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Laminar Plunging Jets - Interfacial Rupture and Inception of Entrainment

Kishore, Aravind
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1397476562

Abstract Details

2014, PhD, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
Interfacial rupture and entrainment are commonly observed, e.g., air bubbles within a container being filled with water from a faucet. The example involves a liquid jet (density, &#961, and viscosity, &#951) plunging into a receiving pool of liquid. Below a critical liquid-jet velocity, the interface develops a cusp-like shape within the receiving pool. The cusp becomes sharper with increasing liquid-jet velocity, and at a critical velocity (V<SUB>c</SUB>), the interface between the liquid and the surrounding fluid (density, &#961<SUB>0</SUB>, and viscosity, &#951<SUB>0</SUB>) ruptures. Interfacial tension (&#963) can no longer preserve the integrity of the interface between the two immiscible fluids, and the plunging jet drags/entrains surrounding fluid into the receiving pool. Subsequently, the entrained fluid breaks up into bubbles within the receiving pool. The focus of this dissertation is the numerical prediction of the critical entrainment inception velocities for laminar plunging jets using the Volume-Of-Fluid (VOF) method, a Computational Fluid Dynamics (CFD) method to simulate multi-fluid flows. Canonical to bottle-filling operations in the industry is the plunging-jet configuration - the liquid jet issues from a nozzle and plunges into a container filled with liquid. Simulations of this configuration require capturing flow phenomena over a large range of length scales (4 orders of magnitude). Results show severe under-prediction of critical entrainment velocities when the maximum resolution is insufficient to capture the sharpening, and eventual rupture, of the interfacial cusp. Higher resolutions resulted in computational meshes with prohibitively large number of cells, and a drastic reduction in time-step values. Experimental results in the literature suggest at least a 100-fold increase in the smallest length scale when the entrained fluid is a liquid instead of air. This narrows the range of length scales in the problem. We exploit the experimental correlation between critical capillary number, Ca<SUB>c</SUB> = &#951 V<SUB>c</SUB>/&#963 and viscosity ratio, &#951<SUB>0</SUB>/&#951 in postulating an alternate approach involving scaling of the pertinent physics by using liquids as entrained fluids. The scaling approach is tested using a rotating cylinder placed at the interface between two fluids. A mesh-independence study using successively finer meshes predicted critical entrainment velocity values within about 1% of each other. Numerical predictions compared well with experimental data, with less than 1% difference in the case where exact experimental data was available, and a maximum of 6% difference for cases where experimental data was extrapolated to make the comparison. These results lend credibility to our approach. The effect of densities of the two fluids manifests as buoyancy force at the interfacial cusp. Remarkably, contrary to a priori notions, our simulation results showed that as &#916&#961 increased, the effect of buoyancy decreased relative to other forces at the interfacial cusp. Finally, we proposed an empirical correlation between Ca<SUB>c</SUB> and &#951<SUB>0</SUB>/&#951 which allows extrapolation of critical entrainment conditions between the rotating-cylinder configuration (with liquids being entrained) to the plunging-jet configuration (with air being entrained). The primary contribution of this research is the physics-based scaling approach utilized to overcome the simulation challenges posed by the physics of interface rupture and entrainment.
Urmila Ghia, Ph.D. (Committee Chair)
Thomas Baer, Ph.D. (Committee Member)
Jerry Feng, Ph.D. (Committee Member)
Shaaban Abdallah, Ph.D. (Committee Member)
Kirti Ghia, Ph.D. (Committee Member)
Milind Jog, Ph.D. (Committee Member)
Kumar Vemaganti, Ph.D. (Committee Member)
119 p.
Mechanics
bottle filling; interface rupture; entrainment; scaling; plunging jet; VOF

Recommended Citations

Citations

  • Kishore, A. (2014). Laminar Plunging Jets - Interfacial Rupture and Inception of Entrainment [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1397476562

    APA Style (7th edition)

  • Kishore, Aravind. Laminar Plunging Jets - Interfacial Rupture and Inception of Entrainment. 2014. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1397476562.

    MLA Style (8th edition)

  • Kishore, Aravind. "Laminar Plunging Jets - Interfacial Rupture and Inception of Entrainment." Doctoral dissertation, University of Cincinnati, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1397476562

    Chicago Manual of Style (17th edition)

ucin1397476562
617
© 2014, some rights reserved.Creative Commons License Laminar Plunging Jets - Interfacial Rupture and Inception of Entrainment by Aravind Kishore is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.