Periodic Regimes Research Articles

Flow over a circular cylinder with a flexible splitter plate

In the present work, we study the flow field around, and forces acting on, a circular cylinder with an attached flexible splitter plate/flap. Two cases of flap length ( $L/D$ ), namely, $L/D = 5$ and $L/D = 2$ have been investigated focusing on the effect of variations in flap flexural rigidity, $EI$ . We find that for a range of $EI$ and Reynolds numbers $Re = UD/\nu$ , a non-dimensional bending stiffness $K^{\ast }=EI/((1/2)\rho U^2 L^3)$ collapses flap motion and forces on the system well, as long as $Re>5000$ . In the $L/D = 5$ flap case, two periodic flap deformation regimes in the form of travelling waves are identified (modes I and II), with mode I occurring at $K^{\ast } \approx 1.5\times 10^{-3}$ and mode II at lower $K^{\ast }$ values ( $K^{\ast }<3\times 10^{-5}$ ). In the $L/D = 2$ flap case, we find a richer set of flapping modes (modes A, B, C and D) that are differentiated by their flapping characteristics (symmetric/asymmetric and amplitude). Force measurements show that the largest drag reduction occurs in mode I ( $L/D = 5$ ) and mode C ( $L/D = 2$ ), which also correspond to the lowest lift and wake fluctuations, with the mode C wake fluctuations being lower than even the rigid splitter plate case. In contrast, the highest fluctuating lift, in both $L/D$ cases, occurs at higher $K^{\ast }$ , when the wake frequency is close to the first structural bending mode frequency of the flap. The observed rich range of flap/splitter plate dynamics could be useful for applications such as drag reduction, vibration suppression, reduction of wake fluctuations and energy harvesting.

Flow regime identification and flow instability analysis of oscillatory flows over twin circular cylinders

Oscillatory flows past two identical circular cylinders are investigated by two-dimensional direct numerical simulations in the parameter space of gap ratio (0.5 ≤ G ≤ 4.0), angle of flow incidence (0° ≤ α ≤ 90°) and Keulegan–Carpenter number (4 ≤ KC ≤ 12) with a constant Reynolds number Re = 150, where G = L/D, KC = UmT/D and Re = UmD/υ with D being the dimeter of the identical cylinders, L the shortest surface-to-surface distance between the two cylinders, Um and T being the velocity amplitude and period of the sinusoidal oscillatory flow, respectively, and α is defined as the angle between the flow direction to the line connecting the centers of the two cylinders. Comparing with the tandem or side-by-side arrangements of twin circular cylinders in oscillatory flows, the staggered twin cylinders (0° < α < 90°) involve more diverse flow regimes, including the periodic, quasi-periodic and chaotic flow states, due to the inherent asymmetric flow interference around the cylinder pair. In addition to introducing four flow regimes for the tandem and side-by-side arrangements, this study newly identifies 11 flow regimes for the staggered twin cylinders. The newly reported flow regimes in this work are collaboratively identified through the flow visualizations, steady streaming, frequency spectra of fluid forces and Lissajous phase diagrams, as well as the temporal-spatial symmetry features of the wake flows. Connecting with the previous work by Zhao and Cheng [“Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers,” J. Fluid Mech. 751, 1–37 (2014)], this study presents overall regime maps in the KC-α plane for varied gap ratios. It is found that the flow regimes previously and presently identified for the tandem and side-by-side arrangements may also appear for the staggered twin cylinders. The present numerical results suggest the sensitive dependence of the flow regimes on the parameters of KC, α, and G. It is also found that a specific flow regime with narrow parameter bands may appear within another flow regime, forming the abnormal regime hole in the regime map. To understand the profound influence of the control parameters on the flow regime transition, and the relevant temporal-spatial symmetry breaking, the linear Floquet stability analysis is conducted in this work. It was confirmed that the variation of the KC number may result in the Ky symmetry breaking over several periodic flow regimes, while the change of the angle of flow incidence may account for the H2 symmetry covering various periodic and quasi-periodic flow regimes. The stability analysis also explains the temporal flow transition and the abnormal occurrence of the regime holes within either quasi-periodic or chaotic flow regimes.

Carbon source priority and availability limit bidirectional electron transfer in freshwater mixed culture electrochemically active bacterial biofilms

This study investigated, if a mixed electroactive bacterial (EAB) culture cultivated heterotrophically at a positive applied potential could be adapted from oxidative to reductive or bidirectional extracellular electron transfer (EET). To this end, a periodic potential reversal regime between − 0.5 and 0.2 V vs. Ag/AgCl was applied. This yielded biofilm detachment and mediated electroautotrophic EET in combination with carbonate, i.e., dissolved CO2, as the sole carbon source, whereby the emerged mixed culture (S1) contained previously unknown EAB. Using acetate (S2) as well as a mixture of acetate and carbonate (S3) as the main carbon sources yielded primarily alternating electrogenic organoheterotropic metabolism with the higher maximum oxidation current densities recorded for mixed carbon media, exceeding on average 1 mA cm−2. More frequent periodic polarization reversal resulted in the increase of maximum oxidative current densities by about 50% for S2-BES and 80% for S3-BES, in comparison to half-batch polarization. The EAB mixed cultures developed accordingly, with S1 represented by mostly aerobes (84.8%) and being very different in composition to S2 and S3, dominated by anaerobes (96.9 and 96.5%, respectively). S2 and S3 biofilms remained attached to the electrodes. There was only minor evidence of fully reversible bidirectional EET. In conclusion the three triplicates fed with organic and/or inorganic carbon sources demonstrated two forms of diauxie: Firstly, S1-BES showed a preference for the electrode as the electron donor via mediated EET. Secondly, S2-BES and S3-BES showed a preference for acetate as electron donor and c-source, as long as this was available, switching to CO2 reduction, when acetate was depleted.Graphical

Fate and migration of enhanced rock weathering products through soil horizons; implications of irrigation and percolation regimes

Terrestrial enhanced rock weathering (ERW) is reckoned as a robust method to contribute to stabilizing atmospheric carbon and combat global warming. The method is particularly a matter of interest in agricultural soil, offering a vast opportunity for the application of crushed silicate minerals and secondary carbonate accumulation and migration. Although the applicability of this practice is well acknowledged, its impact on the geochemical alteration of soil vertical profile, particularly deeper layers, is less discussed in the literature. Moreover, the effect of irrigation and percolation regimes, as influenced by ambient conditions, is also not well-reported and characterized. In the present study, we utilized a high amendment rate (50 t/ha) of wollastonite skarn, a fast-weathering silicate mineral, to uncover the alterations in topsoil and subsoil as well as effluent water over a through a soil column experiment over five months, under more controlled (indoor) and less controlled (outdoor) ambient and irrigation conditions. The results indicate more conspicuous modification of parameters in shallow layers of soil compared to deeper ones, explicitly in the rain-fed setup. Silicate amendment induced an increase of 6.53 and 2.85 tCO2/ha (in the form of pedogenic carbonate (PC)) over the profile of soil (0–60 cm) under periodic and rain-fed water regimes, respectively. The silicate treatment was also found to be effective toward rising pH and electrical conductivity of topsoil (0–15 and 15–30 cm layers) and leachate, and a measurably greater release of Ca2+ and Mg2+ in the column effluent. We estimate a carbon drawdown ratio (carbonate/bicarbonate) of ≈15:1 in this study, showing that PC formation is a more significant weathering indicator than leachate bicarbonate export in the shorter term for a fast-weathering mineral in pH-neutral soils and moderate irrigation regime. Such observations are valuable for developing carbon drawdown quantification methods suitable for a variety of agricultural lands and global regions.

Forecasting Trading-Session Return Volatility in Taiwan Futures Market: A Periodic Regime Switching with Jump Approach

Forecasting Trading-Session Return Volatility in Taiwan Futures Market: A Periodic Regime Switching with Jump Approach

Spiking ruby revisited: self-induced periodic spiking oscillations leading to chaotic state in a Cr:Al2O3 laser with cw 532-nm pumping

This paper reexamines a 60-year-old mystery of spiking behavior in ruby lasers with a cw 532-nm pump, paying special attention to mode matching between the pump and lasing beam within a ruby crystal placed in a semi-confocal laser cavity. Periodic spiking oscillations were observed in a limited pump power regime, where spikes obeying the generic asymmetric hyperbolic function appeared at a repetition rate around 50 kHz and with a 130-150 ns width and 0.1-0.6 µJ energy depending on the pump power. The physics of the spiking behavior based on Kleinman’s mechanical approach and a plausible interpretation for the periodic spiking oscillation in terms of self-induced mode matching between the pump and laser beams through the self-induced Kerr-lens effect are addressed. The statistical nature inherent to spiking and the associated self-organized critical behavior in the quasi-periodic spiking oscillations as well as chaotic states occurring outside the periodic spiking regime are clarified from a nonlinear dynamics point of view and intriguing statistical properties inherent to chaotic oscillations in usual solid-state lasers subjected to external modulations are shown to be present in the self-induced instabilities of the ruby laser

Novel prediction of fluid forces on obstacle in a periodic flow regime using hybrid FEM-ANN simulations

Novel prediction of fluid forces on obstacle in a periodic flow regime using hybrid FEM-ANN simulations

Influence of symmetric/asymmetric boundaries on axisymmetric convection in a cylindrical enclosure in the presence of a weak vertical throughflow

The linear and nonlinear stability of axisymmetric convection of a viscous fluid in a cylindrical enclosure heated from below is investigated for various radius to height ratios. A weak vertical throughflow is imposed in a gravity-aligned or a gravity-opposing manner. Symmetric and asymmetric boundaries of free-free, rigid-rigid and rigid-free types are considered for lower and upper boundaries with isothermal temperature boundary condition. The side-walls are assumed to be rigid and adiabatic. A convergent Maclaurin series representation is considered for the finding of axial trial eigenfunctions. In order to corroborate the results of the present study with those of a previous investigation, the critical Rayleigh number and the number of radial rolls manifesting for any given aspect ratio are determined in the case of no throughflow and an exact match is found. Further, the influence of boundaries and the effect of throughflow on chaotic and periodic regimes of motion are studied with the help of a time series solution and the largest Lyapunov exponent as indicators of chaos. The novelty of the present study is the use of a Maclaurin series representation for the eigenfunctions of the linear problem and using the same in determining the solution with the convective mode.

PERIODIC MODES IN THE MODEL OF A MATHEMATICAL PENDULUM WITH IMPULSE EFFECT

The article is devoted to establishing the conditions for the existence of periodic regimes of the model of a mathematical pendulum with impulse effect. An important aspect is that such a system is subjected to the action of instantaneous forces at the moments when the moving point passes some fixed position. In addition, it is subjected to impulse action at unfixed moments of time, whereby its amount of movement is increased by a certain amount. The paper presents some theoretical aspects, as well as a description of the sequence of moments of time, which describes the mechanism of reducing the problem with impulse action at unfixed moments of time to the problem of finding fixed points of the interval within itself. The relevance and degree of research of the problem is revealed by comparing existing solutions to the problem and finding and adding new ones. Actually, this is the main task of this work. The resulting problem involves investigating the existence of conditions that ensure the existence of cycles to which periodic solutions correspond. In the work, a second-order differential equation with impulse action is investigated in a specific case with a fixed value of the position of the impulse action depending on the values of the parameters in the impulse action function. As a result, two cycles of period three were found. It is also demonstrated by verification that the given cycles form periodic solutions. The obtained results are recorded as detailed and informative as possible. In the work, a clear view of the points that guarantee the existence of periodic regimes in the system of the mathematical pendulum with impulse action is obtained and two graphs are given, that demonstrate the results of the experiment. It is illustrated in colors how the trajectories change after each action of impulse forces. Using a corollary from Sharkovsky's theorem, it is shown that if a function is continuous and has a periodic point of period three, then it has periodic points of any natural period. Therefore, in the system there are such periodic regimes in which the phase point undergoes impulse action exactly n times per period, where n is a natural number.

Chaotic signal generation in a CW K-band gyro-TWT with strong output reflections

We experimentally study the dynamics of a K-band continuous wave gyro-resonant traveling wave tube (gyro-TWT) with strong output reflections. By varying system parameters, we have obtained transitions from periodic self-modulation regimes with line spectra to more complex oscillation regimes. We present the analysis of experimental data verifying the experimental observation of chaotic oscillation regimes. We have shown that chaotic oscillation regimes emerge in a fairly narrow parameter area, about 0.5% of magnetic field strength and about 10% of reflectivity. Maximum oscillation power reaches 0.5 kW at about 2% efficiency. For a gyro-TWT with output reflections operating in the CW mode, the chaotic oscillations are being experimentally observed and systematically analyzed for the first time.

Investigation of nonlinear control of galloping with a linear beam with elastic boundary conditions

The aim of this study is nonlinear passive control of galloping oscillation on overhead transmission lines. The considered system is a linear beam subjected to harmonic and aerodynamic excitations which is coupled to a nonlinear absorber placed on an arbitrary position along the beam. Both extremities of the beam present rotationally and translationally elastic boundary conditions. After projection of spatio-temporal equations of the system on an arbitrary mode of the beam (the mode to be controlled), fast and slow system dynamics are traced which predict periodic or non periodic regimes. All analytical developments are compared with numerical results obtained from direct numerical integration of system equations and also from finite element modeling of the overall structure. Then, nonlinear passive control process of galloping instability by a non smooth nonlinear energy sink (NES) is investigated on a real case of galloping instability on a transmission line cable due to accretion of ice on it.

Controlling the frequency of periodic self-modulation in gyrotrons with external reflections

We develop the theory of electron–wave interaction in gyrotrons with reflections of part of the radiation, focusing on the implementation of self-modulation generation regimes with controlled frequencies. The optimal conditions for the simultaneous excitation of neighboring axial modes of the electrodynamic system of a gyrotron with a reflecting diaphragm in the output waveguide path are found. When the gyrotron is powered by an electron beam under these conditions, periodic self-modulation regimes are realized with the distance between the main spectral components controlled by varying the distance to the reflector. The conclusions of the theory are confirmed by the results of direct particle-in-cells simulation.

Analytical solution to Windkessel models using piecewise linear aortic flow waveform

Objective. Deriving time-domain analytical solutions to two- three- and four-element Windkessel models, which are commonly used in teaching and research to analyse the behaviour of the arterial pressure-flow relationship. Approach. The governing (first-order, non-homogeneous, linear) differential equations are solved analytically, based on a piecewise linear function that can accurately approximate typical aortic flow waveforms. Main results. Closed-form expressions for arterial pressure are obtained both in transient conditions and in steady-state periodic regime. Significance. In most cases Windkessel models are studied in the frequency domain and when studied in the time domain, numerical methods are used. The main advantage of the proposed expressions is that they are an explicit, exact, and easily understood mathematical description of the model behaviour. Moreover, they avoid the use of Fourier analysis or numerical solvers to integrate the differential equations.

Thermal cycle performance of thermocline storage: numerical and experimental exergy analysis

The performance of a dual-media thermocline storage is studied in stationary periodic operation. Successive cycles are carried out until a stabilised behaviour is obtained. Numerical results are compared to experiments realised on a 107 kWh prototype combining thermal oil and alumina. Two performance indicators are studied: utilisation rate and exergy efficiency. The utilisation rate decreases as the thermocline thickens over the cycles, while the exergy efficiency increases over the cycles, mainly due to lower heat losses improving the energy efficiency. Experimental values stabilise around UR = 53% and ηex= 73% at the fifth cycle. A new indicator is introduced: the storage quality factor Ψs, which quantifies the exergy losses due to the process. Experiments and simulations show good agreement, with a slight underestimation of heat losses by the model. Exergetic performance of thermocline storage is thus validated experimentally on a prototype-scale setup in stationary periodic regime, with satisfying value: Ψs≈ 0.99. The influence of stop thresholds on performance is then examined numerically. The utilisation rate decreases with strict thresholds (κch=κd= 0.05) because it prevents the storage to be fully loaded and because the thermocline thickens over the cycles if not extracted from the tank. The exergy efficiency globally increases for hybrid threshold (strict during charge, soft during discharge), with a maximum of ηex= 96.5% for κch= 0.05, κd= 0.95. In that configuration, the time during which the storage is hot is minimised, decreasing heat losses. Besides, setting strict thresholds limits the variation of the outlet temperature and reduces exergy destruction.

Chaos in coupled heteroclinic cycles and its piecewise-constant representation

We consider two robust heteroclinic cycles rotating in opposite directions, coupled by diffusive terms. A complete synchronization is impossible in this system. Numerical studies show that chaos is abundant at low levels of coupling. With increasing coupling strength, several symmetry-changing transitions are observed, and finally, a stable periodic regime appears via an inverse period-doubling cascade. To reveal the behavior at extremely small couplings, a piecewise constant model for the dynamics is proposed. Within this model, we numerically construct a Poincaré map for a chaotic state, which appears to be an expanding non-invertible circle map, thus confirming the abundance of chaos in the small coupling limit. We also show that within the piecewise constant description, there is a set of periodic solutions with different phase shifts between subsystems due to dead zones in the coupling.

Transient mixed convection in a cylindrical cavity with a rotating finned cylinder

This article presents a numerical study of horizontal ring mixed convection with a heated inner cylinder equipped with two fins. Thermal buoyancy forces are maintained by considering the inner and outer cylinders at different uniform temperatures. The flow is generated by the rotation of the inner cylinder with a constant angular velocity (ω) in the counter-clockwise direction while the outer cylinder is held fixed. A finite volume scheme is adopted using the SIMPLE algorithm to solve the transport equations for continuity, momentum and energy. Simulations are made for various combinations of rotating Reynolds (Re = 0 to 1500) and Grashof numbers (Gr = 10 to 106). First, we focused on the criteria and parameters controlling the fully developed periodic regime. Thereafter, the heat transfer rates analyzed through the averaged Nusselt number (instant and over a period) highlights a complex phenomenon. For moderate Grashof numbers (Gr ≤ 103) the overall Nusselt number is not affected by Gr further, Re = 750 constitute a limit for the improvement of the heat transfer beyond which it decreases strongly. For larger Gr (>103), the reverse phenomenon occurs, i.e., the overall mean Nusselt number grows with Gr as Re < 750, then decreases for higher values.

Identification of Periodic Regimes in a Dynamic System

Identification of Periodic Regimes in a Dynamic System

Coupling performance of two tandem and side-by-side inverted piezoelectric flags in an oscillating flow

The flow-induced vibration characteristics and energy extraction performance of two flexible inverted piezoelectric flags arranged in tandem and side-by-side configurations in an oscillating flow are studied. An immersed boundary-lattice Boltzmann method is employed for Reynolds number of 100, mass ratio of 2.9 and non-dimensional bending stiffness of 0.26 which correspond to the maximum flapping amplitude for a single inverted flag in a uniform flow. 2D simulations are conducted by varying the ratio R of the frequency of the oscillating flow to the fundamental natural frequency of the flag and the horizontal velocity amplitude (Au) of the flow. Three coupling regimes at Au=0.5 are identified for both tandem and side-by-side flags: chaotic oscillations regime I (0.1≤R≤1), large periodic and symmetric oscillation regime IIa1.1≤R≤1.5andIIb(2.1≤R≤3.0), and small periodic and asymmetric oscillation regime III(1.6≤R≤2). The maximum mean electrical power coefficient C¯P occurs in regime IIa at R=1.5 with, α (piezo-mechanical coupling parameter) = 0.5, and β (piezo-electric tuning parameter) = 1.5. C¯P is 0.1 for a tandem upstream flag, 0.068 for the tandem downstream flag and 0.1 for both side-by-side flags, and is respectively 120%, 300% and 213%, higher than that of the corresponding flag in the uniform flow. This improvement is attributed to the higher flapping angular amplitude (180°), the higher ratio of the flapping frequency of the flags to the oscillating frequency of the flow (virtually constant at 0.5), and constructive vortex interaction in regime IIa.

Coupled systems with quasi-periodic and chaotic dynamics

The interaction of a system with quasi-periodic autonomous dynamics and a chaotic Rössler system is studied. We have shown that with the growth of the coupling, regimes of two-frequency and three-frequency quasiperiodicity, a periodic regime and a regime of oscillation death sequentially arise. With a small coupling strength, doubling bifurcations of three-frequency tori are observed in the system. A chaotic regime, characterized by two additional zero Lyapunov exponents in spectrum, is revealed. Two-parameter Lyapunov exponent analysis and bifurcation analysis are presented. A new bifurcation scenario of transition from the regime of oscillation death to quasi-periodicity in coupled systems is described.

Dynamics of a Wind Turbine with Two Moving Masses Using the Galloping Effect

A wind power plant is considered using the galloping effect, which includes two elastically connected translationally moving bodies: one is a square prism with a permanent magnet rigidly attached to it, and the other is a material point. Electricity is generated by the movement of a magnet in a coil. The influence of the system parameters on the wind speed at which galloping oscillations occur is analyzed. It is shown that a proper choice of parameters makes it possible to significantly expand the range of wind speeds at which periodic regimes exist, in comparison with a system containing one moving body. Approximations are obtained for the amplitudes and frequencies of the limit cycles arising in the system. The evolution of these cycles with a change in the stiffness of the spring between the bodies is studied. It is established that, for certain values of the parameters, the simultaneous existence of two attracting periodic solutions is possible. Conditions are obtained under which the power generated by such a system is greater than the power generated by a system with one moving mass.