51-1 Efficient Numerical Calculation of Evaporating Sprays in Combustion Chamber Flows R. Schmehl, G. Klose, G. Maier and S. Wittig Lehrstuhl und Institut für Thermische Strömungsmaschinen Universität Karlsruhe (T.H.) 76128 Karlsruhe, Germany Summary Representing two different conceptual approaches, either Eule- rian continuum models or Lagrangian particle models are com- monly applied for the numerical description of dispersed two phase flows. Taking advantage of the positive features inherent to each model, a combination approach is presented in this study for the efficient computation of liquid fuel sprays in combustor flows. In the preconditioning stage, Eulerian transport equa- tions for gas phase and droplet phase are solved simultaneously in a block-iterative scheme based on a coarse discretization of spray boundary conditions at the nozzle. Due to the close cou- pling of both phases, the time expense of this approximate flow field computation is not much higher as for single phase flows. In the refinement stage, Lagrangian droplet tracking is applied with a detailed discretization of initial conditions. To account for complete interaction between gas phase and droplets, gas flow solution and droplet tracking are concatenated by an iter- ative procedure. In this stage, the numerical description of the spray is enhanced by additional modeling of droplet breakup. Results of numerical simulations are compared with measure- ments of the two phase flow in a premix duct of a LPP research combustor. 1 Notation cp specific heat capacity D droplet diameter D0.5 mass median diameter D32 Sauter mean diameter D0.632 characteristic diameter f body force h enthalpy ˙ H enthalpy flux H energy transfer rate I momentum transfer rate k turbulent kinetic energy ˙ m mass flux M mass transfer rate On Ohnesorge number P pressure Pr Prandtl number ˙ Q conductive heat flux Re Reynolds number S source term Sc Schmidt number T temperature Tu degree of turbulence U velocity component We Weber number Y mass fraction Greek Symbols α heat transfer coefficient α k liquid volume fraction β off axis angle ε dissipation rate of k Γ diffusion coefficient µ dynamic viscosity ν kinematic viscosity ρ density τ shear stress Subscripts 0 initial state g,d gas, droplet int interface t turbulent vap vapor 2 Introduction Improving modern gas turbine efficiencies by increasing pres- sure and temperature levels of the combustion process, essen- tially requires sophisticated combustion concepts in order to meet todays strict limitations on pollutant emissions. Funda- mental to these low emissions concepts is a characteristic strat- egy to inject and mix the liquid fuel with the compressed air flow, avoiding local stoichiometric combustion conditions as far as possible. Two promising approaches in this context are the concepts of Lean-Premix-Prevaporize (LPP) and Rich-Quench- Lean (RQL) combustion. In order to develop advanced com- bustor designs with the required flow characteristics, a better understanding of the two phase flow physics is necessary. Two phase flow effects typical for premix ducts of LPP combustors or prefilming air blast atomizers are summarized in Fig. 1. Evaporation Dispersion + Droplet Breakup Spray-wall Interaction Wall Film Flow Atomization Figure 1: Two phase flow effects in a LPP premix duct Due to the enormous increase in computing performance, Com- putational Fluid Dynamics (CFD) offers a promising potential for efficient combustor design and optimization. In particular when compared to experimental studies at elevated pressures, CFD analysis may be employed to reduce turn-around times and costs of combustor design significantly. On the other hand, complex flow phenomena such as turbulence, atomization or chemical reaction still represent some of the most challenging topics for CFD tools. Basically, two different conceptual approaches may be em- ployed for the numerical description of dispersed two phase flows [3]. In analogy to single phase gas flow, the Eulerian ap- proach is based on a continuum model of the spray, resulting in transport equations describing the propagation and evaporation of this droplet phase [28], [6]. In the Lagrangian approach, the spray is modeled by superposition of trajectories calculated for large numbers of representative droplets. Each of the two basic approaches is characterized by specific advantages and restric- tions. In the Eulerian method, the transport equations of the droplet phase are appended to the gas phase transport equations, result- ing in a compact description of the interacting two phase flow system. The essential advantage is a simultaneous solution of the interacting flow fields of gas phase and spray by a single numerical method. Applying a standard block-iterative solver for systems of linearized equations, the information exchange