scholarly journals Microbubble dynamics in a viscous compressible liquid near a rigid boundary

2019 ◽  
Vol 84 (4) ◽  
pp. 696-711 ◽  
Author(s):  
Qianxi Wang ◽  
WenKe Liu ◽  
David M Leppinen ◽  
A D Walmsley
Keyword(s):  
Potential Flow ◽  
Stokes Equations ◽  
Bubble Surface ◽  
Compressible Liquid ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Effects ◽  
Rigid Boundary ◽  
Viscous Potential Flow ◽  
Viscous Compressible Liquid

Abstract This paper is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled using the weakly compressible theory of Wang & Blake (2010, Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave. J. Fluid Mech., 730, 245–272), since the Mach number associated is small. The viscous effects are approximated using the viscous potential flow theory of Joseph & Wang (2004, The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365–377), because the flow field is characterized as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through including corresponding additional terms in the far field condition and the dynamic boundary condition at the bubble surface, respectively. The numerical results are shown in good agreement with the Keller–Miksis equation, experiments and computations based on the Navier–Stokes equations. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed in terms of the compressible and viscous effects.

scholarly journals Bubble dynamics in a compressible liquid in contact with a rigid boundary

2015 ◽  
Vol 5 (5) ◽  
pp. 20150048 ◽  
Author(s):  
Qianxi Wang ◽  
Wenke Liu ◽  
A. M. Zhang ◽  
Yi Sui
Keyword(s):  
Shock Waves ◽  
Thin Layer ◽  
High Speed ◽  
Bubble Radius ◽  
Time History ◽  
Bubble Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Imaging Method ◽  
Rigid Boundary

A bubble initiated near a rigid boundary may be almost in contact with the boundary because of its expansion and migration to the boundary, where a thin layer of water forms between the bubble and the boundary thereafter. This phenomenon is modelled using the weakly compressible theory coupled with the boundary integral method. The wall effects are modelled using the imaging method. The numerical instabilities caused by the near contact of the bubble surface with the boundary are handled by removing a thin layer of water between them and joining the bubble surface with its image to the boundary. Our computations correlate well with experiments for both the first and second cycles of oscillation. The time history of the energy of a bubble system follows a step function, reducing rapidly and significantly because of emission of shock waves at inception of a bubble and at the end of collapse but remaining approximately constant for the rest of the time. The bubble starts being in near contact with the boundary during the first cycle of oscillation when the dimensionless stand-off distance γ = s / R m < 1, where s is the distance of the initial bubble centre from the boundary and R m is the maximum bubble radius. This leads to (i) the direct impact of a high-speed liquid jet on the boundary once it penetrates through the bubble, (ii) the direct contact of the bubble at high temperature and high pressure with the boundary, and (iii) the direct impingement of shock waves on the boundary once emitted. These phenomena have clear potential to damage the boundary, which are believed to be part of the mechanisms of cavitation damage.

Viscous irrotational analysis of the deformation and break-up time of a bubble or drop in uniaxial straining flow

2011 ◽  
Vol 688 ◽  
pp. 390-421
Author(s):  
J. C. Padrino ◽  
D. D. Joseph
Keyword(s):  
Potential Flow ◽  
Stokes Equations ◽  
Extensional Flow ◽  
Time Integration ◽  
Inviscid Limit ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Viscous Potential Flow ◽  
Break Up

AbstractThe nonlinear deformation and break-up of a bubble or drop immersed in a uniaxial extensional flow of an incompressible viscous fluid is analysed by means of viscous potential flow. In this approximation, the flow field is irrotational and viscosity enters through the balance of normal stresses at the interface. The governing equations are solved numerically to track the motion of the interface by coupling a boundary-element method with a time-integration routine. When break-up occurs, the break-up time computed here is compared with results obtained elsewhere from numerical simulations of the Navier–Stokes equations (Revuelta, Rodríguez-Rodríguez & Martínez-Bazán J. Fluid Mech., vol. 551, 2006, p. 175), which thus keeps vorticity in the analysis, for several combinations of the relevant dimensionless parameters of the problem. For the bubble, for Weber numbers $3\leqslant \mathit{We}\leqslant 6$, predictions from viscous potential flow shows good agreement with the results from the Navier–Stokes equations for the bubble break-up time, whereas for larger $\mathit{We}$, the former underpredicts the results given by the latter. When viscosity is included, larger break-up times are predicted with respect to the inviscid case for the same $\mathit{We}$. For the drop, and considering moderate Reynolds numbers, $\mathit{Re}$, increasing the viscous effects of the irrotational motion produces large, elongated drops that take longer to break up in comparison with results for inviscid fluids. For larger $\mathit{Re}$, it comes as a surprise that break-up times smaller than the inviscid limit are obtained. Unfortunately, results from numerical analyses of the incompressible, unsteady Navier–Stokes equations for the case of a drop have not been presented in the literature, to the best of the authors’ knowledge; hence, comparison with the viscous irrotational analysis is not possible.

Optimization of Rotor-Stator-Strut Potential Flow Interaction Including Rotor Feedback Effects

1994 ◽  
Author(s):  
G. Cerri ◽  
P. Boatto ◽  
W. F. O’Brien ◽  
A. Sorrenti
Keyword(s):  
Potential Flow ◽  
Optimization Technique ◽  
Pressure Coefficient ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Blade Profile ◽  
Momentum Coefficient ◽  
Flow Interaction ◽  
Constrained Minimization Problem ◽  
Stator Blade

A method for the optimization of stator blade stagger angles and of strut circumferential position in order to shield a rotor cascade from downstream strut pressure disturbances is presented. Potential flow interaction between rotor, stator and strut rows is analyzed by a boundary integral method for unsteady incompressible 2-D flows, based on singularity superposition over every blade profile. The flow field is solved in terms of velocity, and the pressure field is computed using the unsteady Bernoulli equation. An optimization technique based on a constrained minimization problem is applied; objective functions related to pressure coefficient and lift coefficients are considered. Force coefficients in the tangential and axial directions, and the momentum coefficient acting on the blades are calculated by integrating the pressure distribution over the blade profile. Results of the stagger angle and strut position optimization are presented and discussed. An analysis in the frequency domain is also performed.

Modeling of a Semisubmersible Floating Offshore Wind Platform in Severe Waves

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Irene Rivera-Arreba ◽  
Niek Bruinsma ◽  
Erin E. Bachynski ◽  
Axelle Viré ◽  
Bo T. Paulsen ◽  
...  
Keyword(s):  
Experimental Data ◽  
Potential Flow ◽  
Stokes Equations ◽  
Second Order ◽  
Offshore Wind ◽  
Computationally Efficient ◽  
Viscous Effects ◽  
Floating Platform ◽  
Global Dynamic ◽  
Offshore Industry

Floating offshore wind platforms may be subjected to severe sea states, which include both steep and long waves. The hydrodynamic models used in the offshore industry are typically based on potential-flow theory and/or Morison’s equation. These methods are computationally efficient and can be applied in global dynamic analysis considering wind loads and mooring system dynamics. However, they may not capture important nonlinearities in extreme situations. The present work compares a fully nonlinear numerical wave tank (NWT), based on the viscous Navier–Stokes equations, and a second-order potential-flow model for such situations. A comparison of the NWT performance with the experimental data is first completed for a moored vertical floating cylinder. The OC5-semisubmersible floating platform is then modeled numerically both in this nonlinear NWT and using a second-order potential-flow based solver. To test both models, they are subjected to nonsteep waves and the response in heave and pitch is compared with the experimental data. More extreme conditions are examined with both models. Their comparison shows that if the structure is excited at its heave natural frequency, the dependence of the response in heave on the wave height and the viscous effects cannot be captured by the adjusted potential-flow based model. However, closer to the inertia dominated region, the two models yield similar responses in pitch and heave.

Lubrication analysis and boundary integral simulations of a viscous micropump

2000 ◽  
Vol 416 ◽  
pp. 197-216 ◽  
Author(s):  
RICHARD F. DAY ◽  
H. A. STONE
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Direction ◽  
Maximum Flow ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Micropump ◽  
Analytical Relations ◽  
Rate Optimization

Several recent papers discuss a viscous micropump consisting of Poiseuille flow of fluid between two plates with a cylinder placed along the gap perpendicular to the flow direction (e.g. Sen, Wajerski & Gad-el-Hak 1996). If the cylinder is not centred, rotating it will generate a net flow and an additional pressure drop along the channel, due to the net tangential viscous stresses along its surface. The research reported here complements existing work by examining the lubrication limit where the gaps between the cylinder and the walls are small compared to the cylinder radius. Lubrication analysis provides analytical relations among the flow rate, torque, pressure drop and rotation rate. Optimization of the flow parameters is shown in order to determine the optimal geometry of the device, which can be used by micro-electrical-mechanical systems designers. It is also shown, for example, that a device cannot be developed that achieves maximum flow rate and rotation simultaneously. In addition, since the Reynolds number can be smaller than 1, the Stokes equations are solved for this configuration using a numerical boundary integral method. The numerical results match the lubrication solution for small gaps, and determine the limits of validity for using the lubrication results.

A BOUNDARY INTEGRAL METHOD FOR ACOUSTIC SOURCE LOCALIZATION IN A WAVEGUIDE WITH INCLUSIONS

1994 ◽  
Vol 02 (02) ◽  
pp. 133-145 ◽  
Author(s):  
YONGZHI XU ◽  
YI YAN
Keyword(s):  
Source Localization ◽  
Sound Source ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Rigid Boundary ◽  
Matched Field Processing ◽  
Acoustic Source Localization ◽  
Continuous Waves ◽  
Hydrophone Array ◽  
Computation Load

In this paper, we continue our study on combining the matched field processing with the boundary integral equation (BIE) method of scattering theory to solve a sound source localization problem in a shallow ocean with a large inclusion which has a rigid boundary. We consider an enviroment where continuous waves (CW) are produced by a sound source, scattered by the inclusion, and then received by a hydrophone array. The symmetry of the waveguide is destroyed by the existence of the inclusion, and a proper procedure is therefore required to avoid the mismatching. We present a numerical scheme which makes use of the separation of the source and the detection array, and a BIE method. The separation greatly reduces the computation load. The BIE method preserves a certain accuracy on one hand and minimizes arithmetic operations on the other. Some numerical simulations using this scheme are presented.

A spectral boundary element approach to three-dimensional Stokes flow

1995 ◽  
Vol 298 ◽  
pp. 167-192 ◽  
Author(s):  
G. P. Muldowney ◽  
J. J. L. Higdon
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Spectral Element ◽  
Companion Paper ◽  
Porous Membrane ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Reynolds Number Flow ◽  
Periodic Models ◽  
Element Approach

A novel method is introduced for solving the three-dimensional Stokes equations via a spectral element approach to the boundary integral method. The accuracy and convergence of the method are illustrated through applications involving rigid particles, deformable droplets and interacting particles. New physical results are obtained for two applications in low Reynolds number flow: the permeability of periodic models of a porous membrane and the instability of a toroidal droplet subject to non-axisymmetric perturbations. Further applications are described in the companion paper (Higdon & Muldowney 1995).

The motion of a rigid body in viscous fluid bounded by a plane wall

1989 ◽  
Vol 207 ◽  
pp. 29-72 ◽  
Author(s):  
Richard Hsu ◽  
Peter Ganatos
Keyword(s):  
Aspect Ratio ◽  
Stokes Equations ◽  
Hydrodynamic Force ◽  
Orientation Angle ◽  
Boundary Integral ◽  
The Body ◽  
Boundary Integral Method ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Planar Wall

The boundary-integral method is used to calculate the hydrodynamic force and torque on an arbitrary body of revolution whose axis of symmetry is oriented at an arbitrary angle relative to a planar wall in the zero-Reynolds-number limit. The singular solution of the Stokes equations in the presence of a planar wall is used to formulate the integral equations, which are then reduced to a system of linear algebraic equations by satisfying the no-slip boundary conditions on the body surface using the boundary collocation method or weighted residual technique.Numerical tests for the special case of a sphere moving parallel or perpendicular to a planar wall show that the present theory is accurate to at least three significant figures when compared with the exact solutions for gap widths as small as only one-tenth of the particle radius. Higher accuracy can be achieved and solutions can be obtained for smaller gap widths at the expense of more computation time and larger storage requirements.The hydrodynamic force and torque on a spheroid with varying aspect ratio and orientation angle relative to the planar wall are obtained. The theory is also applied to study the motion of a toroidal particle or biconcave shaped disc adjacent to a planar wall. The coincidence of the drag and torque of a biconcave-shaped body and a torus having an aspect ratio b/a = 2 with the same surface area shows that in this case the hole of a torus has little influence on the flow field. On the other hand, for an aspect ratio b/a = 10, the effect of the hole is significant. It is also shown that when the body is not very close to the wall, an oblate spheroid can be used as a good approximation of a biconcave-shaped disc.

scholarly journals Amplitude Induced Nonlinearity in Piston Mode Resonant Flow: A Fully Viscous Numerical Analysis

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Luca Bonfiglio ◽  
Stefano Brizzolara
Keyword(s):  
Free Surface ◽  
Vortex Shedding ◽  
Potential Flow ◽  
Stokes Equations ◽  
Body Wave ◽  
Oscillation Amplitude ◽  
Computational Technique ◽  
Linear Potential ◽  
Viscous Effects ◽  
Piston Mode

Near field flow characteristics around catamarans close to resonant conditions involve violent viscous flow such as energetic vortex shedding and steep wave making. This paper presents a systematic and comprehensive numerical investigation of these phenomena at various oscillating frequencies and separation distances of twin sections. The numerical model is based on the solution of Navier–Stokes equations assuming laminar-flow conditions with a volume of fluid (VOF) approach which has proven to be particularly effective in predicting strongly nonlinear radiated waves which directly affect the magnitude of the hydrodynamic forces around resonant frequencies. Considered nonlinear effects include wave breaking, vortex shedding and wave-body wave-wave interactions. The method is first validated using available experiments on twin circular sections: the agreement in a very wide frequency range is improved over traditional linear potential flow based solutions. Particular attention is given to the prediction of added mass and damping coefficients at resonant conditions where linear potential flow methods fail, if empirical viscous corrections are not included. The results of the systematic investigation show for the first time how the so-called piston-mode motion characteristics are nonlinearly dependent on the gap width and motion amplitude. At low oscillation amplitudes, flow velocity reduces and so does the energy lost for viscous effects. On the other hand for higher oscillation amplitude, the internal free surface breaks dissipating energy hence reducing the piston mode amplitude. These effects cannot be numerically demonstrated without a computational technique able to capture free surface nonlinearity and viscous effects.

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