Note: All transient jet data taken and the full code for the 1-D jet model are detailed in papers  and  and are available for download and use with citation at the link below.
The performance of internal combustion engines that use direct injection strategies is strongly dependent upon the fluid mechanics associated with the fuel injection process. While a significant amount of literature has been published on the behavior of free shear flows with quasi-steady flow rates, little documentation is available on the impact of transient rate of injection on jet characteristics and the subsequent combustion process in engines.
High-speed optical measurements of unsteady liquid fuel jets under a variety of engine conditions have been acquired in the optical engine laboratory at the Engine Research Center. These simultaneous measurements included shadowgraphy of fuel vapor, Mie scattering of liquid fuel, and OH* chemiluminescence for high temperature combustion.
A new adaptive edgefinding algorithm capable of dealing with non-constant backgrounds and illumination levels was developed using the Otsu  technique. When comparing the transient jet penetration results to 1-D estimations informed by quasi-steady scalings  and that allow for experimental ROI inputs but do not consider the jet breakup length [5,6], deviations are apparent.
However, if the initial jet penetration is estimated based on the ROI by assuming an inviscid liquid column of constant diameter (shown in yellow above), it matches the initial penetration well. Therefore, there is a period of time where a portion of the injected fuel retains its initial momentum and is relatively undisturbed by the ambient air: the distance over which this occurs is the “jet breakup length.”
The above GIFs show samples of the visible jet and chemiluminescence videos taken at each case. The liftoff length video is shown in its processed form, after the Otsu technique has been applied. The predictions of prevalent quasi-steady literature assumes early scaling with time of t1 and long-term scaling with time of t1/2. The three-zone scaling with time for these transient jets is shown below.
It is clear that although the power scaling of penetration with time decreases as the jet penetrates, the spread of values at each region is quite large. Also, the average initial scaling is greater than unity, the value predicted by the literature for quasi-steady jets. The fit quality also decreases closer to the injector tip. It is evident that in the early penetration times, a single quasi-steady relationship does not apply for transient jets, leading to the development of the 1-D model, explained here.
 Neal, N. and Rothamer, D., “Measurement and Characterization of Fully Transient Diesel Fuel Jet Processes in an Optical Engine with Production Injectors,” Experiments in Fluids, Vol. 57, No. 10, pp. 1-19, 2016.
 Neal, N. and Rothamer, D., “Evolving 1-D Transient Jet Modeling by Integrating Jet Breakup Physics,” International Journal of Engine Research, Vol. Submitted for publication, No., 2016.
 Gonzalez, R. Digital image processing. Prentice Hall, Upper Saddle River, N.J, 2008.
 Hiroyasu, H. and Arai, M., “Structures of Fuel Sprays in Diesel Engines,” SAE Technical Paper, 900475, 1990.
 Musculus, M.P.B. and Kattke, K., “Entrainment Waves in Diesel Jets,” SAE Technical Paper, Vol. 2009-01-1355, No., 2009.
 Pastor, J.V., Lopez, J.J., Garcia, J.M., and Pastor, J.M., “A 1D Model for the Description of Mixing-Controlled Inert Diesel Sprays,” Fuel, Vol. 87, No. 13-14, pp. 2871-2885, Oct 2008.