Self-oscillation Research Articles

Dynamic behaviour of a full-load cavitation vortex in a Francis turbine draft tube excited at its eigenfrequencies

The operating range of Francis turbines is limited at full-load conditions by the formation of a cavitation vortex rope that may enter self-oscillations under certain conditions. This induces severe pressure pulsations in the entire system, as well as output power swings putting at risk the integrity of the electro-mechanical components. The understanding of the underlying physical mechanisms and the prediction of the stability of hydropower units at full-load conditions are therefore crucial to ensure a safe extension of their operating range. In the present paper, the dynamic behaviour of a stable cavitation vortex rope at full load is investigated by high-speed visualizations while the test rig is excited at its first and second hydroacoustic eigenfrequencies. It is first demonstrated that the cavitation volume and the pressure in the draft tube are more likely to oscillate at the first eigenfrequency, in agreement with the observations of self-excited oscillations at the first eigenfrequency of the cavitation vortex rope during unstable full-load conditions. In addition, it is observed that the amplitude of both the cavitation volume and pressure fluctuations in the draft tube reach a limit value when the amplitude of the excitation is further increased. Further investigations will determine if this behaviour can be generalized to any full-load conditions and will focus on the determination of the hydro-acoustic parameters of the draft tube cavitation flow based on the behaviour of the vortex rope during forced oscillations.

Experimental study of the flow regime effect on the stability of collapsible tubes conveying fluid

Experimental studies of the stability of the collapsible tubes conveying fluid have been previously conducted in the context of cardiovascular mechanics mostly for turbulent flows, although blood flows are laminar under normal conditions. In this paper, the turbulent and laminar regimes with equal flow rates and pressure drops are investigated experimentally to identify the stability boundary and self-exciting oscillation modes of Penrose tubes conveying fluid in the Starling resistor. Four oscillation modes for laminar and for turbulent regimes were observed visually and by measuring the pressure drop and the output pressure. Comparison of amplitudes, frequencies, and boundaries between different oscillation modes for equivalent laminar and turbulent flow regimes is performed.

Modeling of self-excited oscillation of non-equilibrium condensation in transonic moist air flow

Atmospheric air is a popular working fluid in gas power plants and turbomachinery which always contains water vapor. The vapor condensation occurs in transonic flow when the temperature drops below dew point during the accelerating expansion and affects the performance of equipment and safety. The unsteady condensation model based on nucleation and droplet growth model, and the Shear Stress Transport (SST) viscous turbulence model for moist air condensing in transonic flows was proposed. The prediction accuracy of steady and unsteady condensing flows was validated by experimental data and theory. The unsteady frequency and fluctuation intensity of pressures for symmetric and asymmetric condensing oscillation modes were discussed. A new formula (f0 = 1.992Φ01.539ws0.3853) of dimensional frequency related with inlet relative humidity and saturated vapor mass fraction was obtained. Then, periodic mass flux, pressure loss and droplet mass generation rate distributions at different carrier gas pressure were analyzed. The pressure loss coefficient represents the energy loss. As the carrier gas pressure increases, the mass flow rate increases, but the energy of condensation-induced shock decreases. Combined with the analysis of the distribution of liquid mass fraction, it is also found that Mach number and pressure fluctuation are induced by condensation wave due to heat release. Finally, the velocity phase diagrams and heat addition of per unit volume at different oscillation modes were assessed. It reveals the maximum heat addition amounts of per unit volume for three symmetric modes are 1.28 × 103, 1.48 × 103 and 1.54 × 103 MW m−3 along the increase of humidity.

Asteroseismology of Close Binary Stars: Tides and Mass Transfer

The study of stellar oscillations allows us to infer the properties of stellar interiors. Meanwhile, fundamental parameters such as mass and radius can be obtained by studying stars in binary systems. The synergy between binarity and asteroseismology can constrain the parameter space of stellar properties and facilitate the asteroseismic inference. On the other hand, binarity also introduces additional complexities such tides and mass transfer. From an observational perspective, we briefly review the recent advances in the study of tidal effects on stellar oscillations, focusing on upper main sequence stars (F-, A-, or OB- type). The effect can be roughly divided into two categories. The first one concerns the tidally excited oscillations (TEOs) in eccentric binaries where TEOs are mostly due to resonances between dynamical tides and gravity modes of the star. TEOs appear as orbital-harmonic oscillations on top of the eccentric ellipsoidal light curve variations (the 'heartbeat' feature). The second category is regarding the self-excited oscillations perturbed by static tides in circularized and synchronized close binaries. It includes the tidal deformation of the propagation cavity and its effect on eigenfrequencies, eigenfunctions, and the pulsation alignment. We list binary systems that show these two types of tidal effect and summarise the orbital and pulsation observables. We also discuss the theoretical approaches used to model these tidal oscillations and relevant complications such as non-linear mode coupling and resonance locking. Further information can be extracted from the observations of these oscillations which will improve our understanding of tides. We also discuss the effect of mass transfer, the extreme result of tides, on stellar oscillations. We bring to the readers' attention: 1) oscillating stars undergoing mass accretion (A-, F-, and OB type pulsators and white dwarfs), for which the pulsation properties may be changed significantly by accretion; 2) post-mass transfer pulsators, which have undergone a stable or unstable Roche-Lobe overflow. These pulsators have great potential in probing detailed physical processes in stellar interiors and mass transfer, as well as in studying the binary star populations.

Asteroseismology of Close Binary Stars: Tides and Mass Transfer

The study of stellar oscillations allows us to infer the properties of stellar interiors. Meanwhile, fundamental parameters such as mass and radius can be obtained by studying stars in binary systems. The synergy between binarity and asteroseismology can constrain the parameter space of stellar properties and facilitate the asteroseismic inference. On the other hand, binarity also introduces additional complexities such tides and mass transfer. From an observational perspective, we briefly review the recent advances in the study of tidal effects on stellar oscillations, focusing on upper main sequence stars (F-, A-, or OB- type). The effect can be roughly divided into two categories. The first one concerns the tidally excited oscillations (TEOs) in eccentric binaries where TEOs are mostly due to resonances between dynamical tides and gravity modes of the star. TEOs appear as orbital-harmonic oscillations on top of the eccentric ellipsoidal light curve variations (the “heartbeat” feature). The second category is regarding the self-excited oscillations perturbed by static tides in circularized and synchronized close binaries. It includes the tidal deformation of the propagation cavity and its effect on eigenfrequencies, eigenfunctions, and the pulsation alignment. We list binary systems that show these two types of tidal effect and summarize the orbital and pulsation observables. We also discuss the theoretical approaches used to model these tidal oscillations and relevant complications such as non-linear mode coupling and resonance locking. Further information can be extracted from the observations of these oscillations which will improve our understanding of tides. We also discuss the effect of mass transfer, the extreme result of tides, on stellar oscillations. We bring to the readers' attention: (1) oscillating stars undergoing mass accretion (A-, F-, and OB type pulsators and white dwarfs), for which the pulsation properties may be changed significantly by accretion; (2) post-mass transfer pulsators, which have undergone a stable or unstable Roche-Lobe overflow. These pulsators have great potential in probing detailed physical processes in stellar interiors and mass transfer, as well as in studying the binary star populations.

Numerical study on the flow and heat transfer of water-based Al2O3 forced pulsating nanofluids based on self-excited oscillation chamber structure

In this study, the flow and heat transfer characteristics of the forced pulsating Al2O3-water nanofluid were numerically studied. The pulsating excitation of the nanofluid is provided by the Helmhertz self-excited oscillating cavity. The large eddy simulation method is used to solve the equation, and the local Nusselt number and heat transfer performance index are used to analyze the heat transfer characteristics of the nanofluid in the self-excited oscillation heat exchange tube. In addition, the effect of different downstream tube diameters on heat transfer enhancement is discussed. The research results show that the existence of the countercurrent vortex can increase the disturbance of the near-wall fluid, thereby improving the mixing degree of the near-wall fluid and the central mainstream. As the countercurrent vortex migrates downstream, pulse enhanced heat transfer is realized. Furthermore, it was also found that when the downstream tube diameter d2 = 1.8d1, the periodic effect of the local Nusselt number of the wall is the best and the heat transfer performance index has the most stable pulsation effect within a pulsation cycle. But when d2 = 2.0d1, the change curve of heat transfer performance index in a pulsating period is the highest, the maximum value is 3.95.

Nonlinear feedback anti-control of limit cycle and chaos in a mechanical oscillator: theory and experiment

Though engineers believe that self-excited oscillation and chaos is detrimental, recent research has revealed that self-excited periodic and chaotic oscillation can be effectively utilized in many engineering processes and devices for significant benefits. Then a simple nonlinear acceleration feedback controller is proposed to generate self-excited periodic and chaotic oscillation in a mechanical oscillator. Analytical expressions relating the amplitude of limit cycles and control parameters are obtained by the method of multiple time scales. Analytical results are verified by numerical simulations performed in MATLAB–SIMULINK. Existence of chaotic oscillations is confirmed by numerical simulations. An extensive parametric study is carried out to reveal the nature of the chaotic oscillations and its dependence on the controller parameters. Theoretical results are finally verified by experiments. It is generally observed that the same controller can be used to induce both periodic and chaotic oscillations just by flipping the phase of the controller. This is possibly the first example where the same controller can be utilized to generate periodic and chaotic oscillation in a mechanical system. The findings of the paper are believed to be used in macro- and micro-mechanical systems.

Flow Parameters in Dominant Mode Selection of Self-Excited Oscillation in Slat Coves

This paper investigates self-excited oscillation within a slat cove and the flowfield parameters involved in selection of the main oscillation mode. Aeroacoustic experiments are described for aerodynamic noise characteristics on the leading-edge slat of a two-dimensional three-element high-lift configuration. Different geometrical settings are tested at varying angles of attack. A numerical simulation method is used as an auxiliary tool to analyze the flowfield. Based on previous research results and the experimental results obtained in this paper, a ratio of is proposed to evaluate the main mode of self-excited oscillation, where is the shear-layer length within the slat cove, is the boundary-layer thickness near the point of separation, and is the ratio of average vortex convection velocity along the shear layer to the maximum velocity in the shear layer near the cusp. The relationship between the aforementioned ratio and the main mode of oscillation is verified by far-field noise data for a high-lift configuration with different geometrical settings. As the slat translation along the chordwise direction of the main wing increases, the ratio also increases; and the main mode of self-excited oscillation switches from mode II to a transition phase, and then to mode III.

Space-charge induced particle reflection between hybrid AC/DC biased electrodes

Space-charge limited current flow between DC biased electrodes is a widely applicable problem in many areas of physics. Recently, radio-frequency biasing, together with DC self-bias formation, has been studied as a new concept for the extraction of charged particles from an upstream plasma source. Here, we compare particle extraction between systems using this hybrid AC/DC biasing, with conventional DC biased electrodes, and identify important similarity parameters. The injection current first leading to particle reflection strongly depends on the applied AC frequency and voltage magnitude, as well as the initial particle injection velocity, and is in general lower than the DC case. For injection currents above the AC limit, the system becomes unstable, and self-excited space-charge oscillations are generated. A critical parameter is the ratio of the average particle transit time between the electrodes to the AC period, γ = t L/T. As long as γ ≫ 1, the onset of particle reflection can be sufficiently delayed that the extracted current approaches the DC limit.

Investigation of the modes of motion of a hydraulic drive with axial-piston hydraulic motors at low speeds

Technological machines for various purposes, in which hydraulic actuators are widely used, are constantly being improved in terms of power, speed and accuracy of the specified parameters. It requires making certain changes in the design of these actuators that allow them to withstand the operating modes of technological machines within the specified limits. The article considers the results of the study of the operation modes of a nonlinear hydraulic actuator with axial-piston hydraulic motors under the conditions of parametric excitation of self-oscillations due to the nonlinear nature of the friction moment in the front distributor of the hydraulic motor. The authors propose mathematical models of the modes of operation of this hydraulic drive at low speeds. They present a linearized mathematical model and the results of the study of this hydraulic drive in the form of amplitude-frequency characteristics obtained using the harmonic linearization of the dynamic equations. The results of the study allow us to estimate the parametric oscillations of the hydraulic actuator and to evaluate the minimum value of the constant component of the speed corresponding to the beginning of periodic intermittent motions, which leads to a decrease in the accuracy of performing technological movements of the actuators of technological machines.

Simulation Analysis of Ferro resonance of Generator-Transformer Group Shock Tripping

As a common self-excited oscillation in power systems, ferromagnetic resonance has a great threat to the insulation of electrical equipment due to overvoltage and overcurrent. The magnetizing inductance of electromagnetic voltage transformers has nonlinear characteristics, which tend to saturate the excitation and cause circuit resonance and generate resonance overvoltage. The ferromagnetic resonance overvoltage caused by the saturation of the transformer has greatly affected the safe and stable operation of the power grid. Therefore, it is very necessary to analyze, calculate and simulate the ferromagnetic resonance overvoltage, and to study the measures to eliminate resonance. Through theoretical calculation and simulation analysis of a hydroelectric power plant generator-transformer group reverse transmission impulse tripping fault, the cause of its ferromagnetic resonance was analysed, and relevant operation and maintenance suggestions were put forward to provide a basis for further research.

Математичне моделювання жорстких режимів збудження кавітаційних ав-токоливань у системі живлення рідинних ракетних двигунів

Hard self-oscillation excitation differs from soft excitation in that self-oscillations are set up only if the initial departure of an oscillating system from equilibrium is strong enough. Experimental studies of cavitation oscillations in hydraulic systems with cavitating pumps of liquid-propellant rocket engines ((LPREs) include works that describe hard excitation of cavitation oscillations. By mow, hard excitation regimes have not been explained theoretically, to let alone their mathematical simulation. This paper presents a mathematical model of hard excitation of cavitation oscillations in a LPRE feed system, which comprises a mathematical model of cavitation self-oscillations in a LPRE feed system that accounts for pump choking and an external disturbance model. A mechanism of hard excitation of cavitation oscillations in a LPRE feed system is proposed. It is well known that hard excitation of cavitation self-oscillations may take place in cases where the pump feed system is near the boundary of the cavitation self-oscillation region. In this case, the self-oscillation amplitudes are small, and they are limited only by one nonlinearity (cavity volume vs. pump inlet pressure and flow relationship). Under excitation of sufficient intensity, the pump inlet pressure and flow find themselves in the choking characteristic; this may be responsible for choking and developed cavitation self-oscillations, which remain of interrupted type and do not go into the initial small-amplitude oscillations even after excitation removal. A mathematical simulation of hard excitation of cavitation self-oscillations was conducted to determine the parameters of cavitation self-oscillations in a bench feed system of a test pump. The simulation results show that without an external disturbance the pump system exhibits small-amplitude self-oscillations. On an external disturbance, developed (interrupted) cavitation oscillations are set up in the system, which is in agreement with experimental data. The proposed mathematical model of hard excitation of cavitation self-oscillations in a LPRE feed system allows one to simulate a case observed in an experiment in which it was possible to eliminate cavitation self-oscillations by an external disturbance.

Self-excited oscillations in an inverted cart–pendulum based on the two-relay approach

Solving the orbital stabilization of a class of underactuated systems near its open-loop unstable equilibrium point is a challenging task but useful in repetitive tasks. This paper addresses the control problem of an inverted cart–pendulum’s motion driven by a two-relay controller. This controller is tuned to set the desired amplitude and frequency using the locus of the perturbed relay system, which is a frequency-domain method. We solved the periodic motion of the pendulum occurring in its open-loop unstable equilibrium point. The experimental results showed that the proposed two-relay controller forced the pendulum into a periodic motion around the upright position.

Numerical modeling of a high power triode-based self-excited oscillator: a path forward more efficient designs and a better frequency stability of low cost high power RF sources

Triode-based circuits are still the less expensive and more reliable high power sources for industrial applications between 13.56 and 40.68 Mhz. Among them, self-excited oscillators feature the lower cost but with a frequency stability preventing them to address all ISM frequencies and applications. This article demonstrates the possibility to model numerically self-excited oscillators with power triodes using a class-C practical circuit. Advantages over existing analytical calculations and graphical derivations are shown. A method is proposed to evaluate the frequency stability in presence of internal imperfections and external perturbations. These tools offer the possibility to design and analyze more efficiently this family of oscillators especially for demanding applications regarding frequency stability.

Numerical investigation on the porosity effect of a bias-flow perforated liner on attenuating self-excited thermoacoustic oscillations

Self-excited thermoacoustic oscillations are unwanted in propulsion and stationary gas turbines due to the undesirable structural and heating damage to the engine systems. To prevent overheating and damping noise, perforated liners are widely applied in engines. It is a cylindrical metal sheet perforated with a number of millimetre-size circle orifices. In this work, numerical studies are conducted on an acoustically open-open thermoacoustic combustor with premixed propane and air fuelled and burnt. A perforated liner with a porosity σ is implemented downstream of the combustor in the presence of a cooling flow (also known as bias flow). The effects of (1) the cooling mass flow rate ṁb and (2) the porosity σp are examined one at a time. It is found that in the absence of the cooling flow, i.e., ṁb = 0, the perforated liner’s acoustic damping effect is quite small. Increasing is found to increase the liners damping performance in terms of attenuating the thermoacoustic oscillations, due to the enhanced vortex shedding generated over the rims of the perforated holes. In addition, there is an optimum cooling flow rate corresponding to the maximum acoustic damping effect of the liner. Furthermore, for a given mass flow rate, there is an optimum porosity.

Effect of time delay on the generation of oscillation in a single degree-of-freedom mass-spring-damper system by nonlinear velocity feedback

The present paper investigates the effect of time delay in a particular type of single degree-of-freedom self-excited oscillator. The self-excited vibration is generated in the system by using linear velocity feedback (to destabilize the static equilibrium of the system) with a nonlinear Rayleigh type feedback (to limit the growth of the instability into a stable limit cycle). The general method of describing function is employed to study the dynamics with the presence of time delay. Also, the analytical results are verified with the simulation result. Without time delay, the control law can generate a stable limit cycle with the proper choice of control parameters. However, the presence of time delay introduces a globally unstable limit cycle in the system with a stable one. Though the amplitude of the stable limit cycle dies down with the increase of time delay and finally vanishes by stabilizing the static equilibrium of the system. The effect of control parameters is also studied.

Nonlinear thermoacoustic instability investigation on ammonia-hydrogen combustion in a longitudinal combustor with double-ring inlets

The greenhouse effect induced by the combustion of hydrocarbon fuel is an urgent environmental problem. Ammonia gas, as a renewable energy with a high proportion of hydrogen content, can achieve zero CO2 emission. In order to ignite ammonia and obtain continual flame, a partial premix entry condition of NH3/H2/O2 with double-ring inlets is adopted. The RNG k-ε model and EDC model are used to analyse the self-excited oscillation and the total heat release. After the numerical results and experimental data are validated, the following aspects are investigated: (1) total mass flow rate; (2) mass fraction of hydrogen; (3) mass flow ratio of inlets; and (4) the temperature of the heat exchanger. The results are compared with the traditional single-ring structure under the same condition. It is found that the exothermic heat of double-ring structure increases by 98.7% on average. The frequency of intermittent oscillation increases with the decrease in HN3 proportion. When pure hydrogen is passed through the outer ring, the combustion limit can be greatly expanded even if the inlet mass fraction of hydrogen is very small. This study contributes to provide an alternative method to enhance ammonia combustion and improve its flammability limit.

Study on the effects of wheel-rail friction self-excited vibration and feedback vibration of corrugated irregularity on rail corrugation

Both the self-excited vibration of the wheel-rail system and the feedback vibration of track irregularity have certain effects on the rail corrugation. The present paper focuses on the effects of wheel-rail friction self-excited vibration and feedback vibration of corrugated irregularity on rail corrugation. Taking the typical rail corrugation on the low rail of the small-radius curve of the metro as the research object, the relevant wheel-rail finite element model and the worn rail surface of corrugated irregularity are established. Then, considering the influences of the wheel-rail friction self-excited oscillation and feedback vibration of corrugated irregularity, the stability and dynamic response of wheel-rail system on smooth and worn rail surfaces are studied to explore the dynamic origin of rail corrugation. Furthermore, the effects of the friction coefficient, corrugation depth and corrugation wavelength on the development of rail corrugation are studied, respectively. The results show that the wheel-rail friction-induced vibration may cause the rail corrugation and the feedback vibration of corrugated irregularity may aggravate the development of the subsequent rail corrugation. Then, the increase of the wheel-rail friction coefficient will increase the possibility of rai corrugation whether the rail surface is smooth or wear. When the wheel-rail friction coefficient is less than 0.2, no unstable vibration occurs. Moreover, the development of wear depth and the expansion rate to the surrounding rail of subsequent rail corrugation will be further intensified with the corrugation depth increases. Furthermore, when a corrugation wavelength is less than 60 mm, the feedback vibration of rail corrugation will aggravate the development of rail corrugation. Otherwise, the development rate of rail corrugation will gradually slow down with the corrugation wavelength increases continuously.

3D convolutional selective autoencoder for instability detection in combustion systems

While analytical solutions of critical (phase) transitions in dynamical systems are abundant for simple nonlinear systems, such analysis remains intractable for real-life dynamical systems. A key example is thermoacoustic instability in combustion, where prediction or early detection of the onset of instability is a hard technical challenge, which needs to be addressed to build safer and more energy-efficient gas turbine engines powering aerospace and energy industries. The instabilities arising in combustion chambers of engines are mathematically too complex to model. To address this issue in a data-driven manner instead, we propose a novel deep learning architecture called 3D convolutional selective autoencoder (3D-CSAE) to detect the evolution of self-excited oscillations using spatiotemporal data, i.e., hi-speed videos taken from a swirl-stabilized combustor (laboratory surrogate of gas turbine engine combustor). 3D-CSAE consists of filters to learn, in a hierarchical fashion, the complex visual and dynamic features related to combustion instability from the training videos (i.e., two spatial dimensions for the image frames and the third dimension for time). We train the 3D-CSAE on frames of videos obtained from a limited set of operating conditions. We select the 3D-CSAE hyper-parameters that are effective for characterizing hierarchical and multiscale instability structure evolution by utilizing the dynamic information available in the video. The proposed model clearly shows performance improvement in detecting the precursors and the onset of instability. The machine learning-driven results are verified with physics-based off-line measures. Advanced active control mechanisms can directly leverage the proposed online detection capability of 3D-CSAE to mitigate the adverse effects of combustion instabilities on the engine operating under various stringent requirements and conditions.

On the importance of time delay and noise in thermoacoustic modeling

Identification of thermoacoustic systems usually requires low-order modeling, often obtained by means of a Galerkin projection onto a single acoustic mode. The resulting dissipative self-excited oscillator equation describes the dynamic balance between acoustic energy sources (i.e. the flame) and sinks. Previous works studied the case of a nonlinear flame response and a driving background noise or a nonlinear delayed flame response in a deterministic setting. In the present work, we extend previous efforts considering a generic nonlinear delayed flame response with noise. In the case where both the delay and the noise are considered, we show that the widely-used cubic nonlinear saturation function is inadequate because it can lead to diverging solutions, due to the unboundedness of the respective describing function. We present an analytical treatment for a generic saturation function, which is benchmarked against an arctangent saturation function which does not exhibit this shortcoming. From a linear stability analysis, the delayed equation is found to present intrinsic thermoacoustic (ITA) eigenvalues, showing that a one-mode approximation can still retain information on both the acoustic and the ITA dynamics if a delayed flame model is adopted. Additionally, the model is found to present rich nonlinear dynamics (e.g. bistability) and to reproduce mode switching between two close frequencies, which is a feature often observed experimentally in thermoacoustic systems. We show that the derivation of quantitatively accurate equations for the slowly varying amplitude and phase is not trivial. To this regard, three sets of equations are introduced and a detailed discussion is dedicated to investigate their capability to model the original system dynamics. It is concluded that, for thermoacoustic applications, one of the presented sets more accurately models the delayed interaction between the acoustics and the flame response and should therefore be considered for system identification purposes. Additionally, a statistical characterization of the oscillation shows the need for more advanced modeling of amplitude and phase processes. We present novel equations based on perturbation methods and benchmark them with respect to classical results. The study explores a large nondimensional parameter space which encompasses a wide range of thermoacoustic systems.