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Journal articles on the topic 'Oscillator flows'
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1
Portillo, Daniel J., Eugene Hoffman, Matt Garcia, Elijah LaLonde, Christopher Combs, and R. Lyle Hood. "The Effects of Compressibility on the Performance and Modal Structures of a Sweeping Jet Emitted from Various Scales of a Fluidic Oscillator." Fluids 7, no. 7 (July 21, 2022): 251. http://dx.doi.org/10.3390/fluids7070251.
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Investigations of fluidic oscillators, or sweeping jet actuators, have primarily been conducted within the incompressible flow regime, which limits the accuracy of estimating fluidic oscillator performance for compressible flows. The objective of this study was to evaluate the effects of gas compressibility on the performance of a fluidic oscillator. A commonly used fluidic oscillator geometry (the Bray geometry) was scaled to five different sizes, 3D printed, and tested over a range of air flow rates. High-speed Schlieren images captured the sweeping jet exiting the fluidic oscillators, and custom MATLAB algorithms were used to calculate the oscillation frequencies and angles. A spectral proper orthogonal decomposition (SPOD) method was used to identify and compare the mode structures within the flow fields. All the results were compared using dimensionless parameters to observe performance trends. The results showed that the oscillation frequencies were directly proportional to the flow rate, while the oscillation angles were inversely proportional to the flow rate, regardless of scale size. The angular velocities were not proportional to the flow rate or scale size and exhibited maxima within the evaluated ranges. For all scale sizes, the mode structures were symmetric across the centerlines of the fluidic oscillators and extended further beyond the fluidic oscillators at higher flow rates. These results enable the prediction of fluidic oscillator performance, which can significantly improve the design process for an application where a fluidic oscillator may be used, such as aerospace applications, power generation, heat exchangers, or medical devices.
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Shardt, Orest, Hassan Masoud, and Howard A. Stone. "Oscillatory Marangoni flows with inertia." Journal of Fluid Mechanics 803 (August 19, 2016): 94–118. http://dx.doi.org/10.1017/jfm.2016.507.
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When the surface of a liquid has a non-uniform distribution of a surfactant that lowers surface tension, the resulting variation in surface tension drives a flow that spreads the surfactant towards a uniform distribution. We study the spreading dynamics of an insoluble and non-diffusing surfactant on an initially motionless liquid. We derive solutions for the evolution over time of sinusoidal variations in surfactant concentration with a small initial amplitude relative to the average concentration. In this limit, the coupled flow and surfactant transport equations are linear. In contrast to exponential decay when the inertia of the flow is negligible, the solution for unsteady Stokes flow exhibits oscillations when inertia is sufficient to spread the surfactant beyond a uniform distribution. This oscillatory behaviour exhibits two properties that distinguish it from that of a simple harmonic oscillator: the amplitude changes sign at most three times, and the decay at late times follows a power law with an exponent of $-3/2$. As the surface oscillates, the structure of the subsurface flow alternates between one and two rows of counter-rotating vortices, starting with one row and ending with two during the late-time monotonic decay. We also examine numerically the evolution of the surfactant distribution when the system is nonlinear due to a large initial amplitude.
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Kovacic, Ivana, Matthew Cartmell, and Miodrag Zukovic. "Mixed-mode dynamics of certain bistable oscillators: behavioural mapping, approximations for motion and links with van der Pol oscillators." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (December 2015): 20150638. http://dx.doi.org/10.1098/rspa.2015.0638.
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This study is concerned with a new generalized mathematical model for single degree-of-freedom bistable oscillators with harmonic excitation of low-frequency, linear viscous damping and a restoring force that contains a negative linear term and a positive nonlinear term which is a power-form function of the generalized coordinate. Comprehensive numerical mapping of the range of bifurcatory behaviour shows that such non-autonomous systems can experience mixed-mode oscillations, including bursting oscillations (fast flow oscillations around the outer curves of a slow flow), and relaxation oscillations like a classical (autonomous) van der Pol oscillator. After studying the global system dynamics the focus of the investigations is on cubic oscillators of this type. Approximate techniques are presented to quantify their response, i.e. to determine approximations for both the slow and fast flows. In addition, a clear analogy between the behaviour of two archetypical oscillators—the non-autonomous bistable oscillator operating at low frequency and the strongly damped autonomous van der Pol oscillator—is established for the first time.
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LUO, ALBERT C. J., and MOZHDEH S. FARAJI MOSADMAN. "SINGULARITY, SWITCHABILITY AND BIFURCATIONS IN A 2-DOF, PERIODICALLY FORCED, FRICTIONAL OSCILLATOR." International Journal of Bifurcation and Chaos 23, no. 03 (March 2013): 1330009. http://dx.doi.org/10.1142/s0218127413300097.
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In this paper, the analytical dynamics for singularity, switchability, and bifurcations of a 2-DOF friction-induced oscillator is investigated. The analytical conditions of the domain flow switchability at the boundaries and edges are developed from the theory of discontinuous dynamical systems, and the switchability conditions of boundary flows from domain and edge flows are presented. From the singularity and switchability of flow to the boundary, grazing, sliding and edge bifurcations are obtained. For a better understanding of the motion complexity of such a frictional oscillator, switching sets and mappings are introduced, and mapping structures for periodic motions are adopted. Using an eigenvalue analysis, the stability and bifurcation analysis of periodic motions in the friction-induced system is carried out. Analytical predictions and parameter maps of periodic motions are performed. Illustrations of periodic motions and the analytical conditions are completed. The analytical conditions and methodology can be applied to the multi-degrees-of-freedom frictional oscillators in the same fashion.
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Vodinchar, Gleb. "Hereditary Oscillator Associated with the Model of a Large-Scale αω-Dynamo." Mathematics 8, no. 11 (November 19, 2020): 2065. http://dx.doi.org/10.3390/math8112065.
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Cosmic magnetic fields possess complex time dynamics. They are characterized by abrupt polarity changes (reversals), fluctuations of fixed polarity, bursts and attenuations. These dynamic conditions can replace each other, including both regular and chaotic components. Memory in dynamo systems manifests itself in a feedback mechanism when a strong magnetic field begins to change the properties of turbulent flows. A hereditary oscillator can be the simplest model of such complex oscillatory systems with memory. The article suggests the construction of such oscillator by means of two-mode approximation of magnetic field components in the αω-dynamo model. The hereditary member describes the suppression of a field turbulent generator by magnetic helicity and determines the shape of oscillator potential. The article describes the implicit difference scheme for numerical research of oscillator. It also describes the results of numerical simulation for two cases—instantaneous feedback and delay in feedback. The results of simulation are interpreted in terms of oscillator theory. It is shown that the observed dynamic regimes in the model go well with the change of potential shape.
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Serrar, Abderrahim, Mohamed El Khlifi, and Azeddine Kourta. "Characterisation and comparison of unsteady actuators: a fluidic oscillator and a sweeping jet." International Journal of Numerical Methods for Heat & Fluid Flow 32, no. 4 (October 4, 2021): 1237–54. http://dx.doi.org/10.1108/hff-07-2021-0474.
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Purpose The purpose of this study is to compare two unsteady actuators: an oscillator and a sweeping jet. Both actuators can produce an oscillating jet of different amplitudes and frequencies without any moving parts, making them an attractive actuator concept. The Coanda effect phenomenon can explain the operating principles of these two unsteady actuators. Design/methodology/approach A numerical study was conducted to compare the amplitudes and frequencies of fluidic and sweeping jet (SJ) oscillators to obtain an efficient actuator to control separated flows at high Reynolds numbers. For this goal, two-dimensional unsteady Reynolds-averaged Navier-Stokes simulations were carried out using computational fluid dynamics (CFD) fluent code to evaluate the actuator performances. The discrete fast Fourier transform method determined the oscillation frequencies. Findings The oscillation frequencies gradually increase as the inlet pressure increases. The characteristics and dimensions of the vortices produced in the mixing chamber and feedback loops vary overtime when the injected fluid is swept sideways. The frequencies supplied by the SJ are stronger than those obtained by the fluidic oscillator, which may contribute to improving the aerodynamic performance at a lower power supply cost. Originality/value The existence of the splitter in the fluidic oscillator led to the production of separate pulses, which would be useful in various industrial applications, including active control of combustion and mixing processes while other applications such as flow separation control require SJs. With the latter actuator higher and interesting frequencies can be obtained, leading to efficient flow control.
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KHEIRANDISH, F., and M. AMOOSHAHI. "RADIATION REACTION AND QUANTUM DAMPED HARMONIC OSCILLATOR." Modern Physics Letters A 20, no. 39 (December 21, 2005): 3025–34. http://dx.doi.org/10.1142/s0217732305018384.
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By taking a Klein–Gordon field as the environment of a harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), we find out the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator. Applying perturbation method, we obtain some transition probabilities indicating the way energy flows between oscillator, reservoir and quantum vacuum.
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Ma, Zhao Wei, Tiang Jiang Hu, Han Zhou, Guang Ming Wang, and Dai Bing Zhang. "Modeling of Fish Adaptive Behaviors in Unsteady Flows." Applied Mechanics and Materials 461 (November 2013): 313–19. http://dx.doi.org/10.4028/www.scientific.net/amm.461.313.
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Fish can swim swiftly in complicated flow environments, which conceives inspirations for man-made underwater vehicles. This paper concentrates on observation and modeling of fish adaptive behaviors in unsteady flows. A good representative of bony fish, crucian, is taken as the experimental specimen for investigating biological adaptation with response to alteration of surrounding flow patterns. Difference of swimming parameters is confirmed by recorded samples within several flow patterns. Furthermore, a bio-inspired gait model is constructed to stimulate fish adaptive behaviors, since the traditional model is hardly suitable. The model is inspired and supported by biological neural oscillators. By using the developed neural oscillator model, not only certain rhythmic motions under a steady flow pattern can be generated, but also behavioral transitions between multiple different patterns within unsteady flows come true. Experimental results validate the effectiveness of the developed neural model in continuously and smoothly regulating fish propulsive patterns within unsteady flows.
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BILLINGHAM, JOHN. "Modelling the response of a vibrating-element density meter in a two-phase mixture." Journal of Fluid Mechanics 340 (June 10, 1997): 343–60. http://dx.doi.org/10.1017/s0022112097005600.
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A vibrating-element density meter is a mechanical oscillator with known properties, for example a tuning fork or a simple rod, driven to vibrate at a known frequency. The oscillator is immersed in a fluid and the resonant frequency measured. The density of the fluid can then be inferred. We consider an idealized meter immersed in two-phase flows of various types, and investigate whether a simple single-phase interpretation allows us to deduce the density of the mixture. We find that, when the density contrast between the two fluids is not great, the simple interpretation gives good results, for example in oil/water flows. However, when the density contrast is significant, for example in gas/liquid flows, the simple interpretation is highly inaccurate.
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Cang, Shijian, Yueyue Shan, and Zenghui Wang. "Conservative dynamics in a novel class of 3D generalized thermostatted systems." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 8 (August 2022): 083143. http://dx.doi.org/10.1063/5.0101570.
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This paper reports a method to derive a novel class of 3D generalized thermostatted oscillators from a simple damped harmonic oscillator. Its detailed procedure is obtained through a mathematical derivation. Then, we propose an example system to show the effectiveness of the method. Furthermore, the numerical analysis is performed to investigate its rich conservative dynamics, including chaotic sea, hierarchical invariant tori, and the coexistence of chaotic seas and invariant tori with islands-around-islands hierarchy, even if there are three dissipative terms in the example system. To verify the existence of conservative chaos at the physical level, an analog circuit is presented to observe the existing conservative chaotic flows in National Instruments multisim. We finally provide two systems, which can produce conservative chaotic flows with more complicated topologies, and draw our conclusions.
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Girfoglio, M., F. De Rosa, G. Coppola, and L. de Luca. "Unsteady critical liquid sheet flows." Journal of Fluid Mechanics 821 (May 18, 2017): 219–47. http://dx.doi.org/10.1017/jfm.2017.241.
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The unsteady global dynamics of a gravitational liquid sheet interacting with a one-sided adjacent air enclosure (commonly referred to as nappe oscillation configuration) is addressed under the assumptions of potential flow and the presence of surface tension effects. From a theoretical viewpoint the problem is challenging, because from previous literature it is known that the equation governing the evolution of small disturbances exhibits a singularity at the vertical station where the local flow velocity equals the capillary wave velocity (local critical condition), although the solution to the problem has not yet been found. The equation governing the local dynamics resembles one featuring the forced vibrations of a string of finite length, formulated in the reference frame moving with the flow velocity, and exhibits both slow and fast characteristic curves. From the global system perspective the nappe behaves as a driven damped spring–mass oscillator, where the inertial effects are linked to the liquid sheet mass and the spring is represented by the equivalent stiffness of the air enclosure acting on the displacement of the compliant nappe centreline. A suited procedure is developed to remove the singularity of the integro-differential operator for Weber numbers less than unity. The investigation is carried out by means of a modal (i.e. time asymptotic) linear approach, which is corroborated by numerical simulations of the governing equation and supported by systematic comparisons with experimental data from the literature, available in the supercritical regime only. As regards the critical regime for the unit Weber number, the major theoretical result is a sharp increase in oscillation frequency as the flow Weber number is gradually reduced from supercritical to subcritical values due to the shift of the prevailing mode from the slow one to the fast one.
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MOLERO, F. J., J. C. VAN DER MEER, S. FERRER, and F. J. CÉSPEDES. "THE 2-D SEXTIC HAMILTONIAN OSCILLATOR." International Journal of Bifurcation and Chaos 23, no. 06 (June 2013): 1330019. http://dx.doi.org/10.1142/s021812741330019x.
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The 2-D sextic oscillator is studied as a family of axial symmetric parametric integrable Hamiltonian systems, presenting a bifurcation analysis of the different flows. It includes the "elliptic core" model in 1-D nonlinear oscillators, recently proposed in the literature. We make use of the energy-momentum mapping, which will give us the fundamental fibration of the four-dimensional phase space. Special attention is given to the singular values of the energy-momentum mapping connected with rectilinear and circular orbits. They are related to the saddle-center and pitchfork scenarios with the associated homoclinic and heteroclinic trajectories. We also study how the geometry of the phase space evolves during the transition from the one-dimensional to the two-dimensional model. Within an elliptic function approach, the solutions are given using Legendre elliptic integrals of the first and third kind and the corresponding Jacobi elliptic functions.
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LUO, ALBERT C. J. "GLOBAL TANGENCY AND TRANSVERSALITY OF PERIODIC FLOWS AND CHAOS IN A PERIODICALLY FORCED, DAMPED DUFFING OSCILLATOR." International Journal of Bifurcation and Chaos 18, no. 01 (January 2008): 1–49. http://dx.doi.org/10.1142/s0218127408020148.
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This paper presents how to apply a newly developed general theory for the global transversality and tangency of flows in n-dimensional nonlinear dynamical systems to a 2-D nonlinear dynamical system (i.e. a periodically forced, damped Duffing oscillator). The global tangency and transversality of the periodic and chaotic motions to the separatrix for such a nonlinear system are discussed to help us understand the complexity of chaos in nonlinear dynamical systems. This paper presents the concept that the global transversality and tangency to the separatrix are independent of the Melnikov function (or the energy increment). Chaos in nonlinear dynamical systems makes the exact energy increment quantity to be chaotic no matter if the nonlinear dynamical systems have separatrices or not. The simple zero of the Melnikov function cannot be used to simply determine the existence of chaos in nonlinear dynamical systems. Through this paper, the expectation is that, from now on, one can use the alternative aspect to look into the complexity of chaos in nonlinear dynamical systems. Therefore, in this paper, the analytical conditions for global transversality and tangency of 2-D nonlinear dynamical systems are presented. The first integral quantity increment (i.e. the energy increment) for a certain time interval is achieved for periodic flows and chaos in the 2-D nonlinear dynamical systems. Under the perturbation assumptions and convergent conditions, the Melnikov function is recovered from the first integral quantity increment. A periodically forced, damped Duffing oscillator with a separatrix is investigated as a sampled problem. The corresponding analytical conditions for the global transversality and tangency to the separatrix are obtained and verified by numerical simulations. The switching planes and the corresponding local and global mappings are defined on the separatrix. The mapping structures are developed for local and global periodic flows passing through the separatrix. The mapping structures of global chaos in the damped Duffing oscillator are also discussed. Bifurcation scenarios of the damped Duffing oscillator are presented through the traditional Poincaré mapping section and the switching planes. The first integral quantity increment (i.e. L-function) is presented to observe the periodicity of flows. In addition, the global tangency of periodic flows in such an oscillator is measured by the G-function and G(1)-function, and is verified by numerical simulations. The first integral quantity increment of periodic flows is zero for their complete periodic cycles. Numerical simulations of chaos in such a Duffing oscillator are carried out through the Poincaré mapping sections. The conservative energy distribution, G-function and L-function along the displacement of Poincaré mapping points are presented to observe the complexity of chaos. The first integral quantity increment (i.e. L-function) of chaotic flows at the Poincaré mapping points is nonzero and chaotic. The switching planes of chaos are presented on the separatrix for a better understanding of the global transversality to the separatrix. The switching point distribution on the separatrix is presented and the switching G-function on the separatrix is given to show the global transversality of chaos on the separatrix. The analytical conditions are obtained from the new theory rather than the Melnikov method. The new conditions for the global transversality and tangency are more accurate and independent of the small parameters.
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BLACKBURN, H. M., and R. D. HENDERSON. "A study of two-dimensional flow past an oscillating cylinder." Journal of Fluid Mechanics 385 (April 25, 1999): 255–86. http://dx.doi.org/10.1017/s0022112099004309.
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In this paper we describe a detailed study of the wake structures and flow dynamics associated with simulated two-dimensional flows past a circular cylinder that is either stationary or in simple harmonic cross-flow oscillation. Results are examined for Re=500 and a fixed motion amplitude of ymax/D=0.25. The study concentrates on a domain of oscillation frequencies near the natural shedding frequency of the fixed cylinder. In addition to the change in phase of vortex shedding with respect to cylinder motion observed in previous experimental studies, we note a central band of frequencies for which the wake exhibits long-time-scale relaxation oscillator behaviour. Time-periodic states with asymmetric wake structures and non-zero mean lift were also observed for oscillation frequencies near the lower edge of the relaxation oscillator band. In this regime we compute a number of bifurcations between different wake configurations and show that the flow state is not a unique function of the oscillation frequency. Results are interpreted using an analysis of vorticity generation and transport in the base region of the cylinder. We suggest that the dynamics of the change in phase of shedding arise from a competition between two different mechanisms of vorticity production.
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Pando, Miguel Fosas de, Peter J. Schmid, and Denis Sipp. "Nonlinear Model-order Reduction for Oscillator Flows Using POD-DEIM." Procedia IUTAM 14 (2015): 329–36. http://dx.doi.org/10.1016/j.piutam.2015.03.056.
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Fu, Xilin, and Yanyan Zhang. "Stick motions and grazing flows in an inclined impact oscillator." Chaos, Solitons & Fractals 76 (July 2015): 218–30. http://dx.doi.org/10.1016/j.chaos.2015.04.005.
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Horwitz, Lawrence Paul, Vishnu S. Namboothiri, Gautham Varma K, Asher Yahalom, Yosef Strauss, and Jacob Levitan. "Raychaudhuri Equation, Geometrical Flows and Geometrical Entropy." Symmetry 13, no. 6 (May 28, 2021): 957. http://dx.doi.org/10.3390/sym13060957.
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The Raychaudhuri equation is derived by assuming geometric flow in space–time M of n+1 dimensions. The equation turns into a harmonic oscillator form under suitable transformations. Thereby, a relation between geometrical entropy and mean geodesic deviation is established. This has a connection to chaos theory where the trajectories diverge exponentially. We discuss its application to cosmology and black holes. Thus, we establish a connection between chaos theory and general relativity.
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Li, Larry K. B., and Matthew P. Juniper. "Lock-in and quasiperiodicity in a forced hydrodynamically self-excited jet." Journal of Fluid Mechanics 726 (June 11, 2013): 624–55. http://dx.doi.org/10.1017/jfm.2013.223.
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AbstractThe ability of hydrodynamically self-excited jets to lock into strong external forcing is well known. Their dynamics before lock-in and the specific bifurcations through which they lock in, however, are less well known. In this experimental study, we acoustically force a low-density jet around its natural global frequency. We examine its response leading up to lock-in and compare this to that of a forced van der Pol oscillator. We find that, when forced at increasing amplitudes, the jet undergoes a sequence of two nonlinear transitions: (i) from periodicity to ${ \mathbb{T} }^{2} $ quasiperiodicity via a torus-birth bifurcation; and then (ii) from ${ \mathbb{T} }^{2} $ quasiperiodicity to 1:1 lock-in via either a saddle-node bifurcation with frequency pulling, if the forcing and natural frequencies are close together, or a torus-death bifurcation without frequency pulling, but with a gradual suppression of the natural mode, if the two frequencies are far apart. We also find that the jet locks in most readily when forced close to its natural frequency, but that the details contain two asymmetries: the jet (i) locks in more readily and (ii) oscillates more strongly when it is forced below its natural frequency than when it is forced above it. Except for the second asymmetry, all of these transitions, bifurcations and dynamics are accurately reproduced by the forced van der Pol oscillator. This shows that this complex (infinite-dimensional) forced self-excited jet can be modelled reasonably well as a simple (three-dimensional) forced self-excited oscillator. This result adds to the growing evidence that open self-excited flows behave essentially like low-dimensional nonlinear dynamical systems. It also strengthens the universality of such flows, raising the possibility that more of them, including some industrially relevant flames, can be similarly modelled.
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GALINAT, SOPHIE, FRÉDÉRIC RISSO, OLIVIER MASBERNAT, and PASCAL GUIRAUD. "Dynamics of drop breakup in inhomogeneous turbulence at various volume fractions." Journal of Fluid Mechanics 578 (April 26, 2007): 85–94. http://dx.doi.org/10.1017/s0022112007005186.
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We report experimental and numerical determinations of the breakup probability of a drop travelling through inhomogeneous turbulent flow generated in a pipe downstream of a restriction. The model couples the Rayleigh–Lamb theory of drop oscillations with the Kolmogorov–Hinze theory of turbulent breakup. The interface deformation is modelled by a linear oscillator forced by the Lagrangian turbulent Weber number measured in experiments. The interface is assumed to rupture when either (i) the instantaneous Weber number exceeds a critical value or (ii) the predicted deformation exceeds a given threshold. Seven flow configurations have been tested, corresponding to various Reynolds numbers, damping coefficients and drop volume fractions. The history of the drop deformation proves to play an important role, and simulations assuming a critical Weber number fail to reproduce the experiments. Simulations assuming a critical deformation predict well the main features observed in the experiments. The linear oscillator appears able to describe the main feature of the dynamics of the drop deformation in inhomogeneous turbulence. Provided the oscillation frequency and the damping rate are known, the model can be used to compute the breakup probability in concentrated dispersed two-phase flows.
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Liu, Guo Hua, Li Sui, and Geng Chen Shi. "The Electricity Performance of Flexible Piezoelectric Generator." Applied Mechanics and Materials 556-562 (May 2014): 2035–38. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.2035.
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A FPEG (flexible piezoelectric generator) composed of PVDF (polyvinylidene fluoride) piezoelectric film, conducting resin and titanium alloy substrate, which occupies less room and produces electrical energy while the axial wind flows through the oscillator surface. When the axial wind flows through the generator surface, generator begins to vibrate and produce electrical energy, as the wind speed reaches a critical value, generator yields resonance phenomenon. In this paper, more work was placed on how the substrate structure parameters such as length, width and thickness affected the power generation capacity in resonance mode.
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KOSO, Toru, Tetsuya SAITO, and Keita TSUKAHARA. "G904 Self-induced Oscillation of Low Reynolds Number Jet Flows in a Fluidic Oscillator with a Target(2)." Proceedings of the Fluids engineering conference 2007 (2007): _G904–1_—_G904–4_. http://dx.doi.org/10.1299/jsmefed.2007._g904-1_.
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KOSO, Toru, Tetsuya SAITO, and Keita TSUKAHARA. "G904 Self-induced Oscillation of Low Reynolds Number Jet Flows in a Fluidic Oscillator with a Target(1)." Proceedings of the Fluids engineering conference 2007 (2007): _G904—a_. http://dx.doi.org/10.1299/jsmefed.2007._g904-a_.
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Qu, Yang, Piguang Wang, Shixiao Fu, and Mi Zhao. "Numerical study on vortex-induced vibrations of a flexible cylinder subjected to multi-directional flows." Physics of Fluids 35, no. 3 (March 2023): 037104. http://dx.doi.org/10.1063/5.0138063.
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Vortex-induced vibrations (VIVs) of a flexible cylinder subjected to multi-directional flows have been studied based on a wake oscillator model. The multi-directional flow comprises two slabs of flows in different directions, with each slab having a uniform uni-directional profile. The dynamics of the flexible cylinder is described based on the linear Euler–Bernoulli beam theory, and a wake oscillator model is uniformly distributed along the cylinder to model the hydrodynamic force acting on it. The dynamics of the coupled system has been solved numerically using the finite element method, and simulations have been conducted with the cylinder subjected to multi-directional flows with different angles between the two slabs. A large number of different initial conditions have been applied, and more than one steady-state response has been captured. The steady-state responses exhibit two different patterns: one is characterized by two waves traveling in opposite directions, while the other is dominated by a single traveling wave. The cross-flow VIV primarily occurs in the local cross-flow direction, and a transition of its vibrating direction happens at the interface of the two flows. Such transition is not observed in the inline VIV, and significant vibrations at the double frequency appear in both local cross-flow and inline directions. Energy analysis shows that this transition is boosted by a specific energy transfer pattern between the structure and the flow, which excites the vibration of the cylinder in some directions while damps it in others.
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Poulin, F. J. "The Linear Stability of Time-Dependent Baroclinic Shear." Journal of Physical Oceanography 40, no. 3 (March 1, 2010): 568–81. http://dx.doi.org/10.1175/2009jpo4094.1.
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Abstract This article aims to advance the understanding of inherent randomness in geophysical fluids by considering the particular example of baroclinic shear flows that are spatially uniform in the horizontal directions and aperiodic in time. The time variability of the shear is chosen to be the Kubo oscillator, which is a family of time-dependent bounded noise that is oscillatory in nature with various degrees of stochasticity. The author analyzed the linear stability of a wide range of temporally periodic and aperiodic shears with a zero and nonzero mean to get a more complete understanding of the effect of oscillations in shear flows in the context of the two-layer quasigeostrophic Phillips model. It is determined that the parametric mode, which exists in the periodic limit, also exists in the range of small and moderate stochasticities but vanishes in highly erratic flows. Moreover, random variations weaken the effects of periodicity and yield growth rates more similar to that of the time-averaged steady-state analog. This signifies that the periodic shear flows possess the most extreme case of stabilization and destabilization and are thus anomalous. In the limit of an f plane, the linear stability problem is solved exactly to reveal that individual solutions to the linear dynamics with time-dependent baroclinic shear have growth rates that are equal to that of the time-averaged steady state. This implies that baroclinic shear flows with zero means are linearly stable in that they do not grow exponentially in time. This means that the stochastic mode that was found to exist in the Mathieu equation does not arise in this model. However, because the perturbations grow algebraically, the aperiodic baroclinic shear on an f plane can give rise to nonlinear instabilities.
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Luo, Albert C. J. "Periodic Flows to Chaos Based on Discrete Implicit Mappings of Continuous Nonlinear Systems." International Journal of Bifurcation and Chaos 25, no. 03 (March 2015): 1550044. http://dx.doi.org/10.1142/s0218127415500443.
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This paper presents a semi-analytical method for periodic flows in continuous nonlinear dynamical systems. For the semi-analytical approach, differential equations of nonlinear dynamical systems are discretized to obtain implicit maps, and a mapping structure based on the implicit maps is employed for a periodic flow. From mapping structures, periodic flows in nonlinear dynamical systems are predicted analytically and the corresponding stability and bifurcations of the periodic flows are determined through the eigenvalue analysis. The periodic flows predicted by the single-step implicit maps are discussed first, and the periodic flows predicted by the multistep implicit maps are also presented. Periodic flows in time-delay nonlinear dynamical systems are discussed by the single-step and multistep implicit maps. The time-delay nodes in discretization of time-delay nonlinear systems were treated by both an interpolation and a direct integration. Based on the discrete nodes of periodic flows in nonlinear dynamical systems with/without time-delay, the discrete Fourier series responses of periodic flows are presented. To demonstrate the methodology, the bifurcation tree of period-1 motion to chaos in a Duffing oscillator is presented as a sampled problem. The method presented in this paper can be applied to nonlinear dynamical systems, which cannot be solved directly by analytical methods.
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Dang, Van Bac, and Sung-Jin Kim. "Water-head-driven microfluidic oscillators for autonomous control of periodic flows and generation of aqueous two-phase system droplets." Lab on a Chip 17, no. 2 (2017): 286–92. http://dx.doi.org/10.1039/c6lc00911e.
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Kanavets, V. I., Yu D. Mozgovoi, and S. A. Khritkin. "Self-excitation and synchronization in a multibeam microwave generator with electron-oscillator flows." Journal of Communications Technology and Electronics 51, no. 3 (March 2006): 339–44. http://dx.doi.org/10.1134/s1064226906030120.
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Simić, Slobodan N. "On the sub-Riemannian geometry of contact Anosov flows." Journal of Topology and Analysis 08, no. 01 (February 23, 2016): 187–205. http://dx.doi.org/10.1142/s1793525316500072.
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We investigate certain natural connections between sub-Riemannian geometry and hyperbolic dynamical systems. In particular, we study dynamically defined horizontal distributions which split into two integrable ones and ask: how is the energy of a sub-Riemannian geodesic shared between its projections onto the integrable summands? We show that if the horizontal distribution is the sum of the strong stable and strong unstable distributions of a special type of a contact Anosov flow in three dimensions, then for any short enough sub-Riemannian geodesic connecting points on the same orbit of the Anosov flow, the energy of the geodesic is shared equally between its projections onto the stable and unstable bundles. The proof relies on a connection between the geodesic equations and the harmonic oscillator equation, and its explicit solution by the Jacobi elliptic functions. Using a different idea, we prove an analogous result in higher dimensions for the geodesic flow of a closed Riemannian manifold of constant negative curvature.
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LUO, ALBERT C. J., and JIANZHE HUANG. "ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 04 (April 2012): 1250093. http://dx.doi.org/10.1142/s0218127412500939.
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In this paper, the analytical solutions for period-m flows and chaos in nonlinear dynamical systems are presented through the generalized harmonic balance method. The nonlinear damping, periodically forced, Duffing oscillator was investigated as an example to demonstrate the analytical solutions of periodic motions and chaos. Through this investigation, the mechanism for a period-m motion jumping to another period-n motion in numerical computation is found. In this problem, the Hopf bifurcation of periodic motions is equivalent to the period-doubling bifurcation via Poincare mappings of dynamical systems. The stable and unstable period-m motions can be obtained analytically. Even more, the stable and unstable chaotic motions can be achieved analytically. The methodology presented in this paper can be applied to other nonlinear vibration systems, which is independent of small parameters.
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WEBB, G. M., E. Kh KAGHASHVILI, and G. P. ZANK. "Magnetohydrodynamic wave mixing in shear flows: Hamiltonian equations and wave action." Journal of Plasma Physics 73, no. 1 (February 2007): 15–68. http://dx.doi.org/10.1017/s0022377806004399.
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Abstract.Magnetohydrodynamic wave interactions in a linear shear flow are investigated using the Lagrangian fluid displacement ξ and entropy perturbation Δ S, in which a spatial Fourier solution is obtained in the frame of the background shear flow (Kelvin's method). The equations reduce to three coupled oscillator equations, with time-dependent coefficients and with source terms proportional to the entropy perturbation. In the absence of entropy perturbations, the system admits a wave action conservation integral consisting of positive and negative energy waves. Variational and Hamiltonian forms of the equations are obtained. Examples of wave amplification phenomena and sharp resonant-type wave interactions are obtained. Implications for the interaction of magnetohydrodynamic waves in the shear flow between fast, polar coronal-hole solar wind and slow, streamer belt solar wind are discussed.
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Bouchgl, J., and M. Souhar. "Control of the Interfacial Instabilities in a circular Hele-Shaw cell oscillating with a periodic angular velocity." MATEC Web of Conferences 286 (2019): 07014. http://dx.doi.org/10.1051/matecconf/201928607014.
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The stability of an interface of two viscous immiscible fluids of different densities and confined in a Hele-Shaw cell which is oscillating with periodic angular velocityis investigated. A linear stability analysis of the viscous and time-dependent basic flows, generated by a periodic rotation, leads to a time periodic oscillator describing the evolution of the interface amplitude. In this study, we examine mainly the effect of the frequency of the periodic rotation on the interfacial instability that occurs at the interface.
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Lai, F. C., P. J. McKinney, and J. H. Davidson. "Oscillatory Electrohydrodynamic Gas Flows." Journal of Fluids Engineering 117, no. 3 (September 1, 1995): 491–97. http://dx.doi.org/10.1115/1.2817289.
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Prior numerical solutions of electrohydrodynamic flows in a positive-corona, wire-plate electrostatic precipitator are extended to reveal steady-periodic electrohydrodynamic flows. Previously, only steady solutions were reported. The present study includes results for flows with Reynolds numbers from 0 to 4800 and with dimensionless electric number ranging from 0.06 to ∞. Results indicate that two regimes of low frequency oscillatory flow occur. The first regime is characterized by a single recirculating vortex that oscillates in strength between one and five Hertz. The second regime is characterized by two counter-rotating vortices that oscillate in strength at a frequency near one Hertz.
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Burq, Nicolas. "Large-time dynamics for the one-dimensional Schrödinger equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 2 (April 2011): 227–51. http://dx.doi.org/10.1017/s0308210509000018.
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Famous results by Rademacher, Kolmogorov and Paley and Zygmund state that random series on the torus enjoy better Lp bounds that the deterministic bounds. We present a natural extension of these harmonic analysis results to a partial-differential-equations setting. Specifically, we consider the one-dimensional nonlinear harmonic oscillator i∂tu + Δu − |x|2u = |u|r−1u, and exhibit examples for which the solutions are better behaved for randomly chosen initial data than would be predicted by the deterministic theory. In particular, on a deterministic point of view, the nonlinear harmonic oscillator equation is well posed in L2(ℝ) if and only if r ≤ 5. However, we shall prove that, for all nonlinearities |u|r−1u, r > 1, not only is the equation well posed for a large set of initial data whose Sobolev regularity is below L2, but also the flows enjoy very nice large-time probabilistic behaviour.These results are joint work with Laurent Thomann and Nikolay Tzvetkov.
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Sun, Chen-li, Yu Jen Lin, Chia-I. Rau, and Shao-Yu Chiu. "Flow characterization and mixing performance of weakly-shear-thinning fluid flows in a microfluidic oscillator." Journal of Non-Newtonian Fluid Mechanics 239 (January 2017): 1–12. http://dx.doi.org/10.1016/j.jnnfm.2016.11.003.
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Balasuriya, Sanjeeva. "A Numerical Scheme for Computing Stable and Unstable Manifolds in Nonautonomous Flows." International Journal of Bifurcation and Chaos 26, no. 14 (December 30, 2016): 1630041. http://dx.doi.org/10.1142/s021812741630041x.
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There are many methods for computing stable and unstable manifolds in autonomous flows. When the flow is nonautonomous, however, difficulties arise since the hyperbolic trajectory to which these manifolds are anchored, and the local manifold emanation directions, are changing with time. This article utilizes recent results which approximate the time-variation of both these quantities to design a numerical algorithm which can obtain high resolution in global nonautonomous stable and unstable manifolds. In particular, good numerical approximation is possible locally near the anchor trajectory. Nonautonomous manifolds are computed for two examples: a Rossby wave situation which is highly chaotic, and a nonautonomus (time-aperiodic) Duffing oscillator model in which the manifold emanation directions are rapidly changing. The numerical method is validated and analyzed in these cases using finite-time Lyapunov exponent fields and exactly known nonautonomous manifolds.
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Misawa, Tetsuya. "Symplectic Integrators to Stochastic Hamiltonian Dynamical Systems Derived from Composition Methods." Mathematical Problems in Engineering 2010 (2010): 1–12. http://dx.doi.org/10.1155/2010/384937.
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“Symplectic” schemes for stochastic Hamiltonian dynamical systems are formulated through “composition methods (or operator splitting methods)” proposed by Misawa (2001). In the proposed methods, a symplectic map, which is given by the solution of a stochastic Hamiltonian system, is approximated by composition of the stochastic flows derived from simpler Hamiltonian vector fields. The global error orders of the numerical schemes derived from the stochastic composition methods are provided. To examine the superiority of the new schemes, some illustrative numerical simulations on the basis of the proposed schemes are carried out for a stochastic harmonic oscillator system.
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Balasubramanian, S., and R. A. Skop. "A NONLINEAR OSCILLATOR MODEL FOR VORTEX SHEDDING FROM CYLINDERS AND CONES IN UNIFORM AND SHEAR FLOWS." Journal of Fluids and Structures 10, no. 3 (April 1996): 197–214. http://dx.doi.org/10.1006/jfls.1996.0013.
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Rypina, Irina I., and Lawrence J. Pratt. "Trajectory encounter volume as a diagnostic of mixing potential in fluid flows." Nonlinear Processes in Geophysics 24, no. 2 (May 3, 2017): 189–202. http://dx.doi.org/10.5194/npg-24-189-2017.
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Abstract. Fluid parcels can exchange water properties when coming into contact with each other, leading to mixing. The trajectory encounter mass and a related simplified quantity, the encounter volume, are introduced as a measure of the mixing potential of a flow. The encounter volume quantifies the volume of fluid that passes close to a reference trajectory over a finite time interval. Regions characterized by a low encounter volume, such as the cores of coherent eddies, have a low mixing potential, whereas turbulent or chaotic regions characterized by a large encounter volume have a high mixing potential. The encounter volume diagnostic is used to characterize the mixing potential in three flows of increasing complexity: the Duffing oscillator, the Bickley jet and the altimetry-based velocity in the Gulf Stream extension region. An additional example is presented in which the encounter volume is combined with the u∗ approach of Pratt et al. (2016) to characterize the mixing potential for a specific tracer distribution in the Bickley jet flow. Analytical relationships are derived that connect the encounter volume to the shear and strain rates for linear shear and linear strain flows, respectively. It is shown that in both flows the encounter volume is proportional to time.
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Afanasyev, A. N., T. Van Doorsselaere, and V. M. Nakariakov. "Excitation of decay-less transverse oscillations of coronal loops by random motions." Astronomy & Astrophysics 633 (January 2020): L8. http://dx.doi.org/10.1051/0004-6361/201937187.
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Context. The relatively large-amplitude decaying regime of transverse oscillations of coronal loops has been known for two decades and has been interpreted in terms of magnetohydrodynamic kink modes of cylindrical plasma waveguides. In this regime oscillations decay in several cycles. Recent observational analysis has revealed so-called decay-less, small-amplitude oscillations, in which a multi-harmonic structure has been detected. Several models have been proposed to explain these oscillations. In particular, decay-less oscillations have been described in terms of standing kink waves driven with continuous mono-periodic motions of loop footpoints, in terms of a simple oscillator model of forced oscillations due to harmonic external force, and as a self-oscillatory process due to the interaction of a loop with quasi-steady flows. However, an alternative mechanism is needed to explain the simultaneous excitation of several longitudinal harmonics of the oscillation. Aims. We study the mechanism of random excitation of decay-less transverse oscillations of coronal loops. Methods. With a spatially one-dimensional and time-dependent analytical model taking into account effects of the wave damping and kink speed variation along the loop, we considered transverse loop oscillations driven by random motions of footpoints. The footpoint motions were modelled by broad-band coloured noise. Results. We found the excitation of loop eigenmodes and analysed their frequency ratios as well as the spatial structure of the oscillations along the loop. The obtained results successfully reproduce the observed properties of decay-less oscillations. In particular, excitation of eigenmodes of a loop as a resonator can explain the observed quasi-monochromatic nature of decay-less oscillations and the generation of multiple harmonics detected recently. Conclusions. We propose a mechanism that can interpret decay-less transverse oscillations of coronal loops in terms of kink waves randomly driven at the loop footpoints.
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Garrett, Timothy J. "Modes of growth in dynamic systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2145 (May 23, 2012): 2532–49. http://dx.doi.org/10.1098/rspa.2012.0039.
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Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how system growth can be constrained to a few distinct modes that depend on the time integral of past flows and the current availability of material and energetic resources. These modes include a law of diminishing returns, logistic behaviour and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator–prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviours in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.
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Glesser, M., V. Valeau, and A. Sakout. "Vortex sound in unconfined flows: Application to the coupling of a jet-slot oscillator with a resonator." Journal of Sound and Vibration 314, no. 3-5 (July 2008): 635–49. http://dx.doi.org/10.1016/j.jsv.2008.01.012.
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Filippi, Margaux, Irina I. Rypina, Alireza Hadjighasem, and Thomas Peacock. "An Optimized-Parameter Spectral Clustering Approach to Coherent Structure Detection in Geophysical Flows." Fluids 6, no. 1 (January 12, 2021): 39. http://dx.doi.org/10.3390/fluids6010039.
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In Lagrangian dynamics, the detection of coherent clusters can help understand the organization of transport by identifying regions with coherent trajectory patterns. Many clustering algorithms, however, rely on user-input parameters, requiring a priori knowledge about the flow and making the outcome subjective. Building on the conventional spectral clustering method of Hadjighasem et al. (2016), a new optimized-parameter spectral clustering approach is developed that automatically identifies optimal parameters within pre-defined ranges. A noise-based metric for quantifying the coherence of the resulting coherent clusters is also introduced. The optimized-parameter spectral clustering is applied to two benchmark analytical flows, the Bickley Jet and the asymmetric Duffing oscillator, and to a realistic, numerically generated oceanic coastal flow. In the latter case, the identified model-based clusters are tested using observed trajectories of real drifters. In all examples, our approach succeeded in performing the partition of the domain into coherent clusters with minimal inter-cluster similarity and maximum intra-cluster similarity. For the coastal flow, the resulting coherent clusters are qualitatively similar over the same phase of the tide on different days and even different years, whereas coherent clusters for the opposite tidal phase are qualitatively different.
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Symon, Sean, Denis Sipp, and Beverley J. McKeon. "A tale of two airfoils: resolvent-based modelling of an oscillator versus an amplifier from an experimental mean." Journal of Fluid Mechanics 881 (October 24, 2019): 51–83. http://dx.doi.org/10.1017/jfm.2019.747.
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The flows around a NACA 0018 airfoil at a chord-based Reynolds number of $Re=10\,250$ and angles of attack of $\unicode[STIX]{x1D6FC}=0^{\circ }$ and $\unicode[STIX]{x1D6FC}=10^{\circ }$ are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity fields are data assimilated so that they are solutions of the incompressible Reynolds-averaged Navier–Stokes equations forced by Reynolds stress terms which are derived from experimental data. Resolvent analysis of the data-assimilated mean velocity fields reveals low-rank behaviour only in the vicinity of the shedding frequency for $\unicode[STIX]{x1D6FC}=0^{\circ }$ and none of its harmonics. The resolvent operator for the $\unicode[STIX]{x1D6FC}=10^{\circ }$ case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by spectral proper orthogonal decomposition. It is also shown that the second linear mechanism, corresponding to the Kelvin–Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as an input for resolvent analysis due to missing data near the leading edge. For both cases, resolvent modes resemble those from spectral proper orthogonal decomposition when the resolvent operator is low rank. The $\unicode[STIX]{x1D6FC}=0^{\circ }$ case is classified as an oscillator and its harmonics, where the resolvent operator is not low rank, are modelled using parasitic modes as opposed to classical resolvent modes which are the most amplified. The $\unicode[STIX]{x1D6FC}=10^{\circ }$ case behaves more like an amplifier and its nonlinear forcing is far less structured. The two cases suggest that resolvent-based modelling can be achieved for more complex flows with limited experimental measurements.
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Momen, Mostafa, and Elie Bou-Zeid. "Large-Eddy Simulations and Damped-Oscillator Models of the Unsteady Ekman Boundary Layer*." Journal of the Atmospheric Sciences 73, no. 1 (December 11, 2015): 25–40. http://dx.doi.org/10.1175/jas-d-15-0038.1.
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Abstract The Ekman boundary layer (EBL) is a central problem in geophysical fluid dynamics that emerges when the pressure gradient force, the Coriolis force, and the frictional force interact in a flow. The unsteady version of the problem, which occurs when these forces are not in equilibrium, is solvable analytically only for a limited set of forcing variability regimes, and the resulting solutions are intricate and not always easy to interpret. In this paper, large-eddy simulations (LESs) of neutral atmospheric EBLs are conducted under various unsteady forcings to reveal the range of physical characteristics of the flow. Subsequently, it is demonstrated that the dynamics of the unsteady EBL can be reduced to a second-order ordinary differential equation that is very similar to the dynamical equation of a damped oscillator, such as a mass–spring–damper system. The validation of the proposed reduced model is performed by comparing its analytical solutions to LES results, revealing very good agreement. The reduced model can be solved for a wide range of variable forcing conditions, and this feature is exploited in the paper to elucidate the physical origin of the inertia (mass), energy storage (spring), and energy dissipation (damper) attributes of Ekman flows.
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Xue, Kangrui, Ryan M. Aronson, Jui-Hsien Wang, Timothy R. Langlois, and Doug L. James. "Improved Water Sound Synthesis using Coupled Bubbles." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–13. http://dx.doi.org/10.1145/3592424.
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We introduce a practical framework for synthesizing bubble-based water sounds that captures the rich inter-bubble coupling effects responsible for low-frequency acoustic emissions from bubble clouds. We propose coupled-bubble oscillator models with regularized singularities, and techniques to reduce the computational cost of time stepping with dense, time-varying mass matrices. Airborne acoustic emissions are estimated using finite-difference time-domain (FDTD) methods. We propose a simple, analytical surface-acceleration model, and a sample-and-hold GPU wavesolver that is simple and faster than prior CPU wavesolvers. Sound synthesis results are demonstrated using bubbly flows from incompressible, two-phase simulations, as well as procedurally generated examples using single-phase FLIP fluid animations. Our results demonstrate sound simulations with hundreds of thousands of bubbles, and perceptually significant frequency transformations with fuller low-frequency content.
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Meskell, Craig, and Alberto Pellegrino. "Vortex Shedding Lock-In due to Pitching Oscillation of a Wind Turbine Blade Section at High Angles of Attack." International Journal of Aerospace Engineering 2019 (March 11, 2019): 1–12. http://dx.doi.org/10.1155/2019/6919505.
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The unsteady flow around a pitching two-dimensional airfoil section (NREL S809) has been simulated using unsteady RANS with the transition SST turbulence model. This geometry is chosen to represent a wind turbine blade in a standstill configuration. The Reynolds number is Re=106 based on a chord length of 1 m. A prescribed sinusoidal pitching motion has been applied at a fixed amplitude of 7° for a range of high angles of attack 30°<α<150°. At these incidences, the airfoil will behave more like a bluff body and may experience periodic vortex shedding. It is well known that, in bluff body flows, oscillations can lead to a lock-in (lock-in) of the vortex shedding frequency, fv, with the body’s motion frequency, fp. In order to investigate the susceptibility of airfoil to lock-in, the frequency ratio r (r=fp/fv0) has been varied around r=1. The lock-in region boundaries have been proposed, and an analysis of the effect of the oscillation amplitude has been conducted. The lock-in map obtained suggests that, for the vibration amplitude considered, the risk of vortex-induced vibration is more significant in the regions of α≈40° and α≈140°, i.e., for shallower characteristic lengths. Finally, a lumped parameter wake oscillator model has been proposed for pitching airfoils. This simple model is in qualitative agreement with the CFD results.
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Lui, Hugo F. S., and William R. Wolf. "Construction of reduced-order models for fluid flows using deep feedforward neural networks." Journal of Fluid Mechanics 872 (June 14, 2019): 963–94. http://dx.doi.org/10.1017/jfm.2019.358.
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We present a numerical methodology for construction of reduced-order models (ROMs) of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition is applied to reduce the dimensionality of the model and, at the same time, filter the proper orthogonal decomposition temporal modes. The regression step is performed by a deep feedforward neural network (DNN), and the current framework is implemented in a context similar to the sparse identification of nonlinear dynamics algorithm. A discussion on the optimization of the DNN hyperparameters is provided for obtaining the best ROMs and an assessment of these models is presented for a canonical nonlinear oscillator and the compressible flow past a cylinder. Then the method is tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced-order model is able to capture the dynamics of the leading edge stall vortex and the subsequent trailing edge vortex. For the cases analysed, the numerical framework allows the prediction of the flow field beyond the training window using larger time increments than those employed by the full-order model. We also demonstrate the robustness of the current ROMs constructed via DNNs through a comparison with sparse regression. The DNN approach is able to learn transient features of the flow and presents more accurate and stable long-term predictions compared to sparse regression.
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Tatsios, Giorgos, Alexandros Tsimpoukis, and Dimitris Valougeorgis. "The Half-Range Moment Method in Harmonically Oscillating Rarefied Gas Flows." Fluids 6, no. 1 (January 1, 2021): 17. http://dx.doi.org/10.3390/fluids6010017.
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The formulation of the half-range moment method (HRMM), well defined in steady rarefied gas flows, is extended to linear oscillatory rarefied gas flows, driven by oscillating boundaries. The oscillatory Stokes (also known as Stokes second problem) and the oscillatory Couette flows, as representative ones for harmonically oscillating half-space and finite-medium flow setups respectively, are solved. The moment equations are derived from the linearized time-dependent BGK kinetic equation, operating accordingly over the positive and negative halves of the molecular velocity space. Moreover, the boundary conditions of the “positive” and “negative” moment equations are accordingly constructed from the half-range moments of the boundary conditions of the outgoing distribution function, assuming purely diffuse reflection. The oscillatory Stokes flow is characterized by the oscillation parameter, while the oscillatory Couette flow by the oscillation and rarefaction parameters. HRMM results for the amplitude and phase of the velocity and shear stress in a wide range of the flow parameters are presented and compared with corresponding results, obtained by the discrete velocity method (DVM). In the oscillatory Stokes flow the so-called penetration depth is also computed. When the oscillation frequency is lower than the collision frequency excellent agreement is observed, while when it is about the same or larger some differences are present. Overall, it is demonstrated that the HRMM can be applied to linear oscillatory rarefied gas flows, providing accurate results in a very wide range of the involved flow parameters. Since the computational effort is negligible, it is worthwhile to consider the efficient implementation of the HRMM to stationary and transient multidimensional rarefied gas flows.
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Yamano, Akio, Atsuhiko Shintani, Tomohiro Ito, and Chihiro Nakagawa. "Evaluation of Driving Method of the Flexible Body Moving in Narrow Flow Passage." Journal of Robotics and Mechatronics 26, no. 3 (June 20, 2014): 349–57. http://dx.doi.org/10.20965/jrm.2014.p0349.
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<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00260003/08.jpg"" width=""300"" />Analytical model</span></div> A flexible fish-like biomimetic robot developed for use in narrow passage flows was downsized using shape memory alloy (SMA) actuators. We constructed a fluid-body-coupled model of the robot and considered undulatory swimming and the effect of nonlinear SMA characteristics. An experimental model was also constructed to confirm the analytical model’s feasibility. Shrinkage due to temperature depends on the temperature of the SMA actuator, in which overheating may decrease the fin-vibration amplitude. To avoid this problem, a new driving method was introduced that used a self-excited oscillator with an actuator. Simulation results showed that this method achieves constant thrust in the moving body. </span>
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SELVAM, B., L. TALON, L. LESSHAFFT, and E. MEIBURG. "Convective/absolute instability in miscible core-annular flow. Part 2. Numerical simulations and nonlinear global modes." Journal of Fluid Mechanics 618 (January 10, 2009): 323–48. http://dx.doi.org/10.1017/s0022112008004242.
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The convective/absolute nature of the instability of miscible core-annular flow with variable viscosity is investigated via linear stability analysis and nonlinear simulations. From linear analysis, it is found that miscible core-annular flows with the more viscous fluid in the core are at most convectively unstable. On the other hand, flows with the less viscous fluid in the core exhibit absolute instability at high viscosity ratios, over a limited range of core radii. Nonlinear direct numerical simulations in a semi-infinite domain display self-excited intrinsic oscillations if and only if the underlying base flow exhibits absolute instability. This oscillator-type flow behaviour is demonstrated to be associated with the presence of a nonlinear global mode. Both the parameter range of global instability and the intrinsically selected frequency of nonlinear oscillations, as observed in the simulation, are accurately predicted from linear criteria. In convectively unstable situations, the flow is shown to respond to external forcing over an unstable range of frequencies, in quantitative agreement with linear theory. As discussed in part 1 of this study (d'Olce, Martin, Rakotomalala, Salin and Talon,J. Fluid Mech., vol. 618, 2008, pp. 305–322), self-excited synchronized oscillations were also observed experimentally. An interpretation of these experiments is attempted on the basis of the numerical results presented here.