David P. Schmidt

Modeling high-speed viscous liquid sheet atomization

Abstract A linear stability analysis is presented for a liquid sheet that includes the effects of the surrounding gas, surface tension and the liquid viscosity on the wave growth process. An inviscid dispersion relation is used to identify the transition from a long wavelength regime to a short wavelength regime, analogous to the first and second wind induced breakup regimes of cylindrical liquid jets. This transition, which is found to occur at a gas Weber number of 27/16, is used to simplify the viscous dispersion relation for use in multi-dimensional simulations of sheet breakup. The resulting dispersion relation is used to predict the maximum unstable growth rate and wave length, the sheet breakup length and the resulting drop size for pressure-swirl atomizers. The predicted drop size is used as a boundary condition in a multi-dimensional spray model. The results show that the model is able to accurately predict liquid spray penetration, local Sauter mean diameter and overall spray shape.

The internal flow of diesel fuel injector nozzles: A review

Abstract Diesel fuel injector nozzles have a significant effect on the quality of spray and charge preparation. However, the mechanism and degree of this effect is unclear. The complexity of the internal nozzle flow has hindered the study of the fuel injection process. Diesel fuel injector nozzle flows are highly turbulent and usually two-phase. Several experiments have shown the presence of cavitation in the nozzles to be a dominating effect. Recent experimental work has revealed new qualitative details about the cavitation in fuel injector nozzles. The cavity tends to be smooth near the inlet, transitioning to a more ruffled appearance downstream. These flows are also strongly asymmetric in realistic geometries. Additionally, photographs have shown string cavitation inside the sac volume extending into the nozzles. The strings appear to be a form of stratified two-phase flow, like the cavities near the inlet corner. Like the cavities, the strings break down into bubbly flow near the exit of the nozzle. Future experiments in this field should address the exact nature of the two-phase flow at the exit. In spite of these difficulties, useful models for the flow in fuel injector nozzles have been developed. Analytical models work very well for the steady state behaviour of axisymmetric nozzles. Multi-dimensional models have proved to be useful for more general geometries and attempt to predict transient behaviour. There is currently no consensus on the basic physics behind the multi-dimensional models. Despite this controversy, there are several models available that have succeeded in predicting gross cavitation behaviour. The implications of the recent experimental investigations are that future cavitation models should include the ability to simulate more than one kind of cavitation. Typically, a model assumes that the cavitation is either a smooth cavity or a bubbly mixture. In general, the ideal cavitation model must capture either kind of behaviour.

Aerosol generation by reactive boiling ejection of molten cellulose

The generation of primary aerosols from biomass hinders the production of biofuels by pyrolysis, intensifies the environmental impact of forest fires, and exacerbates the health implications associated with cigarette smoking. High speed photography is utilized to elucidate the ejection mechanism of aerosol particles from thermally decomposing cellulose at the timescale of milliseconds. Fluid modeling, based on first principles, and experimental measurement of the ejection phenomenon supports the proposed mechanism of interfacial gas bubble collapse forming a liquid jet which subsequently fragments to form ejected aerosol particles capable of transporting nonvolatile chemicals. Identification of the bubble-collapse/ejection mechanism of intermediate cellulose confirms the transportation of nonvolatile material to the gas phase and provides fundamental understanding for predicting the rate of aerosol generation.

Modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations

The three-dimensional, moving mesh interface tracking (MMIT) method coupled with local mesh adaptations by Quan and Schmidt [S.P. Quan, D.P. Schmidt, A moving mesh interface tracking method for 3D incompressible two-phase flows, J. Comput. Phys. 221 (2007) 761-780] demonstrated the capability to accurately simulate multiphase flows, to handle large deformation, and also to perform interface pinch-off for some specific cases. However, another challenge, i.e. how to handle interface merging (such as droplet coalescence) has not been addressed. In this paper, we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup. These two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region. After the conversion, the newly created interface is usually ragged, and a local projection method is employed to smooth the interface. Extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes. Simulations of droplet pair collisions including both head-on and off-center coalescences show that the mesh adaptations are capable of resolving very small length scales, and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows. The potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed.

Direct Numerical Study of a Liquid Droplet Impulsively Accelerated by Gaseous Flow

A liquid spherical droplet impulsively accelerated by a gaseous flow is simulated in order to investigate the drag force and the deformation. The dynamics of the droplet immersed in a gaseous flow are investigated by solving the incompressible Navier-Stokes equations using a finite volume staggered mesh method coupled with a moving mesh interface tracking scheme. The benefit of the current scheme is that the interface conditions are implemented directly on an explicitly located interface with zero thickness. The droplet shape changes as it is accelerated, and the deformation factor of the droplet is as small as 0.2, so mesh adaptation methods are employed to achieve good mesh quality and to capture the interface curvature. The total drag coefficients are found to be larger than typical steady-state drag coefficients of solid spheres at the same Reynolds numbers. This agrees with the observation of Temkin et al. [J. Fluid Mech. 96, 133 (1980)] that the unsteady drag of decelerating relative flows was alway...

Reducing Grid Dependency in Droplet Collision Modeling

Droplet collision models have been criticized for creating large mesh dependency in spray calculations. These numerical errors are very troublesome; they behave erratically and interfere with the predictive ability of physical models. The collision method used in KIVA can cause mesh dependent changes in average drop size of over 40 microns. In order to reduce mesh dependency a new method has been developed for calculating the incidence of collision. The solution is to create a special collision mesh that is optimized for accuracy. The mesh is created automatically during the spray calculation. Additionally, a different stochastic collision sampling technique is also used. The new method, called the NTC algorithm, was incorporated into KIVA and found to be much faster than older algorithms. Calculations with 60,000 parcels required only a few CPU minutes. With the new NTC method and collision mesh, the mesh dependence of the drop size is only nine microns. This remaining mesh dependency is found to be due to the drag calculations and is not the fault of the collision algorithm.

Second-Order Spatial Accuracy in Lagrangian–Eulerian Spray Calculations

ABSTRACT The current work establishes the order of accuracy of existing Lagrangian–Eulerian tracking methods and requirements for second-order spatial accuracy. A simple, unconditionally stable method can be used for basic velocity integration, and linear interpolation is required for gas-to-liquid coupling. A theoretical approach is presented for calculating spatial errors in liquid-to-gas coupling, which indicates that a simple “nearest-neighbor” approach is adequate for second-order accuracy. This result is contrary to past observations in the literature, but it is confirmed with convergence tests. Numerical test results include two-phase simulations with a Monte Carlo treatment of particle injection.

Numerical simulation of head-on droplet collision : Effect of viscosity on maximum deformation

Numerical simulation of head-on collision of two equal-size droplets is conducted to observe the effect of viscosity on the maximum deformation amplitude using a moving-mesh finite-volume method. Recent experimental results by Willis and Orme [Exp. Fluids 34, 28 (2003)] have shown that the maximum deformation amplitude depends on the viscosity coefficient, and thus the percentage of energy that is dissipated until the instant of maximum deformation increases with the increasing fluid viscosity. This observation contradicts previous results by Jiang, Umemura, and Law [J. Fluid Mech. 234, 171 (1992)]. The numerical results in this Letter show that the dissipated energy and the maximum deformation depend on the collision Reynolds number, which is consistent with Willis and Orme (2003). However, this dependence decreases with increasing Reynolds number, which suggests that the effect caused by viscosity on maximum deformation becomes insignificant at sufficiently high Reynolds number.

High-resolution large eddy simulations of cavitating gasoline–ethanol blends

Cavitation plays an important role in the formation of sprays in fuel injection systems. With the increasing use of gasoline–ethanol blends, there is a need to understand how changes in fluid properties due to the use of these fuels can alter cavitation behavior. Gasoline–ethanol blends are azeotropic mixtures whose properties are difficult to model. We have tabulated the thermodynamic properties of gasoline–ethanol blends using a method developed for flash-boiling simulations. The properties of neat gasoline and ethanol were obtained from National Institute of Standards and Technology REFPROP data, and blends from 0% to 85% ethanol by mass have been tabulated. We have undertaken high-resolution three-dimensional numerical simulations of cavitating flow in a 500-µm-diameter submerged nozzle using the in-house HRMFoam homogeneous relaxation model constructed from the OpenFOAM toolkit. The simulations are conducted at 1 MPa inlet pressure and atmospheric outlet pressure, corresponding to a cavitation number range of 1.066–1.084 and a Reynolds number range of 15,000–40,000. For the pure gasoline case, the numerical simulations are compared with synchrotron X-ray radiography measurements. Despite significant variation in the fluid properties, the distribution of cavitation vapor in the nozzle is relatively unaffected by the gasoline–ethanol ratio. The vapor remains attached to the nozzle wall, resulting in an unstable annular two-phase jet in the outlet. Including turbulence at the conditions studied does not significantly change mixing behavior, because the thermal nonequilibrium at the vapor–liquid interfaces acts to low-pass filter the turbulent fluctuations in both the nozzle boundary layer and jet mixing layer.

A numerical study of the relaxation and breakup of an elongated drop in a viscous liquid

The relaxation and breakup of an elongated droplet in a viscous and initially quiescent fluid is studied by solving the full Navier-Stokes equations using a three-dimensional finite volume method coupled with a moving mesh interface tracking (MMIT) scheme to locate the interface. The two fluids are assumed incompressible and immiscible. The interface is represented as a surface triangle mesh with zero thickness that moves with the fluid. Therefore, the jump and continuity conditions across the interface are implemented directly, without any smoothing of the fluid properties. Mesh adaptations on a tetrahedral mesh are employed to permit large deformation and to capture the changing curvature. Mesh separation is implemented to allow pinch-off. The detailed investigations of the relaxation and breakup process are presented in a more general flow regime compared to the previous works by Stone & Leal (J. Fluid Mech., vol. 198, 1989, p. 399) and Tong & Wang (Phys. Fluids, vol. 19, 2007, 092101), including the flow field of the both phases. The simulation results reveal that the vortex rings due to the interface motion and the conservation of mass play an important role in the relaxation and pinch-off process. The vortex rings are created and collapsed during the process. The effects of viscosity ratio, density ratio and length ratio on the relaxation and breakup are studied. The simulations indicate that the fluid velocity field and the neck shape are distinctly different for viscosity ratios larger and smaller than O(1), and thus a different end-pinching mechanism is observed for each regime. The length ratio also significantly affects the relaxation process and the velocity distributions, but not the neck shape. The influence of the density ratio on the relaxation and breakup process is minimal. However, the droplet evolution is retarded due to the large density of the suspending flow. The formation of a satellite droplet is observed, and the volume of the satellite droplet depends strongly on the length ratio and the viscosity ratio.