Franz X. Tanner

A Cascade Atomization and Drop Breakup Model for the Simulation of High-Pressure Liquid Jets

A further development of the ETAB atomization and drop breakup model for high pressure-driven liquid fuel jets, has been developed, tuned and validated. As in the ETAB model, this breakup model reflects a cascade of drop breakups, where the breakup criterion is determined by the Taylor drop oscillator and each breakup event resembles experimentally observed breakup mechanisms. A fragmented liquid core due to inner-nozzle disturbances is achieved by injecting large droplets subject to this breakup cascade. These large droplets are equipped with appropriate initial deformation velocities in order to obtain experimentally observed breakup lengths. In contrast to the ETAB model which consideres only the bag breakup or the stripping breakup mechanism, the new model has been extended to include the catastrophic breakup regime. In addition, a continuity condition on the breakup parameters has lead to the reduction of one model constant. Further, the primary breakup has been adjusted in order to avoid the nonlinear dependence of the spray angle on the breakup length. The model has been tuned and validated by means of experimental data for non-evaporating, evaporating and reacting sprays under controlled conditions in constant-volume or constant-pressure combustion vessels using a KIVA-based code.

Computational Optimization of Split Injections and EGR in a Diesel Engine Using an Adaptive Gradient-Based Algorithm

The objective of this study is the development of a computationally ecient CFD-based tool for nding optimal engine operating conditions with respect to fuel consumption and emissions. The optimization algorithm employed is based on the steepest descent method where an adaptive cost function is minimized along each line search using an eective backtracking strategy. The adaptive cost function is based on the penalty method, where the penalty coecient is increased after every line search. The parameter space is normalized and, thus, the optimization occurs over the unit cube in higherdimensional space. The application of this optimization tool is demonstrated for the Sulzer S20, a central-injection, non-road DI diesel engine. The optimization parameters are the start of injection of the two pulses, the duration of each pulse, the duration of the dwell, the exhaust gas recirculation rate and the boost pressure. A zero-dimensional engine code is used to simulate the exhaust and intake strokes to predict the conditions at the closure of the inlet valves. These data are then used as initial values for the three-dimensional CFD simulation which, in turn, computes the the emissions and specic fuel consumption. Simulations were performed for two dierent cost functions with dierent emphasis on the fuel consumption. The best case showed that the nitric oxide and the particulates could be reduced by over 83% and almost 24%, respectively, below the EPA mandates while maintaining a reasonable value of specic fuel consumption. Moreover, the path taken by the algorithm from the starting point to the optimum has been investigated to understand the inuence of each parameter on the process of optimization.

Numerical Investigation of the Formation and Detachment of Droplets from Pores in a Shear Flow Field

The formation and detachment behavior of droplets from a pore opening into a simple shear field within a channel gap is investigated using numerical simulations. The mathematical model consists of the governing equations for an incompressible two‐phase flow problem with a moving contact line. These equations are numerically solved using the volume‐of‐fluid method implemented in the open source software OpenFOAM. A parameter study was performed to determine the effect of relevant dimensionless parameters on the formation and detachment behavior of the droplets. These dimensionless parameters involve the pore size, pore flow rate, gap shear rate, interfacial tension, and the viscosity and density of the two fluid phases. For the parameter range considered in this study, different degrees of jetting behavior were observed. Also, the sizes of the detached droplets were seen to decrease as the gap shear rate increased, and increase with the pore flow rate, with the gap shear rate having a larger effect.

Droplet Freezing and Solidification

Freezing and solidification processes are discussed and modeled for liquid droplets which undergo first-order phase transitions. First, a four-stage model is presented which accounts for supercooling, nucleation, recalescence, and crystallization. Subsequently, a more detailed discussion of a three-stage solidification model for droplets that do not exhibit supercooling is given. Aspects of the three-stage model validation are presented for a single cocoa butter drop and for a cocoa butter spray.

Development and evaluation of a micro-macro algorithm for the simulation of polymer flow

A micro-macro algorithm for the calculation of polymer flow is developed and numerically evaluated. The system being solved consists of the momentum and mass conservation equations from continuum mechanics coupled with a microscopic-based rheological model for polymer stress. Standard finite element techniques are used to solve the conservation equations for velocity and pressure, while stochastic simulation techniques are used to compute polymer stress from the simulated polymer dynamics in the rheological model. The rheological model considered combines aspects of reptation, network and continuum models. Two types of spatial approximation are considered for the configuration fields defining the dynamics in the model: piecewise constant and piecewise linear. The micro-macro algorithm is evaluated by simulating the abrupt planar die entry flow of a polyisobutylene solution described in the literature. The computed velocity and stress fields are found to be essentially independent of mesh size and ensemble size, while there is some dependence of the results on the order of spatial approximation to the configuration fields close to the die entry. Comparison with experimental data shows that the piecewise linear approximation leads to better predictions of the centerline first normal stress difference. Finally, the computational time associated with the piecewise constant spatial approximation is found to be about 2.5 times lower than that associated with the piecewise linear approximation. This is the result of the more efficient time integration scheme that is possible with the former type of approximation due to the pointwise incompressibility guaranteed by the choice of velocity-pressure finite element.

Numerical simulations of the breakup of emulsion droplets inside a spraying nozzle

Numerical simulations are used to investigate the breakup of emulsion drops within a spraying nozzle. The simulations are performed by solving a two-phase flow problem in the nozzle in which individual drops are tracked through the flow field. A modified version of an OpenFOAM® solver is used as a basis for the simulations. The numerical algorithm employs the finite volume method for solving the mass and momentum conservation equations and a volume-of-fluid approach for capturing the fluid-fluid interface. Dynamic meshing is used to maintain a sufficiently refined mesh around a drop as it moves through the flow field. The dispersed phase is Newtonian, while a Newtonian and a shear-thinning non-Newtonian continuous phase are used. The simulations show two types of breakup behavior. Larger drops break up via tipstreaming in which small drops are detached from the tail of the mother drop, while smaller drops break up via filament fracturing in which the daughter drops were formed via pinching at several loca...

Continuum-Based Methods for Sprays

In this chapter, the mathematical description of spray processes is presented. After a brief summary of the basic mathematical concepts used, a discussion of the conservation equations is given, followed by a brief introduction to turbulence. Subsequently, a discussion of turbulence modeling is presented including Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) modeling. Once this basic background is established, the discussion of the averaged or filtered conservation equations in conjunction with the liquid phase equations is given. The chapter ends with a discussion of the discretization of the equation system and the main algorithms used for the numerical solutions.

Modeling and Validation of a Three‐Stage Solidification Model for Sprays

A three‐stage freezing model and its validation are presented. In the first stage, the cooling of the droplet down to the freezing temperature is described as a convective heat transfer process in turbulent flow. In the second stage, when the droplet has reached the freezing temperature, the solidification process is initiated via nucleation and crystal growth. The latent heat release is related to the amount of heat convected away from the droplet and the rate of solidification is expressed with a freezing progress variable. After completion of the solidification process, in stage three, the cooling of the solidified droplet (particle) is described again by a convective heat transfer process until the particle approaches the temperature of the gaseous environment. The model has been validated by experimental data of a single cocoa butter droplet suspended in air. The subsequent spray validations have been performed with data obtained from a cocoa butter melt in an experimental spray tower using the open‐...