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Document Type

Open Access

Degree Program

Mechanical Engineering

Degree Type

Master of Science in Mechanical Engineering (M.S.M.E.)

Year Degree Awarded


Month Degree Awarded



Atomization of fuel is essential in controlling combustion inside a direct injection engine. Controlling combustion helps in reducing emissions and boosting efficiency. Cavitation is one of the factors that significantly affect the nature of spray in a combustion chamber. Typical fuel injector nozzles are small and operate at a very high pressure, which limit the study of internal nozzle behavior. The time and length scales further limit the experimental study of a fuel injector nozzle. Simulating cavitation in a fuel injector will help in understanding the phenomenon and will assist in further development.

The construction of any simulation of cavitating injector nozzles begins with the fundamental assumptions of which phenomena will be included and which will be neglected. To date, there has been no consensus about whether it is acceptable to assume that small, high-speed cavitating nozzles are in thermal or inertial equilibrium. This diversity of opinions leads to a variety of modeling approaches. If one assumes that the nozzle is in thermal equilibrium, then there is presumably no significant delay in bubble growth or collapse due to heat transfer. Heat transfer is infinitely fast and inertial effects limit phase change. The assumption of inertial equilibrium means that the two phases have negligible slip velocity. Alternatively, on the sub-grid scale level, one may also consider the possibility of small bubbles whose size responds to changes in pressure. Schmidt et al. developed a two dimensional transient homogeneous equilibrium model which was intended for simulating a small, high speed nozzle flows. The HEM uses the assumption of thermal equilibrium to simulate cavitation. It assumes the two-phase flow inside a nozzle in homogeneous mixture of vapor and liquid. This work presents the simulation of high-speed nozzle, using the HEM for cavitation, in a multidimensional and parallel framework. The model is extended to simulate the non-linear effects of the pure phase in the flow and the numerical approach is modified to achieve stable result in multidimensional framework.

Two-dimensional validations have been presented with simulation of a venturi nozzle, a sharp nozzle and a throttle from Winklhofer et al. Three-dimensional validations have been presented with simulation of ‘spray A’ and ‘spray H’ injectors from the Engine Combustion Network. The simulated results show that equilibrium assumptions are sufficient to predict the mass flow rate and cavitation incidence in small, high-speed nozzle flows.

First Advisor

David P. Schmidt

Second Advisor

Blair Perot