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Research Papers: Flows in Complex Systems

Supersonic Liquid Jets Into Quiescent Gaseous Media: An Adaptive Numerical Study

[+] Author and Article Information
Sahand Majidi

School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439957131, Iran
e-mail: majidisahand@ut.ac.ir

Asghar Afshari

Mem. ASME
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439957131, Iran
e-mail: afsharia@ut.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 9, 2015; final manuscript received September 9, 2015; published online October 26, 2015. Assoc. Editor: Francine Battaglia.

J. Fluids Eng 138(1), 011103 (Oct 26, 2015) (15 pages) Paper No: FE-15-1252; doi: 10.1115/1.4031612 History: Received April 09, 2015; Revised September 09, 2015

A computational tool is introduced and applied to the emergence of supersonic liquid jets in quiescent compressible gas. A diffuse interface wave propagation method along with an interface sharpening technique is employed to solve the governing equations of compressible multiphase flows. Adaptive mesh refinement (AMR) strategy is utilized to improve the ability of the solver in better resolving the flow features. The accuracy of our method is benchmarked with four experimental and numerical test problems. Then, the evolution of supersonic liquid jets in compressible gaseous media is simulated; demonstrating a good agreement with experimental observations. Moreover, the impact of physical parameters, such as increment in ambient pressure and inlet velocity on the flow characteristics, is examined. The results indicate that the penetration length of the liquid jet decreases with an increase in the ambient pressure. The values of this parameter compare reasonably well with the experiment-based correlations. Further, with lower ambient pressure the Mach cone generated ahead of the liquid jet has a narrower half angle, situated closer to the jet tip. A similar behavior is demonstrated by the induced shock-front when the inlet Mach number of the liquid jet is increased. The simulations indicate the applicability of our numerical methodology to supersonic liquid jet flows for the analysis of shock waves dynamics and shock–interface interaction.

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Figures

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Fig. 1

One-dimensional air–helium shock-tube problem at t = 0.15: (a) density distribution, (b) pressure distribution, (c) velocity distribution, and (d) volume fraction distribution

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Fig. 2

One-dimensional gas–water shock–interface interaction problem at t = 0.00024: (a) density distribution, (b) pressure distribution, and (c) velocity distribution

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Fig. 3

A schematic of the computational domain for shock–bubble interaction test case

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Fig. 4

Wave propagation and flow structure in shock–bubble interaction case. Left column represents numerical schlieren images and right column shows experimental shadowgraphs of Haas and Sturtevant [68]: (a) 32 μs, (b) 62 μs, (c) 82 μs, and (d) 427 μs.

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Fig. 5

Grid refinement tests for shock–bubble interaction case performed using the same base grid resolution: (a) without refinement, (b) with one mesh refinement level, and (c) with two mesh refinement levels

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Fig. 6

Schematic of the computational domain for cavity collapse problem

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Fig. 7

Bubble collapse problem. Left column represents present numerical images while right column shows numerical results of Nourgaliev et al. [54]. In the upper part of the images, contours of Mach number are displayed while pressure contours are shown in the lower part. Solid lines indicate the phase interface: (a) 1.6 μs, (b) 2.2 μs, (c) 3.1 μs, (d) 3.8 μs, and (e) 4.2 μs.

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Fig. 8

Air cavity collapse in gelatine from the experimental study of Bourne and Field [70]

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Fig. 9

Volume fraction distribution in grid refinement tests for bubble collapse problem: (a) without refinement, (b) with one mesh refinement level, and (c) with two mesh refinement levels

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Fig. 10

Mass conservation history for cavity collapse in water

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Fig. 11

Volume fraction distribution compared for two simulations of cavity collapse problem using AMR technique with two levels of mesh refinement

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Fig. 12

Comparison of result obtained using GFM [73] and present algorithm: (a) distribution of pressure contours in the entire computational domain and (b) volume fraction distribution in the zoomed area encompassing the bubble

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Fig. 13

Schematic representation of the computational domain used in the simulation of supersonic liquid jet flow

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Fig. 14

Schlieren image (upper part) and density distribution (lower part) of the emergence of the supersonic liquid jets. On the upper part of the images, numerical schlieren images and interface (solid line) are shown. Density distributions are shown in the lower part: (a) 8 μs, (b) 16 μs, and (c) 24 μs.

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Fig. 15

Schlieren image (upper part) and mesh level distribution (lower part) of the emergence of the supersonic liquid jets

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Fig. 16

Interface deformations for two different levels of mesh refinements

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Fig. 17

Penetration lengths obtained from simulations with different refinement levels

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Fig. 21

Numerical schlieren images of two supersonic liquid jets at the same penetration lengths but with different inlet velocities. The upper and lower jets have inlet Mach numbers of 4.4 and 2.2, respectively. The solid line represents the phase interface and dashed line indicates axis of symmetry.

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Fig. 20

Penetration length of supersonic liquid jets with different density ratios

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Fig. 22

Ambient pressure and volume fraction distribution along the centerline for two supersonic jets at the same penetration length with different inlet Mach numbers

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Fig. 18

Velocity vector field and density distribution of the gaseous phase. Liquid phase is eliminated for clarity. The white oblique line indicates the separation line in the flow field.

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Fig. 19

Numerical schlieren images of supersonic liquid jets with different density ratios at 30 μs and inlet Mach number equal to 2.2: (a) density ratio = 100, (b) density ratio = 30, and (c) density ratio = 10

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