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Author ORCID Identifier



Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program

Mechanical Engineering

Year Degree Awarded


Month Degree Awarded


First Advisor

David P. Schmidt

Second Advisor

Blair Perot

Third Advisor

Michael Henson

Subject Categories

Computational Engineering | Computer-Aided Engineering and Design | Other Mechanical Engineering


The improvement of combustion systems which use sprays to atomize liquid fuel requires an understanding of that atomization process. Although the secondary break up mechanisms for the far-field of an atomizing spray have been thoroughly studied and well understood for some time, understanding the internal nozzle flow and primary atomization on which the far-field spray depends has proven to be more of a challenge. Flow through fuel injector nozzles can be highly complex and heavily influenced by factors such as turbulence, needle motion, nozzle imperfections, nozzle asymmetry, and phase change. All of this occurs within metallic injectors, making experimental characterization challenging.

A review of computational studies in literature shows a trend towards engineering models based on the Eulerian description of the fluid, rather than the Lagrangian. With this approach, the internal and external flow can be simulated together. This allows for the influence of nozzle geometry on the spray to be captured.

Developments and advancements applicable to these Eulerian solvers are discussed. This includes a new constraint on the turbulent mixing model, as well as the inclusion of a vaporization model and a non-equilibrium phase change model. Additionally, issues regarding thermodynamic and hydrodynamic consistency of compressible flows using a segregated solution approach are addressed, as are issues regarding dynamic mesh motion in a compressible solver. Finally, an efficient way of accounting for high pressure thermodynamic properties is presented.

Applied case studies of diesel direct injection are then described. The single-field Eulerian approach is shown to perform very well at the high Reynolds and Weber numbers present in diesel DI conditions, capturing spray characteristics such as density distribution, penetration, and velocity profiles with a moderate level of accuracy. While transient needle motion is shown to cause interesting internal flow features, in converging, axisymmetric diesel DI nozzles, modeling of the internal flow is shown to only marginally benefit the solution.

Finally, applied case studies of gasoline direct injection are presented, first with a parameter study varying counterbore depth, pressure drop, and the ambient to saturated pressure ratio. The significant influence of flash-boiling under a low ambient to saturated pressure ratio is shown. Next, a detailed analysis of internal nozzle and near-field flow in flashing and non-flashing multi-hole injection is presented. Excellent agreement to experimental rate of injection is achieved with transient needle motion and qualitative agreement to experimental imaging in the near-field is shown. Complex internal nozzle flow is analyzed and shown to result in string flash-boiling, perturbations and expansions of the spray angle, and oscillation in the ROI.

Single-field multiphase Eulerian modeling is a useful tool for understanding and designing DI atomizers. The next generation of spray models will rely heavily on this approach to better understand and predict the influence of internal and near-field flow on the combustion system.