Free oscillations of a single spherical gas bubble in glycerol have been examined numerically and experimentally at different ambient temperatures and pressures. The bubble was generated using a Q-switched Nd:YAG laser and the unsteady radius measurement was based on a shadowing technique of a He-Ne laser beam. The measurements were compared to computations obtained from two models, first taking into consideration the liquid compressibility and then assuming an incompressible liquid domain, respectively. In both cases the temperature fields inside and outside the bubble were computed by solving the energy equation in both phases as the thermodynamic processes have great importance to the bubble behavior. For high amplitude oscillations the incompressible model provides poor agreement with the measurements and the modeling of the liquid compressibility becomes necessary. In contrast to the standard method, a practical region of applicability for the incompressible approach was determined as a function of the instantaneous Mach and Reynolds numbers, rather than specifying a simple threshold Mach number. (C) 2013 Elsevier Inc. All rights reserved.

Basins of the periodic attractors of a harmonically excited single spherical gas/vapour bubble were examined numerically.As cavitation occurs in the low pressure level regions in engineering applications, the ambient pressure was set slightly below the vapour pressure.In this case the system is not strictly dissipative and the bubble can grow infinitely for sufficiently high pressure amplitudes and/or starting from large initial bubble radii, consequently, the stable bubble motion is not guaranteed.For moderate excitation pressure amplitudes the exact basins of attraction were determined via the computation of the invariant manifolds of the unstable solutions.At sufficiently large amplitudes transversal intersection of the manifolds can take place, indicating the presence of a Smale horseshoe map and the chaotic behaviour of system.The incidence of this kind of chaotic motion was predicted by the small parameter perturbation method of Melnikov.

In this paper the harmonic response of the excited classical Rayleigh-Plesset equation is examined. Unlike the majority of the corresponding literature, the ambient pressure is set slightly below the vapour pressure, as this is the pressure level of interest in many engineering applications. Due to the low ambient pressure, the system is non-strictly dissipative and the bubble may keep growing infinitely at sufficiently high excitation amplitudes. Period 1, 2 and 3 solutions were traced in the excitation amplitude-frequency parameter space with the help of continuation techniques. The computations revealed that high-frequency excitation typically stabilizes the bubble motion and prevents its infinite growth, even in the case of high excitation amplitudes. The winding numbers corresponding to the bifurcation curves were also computed. By taking their limit for period doubling sequences, predictions were given for the presence of solutions with odd periods (e.g. 3 or 9), which were verified numerically.

Measurement results on the cavitating vortex shedding behind sharp-edged rectangular bodies are presented, intended to provide benchmark cases for the validation of unsteady cavitation models of CFD codes. Rectangular bodies of increasing aspect ratio (1, 2, 3 and 4) were used with a constant 25mm height (12.5% blockage ratio). The water velocity in the 0.2x0.05m test section of the channel was varied between 1 and 12 m/s resulting in a Reynolds number in the range of (0.4-3.5)x105. Pressure signals were measured at several locations, notably in the wake. Dominant frequencies and Strouhal numbers are reported from cavitation-free flow (classic von Kármán vortex shedding) up to supercavitation as a function of the free-stream Reynolds number. The results are in good agreement with the literature in case of the square cylinder. We experienced a slight increase of the dominant Strouhal number with increasing aspect ratio. This result is somewhat inconsistent with the literature, in which a fall of the Strouhal number can be observed at side ratio 2. This may be the consequence of the different ranges of Reynolds numbers. It was also found that between the inception of cavitation and the formation of supercavitation the Strouhal number is not affected by cavitation.

The standard approach to analyse the bubble motion is the well known Rayleigh–Plesset equation. When applying the toolbox of nonlinear dynamical systems to this problem several aspects of physical modelling are usually sacrificed. Particularly in vapour bubbles the heat transfer in the liquid domain has a significant effect on the bubble motion; therefore the nonlinear energy equation coupled with the Rayleigh–Plesset equation must be solved. The main aim of this paper is to find an efficient numerical method to transform the energy equation into an ODE system, which, after coupling with the Rayleigh–Plesset equation can be analysed with the help of bifurcation theory. Due to the strong nonlinearity and violent bubble motions the computational effort can be high, thus it is essential to reduce the size of the problem as much as possible. In the first part of the paper finite difference, Galerkin and spectral collocation methods are examined and compared in terms of efficiency. In the second part free and forced oscillations are analysed with an emphasis on the influence of heat transfer. In the case of forced oscillations the unstable branches of the amplification diagrams are also computed.

Szabalyozo szelep fojtoelemenek nyilasaban megfigyelt kavitacios zona es CFD szamitas eredmenyeinek osszehasonlitasa. A BME Hidrodinamikai Rendszerek Tanszek laboratoriumaban levő kavitacios csatorna ujjaepitese. A merőszakasz Re-szama eleria 800000-et. Negyzetes hasab Reynolds, Strouhal, Thoma-fele kavitacios szama es a zonahossz merese es a fuggveny kapcsolatok meghatarozasa. A buborek sugaranak valtozasat leiro Rayleigh-Plesset es a kondenzacios-parolgasi hőaramot leiro hővezetesi differencialegyenlet osszekapcsolasa es vizsgalata nemlinearis dinamikai modszerrel. | Observed cavitation zone in control valve openings with results of CFD computations was compared. Cavitation channel at the Laboratory of the Dept. of Hydrodynamic Systems at BME was rebuilt. The Reynolds number in the test section can reach Re = 800000. Reynolds, Strouhal, Thoma cavitation-number and cavity zone length were measured for prisms of rectangular cross section and the functional relationship was determined. The Rayleigh-Plesset differential equation describing the bubble radius rate was coupled with the heat conduction equation describing the heat flow of evaporation/condensation and was solved by methods of nonlinear dynamics.

A palyazatban megfogalmazott kutatasi cellal osszhangban egy olyan modularis felepitesű programcsomagot keszitettunk el, mely alkalmas kulonboző fizikai hatterű, de hasonlo logikai felepitesű aramlastechnikai halozatok dinamikus vizsgalatara. A programcsomagot Matlab kornyezetben kodoltuk. Jelenleg az alabbi elemkonyvtarak allnak rendelkezesre: (1) erhalozatok elemei (viszkoelasztikus cső, sziv, stb.), (2) olajhidraulikus halozatok (munkahenger, volumetrikus szivattyu, utvalto, nyomashatarolo szelep, terfogataram allandosito szelep, stb.), (3) nyomottvizes ivovizhalozat elemek (szivattyu, linearisan rugalmas anyagu cső, visszacsapo szelep, nyomasszabalyzo, legust, stb.) es (4) szennyviz- es csatornahalozatok elemei (nyiltfelszinű prizmatikus csatorna, akna, stb.). Az arterias es venas veraramlas modellezese soran kifejlesztettunk egy viszkoelasztikus anyagmodellt, amelyet beepitettunk a szamitogepes programcsomagba. Megepitettunk egy merőberendezest a viszkoelasztikus csőszakaszok osszeroppanasanak vizsgalatara. Orvos kollegakkal egyuttműkodve megfigyeltuk a veraramlast patkanyvenakban. Kidolgoztunk egy modszert a veraramlas sebessegenek becslesere. Modelleztuk a venas billentyűk műkodeset harom dimenzios kapcsolt aramlastani szimulaciok vegrehajtasaval. | A modular software package has been developed, which makes it possible to easily add hydraulic system elements with different physical background but similar logical build-up. The following libraries were developed: (1) arterial systems (viscoelastic pipe, heart, etc.), (2) power transmission systems (hydraulic cylinder, positive displacement pump, directional valve, pressure relief valve, flow control valve, etc.), (3) pressurized water distribution systems (pump, linearly elastic pipe, check valve, pressure control valve, air vessel, etc.) and (4) wastewater system elements (open-surface prismatic channel, weir, etc.). The software package is continuously used and developed by the colleagues at the Dept. and students. In the project of modeling of the elements of the artery system (heart, artery, vein, etc.) a viscoelastic material model was developed and inserted into the software package used for simulating unsteady 1D flow in pipe networks. A test rig was designed and manufactured for the investigation of collapsing viscoelastic tubes. In cooperation with medical researchers we carried out in vivo measurements on rat veins. A method was developed for the estimation of blood velocity. The operation of venous valves was investigated using fluid-structure interaction methods.

Comparison between experimental and numerical results of the cavitating vortex shedding behind a square cylinder is presented. The side length of the experimental and numerical model was 25 mm and 20 mm, respectively. The water velocity in the 0.2x0.05 m test section of the channel was varied between 1 and 12 m/s resulting in a Reynolds number range of (0.4-3.5)x10^5. In the simulation the mean velocity was increased up to 14 m/s with 1 m/s increment. Dominant frequencies and Strouhal numbers are reported from cavitation-free flow (classical von Kármán vortex shedding) up to supercavitation as a function of the free-stream Reynolds number. It was found that between the inception of cavitation and the formation of supercavitation the Strouhal number is not affected by cavitation. The results are in a fairly good agreement with the literature.

A kutatas az elhang (edge tone) aramlasi konfiguraciora koncentralt. Az elhang egyszerű rendszer, ami egy sik szabadsugarbol, es egy azzal szembe forditott ekből all, es megis meglepően komplex viselkedest mutat. Stacionarius peremfeltetelek mellett is nemlinearis, instacionarius jelensegeket produkal. A szabadsugar tobbe-kevesbe periodikusan leng az ek korul. A projekt folyaman nagyszamu numerikus aramlasszimulaciot vegeztunk ezen a konfiguracion, es szamos, a kiserleti irodalombol ismert jelenseget reprodukaltunk, mint pl. a hidrodinamikai modusok letezeset, a parabolikus es az egyenletes kiomlő sebessegprofil kulonboző viselkedeset, a frekvencianak a fuvoka-ek tavolsagtol valo inverz fuggeset, a z eken valo nyomaseloszlast, stb. Felepitettunk egy kiserleti berendezest, amelyen kulonboző modszerekkel mertuk a lenges frekvenciajat. A kulonboző modszerek egymas kozott is, valamint a kiserletek es a szimulaciok is nagyon jo egyezest mutattak. Az erlangeni egyetemmel kozosen kidolgoztunk egy modszert, amelynek segitsegevel a CFX aramlastechnikai szimulacios szoftvert osszekapcsoltuk a CFS++ akusztikai szoftverrel es sikeresen szimulaltuk az elhang altal kibocsajtott zajt. Jellegre tokeletesen megkaptuk a vart dipolus hangnyomas-iranykarakterisztikat. Vizsgaltuk a ketdimenzios illetve haromdimenzios akusztikai illetve aramlastani szimulaciok hatasat. | The research concentrated on the edge tone configuration. The edge tone is a simple system consisting of a plane jet and a wedge placed opposite to it, which yet produces a surprisingly complex behaviour. It produces nonlinear, unsteady phenomena, while having steady boundary conditions. The jet oscillates around the wedge in a more or less periodic manner. During the project we performed a large number of numerical flow simulations on this configuration and we reproduced several phenomena known from the experimental literature such as the existence of hydrodynamic modes, the different behaviour of the parabolic and the top hat exit velocity profiles, the inverse dependence of the frequency on the nozzle ? wedge distance, the pressure distribution on the wedge, etc. We built an experimental rig and measured the oscillation frequency using various method. The various methods agree very well among each other, as well as the experiments with the simulations. Together with the University of Erlangen we worked out a method to couple the CFX flow simulation software with the CFS++ acoustic simulation software and we simulated the noise emitted by the edge tone successfully. We obtained the expected angular sound pressure distribution typical for dipole sound sources. We investigated the effect of two- and three-dimensional acoustic and flow simulations.

We study some consequences of the absence of microscopic reversibility on financial processes. We analyze high resolution data and find asymmetric time dependent cross correlation functions indicating dominance of some companies in the price formation procedure. These effects can be summarised in a directed netowrk of influence. Furthermore, we show that in the Lux-Marchesi multi agent market model spontaneous fluctuations decay differently from perturbations caused by external effects. The latter are easily controlled in the model, however, in real data the separation of the internal and the external effects is a highly nontrivial task.

The paper addresses the analytical and numerical study of a hydraulic positioning system with PD controlling. Two control valve types are considered; two-stage directional valve exhibiting relay-like behaviour and proportional valve, which is capable of controlling the flow continuously. The mathematical model consists of a set of four nonlinear ordinary differential equations with discontinuous right-hand side, which exhibit self-excited oscillations in a wide parameter range. By using novel analytical techniques, closed formulae are derived for stability conditions. To verify these results, the periodic orbits are also computed as the solutions of a two-point boundary value problem, with the help of the software AUTO. By using this numerical technique, not only the stability boundaries and the properties of the oscillations (amplitude, frequency, etc...) can be computed efficiently but also more realistic and complex systems can be analysed.

A simple compression system model, described by a set of three ordinary nonlinear differential equations (the Moore-Greitzer model) is studied using bifurcation analysis to give a qualitative understanding of the presence of surge and rotating stall. First, three parameter values are chosen and a reduced planar system is studied to detect the local bifurcations of pure surge modes. The global bifurcation diagrams are then completed with the help of the continuation software AUTO. A special feature of this 2D system is a set of parameter values where two Takens-Bogdanov points merge. As a next step, the interaction of surge and rotating stall modes is analysed using the same branch tracking technique. Several novel bifurcation scenarios are described. Two-parameter bifurcation maps are computed and a satisfactory agreement with experimental results is found. An explanation is given for the onset of deep surge, rotating stall, classic surge and the hysteresis effects experienced in measurements.

The quality of an approximating function using measured data may be characterized by the magnitude of difference between approximating and exact functional relationship. Smoothing spline has been used as approximating function. Based on measurements, a method is presented for determining a band around the approximating spline containing the graph of the exact functional relationship between physical variables on a calculable probability level.

Air-flow installations composed of fluid machine, pipes, air-vessels and throttles are disposed towards press ure and mass-flow fluctuations at small mass flow rates. Computational models of lumped and distributed parameters both are suitable to the description of such dynamical behaviour as it has been proved by comparising with experimental results. The dynamical treatment of the fluid machine is of great importance within both models.