Enhancement of the Madabhushi Liquid Jet in Crossflow Breakup Model by a Ligament Breakup Mechanism
Markus Lambert  1, *@  , Thomas Esch  2@  , Markus Braun  1@  , Hossam Elasrag  3@  
1 : ANSYS Germany GmbH
Birkenweg 14a, 64295 Darmstadt -  Germany
2 : ANSYS Germany GmbH
Staudenfeldweg 20, 83624 Otterfing -  Germany
3 : Ansys, Inc.
5930 Cornerstone Ct W San Diego, CA 92121 -  United States
* : Corresponding author

The atomization of a liquid fuel jet in a gaseous crossflows has many practical applications, e.g., fuel injection in gas turbine engines; like lean direct injectors (LDI) and lean premixed prevaporized ducts (LPP), as well as fuel injection in augmentors, scramjet and ramjet combustors.
It can be characterized by three regions [2]. The liquid column region where droplets are shed from the liquid core by surface wave mechanism, the column breakup region where ligaments resulting from the primary breakup break into smaller ligaments and finally into large droplets and a spray region, where the droplets undergo further breakup due to external aerodynamic forces.
The Madabhushi breakup model [1] is suitable for numerical simulations of liquid jets in subsonic crossflow. In this framework, the effects of primary breakup in the liquid core are simulated by the Wave model, and the effects of ligament breakup after column breakup as well as the secondary breakup in the spray are simulated by a model suggested by Pilch and Erdman [3].
The original Madabhushi formulation has the tendency to overestimate the child droplet diameters after column breakup. A model extension is proposed that overcomes this limitation and allows for a more realistic size distribution after initial ligament breakup.

The model extension was compared to experimental data at different jet-to-air-momentum
ratios (J=10,20 We=1500) provided by Gopola et al. [4], Sekar et al. [5] and showed good agreement with measurement data.

[1] Madabhushi R. K., “A Model for Numerical Simulation of Breakup of a Liquid Jet
in Crossflow”, Atomization and Sprays, vol. 13, pp 413-424, 2003.
[2] Wu P. K., Kirkendall K. A. and Fuller R. P., “Breakup Processes of Liquid Jets
in Subsonic Crossflow”, J. Propulsion and Power, vol. 13, pp. 64-73, 1997
[3] Pilch M. and Erdman C. A., “Use of Breakup Time Data and Velocity History Data to Predict the Maximum Size of Stable Fragments for Acceleration-Induced Breakup of a Liquid Drop”, Int. J. Multiphase Flow, vol. 13, pp. 741–757, 1987.
[4] Gopala, Y., Zhang, P., Bibik, O., Lubarsky, E., Zinn, B.,T., 2010,
“Liquid Jet in Crossflow – Trajectory Correlations based on the Column Breakup Point”,
AIAA 2010-214, 48th AIAA Aerospace Sciences Meeting, Florida, USA
[5] Sekar J., Rao A., Pillutla S., Danis A. and Hsieh S.Y., “Liquid Jet in Cross Flow Modeling”, Proceedings of ASME Turbo Expo 2014: Turbine Technical Conference and Exposition,
June 16 – 20, 2014, Düsseldorf, Germany

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