1
|
Pandey V. Asymmetricity and sign reversal of secondary Bjerknes force from strong nonlinear coupling in cavitation bubble pairs. Phys Rev E 2019; 99:042209. [PMID: 31108625 DOI: 10.1103/physreve.99.042209] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/10/2018] [Indexed: 06/09/2023]
Abstract
Most of the current applications of acoustic cavitation use bubble clusters that exhibit multibubble dynamics. This necessitates a complete understanding of the mutual nonlinear coupling between individual bubbles. In this study, strong nonlinear coupling is investigated in bubble pairs which is the simplest case of a bubble-cluster. This leads to the derivation of a more comprehensive set of coupled Keller-Miksis equations (KMEs) that contain nonlinear coupling terms of higher order. The governing KMEs take into account the convective contribution that stems from the Navier-Stokes equation. The system of KMEs is numerically solved for acoustically excited bubble pairs. It is shown that the higher-order corrections are important in the estimation of secondary Bjerknes force for closely spaced bubbles. Further, asymmetricity is witnessed in both magnitude and sign reversal of the secondary Bjerknes force in weak, regular, and strong acoustic fields. The obtained results are examined in the light of published scientific literature. It is expected that the findings reported in this paper may have implications in industries where there is a requirement to have a control on cavitation and its effects.
Collapse
Affiliation(s)
- Vikash Pandey
- Centre for Ecological and Evolutionary Synthesis (CEES), Department of Biosciences, University of Oslo, P.O. Box 1066, NO-0316, Oslo, Norway† and Research Centre for Arctic Petroleum Exploration (ARCEx), Department of Geosciences, UiT The Arctic University of Norway in Tromsø, P.O. Box 6050, N-9037, Tromsø, Norway
| |
Collapse
|
2
|
Zhou ZR, Zhang YS, Tian BL. Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations. Phys Rev E 2018; 97:033108. [PMID: 29776047 DOI: 10.1103/physreve.97.033108] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2017] [Indexed: 06/08/2023]
Abstract
Implicit large eddy simulations of two-dimensional Rayleigh-Taylor instability at different density ratios (i.e., Atwood number A=0.05, 0.5, and 0.9) are conducted to investigate the late-time dynamics of bubbles. To produce a flow field full of bounded, semibounded, and chaotic bubbles, three problems with distinct perturbations are simulated: (I) periodic sinusoidal perturbation, (II) isolated W-shaped perturbation, and (III) random short-wave perturbations. The evolution of height h, velocity v, and diameter D of the (dominant) bubble with time t are formulated and analyzed. In problem I, during the quasisteady stage, the simulations confirm Goncharov's prediction of the terminal speed v_{∞}=Frsqrt[Agλ/(1+A)], where Fr=1/sqrt[3π]. Moreover, the diameter D at this stage is found to be proportional to the initial perturbation wavelength λ as D≈λ. This differed from Daly's simulation result of D=λ(1+A)/2. In problem II, a W-shaped perturbation is designed to produce a bubble environment similar to that of chaotic bubbles in problem III. We obtain a similar terminal speed relationship as above, but Fr is replaced by Fr_{w}≈0.63. In problem III, the simulations show that h grows quadratically with the bubble acceleration constant α≡h/(Agt^{2})≈0.05, and D expands self-similarly with a steady aspect ratio β≡D/h≈(1+A)/2, which differs from existing theories. Therefore, following the mechanism of self-similar growth, we derive a relationship of β=4α(1+A)/Fr_{w}^{2} to relate the evolution of chaotic bubbles in problem III to that of semibounded bubbles in problem II. The validity of this relationship highlights the fact that the dynamics of chaotic bubbles in problem III are similar to the semibounded isolated bubbles in problem II, but not to that of bounded periodic bubbles in problem I.
Collapse
Affiliation(s)
- Zhi-Rui Zhou
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
| | - You-Sheng Zhang
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
- Center for Applied Physics and Technology, Peking University, Beijing 100871, China
| | - Bao-Lin Tian
- Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
- Center for Applied Physics and Technology, Peking University, Beijing 100871, China
| |
Collapse
|
3
|
Sohn SI. Bubble interaction model for hydrodynamic unstable mixing. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:066312. [PMID: 17677362 DOI: 10.1103/physreve.75.066312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2007] [Revised: 05/30/2007] [Indexed: 05/16/2023]
Abstract
The analytic model for the evolution of single and multiple bubbles in Rayleigh-Taylor mixing is presented for the system of arbitrary density ratio. The model is the extension of Zufiria's potential theory, which is based on the velocity potential with point sources. We present solutions for a single bubble, at various stages, from the model and show that the solutions for the bubble velocity and curvature are in good agreement with numerical results. We demonstrate the evolution of multiple bubbles for finite density contrast and investigate dynamics of bubble competition, whereby leading bubbles grow in size at the expense of neighbors. The model shows that the growth coefficient alpha for the scaling law of the bubble front depends on the Atwood number and increases logarithmically with the initial perturbation amplitude. It is also found that the aspect ratio of the bubble size to the bubble height exhibits a self-similar behavior in the bubble competition process, and its values are insensitive to the Atwood number. The predictions of the model for the similarity parameters are in accordance with experimental and numerical results.
Collapse
Affiliation(s)
- Sung-Ik Sohn
- Department of Mathematics, Kangnung National University, Kangnung 210-702, Korea.
| |
Collapse
|
4
|
Ramaprabhu P, Dimonte G, Young YN, Calder AC, Fryxell B. Limits of the potential flow approach to the single-mode Rayleigh-Taylor problem. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:066308. [PMID: 17280149 DOI: 10.1103/physreve.74.066308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2006] [Revised: 08/09/2006] [Indexed: 05/13/2023]
Abstract
We report on the behavior of a single-wavelength Rayleigh-Taylor flow at late times. The calculations were performed in a long square duct (lambda x lambda x 8lambda), using four different numerical simulations. In contradiction with potential flow theories that predict a constant terminal velocity, the single-wavelength Rayleigh-Taylor problem exhibits late-time acceleration. The onset of acceleration occurs as the bubble penetration depth exceeds the diameter of bubbles, and is observed for low and moderate density differences. Based on our simulations, we provide a phenomenological description of the observed acceleration, and ascribe this behavior to the formation of Kelvin-Helmholtz vortices on the bubble-spike interface that diminish the friction drag, while the associated induced flow propels the bubbles forward. For large density ratios, the formation of secondary instabilities is suppressed, and the bubbles remain terminal consistent with potential flow models.
Collapse
Affiliation(s)
- P Ramaprabhu
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | | | | | | | | |
Collapse
|
5
|
Liu X, George E, Bo W, Glimm J. Turbulent mixing with physical mass diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:056301. [PMID: 16803031 DOI: 10.1103/physreve.73.056301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/04/2006] [Indexed: 05/10/2023]
Abstract
Simulated mixing rates of the Rayleigh-Taylor instability for miscible fluids with physical mass diffusion are shown to agree with experiment; for immiscible fluids with physical values of surface tension the numerical data lie in the center of the range of experimental values. The simulations are based on an improved front tracking algorithm to control numerical surface tension and on improved physical modeling to allow physical values of mass diffusion or surface tension. Compressibility, after correction for variable density effects, has also been shown to have a strong influence on mixing rates. In summary, we find significant dependence of the mixing rates on scale breaking phenomena. We introduce tools to analyze the bubble merger process and confirm that bubble interactions, as in a bubble merger model, drive the mixing growth rate.
Collapse
Affiliation(s)
- Xinfeng Liu
- Department of Applied Mathematics and Statistics, Stony Brook University, New York 11794-3600, USA
| | | | | | | |
Collapse
|
6
|
George E, Glimm J, Li X, Li Y, Liu X. Influence of scale-breaking phenomena on turbulent mixing rates. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:016304. [PMID: 16486274 DOI: 10.1103/physreve.73.016304] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2005] [Indexed: 05/06/2023]
Abstract
Simulations not seen before compare turbulent mixing rates for ideal fluids and for real immiscible fluids with experimental values for the surface tension. The simulated real fluid mixing rates lie near the center of the range of experimental values. A comparison to theoretical predictions relating the mixing rate, the bubble width, and the bubble height fluctuations based on bubble merger models shows good agreement with experiment. The ideal fluid mixing rate is some 50% larger, providing an example of the sensitivity of the mixing rate to physical scale breaking interfacial phenomena; we also observe this sensitivity to numerical scale-breaking artifacts.
Collapse
Affiliation(s)
- Erwin George
- Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, New York 11794-3600, USA.
| | | | | | | | | |
Collapse
|
7
|
Dimonte G. Dependence of turbulent Rayleigh-Taylor instability on initial perturbations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056305. [PMID: 15244930 DOI: 10.1103/physreve.69.056305] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2003] [Revised: 12/02/2003] [Indexed: 05/24/2023]
Abstract
The dependency of the self-similar Rayleigh-Taylor bubble acceleration constant alpha(b)(identical with [(amplitude)/2] x (displacement) x (Atwood number)) on the initial perturbation amplitude h(0k) is described with a model in which the exponential growth of a small amplitude packet of modes makes a continuous nonlinear transition to its "terminal" bubble velocity proportional, variant Fr[equal to(Froude number)(1/2)]. Then, by applying self-similarity (diameter proportional, variant amplitude), alpha(b) is found to increase proportional to Fr and logarithmically with h(0k). The model has two free parameters that are determined from experiments and simulations. The augmentation of long wavelength perturbations by mode coupling is also evaluated. This is found to decrease the sensitivity of alpha(b) on the initial perturbations when they are smaller than the saturation amplitude of the most unstable modes. These results show that alpha(b) can vary by a factor of 2-3 with initial conditions in reasonable agreement with experiments and simulations.
Collapse
Affiliation(s)
- Guy Dimonte
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
8
|
Sohn SI. Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:036703. [PMID: 15089438 DOI: 10.1103/physreve.69.036703] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2003] [Indexed: 05/24/2023]
Abstract
The vortex method is applied to simulations of Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. The numerical results from the vortex method agree well with analytic solutions and other numerical results. The bubble velocity in the RT instability converges to a constant limit, and in the RM instability, the bubble and spike have decaying growth rates, except for the spike of infinite density ratio. For both RT and RM instabilities, bubbles attain constant asymptotic curvatures. It is found that, for the same density ratio, the RT bubble has slightly larger asymptotic curvature than the RM bubble. The vortex sheet strength of the RM interface has different behavior than that of the RT interface. We also examine the validity of theoretical models by comparing the numerical results with theoretical predictions.
Collapse
Affiliation(s)
- Sung-Ik Sohn
- School of Information Engineering, Tongmyong University of Information Technology, Pusan 608-711, Republic of Korea.
| |
Collapse
|
9
|
Shin S, Juric D, Abdel-Khalik S. Hydrodynamic stability of the porous wetted wall protection schemes in IFE reactors. FUSION ENGINEERING AND DESIGN 2003. [DOI: 10.1016/s0920-3796(03)00050-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
10
|
Cheng B, Glimm J, Sharp DH. A three-dimensional renormalization group bubble merger model for Rayleigh-Taylor mixing. CHAOS (WOODBURY, N.Y.) 2002; 12:267-274. [PMID: 12779554 DOI: 10.1063/1.1460942] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
In this paper we formulate a model for the merger of bubbles at the edge of an unstable acceleration driven (Rayleigh-Taylor) mixing layer. Steady acceleration defines a self-similar mixing process, with a time-dependent inverse cascade of structures of increasing size. The time evolution is itself a renormalization group (RNG) evolution, and so the large time asymptotics define a RNG fixed point. We solve the model introduced here at this fixed point. The model predicts the growth rate of a Rayleigh-Taylor chaotic fluid mixing layer. The model has three main components: the velocity of a single bubble in this unstable flow regime, an envelope velocity, which describes collective excitations in the mixing region, and a merger process, which drives an inverse cascade, with a steady increase of bubble size. The present model differs from an earlier two-dimensional (2-D) merger model in several important ways. Beyond the extension of the model to three dimensions, the present model contains one phenomenological parameter, the variance of the bubble radii at fixed time. The model also predicts several experimental numbers: the bubble mixing rate, alpha(b)=h(b)/Agt(2) approximately 0.05-0.06, the mean bubble radius, and the bubble height separation at the time of merger. From these we also obtain the bubble height to the radius aspect ratio. Using the experimental results of Smeeton and Youngs (AWE Report No. O 35/87, 1987) to fix a value for the radius variance, we determine alpha(b) within the range of experimental uncertainty. We also obtain the experimental values for the bubble height to width aspect ratio in agreement with experimental values. (c) 2002 American Institute of Physics.
Collapse
Affiliation(s)
- Baolian Cheng
- Applied Physics Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
| | | | | |
Collapse
|
11
|
Dimonte G, Schneider M. Turbulent Rayleigh-Taylor instability experiments with variable acceleration. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 54:3740-3743. [PMID: 9965524 DOI: 10.1103/physreve.54.3740] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
12
|
Alon U, Hecht J, Ofer D, Shvarts D. Power Laws and Similarity of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Fronts at All Density Ratios. PHYSICAL REVIEW LETTERS 1995; 74:534-537. [PMID: 10058782 DOI: 10.1103/physrevlett.74.534] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
13
|
Alon U, Hecht J, Mukamel D, Shvarts D. Scale invariant mixing rates of hydrodynamically unstable interfaces. PHYSICAL REVIEW LETTERS 1994; 72:2867-2870. [PMID: 10056005 DOI: 10.1103/physrevlett.72.2867] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
|
14
|
Chen Y, Deng Y, Glimm J, Li G, Zhang Q, Sharp DH. A renormalization group scaling analysis for compressible two‐phase flow. ACTA ACUST UNITED AC 1993. [DOI: 10.1063/1.858701] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
|
15
|
Alon U, Shvarts D, Mukamel D. Scale-invariant regime in Rayleigh-Taylor bubble-front dynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 48:1008-1014. [PMID: 9960684 DOI: 10.1103/physreve.48.1008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
|
16
|
Yang Y, Zhang Q. General properties of a multilayer stratified fluids system. ACTA ACUST UNITED AC 1993. [DOI: 10.1063/1.858602] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
|
17
|
Zhang Q. The motion of a single bubble or spike in Rayleigh-Taylor unstable interfaces. ACTA ACUST UNITED AC 1991. [DOI: 10.1016/0899-8248(91)90001-b] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
18
|
Glimm J, Zhang Q, Sharp DH. The renormalization group dynamics of chaotic mixing of unstable interfaces. ACTA ACUST UNITED AC 1991. [DOI: 10.1063/1.858061] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|