Transport in complex flows: reactive, multiphase and supercritical jets

The present work deals with the dynamics of turbulent jet in different configurations and geometries. In particular two aspect, important both in the engineering applications and in the scientific research, are stressed. The first one deals with the mixing in the turbulent jets at near-critical thermodynamic conditions. The second addresses the dynamics of inertial particle in turbulent premixed Bunsen flames. In order to perform a Direct Numerical Simulation (DNS) of a turbulent jet at supercritical conditions a suitable method was developed to mimic the gas thermodynamic behavior. The Van der Waals equation of state has been chosen and an Low Mach number expansion of Navier Stokes equations has been performed. This approach is completely original in the context of real gas equation, and it is considered as useful as the whole Navier Stokes system in the fully compressible formulation especially at very Low Mach number. The new equations are implemented in a numerical code in order to perform the first, in our knowledge, DNS of a fully turbulent coaxial jet in supercritical thermodynamic conditions. The configuration adopted is similar to the coaxial injectors of the liquid rocket engines and consists in an inner jet with liquid-like density and low velocity and in an outer jet characterized by a gas-like density and high velocity. Aim of the simulation is to observe high-density finger-like structures observed in previous experimental visualizations, the so-called “ligaments”, and to understand the mechanism of their formation. In particular these finger-like structure formation is ascribed to the joint effects of the jet dynamics and the thermodynamics condition. In fact the Kelvin-Helmholtz structures, which generates by the peculiar jet configuration, contributes to the “ligaments” formation while the thermodynamic conditions allow these high-density structures to persist in low-density field. In the real gas jet the interface between the high and low density fluid is observed to be thinner than the perfect gas jet, hence the diffusion occurs at smaller and smaller scales. The obtained data are considered useful for the study of the mixing and combustion processes in the near critical conditions. In the LES/RANS context, in addition, DNS data are necessary for the evaluation of sub-grid terms and for development of new models. The dynamics of the inertial particles in turbulent premixed flame is addressed with the same code. The DNS of a reactive Bunsen jet laden with inertial particle is performed. The simulation reproduces a lean Methane/Air premixed flame in the ”flamelet“ regime. The flow is seeded with four particle population of different inertia with the mass density much larger than the fluid one and diameter much smaller than the Kolmogorov length scale. In these conditions, the particle dynamic equation is forced by only the Stokes drag and the one-way coupling regime can be assumed (no fluid-particle or particle-particle interaction occur). A suitable Stokes number is defined as a function of the particle features and of the laminar flame speed and thickness and burned/unburned gas temperature ratio. It is shown that the so-defined “flamelet” Stokes number is the suitable to describe the particle dynamics in the premixed flames. The DNS data are analyzed to address the effects of particle inertia on Particle Image Velocimetry measurements, in particular is observed that the particle inertia induces a time lag in particle to follow the v fluid acceleration across the flame front. This time lag generate a mismatch in the prediction of fluid velocity through the particle velocity. It is shown that the evaluation of high order velocity statistics needs particle with smaller and smaller flamelet Stokes number. The data are analyzed also to address the effects of the interaction between particle inertia and fluctuating flame front on the particle spatial distribution. Two statistical tools are used to this purpose, the Clustering Index, K, and the radial distribution function, g(r). K measures the departure of the actual distribution from the Poissonian distribution, g(r) is the probability to find a couple of particle at a certain distance r. An important outline consists in the presence of particle clusters in the flame brush. In particular also quasi-Lagrangian particles are characterized by not Poissonian spatial distribution as a consequence of the intermittent fluctuation of the instantaneous thin flame front separating two regions with different particle concentration. With the increasing of the Stokes number the cluster intensity increases experiencing a maximum value for order one flamelet Stokes number. All results concerning the particle dynamics are confirmed by experimental measurement on a Bunsen Methane-Air turbulent reacting jet. The obtained results are considered important both for experimental measurements and for soot dynamics and growth strongly influenced by the interaction of particle with the flame front and by their collision.