Numerical study of the kinematic and acoustic characteristics of bubble clusters

Direct numerical simulations are performed to study single gas/vapor bubble and spherical bubble clusters containing 13–352 vapor bubbles in compressible flow fields.The numerical results show that the single cavitation bubble keeps spherical during the collapse process,and the far-field acoustic pressure calculated by the Ffowcs William-Hawkings(FW-H)formulation is basically consistent with the analytical solution obtained based on the volume acceleration calculation.However,the spherical bubble cluster collapses layer by layer due to the strong coupling between bubbles.The closer to the center of the bubble cluster,the shorter the collapse time and the stronger the non-spherical deformation.The collapse of a bubble cluster would generate multiple acoustic pressure peaks,which cannot be accurately predicted by the volume fluctuation sound source theory.The size and volume fraction of the bubble cluster have a significant influence on the collapse time and the distribution of sound pressure.We found that when the volume fraction of a bubble cluster is large,the total collapse time is basically the same as that of its corresponding single bubble with the equal volume.The frequency distribution of sound pressure of a dense bubble cluster is also close to that of its corresponding single bubble.In addition,we found that a bubble cluster with randomly distributed bubble diameters collapses asymmetrically and rebounds in the late stage of the collapse process.The above study reveals part of the mechanism of bubble cluster collapse and sound generation,and provides a theoretical basis for the establishment of cavitation noise model.

A multi-fidelity prediction model for vertical bending moment and total longitudinal stress of a ship based on composite neural network

In ship engineering,the prediction of vertical bending moment(VBM)and total longitudinal stress(TLS)during ship navigation is of utmost importance.In this work,we propose a new prediction paradigm,the multi-fidelity regression model based on multi-fidelity data and artificial neural network(MF-ANN).Specifically,an ANN is used to learn the fundamental physical laws from low-fidelity data and construct an initial input-output model.The predicted values of this initial model are of low accuracy,and then the high-fidelity data are utilized to establish a correction model that can correct the low-fidelity prediction values.Hence,the overall accuracy of prediction can be improved significantly.The feasibility of the multi-fidelity regression model is demonstrated by predicting the VBM,and the robustness of the model is evaluated at the same time.The prediction of TLS on the deck indicates that just a small amount of high-fidelity data can make the prediction accuracy reach a high level,which further illustrates the validity of the proposed MF-ANN.

Aerodynamic modeling and stability analysis of a high-speed train under strong rain and crosswind conditions

With the development of high-speed train,it is considerably concerned about the aerodynamic characteristics and operation safety issues of the high-speed train under extreme weather conditions.The aerodynamic performance of a high-speed train under heavy rain and strong crosswind conditions are modeled using the Eulerian two-phase model in this paper.The impact of heavy rainfall on train aerodynamics is investigated,coupling heavy rain and a strong crosswind.Results show that the lift force,side force,and rolling moment of the train increase significantly with wind speed up to 40 m/s under a rainfall rate of 60 mm/h.when considering the rain and wind conditions.The increases of the lift force,side force,and rolling moment may deteriorate the train operating safety and cause the train to overturn.A quasi-static stability analysis based on the moment balance is used to determine the limit safety speed of a train under different rain and wind levels.The results can provide a frame of reference for the train safe operation under strong rain and crosswind conditions.

Numerical study on the aerodynamic performance and safe running of high-speed trains in sandstorms

The influence of sandstorms on train aerodynamic performance and safe running was studied in response to the frequent occurrence of sandstorm weather in north China.An Eulerian two-phase model in the computational fluid dynamic (CFD) software FLUENT,validated with published data,was used to solve the gas-solid multiphase flow of a sandstorm around a train.The train aerodynamic performance under different sandstorm levels and no sand conditions was then simulated.Results showed that in sandstorm weather,the drag,lift,side forces and overturning moment increase by variable degrees.Based on a numerical analysis of aerodynamic characteristics,an equation of train stability was also derived using the theory of moment balance from the view of dynamics.A recommended speed limit of a train under different sandstorm levels was calculated based on the stability analysis.

Numerical investigation on the drag force of a single bubble and bubble swarm Authors

The bubble drag force correlation plays an important role in the numerical simulation accuracy of gas/liquid flows.In order to systematically investigate the interphase drag force of non-buoyancy driven bubbly flows,a dynamic-positioning body force(DPBF)method is developed in this study.It is proved that this method has an enough computation precision.Using this method,a series of direct numerical simulation(DNS)cases of a single bubble with low-intermediate Re(1≤Re≤200)and a bubble swarm with low Re(5.6≤Re≤45)are carried out and the bubble drag coefficients are calculated.Based on all the DNS data,the drag correlations with dimensionless parameters(Re,We for a single bubble and Re,We,gas fraction for bubble swarm)are systematically investigated and reported in this paper,which can provide a reference to the development of drag force closure model for non-buoyancy driven bubbly flows.

Experimental and numerical studies on the cavitation over flat hydrofoils with and without obstacle

To control the shedding of cavitation, an obstacle is placed on the surface of a flat hydrofoil. Both experimental and numerical studies are carried out. Images of cavitation evolution are recorded by a high-speed camera. 3-D simulations are performed to investigate the cavitating flows around the hydrofoil. The results show that the re-entrant jet plays an important role during the process of cavitation shedding. A kind of U-type shedding is identified during the evolution of the cloud cavitation. The length of the cavity is apparently reduced due to the placement of the obstacle. It is interesting to find that the cavitation shedding changes from the large-scale mode to a small-scale mode, as an obstacle is placed on the hydrofoil surface. As we can observe from both experimental and numerical results, the small-scale cavitation shedding dominates the cavitating flow dynamics, we thereby conclude that the placement of an obstacle is favorable for the inhibition of cavitation shedding.

基于特殊函数法的Rayleigh-Plesset方程理论解研究

Rayleigh-Plesset方程是气泡动力学理论中的基本方程,描述了无限不可压缩流体中,球形气泡的运动,求解Rayleigh-Plesset方程对于进一步深入研究气泡生长、发展和溃灭具有重要意义。该文主要结合Sundman幂变换和特殊函数理论分析了无黏蒸汽泡的Rayleigh-Plesset方程的理论解。研究表明:蒸汽泡动力学演化规律可由超几何函数形式和Weierstrass椭圆函数形式解析表达,当不考虑表面张力时,两种函数均可表示蒸汽泡的演化规律;当考虑表面张力时,蒸汽泡的动力学演化可由部分Weierstrass椭圆函数表达。该文给出了蒸汽泡在两种情况下的参数解析解具体形式,结果表明:常压载荷下的蒸汽泡只能发生一次溃灭,且蒸汽泡的溃灭时间随流体表面张力的增大而减小。

Measurement of two-phase velocities in bubble flows using laser Doppler velocimetry

The measurement of two-phase velocities in bubble flows using laser Doppler velocimetry(LDV)is studied.The key to the problem is to differentiate the LDV signals from bubbles and tracers,based on which the two-phase velocities can be characterized.In this study,two experiments are carried out.Firstly,the bubble-chain experiment is performed to investigate the optical response of bubble surface and the corresponding LDV signal.The optical response shows that the light received by the LDV detector is dominated by the reflection component,which is similar to specular reflection to some extent.There are three typical patterns of signals of large bubbles passing through the measurement volume,all of which are with high amplitude and saturated.Then,the upward-flow experiment is conducted to study the statistical characteristics of large bubbles as well as micro tracers and micro bubbles.The results show that the amplitude of signal of millimeter bubbles is about an order of magnitude larger than that of tracers or micro bubbles.Based on this significant difference of the amplitude,we propose a phase discrimination method to distinguish two-phase signals.The capability of the proposed method is tested in a complex bubble flow,and its reliability is verified by bubble tracking velocimetry(BTV)technology.

Numerical computations of the flow in a finite diverging channel

The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number,initial condition,intersection angle,length of the wedge edges,and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow,then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow,the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°,a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow,although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability,the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment,providing a possible explanation for the hysteresis phenomenon in the experiment.

An experimental study on the velocity fluctuations generated by the flow past fixed spheres

We perform a series of experiments to study the velocity fluctuations generated by the flow past fixed spheres.Planar particle image velocimetry(PIV)is carried out to characterize the properties of the liquid fluctuation.The fluctuation induced by the spheres can be decomposed into the temporal fluctuation and the spatial fluctuation,which represent the contribution of flow instability and spatial inhomogeneity,respectively.In particularly,we focus on the contributions of temporal fluctuations and spatial fluctuations between low and high Reynolds number.At low Reynolds number(20<Re≤200),the total fluctuation mostly comes from the spatial fluctuation and increases as the area of velocity deficit in the wake of the sphere increases.The temporal fluctuation cannot be neglected at larger Reynolds number(200<Re≤700),and the total velocity fluctuation is induced by both flow instability and spatial inhomogeneity.Furthermore,the energy distribution in the flow direction and the span direction also changes drastically as the Reynolds number increases.The wavenumber spectra of fluctuations show a−3 slope at large scale,−5/3 slope at small scale.The starting scale of the−3 slope decreases with the increase of the Reynolds number.Specifically,it is consistent with the integral length scaleΛfor Re>200,but not for Re<200.The ending scale is aroundλ=0.5d and decreases slightly as Re increases.

A descent method for the Dubins traveling salesman problem with neighborhoods

In this study,we focus mainly on the problem of finding the minimum-length path through a set of circular regions by a fixed-wing unmanned aerial vehicle.Such a problem is referred to as the Dubins traveling salesman problem with neighborhoods(DTSPN).Algorithms developed in the literature for solving DTSPN either are computationally demanding or generate low-quality solutions.To achieve a better trade-off between solution quality and computational cost,an efficient gradient-free descent method is designed.The core idea of the descent method is to decompose DTSPN into a series of subproblems,each of which consists of finding the minimum-length path of a Dubins vehicle from a configuration to another configuration via an intermediate circular region.By analyzing the geometric properties of the subproblems,we use a bisection method to solve the subproblems.As a result,the descent method can efficiently address DTSPN by successively solving a series of subproblems.Finally,several numerical experiments are carried out to demonstrate the descent method in comparison with several existing algorithms.

Numerical study of the acoustic spectrum of bubble clusters

This study delved into the acoustic spectrum of bubble clusters,each consisting of 352 vapor bubbles across volume fractions ranging from 0.005%to 40%.The clusters,organized in five distinct layers,were modeled using the volume of fluid(VOF)method to capture the bubble interfaces,and the Ffowcs Williams-Hawkings(FW-H)methodology to compute the far-field acoustic pressure from bubble collapse.Further analysis revealed distinct sound pressure behaviors across different volume fractions:For 25%–40%,time-domain analysis shows that the peak acoustic pressure pulses from the two innermost layers of bubbles are significantly higher than those from the outer layers.In the frequency domain,the octave decay rate of the acoustic pressure levels is relatively low,around−3dB/octave.For 0.5%–25%,four acoustic pressure pulses with similar widths and peak values were observed in the time domain.In the frequency domain,there are three distinct peaks in sound pressure levels(SPL),directly linked to the difference in collapse times of bubbles within the cluster,and the octave decay rate accelerates as the volume fraction decreases,stabilizing at−6dB/octave when the volume fraction is reduced to 17.5%.For 0.005%–0.5%,as the volume fraction decreases from 0.5%to 0.1%,the number of acoustic pressure pulses significantly reduces.Below 0.1%volume fraction,only a single wider pulse is observed.In the frequency domain,the octave decay rate gradually increases with decreasing volume fraction,significantly exceeding−10dB/octave when it drops below 0.1%,reaching up to−11.7dB/octave.