High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

A parameter identification technique of an underlying bubble model of an experimentally observed single bubble in a cluster under dual-frequency external forcing is presented. The measurements are carried out via high-speed camera recordings at a rate of 162750 frames per second. The used frequencies during the experiment are 25 kHz and 50 kHz. With a digital image processing technique, the measured bubble radius as a function of time is determined. The employed governing equation for the parameter fitting is the Keller–Miksis equation being a second order ordinary differential equation. The unknown four-dimensional parameter space is composed by the two pressure amplitudes, the phase shift of the dual-frequency driving and the equilibrium size of the bubble. In order to obtain an optimal parameter set within reasonable time, an in-house initial value problem solver is used running on a graphics processing unit (GPU). The error function measuring the distance between the numerical simulations and the measurement is based on the identification of the maximum bubble radii during each subsequent period of the external forcing. The results show a consistent estimation of both pressure amplitudes. The optima of phase shift and equilibrium bubble size are less significant due to a valley-like shape of the error function. Nevertheless, reasonable values are found that lead to estimations of pressure and temperature peaks during bubble collapse

Bifurcation Structure Of A Periodically Driven Bubble Oscillator Near Blake’s Critical Threshold

It is well-known that gas/vapour bubbles in liquids growth indefinitely if the ambient pressure exceeds Blake’s critical threshold. For several decades of investigations, researchers tried to find numerical evidence for the stabilization of such bubbles by applying a harmonically varying pressure field on the liquid domain (ultrasonic irradiation) in this regime, with only partial success. Since, the applied linearization on the bubble models restricted the findings only for small amplitude radial oscillations. Therefore, the present paper intends to reveal the particularly complex dynamics of a harmonically excited bubble near, but still below Blake’s threshold. The computed solutions with a variety of periodicity, e.g., from period 1 up to period 9, form a well-organised structure with respect to the pressure amplitude of the excitation, provided that the applied frequency is higher than the first subharmonic resonance frequency of the bubble. This predictable behaviour provides a good basis for further investigation to find the relevant stable oscillations beyond Blake’s threshold. Although, the investigated model is the very simple Rayleigh—Plesset equation, the applied numerical technique is free of the restriction of low amplitude oscillations

Optimal Pressure Measurement Layout Design in Water Distribution Network Systems

This paper addresses the problem of locating the optimal pressure measurement points in a hydraulic system to help system management, calibration/validation of hydraulic models and measurement planning. Two approaches are discussed in the present work. The first method splits the hydraulic system by means of community concept borrowed from graph theory and uses merely the topology of the network. The resulting subsystems will have minimum number of external and maximum number of internal connections and leaves the choice of locating the single pressure measurement location per subsystem to a higher-level decision. The second technique is based on the sensitivity analysis of the hydraulic network and places the measurement points at the most sensitive locations, while trying to preserve the spatial diversity of the layout, i.e. preventing the accumulation of the measurement points within a small area of high sensitivity. The performance of both techniques is demonstrated on real-size hydraulic networks. The proposed sampling layouts are compared to classic D-optimality, A-optimality and V-optimality criterion

Frequency and Phase Characteristics of the Edge Tone, Part I

This paper is the first half of a two-part publication. In these papers the well-known low Mach number edge tone configuration is investigated that is one of thecanonical self-sustained flow configurations leading to simple aeroacoustic flow phe-nomena. The configuration consist of a planar free jet that impinges on a wedgeshaped object. Under certain circumstances the jet starts to oscillate more or lessperiodically thereby creating an oscillating force on the wedge that acts as a dipolesound source. The flow of the edge tone is investigated by experimental and numer-ical means and remarkable agreement is found. This first part contains a detailedliterature overview and the qualitative discussion of the authors’ results of a detailedparametric study

Route to shrimps: Dissipation driven formation of shrimp-shaped domains

In this paper, two scenarios for the formation of shrimp-shaped domains [1] are presented. The employed test model is the Keller–Miksis equation that is a second order, harmonically forced nonlinear oscillator describing the dynamics of a single spherical gas bubble placed in a liquid domain. The results have shown that with an increasing dissipation rate (liquid viscosity), shrimp-shaped domains are evolved within the complex structure of each subharmonic resonances in the amplitude-frequency parameter plane of the external forcing. The mechanism is the coalescence and interaction of two pairs of a period-doubling and a saddle-node codimension-two bifurcation curves

Bi-parametric topology of subharmonics of an asymmetric bubble oscillator at high dissipation rate

The subharmonic topology of a nonlinear, asymmetric bubble oscillator (Keller–Miksis equation) in glycerine is investigated in the parameter space of its external excitation (frequency and pressure amplitude). The bi-parametric investigation revealed that the exoskeleton of the topology can be described as the composition of U-shaped subharmonics of periodic orbits. The fine substructure (higher-order ultra-subharmonic resonances) usually appearing via the well-known period n-tupling phenomenon is completely missing due to the high dissipation rate of the viscous liquid. Moreover, a complex internal structure of the subharmonics has been found, which are composed by interconnected bifurcation blocks (in a zig-zag pattern) each describing the skeleton of a shrimp-shaped domain. The employed numerical techniques are the combination of an in-house initial value problem solver written in C++/CUDA C to harness the high processing power of professional graphics cards, and the boundary value problem solver AUTO to compute periodic orbits directly regardless of their stability