional spray ignition example. It is shown that the new spray terms are not significant in the flows considered, however the modelling of the mixture fraction variance equation is critical. Finally, ignition of the experimental spray burner is simulated and compared with the available data, showing reasonable qualitative agreement but over-predicting the speed of flame stabilisation. Introduction Deeper understanding of forced ignition and flame propagation is needed by researchers developing modelling for the design of industrial burners. The ability to model ignition of spray fuelled flow is of particular interest to manufacturers of aviation gas turbines who must satisfy certification bodies that their designs may be re-ignited at high altitude. The numerical simulations in this paper, used to develop the Conditional Moment Closure (CMC) combustion model for ignition problems, were based on the experimental study of spark ignition and flame propagation in a swirling, bluff body stabilised spray combustor by Marchione et al. [1,2]. The configuration investigated is depicted in Fig. 1, and full details may be found in ref. [1]. The main observation of interest to this study is the global propagation process as shown in Fig. 2. The spark was located at radius, r = 0mm and an axial distance from the bluff body of z = 23mm. The experiment used a 3mm spark gap, 200mJ electrical energy, and 400μs duration. Figure 1. Schematic of burner configuration. The CMC model is an advanced turbulent reacting flow model [3]. It has previously been applied to flame propagation problems such as igniting [4] and steady state lifted turbulent jet flames [5] and to two phase combustion in Diesel like sprays [6,7] and other applications [8,9,10]. These authors have used differing sets of CMC equations and differing approximations in their solution. Furthermore, modelling of the spray ignition experiment requires development of a spark ignition model for the CMC. This paper starts with a presentation of a complete first order CMC two phase combustion model, including forced ignition models. The new elements of the two phase model formalism and the spark ignition models are then illustrated using a one dimensional spray ignition example. Finally, ignition of the experimental spray burner is simulated and compared with the available data. Figure 2. 2200Hz fast camera (line of sight) images of the flame evolution at the times indicated for a successful spark located at r = 0, z = 23mm. Spray injection is at the bottom of each image, dimensions 70mm diameter, 80mm height. Experiment by Marchione et al. [1]. Formulation Two Phase Conditional Moment Closure Equations The first order CMC equations for two phase flow have been employed as derived by Rogerson [8], with the conditional temperature equation provided by Richardson [10]. Conditional expectations are denoted Qα≡ where Yα is the variable being averaged on the condition that the mixture fraction ξ equals the sample space variable η. Transport equations are solved for Qα, the conditional expectation for the mass fraction of species α, and QT, the conditional expectation for the temperature. The closed transport equation for the conditionally averaged species mass fractions is given by:                         