John Abraham

Modeling the outcome of drop–drop collisions in Diesel sprays

The sub-models for collisions and coalescence are important components of the spray model in multidimensional computations of Diesel sprays. These models influence the computed drop sizes, which affect the overall characteristics of the spray. Typically, the droplet interaction model is separated into two parts: first, calculating the collision rate between particles, and second, calculating the probability of coalescence once a collision has occurred. While the collision frequency may be estimated from kinetic theory considerations, a criterion has to be specified to determine the outcome of the collisions. The outcome may be bouncing, coalescence, stretching separation, or reflexive separation. The coalescence efficiency is defined as the probability that two drops will permanently merge into one drop, given that a collision between the two drops has occurred. Current approaches to modeling the coalescence efficiency are based on experimental observations of binary water drop collisions under atmospheric conditions. However, in the last decade experimental evidence has become available that suggests that the collision behavior of hydrocarbon drops may differ significantly from that of water drops. More recent experiments suggest that the effects of ambient pressure may also be significant. This paper presents a comparison of the computed outcome of drop collisions in a Diesel spray to that of recently published experimental observations. Possible ways to employ the recent findings in multidimensional spray models are discussed. Results of a model modified to reflect this new information is presented and compared with the original model. Limitations of the new model are discussed.

Three-dimensional multi-relaxation time (MRT) lattice-Boltzmann models for multiphase flow

In this paper, three-dimensional (3D) multi-relaxation time (MRT) lattice-Boltzmann (LB) models for multiphase flow are presented. In contrast to the Bhatnagar-Gross-Krook (BGK) model, a widely employed kinetic model, in MRT models the rates of relaxation processes owing to collisions of particle populations may be independently adjusted. As a result, the MRT models offer a significant improvement in numerical stability of the LB method for simulating fluids with lower viscosities. We show through the Chapman-Enskog multiscale analysis that the continuum limit behavior of 3D MRT LB models corresponds to that of the macroscopic dynamical equations for multiphase flow. We extend the 3D MRT LB models developed to represent multiphase flow with reduced compressibility effects. The multiphase models are evaluated by verifying the Laplace-Young relation for static drops and the frequency of oscillations of drops. The results show satisfactory agreement with available data and significant gains in numerical stability.

How Far does the Liquid Penetrate in a Diesel Engine: Computed Results vs. Measurements?

A multidimensional model is used to study the penetration of the liquid fuel in a constant volume chamber under normal Diesel engine conditions. Comparisons of the liquid fuel penetration as predicted by the model with results from recent experiments show inadequate agreement but, more importantly, a sensitivity to the numerical resolution. A possible origin of this sensitivity is identified through a series of systematic studies of the different components of the spray model. These studies show that the sensitivity of the liquid penetration to the numerical resolution may be related to a dependence of the computed Sauter Mean Radius (SMR) of the drops on the grid resolution. A detailed study of this dependence relates it to the non-uniformity of the spatial distribution of drops in the chamber, in particular, within about 100 diameters of the injector orifice. This non-uniformity leads to the estimate of different number densities and, hence, different collision frequencies, on different grids. The non-u...

Simulations of binary drop collisions with a multiple-relaxation-time lattice-Boltzmann model

In this paper, we report simulations of drop-drop collisions using a multi-relaxation-time multiphase flow lattice Boltzmann model. Employing a multi-relaxation-time (MRT) model in lieu of the Bhatnagar-Gross-Krook (BGK) model used in the standard lattice-Boltzmann equation enables realization of stable computations of drop collisions at relatively lower fluid viscosities without increasing the lattice resolution to prohibitive levels. Head-on and off-center computations of collisions are carried out using axisymmetric and three-dimensional (3D) versions of the MRT model, respectively. Time-resolved results showing the interactions of the interfaces of drops for different characteristic nondimensional parameters are presented. Computations show that at low Weber numbers, We, coalescence with relatively smaller deformation occurs, sometimes entrapping a stable microbubble. At higher We, head-on collisions lead to reflexive separation with or without the formation of satellite droplets. The size of the sate...

Three-dimensional computations of flows in a stratified-charge rotary engine

The first three-dimensional rotary-engine computations are reported of exhaust, intake (with side and peripheral ports, and with different intake turbulence intensities and length scales), compression, homogeneous-charge combustion, dual liquid fuel injection, and dual liquid fuel injection and combustion. The model includes a k-epsilon submodel for turbulence, a stochastic treatment of the fuel drops and a hybrid laminar and mixing-controlled submodel for the conversion of reactant to products. The code is an extensively modified version of KIVA. The latter was developed at the Los Alamos National Laboratory for reciprocating engines. The modifications include: dynamic rezoning of the grid in both the x-y and the x-z planes; adoption of a cartesian coordinate system fixed to the housing with analytical grid generation and grid velocities related to the rotor velocity; inclusion of radial and tangential ports for both intake and exhaust.

Evaluation of an Unsteady Flamelet Progress Variable Model for Autoignition and Flame Lift-Off in Diesel Jets

An unsteady flamelet progress variable (UFPV) model is evaluated for modeling autoignition and flame lift-off in diesel jets. Changes in injection pressure, orifice diameter, ambient temperature, density, and O2 concentration are considered. In implementing the model in a Reynolds-averaged Navier–Stokes (RANS) code, a look-up table of reaction source terms is generated as a function of mixture fraction Z, stoichiometric scalar dissipation rate χst and progress variable Cst by solving the unsteady flamelet equations. It is assumed that the probability density functions (pdfs) of Z, χst, and Cst are statistically independent, and presumed functions are employed for the pdfs. Comparisons with experimental results show that the model is able to predict ignition delay and flame lift-off with reasonable accuracy in the RANS simulations. The quantitative agreement between computed and measured results depends on the definitions employed to quantify autoignition time and lift-off height, but, in general, the agreement is within 25%.

Lattice boltzmann model for axisymmetric multiphase flows

A lattice Boltzmann model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous, and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into account the discrete lattice effects in the Chapman-Enskog multiscale analysis, so that the macroscopic axisymmetric mass and momentum equations for multiphase flows are recovered self-consistently. The model is extended to incorporate reduced compressibility effects. Axisymmetric equilibrium drop formation and oscillations, breakup and formation of satellite droplets from viscous liquid cylindrical jets through Rayleigh capillary instability, and drop collisions are presented. Comparisons of the computed results with available data show satisfactory agreement.

Crown behavior in drop impact on wet walls

Axisymmetric computations of drop impingement on walls with a pre-existing liquid film are reported. A high-density-ratio lattice-Boltzmann model is employed for the computations. The focus of the work is on the behavior of the crown that forms as a result of impingement. When the crown forms, its base radius and height grow with time. Subsequently, it may break up. The influence of wall liquid film thickness, and surrounding gas density and viscosity on crown behavior is investigated. When the liquid film is thin, it is observed that the rate of increase of the radius and height of the crown increases with increasing film thickness. The breakup of the crown is delayed. On thicker films, the rate of increase decreases with increasing film thickness, but the breakup is further delayed. When either gas density or viscosity is increased, the rate of increase of the radius and height decreases and breakup is delayed.

A numerical investigation of flame lift-off in diesel jets

Abstract Flame lift-off heights are modeled in diesel jets by using diffusion flamelet extinction as a criterion for identifying the lift-off. It is shown that the axial distance in the jet where the stoichiometric scalar dissipation rate matches computed extinction scalar dissipation rate correlates with the lift-off height. The influence of injection pressures (40–138 MPa), chamber densities (14.8–58.5 kg/m3), chamber temperatures (1000–1300 K) and O2 molar concentrations (10–21%) are studied. N-heptane is chosen as a surrogate for diesel fuel. Two chemical kinetic mechanisms, a 37-species, 56-step mechanism and a 159-species, 1540-step mechanism, are employed. Consistent with experimental findings, the computed results indicate that the flame lift-off height decreases with increase in chamber temperature, chamber density and oxygen concentration and increases when the injection velocity is increased. It is observed that across the range of chamber conditions considered, the computed extinction scalar dissipation rates correlate well with the measured lift-off heights. When chamber temperatures and O2 concentrations are varied, the results are found to be sensitive to the choice of the chemical kinetic mechanism.

Exploring injected droplet size effects on steady liquid penetration in a Diesel spray with a two-fluid model

An approach to include droplet size effects in a two-fluid model for Diesel sprays when the locally-homogeneous flow (LHF) assumption is employed is developed. The model is then employed to study the effect of droplet sizes on the steady liquid penetration in vaporizing Diesel sprays when several injection and chamber parameters are changed. These parameters include the orifice diameter, injection pressure, ambient temperature and the ambient density. The computed steady liquid penetration is compared with constant volume measurements made under Diesel conditions at the Sandia National Laboratories. It appears that under typical Diesel conditions, the steady liquid penetration is controlled by entrainment and mixing alone. However, at lower ambient densities, droplet sizes may also be important.