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The topology of gas jets injected beneath a surface and subject to liquid cross-flow

  • Simo A. Mäkiharju (a1), In-Ho R. Lee (a2), Grzegorz P. Filip (a2), Kevin J. Maki (a2) and Steven L. Ceccio (a2)...

Abstract

Gas injection into a liquid cross-flow is examined for the case where the gas is injected beneath a horizontal flat surface. For moderate Froude numbers, the gas pocket that is formed will rise toward the flow boundary under the action of buoyancy, a condition that is conducive to the formation of gas layers for friction-drag reduction on the surface. At the location of gas injection, a plume whose geometry is related to the mass and momentum flux of the injected gas and liquid cross-flow is formed, and the influence of buoyancy is minimal. However, as the gas pocket convects downstream, buoyancy brings the gas back upward to the flow boundary, and leads to the bifurcation of the pocket into two distinct branches, forming a stable ‘V’-shape. Under some conditions, the flow between the two gas branches is almost entirely liquid, while for others there exists a bubbly flow or a continuous sheet of gas between the branches. The sweep angle and cross-sectional geometry of the gas branches are related to free-stream speed and boundary-layer thickness of the liquid cross-flow, the mass-injection rate of the gas, the diameter of the injection orifice and the gas outlet mean velocity and gas–jet angle. Data for a range of experimental conditions are used to scale the flow and results are compared to numerical computations of the flow, and these data are used to illustrate the underlying flow processes responsible leading to the formation the stable and straight gas branches. A simple model based on the balance of forces around a stable gas branch is presented and used to scale the observed data, and we use the results of this analysis and the computations to discuss how the process of gas injection may interact with the formation of the stable gas pockets farther downstream.

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Corresponding author

Email address for correspondence: makiharju@berkeley.edu

References

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Abdelwahed, M. S. & Chu, V. H. 1978 Bifurcation of buoyant jets in a crossflow. In Verification of Mathematical and Physical Models in Hydraulic Engineering, pp. 819826. American Society of Civil Engineers.
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335354.
Brandner, P. A., Pearce, B. W. & de Graaf, K. L. 2015 Cavitation about a jet in crossflow. J. Fluid Mech. 768, 141174.
Ceccio, S. L. 2010 Friction drag reduction of external flows with bubble and gas injection. Annu. Rev. Fluid Mech. 42, 183203.
Choi, K. W., Lai, C. C. & Lee, J. H. 2015 Mixing in the intermediate field of dense jets in cross currents. J. Hydraul. Engng 142 (1), 04015041.
Elbing, B., Mäkiharju, S. A., Wiggins, A., Perlin, M., Dowling, D. & Ceccio, S. L. 2013 On the scaling of air layer drag reduction. J. Fluid Mech. 717, 484513.
Elbing, B. R., Winkel, E. S., Lay, K. A., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2008 Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction. J. Fluid Mech. 612, 201236.
Franc, J.-P. & Michel, J.-M. 2004 Fundamentals of Cavitation. Kluwer Academic.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201225.
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Proceedings of the Summer Program, pp. 193208. Center for Turbulence Research.
Insel, M., Gokcay, S. & Helvacioglu, I. H.2010 Flow analysis of an air injection through discrete air lubrication. In International Conference on Ship Drag Reduction 2010, Paper no. 13.
Lee, I.-H. R.2015 Scaling of gas diffusion into limited partial cavity and interaction of vertical jet with cross-flow beneath horizontal surface. PhD thesis, University of Michigan.
Mahesh, K. 2013 The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45, 379407.
Mäkiharju, S. A., Perlin, M. & Ceccio, S. L. 2012 On the energy economics of air lubrication drag reduction. Intl J. Naval Arch. Ocean Engng 4 (4), 412422.
Pignoux, S.1998 Structure interne d’un jet de gaz injecté perpendiculairement à une couche limite turbulente verticale d’eau. PhD thesis, University of Poitiers, France.
Reynolds, W. C., Parekh, D. E., Juvet, P. J. D. & Lee, M. J. D. 2003 Bifurcating and blooming jets. Annu. Rev. Fluid Mech. 35 (1), 295315.
Sanders, W. C., Winkel, E., Dowling, D. R., Perlin, M. & Ceccio, S. L. 2006 Bubble friction drag reduction in a high Reynolds number flat plate turbulent boundary layer. J. Fluid Mech. 552, 353380.
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31, 567603.
Towns, J., Cockerill, T., Dahan, M., Foster, I., Gaither, K., Grimshaw, A., Hazelwood, V., Lathrop, S., Lifka, D., Peterson., G. D. et al. 2014 XSEDE: accelerating scientific discovery. Comput. Sci. Engng 16, 6274.
Vigneau, O., Pignoux, S., Carreau, J.-L. & Roger, F. 2001a Influence of the wall boundary layer thickness on a gas jet injected into a liquid crossflow. Exp. Fluids 30, 458466.
Vigneau, O., Pignoux, S., Carreau, J.-L. & Roger, F. 2001b Interaction of multiple gas jets horizontally injected into a vertical water stream. Flow Turbul. Combust. 66, 183208.
Wace, P. F., Morrell, M. S. & Woodrow, J. 1987 Bubble formation in transverse liquid flow. Chem. Engng Commun. 62 (1–6), 93106.
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