47067-G9
Turbulent Mixing in the Presence of Liquid Droplets with Application to Spray Combustion
Objective:- The overarching goal of the project is to understand the complex physical interactions in spray combustion. In this performance period, the research team at UT studied the impact of droplet inertia on spray evaporation and combustion. In most automobile and aircraft engines, the liquid fuel is atomized and sprayed into the combustion chamber, where the droplets undergo evaporation and combustion. The atomized droplets have finite volume and mass, and are usually heavy enough to possess non-negligible inertia. This inertia leads to non-uniform droplet dispersion inside the combustion chamber. Consequently, some regions could have a surplus of fuel and not enough oxidizer while other regions could be lean in composition. These spatial and temporal changes lead to a complex combustion process that is very unique to such systems. By understanding how droplet inertia affects the combustion process, better atomizer nozzles could be designed. Further, spray dispersion augmentation through flow control could also be pursued. In the last year, the research team funded through the PRF grant has completed a systematic study of inertia effects on combustion. These activities are reported below. Methodology:- To understand the fundamental physics, simulations should invoke the least amount of assumptions. For this purpose, a direct numerical simulation (DNS) approach was followed. In this work, spray dispersion, evaporation, and combustion of n-heptane fuel droplets in a turbulent jet was studied. DNS resolves all flow and time scales associated with the gas-phase. The code used a low-Mach number assumption to remove the acoustic components. The momentum equations were discretized using a second-order energy-conserving scheme. Gas-phase combustion was described using a one-step chemistry model with Arrhenius-type source terms. The parameters used in this model were extracted from data for n-heptane combustion. In order to include this chemistry model, scalar transport equations for the fuel, oxidizer, and product mass-fractions as well as temperature need to be solved. The scalar equations were evolved using a third-order upwind scheme. The droplet population was evolved using a Lagrangian method. This approach assumes that the droplet sizes are very small compared to the smallest turbulence length-scale. It is noted here that this assumption restricts the maximum Reynolds number that can be simulated for a given droplet size. In the Lagrangian approach, an ensemble of representative droplets is evolved along with the gas-phase equations. The droplets carry a set of properties including position, velocity, and composition. The droplet equations are ordinary different equations that were integrated using a Runge-Kutta third order scheme. Droplet evolution will require gas-phase properties that need to be interpolated to the droplet location. A trilinear interpolation scheme was used. Since the droplets contribute to fuel mass and drag on the gas-phase flow, these sources need to be transferred back to the gas-phase equations. A volume-averaging method was used to compute these source terms. The domain size was 640 X 320 X 320 in the three coordinate directions. In addition, nearly 10 million droplets were present in the domain at any given instant. Due to the large computational cost, an MPI-based parallelization strategy was used. The code was run on 128-256 processors. Each case took roughly 100 hours of computing time. Results:- Three different flow cases were considered. Droplet inertia is measured in terms on a non-dimensional Stokes number, which is the ratio of the particle response time to an appropriate turbulence time-scale. The Stokes number is proportional to the droplet diameter. Three different Stokes numbers of 0.1, 1, and 5 were considered. It was found that the inertia effects could be grouped into two broad categories. When the Stokes number is very large or small, the droplets do not exhibit any organized structures, and the evaporation process is dictated purely by the gas-phase composition. For the same mass loading, more small droplets are present. This was found to result in premixed flame propagation with lean composition in most of the domain. When the Stokes number was large, the number of droplets was fewer leading to intense local regions of evaporation. Consequently, partially premixed flame propagation was observed. Stokes number of 1 forms a different category characterized by coherent droplet structures. Preferential concentration of droplets in two-dimensional layers led to local pockets of fuel with the reaction zone located outside these layers. Consequently, the flame propagation was nearly non-premixed. These differences showed that models for single-phase combustion would not accurately describe spray combustion. Second, it showed that local organization of sprays play an important role in defining the flame propagation mode. In the second year of this project, we will focus on developing a preliminary model for identifying the propagation mode based on macroscopic properties of the droplets and the gas-phase composition.
