Random flutter of a 2-DOF nonlinear airfoil in pitch and plunge with freeplay in pitch

The two-degree-of-freedom (2-DOF) airfoil system with freeplay nonlinearity in pitch is investigated numerically. The relation between eigenvalues and flutter speed has been analyzed. The effect of parameters of the freeplay nonlinearity on the system responses is obtained. The probability density function (PDF) and phase plane of the deterministic system have been studied and the results show that the amplitude of limit cycle oscillation (LCO) grows with mean airspeeds increasing. Marginal PDFs, bidimensional PDFs, random bifurcation, and the largest Lyapunov exponent are used in investigation of the random system. The results show that, for low and intermediate level turbulences, the marginal PDFs of system exhibit different characters at different airspeed ranges. However, for high level turbulence the marginal PDFs are similar in the whole airspeed region. The bidimensional PDF has different shapes in low level turbulence at pre- and post-flutter speeds, but the PDF keeps similar shape in high level turbulence. The random bifurcation analysis indicates the P-bifurcation can happen at both pre- and post-flutter speeds but the D-bifurcation never occurs. Numerical simulations approve the results.     

Response analysis of a pitch–plunge airfoil with structural and aerodynamic nonlinearities subjected to randomly fluctuating flows

This study focuses on numerically investigating the response dynamics of a pitch–plunge airfoil with structural nonlinearity under dynamic stall conditions. The aeroelastic responses are investigated for both deterministic and randomly time varying flow conditions. To that end, a pitch–plunge airfoil under dynamic stall condition is considered and the nonlinear aerodynamic loads are computed using a Leishman–Beddoes formulation. It is shown that the presence of structural nonlinearities can give rise to a variety of dynamical responses in the pre-flutter regime. Next, a response analysis under the presence of a randomly fluctuating wind is carried out. It is demonstrated that the route to flutter occurs via a regime of pre-flutter oscillations called intermittency. Finally, the manifestation of these stochastic responses is characterized by invoking stochastic bifurcation concepts. The route to flutter via intermittency is presented in terms of topological changes occurring in the joint-probability density function of the state variables.     

Dimensionless modeling and nonlinear analysis of a coupled pitch–plunge–leadlag airfoil-based piezoaeroelastic energy harvesting system

In this paper, an airfoil-based piezoaeroelastic energy harvesting system is proposed with an additional supporting device to harvest the mechanical energy from the leadlag motion. A dimensionless dynamic model is built considering the large-effective-angle-of-attack vibrations causing (1) the nonlinear coupling between the pitch–plunge–leadlag motions, (2) the inertia nonlinearity, and (3) the aerodynamic nonlinearity modeled by the ONERA dynamic stall model. Cubic hardening stiffness is introduced in the pitch degree of freedom for persistent vibrations with acceptable amplitude beyond the flutter boundary. The nonlinear aeroelastic response and the average power output are numerically studied. Limit cycle oscillations are observed and, as the flow velocity exceeds a secondary critical speed, the system experiences complex vibrations. The power output from the leadlag motion is smaller than that from the plunge motion, whereas the gap is narrowed with increasing flow velocity. Case studies are performed toward the effects of several dimensionless system parameters, including the nonlinear torsional stiffness, airfoil mass eccentricity, airfoil radius of gyration, mass of the supporting devices, and load resistances in the external circuits. The optimal parameter values for the power outputs from the plunge and leadlag motions are, respectively, obtained. Beyond the secondary critical speed, it is shown that the variations of the power outputs with those parameters become irregular with fluctuations and multiple local maximums. The bifurcation analysis shows the mutual transitions between the limit cycle oscillations, multi-periodic vibrations, and possible chaos. The influences of these complex vibrations on the power outputs are discussed.     

Quasi-steady prediction of coupled bending–torsion flutter under rotating stall

A method is presented in this paper to predict cascade flutter under subsonic stalled flow condition in a quasi-steady manner. The ability to predict the occurrence of aeroelastic flutter is highly important from the compressor design point of view. In the present work, the well known Moore–Greitzer compression system model is used to evaluate the flow under rotating stall and the linearized aerodynamic theory of Whitehead is used to estimate the blade loading. The cascade stability is then predicted by solving the structural model, which is posed as a complex eigenvalue problem. The possibility of occurrence of flutter in both bending and torsional modes is considered and the latter is found to be the dominant one, under subsonic stalled flow, for a large range of frequency ratios examined. It is also shown that the design of compressor blades at frequency ratios close to unity may result in rapid initiation of torsional flutter in the presence of stalled flow. A frequency ratio of 0.9 is primarily emphasized for most part of the study as many interesting features are revealed and the results are physically interpreted. Roughly a pitchfork pattern of energy distribution appears to occur between bending mode and torsional mode which ensures that only one flutter mode is possible at any instant in time. A bifurcation from bending flutter to torsional flutter is shown to occur during which the frequency of the two vibrating modes appear to coalesce for a very short period of time.     

Experimental investigation of dynamics of premixed acetylene–air flames in a micro-combustor

This paper describes a detailed experimental study performed to investigate the flame propagation behaviour of premixed flames in micro-channels. A novel, modular, stackable micro-combustor was developed for this purpose. For a chosen planar channel geometry, the flow condition and the mixture equivalence ratio of premixed acetylene–air were varied to investigate various modes of operation. Three different modes of operation were observed; they were (i) stable periodic operation – consisting of ignition, flame propagation, flame extinction, and re-ignition, (ii) a-periodic operation, and (iii) anchored flame condition. The present work also aims to provide quantitative information on the dynamics of premixed acetylene–air flames propagating inside micro-channels. A novel measurement approach based on OH^* chemiluminescence measurements employing a single photomultiplier unit was developed for this purpose. The data recorded were post processed using an in-house developed MATLAB code to evaluate the mean flame propagation speed measured between three different spatial locations along the length of the micro-channel. The results from the flame propagation speed measurements performed during ‘periodic’ mode of operation indicated that the flame travelled at higher propagation speed in the mid-length region of the channel compared to that at the initial entry point, suggesting flame acceleration. This flame acceleration could be attributed to a situation where the flame experienced different local equivalence ratio conditions at different upstream locations. The results suggest that after completion of a cycle of operation consisting of ignition, flame propagation and flame extinction, the fresh mixture that filled the channel was diluted with the exhaust gas from the previous cycle. This pocket of diluted mixture convected downstream with time, thus enabling the spatial variation in local equivalence ratio along the micro-channel.     

Experimental study of vortex–structure interaction noise radiated from rod–airfoil configurations

Vortex–structure interaction noise radiated from an airfoil embedded in the wake of a rod is investigated experimentally in an anechoic wind tunnel by means of a phased microphone array for acoustic tests and particle image velocimetry (PIV) for the flow field measurements. The rod–airfoil configuration is varied by changing the rod diameter (D), adjusting the cross-stream position (Y) of the rod and the streamwise gap (L) between the rod and the airfoil leading edge. Two noise control concepts, including “air blowing” on the upstream rod and a soft-vane leading edge on the airfoil, are applied to control the vortex–structure interaction noise. The motivation behind this study is to investigate the effects of the three parameters on the characteristics of the radiated noise and then explore the influences of the noise control concepts. Both the vortex–structure interaction noise and the rod vortex shedding tonal noise are analysed. The acoustic test results show that both the position and magnitude of the dominant noise source of the rod–airfoil model are highly dependent on the parameters considered. In the case where the vortex–structure interaction noise is dominant, the application of the air blowing and the soft vane can effectively attenuate the interaction noise. Flow field measurements suggest that the intensity of the vortex–structure interaction and the flow impingement on the airfoil leading edge are suppressed by the control methods, giving a reduction in noise.     

Experimental investigation of transients-induced fluid–structure interaction in a pipeline with multiple-axial supports

Fluid–Structure Interaction (FSI) in pipes can significantly affect pressure fluctuations during water hammer event. In transmission pipelines, anchors with axial stops have an important role in the waterhammer-induced FSI as they can suppress or allow the propagation of additional stress waves in the pipe wall. More specifically, a reduction in the number of axial stops and/or their stiffness causes significant oscillations in the observed pressure signal due to the enhancement of Poisson’s coupling. To confirm these physical arguments, this research conducts experimental investigations and then processes the collected pressure signals. The laboratory tests were run on an anchored pipeline with multiple axial supports which some of them removed at some sections to emerge Poisson’s coupling. The collected pressure signals are analyzed in the time and frequency domain in order to decipher fluctuations that stem from Poisson coupling and other anchors effects. The analysis of the laboratory data reveals that the pattern of the time signals of pressure is primarily affected by the stiffness and location of the supports. Likewise, the properties of structural boundaries characterize the frequency spectrum of the transient pressures, which is manifested by altering the amplitudes corresponding to dominant frequencies of the system. The study is of particular importance in practice of transient based defect detections and pipe system design.     

Assessment of added mass effects on flutter boundaries using the Leishman–Beddoes dynamic stall model

We consider the dynamics of a typical airfoil section both in forced and free oscillations and investigate the importance of the added mass terms, i.e. the second derivatives in time of the pitch angle and plunge displacement. The structural behaviour is modelled by linear springs in pitch and plunge and the aerodynamic loading represented by our interpretation of the state-space version of the Leishman–Beddoes semi-empirical model. The added mass terms are often neglected since this leads to an explicit system of ODEs amenable for solution using standard ODE solvers. We analyse the effect of neglecting the added mass terms in forced oscillations about a set of mean angles of incidence by comparing the solutions obtained with the explicit and implicit systems of ODEs and conclude that their differences amount to a time lag that increases at a constant rate with increases of the reduced frequency. To determine the effect of the added mass terms in free oscillations, we introduce a spring offset angle to obtain static equilibrium positions at various degrees of incidence. We analyse the stability of the explicit and implicit aeroelastic systems about those positions and compare the locations of the respective flutter points calculated as Hopf bifurcation points. For low values of the spring offset angle, added mass effects are significant for low values of the mass ratio, or the ratio of natural frequencies, of the aeroelastic system. For high values of the spring offset angle, corresponding to stall flutter, we observe that their effect is greater for large values of the mass ratio.     

Effects of the dynamic wheel–rail interaction on the ground vibration generated by a moving train

Based on Biot’s fully dynamic poroelastic theory, the dynamic responses of the poroelastic half-space soil medium due to quasi-static and dynamic loads from a moving train are investigated semi-analytically. The dynamic loads are assumed to be generated from the rail surface irregularities. The vehicle dynamics model is used to simulate the axle loads (quasi-static loads) and the dynamic loads from a moving train. The compatibility of the displacements at wheel–rail contact points couple the vehicle and the track–ground subsystem, and yield equations for the dynamic wheel–rail loads. A linearized Hertzian contact spring between the wheel and rail is introduced to calculate the dynamic loads. Using the Fourier transform, the governing equations for the poroelastic half-space are then solved in the frequency–wavenumber domain. The time domain responses are evaluated by the fast inverse Fourier transform. Numerical results show that the dynamic loads can make important contribution to dynamic response of the poroelastic half-space for different train speed, and the dynamically induced responses lie in a higher frequency range. The ground vibrations caused by the moving train can be intensified as the primary suspension stiffness of the vehicle increases.     

Nonlinear dynamic buckling of pinned–fixed shallow arches under a sudden central concentrated load

The structural behavior of a shallow arch is highly nonlinear, and so when the amplitude of the oscillation of the arch produced by a suddenly-applied load is sufficiently large, the oscillation of the arch may reach a position on its unstable equilibrium paths that leads the arch to buckle dynamically. This paper uses an energy method to investigate the nonlinear elastic dynamic in-plane buckling of a pinned–fixed shallow circular arch under a central concentrated load that is applied suddenly and with an infinite duration. The principle of conservation of energy is used to establish the criterion for dynamic buckling of the arch, and the analytical solution for the dynamic buckling load is derived. Two methods are proposed to determine the dynamic buckling load. It is shown that under a suddenly-applied central load, a shallow pinned–fixed arch with a high modified slenderness (which is defined in the paper) has a lower dynamic buckling load and an upper dynamic buckling load, while an arch with a low modified slenderness has a unique dynamic buckling load.     

The effect of dynamic normal force on the stick–slip vibration characteristics

Nonlinear Dynamics - In the experiment, we observed such a phenomenon: the alternating normal force changes the vibration state of a friction system. A single-degree-of-freedom mathematical model...     

Experimental investigation into the detonation characteristics of hybrid RDX–ethylene–air mixtures

An experimental study is conducted to determine the detonation characteristics of 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) particles dispersed in a gaseous fuel air mixture in a vertical detonation tube with an inner diameter of 200 mm and a height of 5400 mm. Experiments are performed in both ethylene–air mixtures and RDX–ethylene–air hybrid mixtures. The detonation front pressure and velocity are measured with six pressure transducers along the detonation tube. The results show that the addition of RDX assists 4.0 vol.% ethylene–air mixtures in achieving detonation. The detonation front pressure increases noticeably with dust concentration up to \(474\hbox { g/m}^{3}\) in the RDX–ethylene–air hybrid mixtures, but the velocity only increases slightly. The cellular structures of RDX–ethylene–air hybrid mixtures and ethylene–air mixtures were obtained with the use of smoked foils and exhibit irregular structures. It is found that the measured cell size has a U-shaped curve with respect to RDX concentration.     

Experimental investigation of wall film renewal in liquid–liquid slug flow

Liquid–liquid slug flow offers the unique characteristics of high heat and mass transfer combined with a narrow residence time distribution in continuous flow and has thus attracted considerable attention in the field of microfluidics. To exploit its advantages in the successful design and operation of micro-reactors, a precise understanding of the mass transfer processes is essential. In the present work, the role of the thin continuous liquid film formed on the capillary wall in mass transfer is investigated. Fluorescence microscopy is used to determine the exchange between wall film and continuous phase segments to determine if the film is continuously renewed and can therefore be considered to contribute interfacial area available for mass transfer. The distinct wetting properties of different capillary materials are utilized in the experimental set-up to achieve a reproducible and non-invasive release of tracer. The degree of wall film mass transfer as a function of velocity, interfacial area and wall-film thickness is established.     

Experimental investigation on heat transfer of forced convection condensation of ethanol–water vapor mixtures on a vertical mini-tube

In this paper, condensation heat transfer characteristics of ethanol–water vapor mixtures on a vertical mini-vertical tube with 1.221 mm outside diameter were investigated experimentally. The experiments were performed at different velocities and pressures over a wide range of ethanol mass fractions in vapor. The test results indicated that, with respect to the change of the vapor-to-surface temperature difference, the condensation curves of the heat transfer coefficients revealed nonlinear characteristics, and had peak values. At 2 % ethanol mass fraction in vapor, the condensation heat transfer coefficient value of the ethanol–water vapor mixture was found to have a maximum heat transfer coefficient of 50 kW m^?2 K^?1, which was 3–4 times than that of pure steam. The condensation heat transfer coefficients decreased with increased ethanol mass fraction in vapor. The vapor pressure and vapor velocity had a positive effect on the condensation heat transfer coefficients of ethanol–water vapor mixtures.     

Experimental investigation of Marangoni condensation of ethanol–water mixture vapors on vertical tube

The heat transfer characteristics of the condensation of ethanol–water binary vapor on vertical tubes with the pipe diameter of 10 mm were investigated experimentally. The results showed that, with the change of the vapor-to-surface temperature difference, the condensation heat transfer coefficients revealed nonlinear characteristics with peak values under a wide variety of operating conditions. With the increasing pressure or velocity of the vapor, the heat transfer coefficients increased subsequently. The effect of vapor pressure or velocity on heat transfer coefficients reduced with the increasing ethanol mass fraction. It was noteworthy that, under low ethanol mass fractions (0.5–2%), the heat transfer coefficients augmented significantly, were about 5–8 times greater than that of pure steam. The comparison for different test blocks indicated that the condensation heat transfer coefficients for different pipe diameters were about the same value under the same operating condition. Significant heat transfer enhancement by Marangoni condensation could be achieved for full range of pipe diameter used in industrial condensers.     

Nonlinear coupled vibration of electrostatically actuated clamped–clamped microbeams under higher-order modes excitation

Nonlinear modal interactions have recently become the focus of intense research in micro-resonators for their use to improve oscillator performance and probe the frontiers of fundamental physics. Understanding and controlling nonlinear coupling between vibrational modes is critical for the development of advanced micromechanical devices. This article aims to theoretically investigate the influence of antisymmetry mode on nonlinear dynamic characteristics of electrically actuated microbeam via considering nonlinear modal interactions. Under higher-order modes excitation, two nonlinear coupled flexural modes to describe microbeam-based resonators are obtained by using Hamilton’s principle and Galerkin method. Then, the Method of Multiple Scales is applied to determine the response and stability of the system for small amplitude vibration. Through Hopf bifurcation analysis, the bifurcation sets for antisymmetry mode vibration are theoretically derived, and the mechanism of energy transfer between antisymmetry mode and symmetry mode is detailed studied. The pseudo-trajectory processing method is introduced to investigate the influence of external drive on amplitude and bifurcation behavior. Results show that nonlinear modal interactions can transit vibration energy from one mode to nearby mode. In what follows, an effective way is proposed to suppress midpoint displacement of the microbeam and to reduce the possibility of large deflection. The quantitative relationship between vibrational modes is also obtained. The displacement of one mode can be predicted by detecting another mode, which shows great potential of developing parameter design in MEMS. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.