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Heavy-duty land-based gas turbines with can-annular combustors typically exhibit a set of thermoacoustic modes with similar frequencies, due to their rotational symmetry and the weak coupling between neighbouring cans. The Bloch boundary condition is often used to simplify these combustors. Because the widely used (quasi-)one-dimensional model cannot naturally consider high-order modal components in the three-dimensional acoustic field, it is valid only when the frequency is sufficiently low and the length of the can-to-can interaction gap is sufficiently short. In this paper, we present a theoretical model using the mode-matching method to consider high-order modal components. A reflection coefficient matrix is used to accurately describe the acoustic characteristics of the gap area. This reflection coefficient matrix is found to depend on the nondimensional cross-sectional area ratio, the Helmholtz number based on the length of the gap area, and the Bloch number. To facilitate a full low-order network modelling of the high-frequency thermoacoustic modes in can-annular combustors, a flame transfer matrix is also used to describe the modal coupling effect across the flame. Based on this model, the thermoacoustic problem of a four-flame can-annular combustor is studied as an example. It is shown that the frequency and growth rate of the thermoacoustic modes can be predicted accurately using the reflection coefficient matrix and flame transfer matrix. The effects of high-order modal components across the flame and in the gap areas are studied separately. The results show that the model containing both of the two coupling effects has the widest range of validity. These couplings can be ignored if only low-frequency plane acoustic waves are considered but need to be carefully considered for higher frequency modes. Moreover, when multiple flames are considered, asymmetric flame distributions are found to more easily lead to modal coupling compared to symmetric flame distributions. All results are validated by comparing with the numerical solutions of the full two-dimensional Helmholtz equation using the finite element method. • The crosstalk effect in the gap area is modelled using the mode matching method. • The jump condition across multiple flames is modelled using the mode matching method. • The effect of modal coupling across the flame and in the gap area is investigated. • A 2D theoretical model is developed to predict the thermoacoustic mode in can-annular combustors. [ABSTRACT FROM AUTHOR]

Thermoacoustic instabilities in annular gas turbine combustors often involve modes which vary in both the longitudinal and circumferential directions. Recent experimental studies show that during limit cycle oscillations, different thermoacoustic modes may be uncoupled, as is the case in purely longitudinal or circumferential spinning modes. They may also be coupled, for example two counter-rotating circumferential modes combining to give standing or mixed modes, and coupling between circumferential and longitudinal modes giving rise to the slanted mode. Accurately predicting such modal couplings and the resulting spatial pattern of limit cycle oscillations remains an open challenge. This work uses a 2-D low-order network model based on modal expansions, validated against a full 3-D Helmholtz solver, to systematically investigate these couplings. For the first time, low-order network modelling is shown to capture limit cycle oscillations exhibiting both uncoupled and nonlinearly coupled modes, the latter including coupling between counter-rotating circumferential modes and between longitudinal and circumferential modes. It is shown that limit cycle solutions with totally different mode patterns (longitudinal, circumferential spinning, circumferential standing and slanted) can all exist in a given thermoacoustic system, with switches between modal patterns arising from slight changes in parameters such as the flame time delay. [ABSTRACT FROM AUTHOR]

Abstract Helmholtz resonators (HRs) are widely used to damp acoustic oscillations, including in the combustors of aero-engines and power gas turbines where they damp thermoacoustic oscillations. The geometries of such combustors are often annular in shape, which means that low frequency acoustic modes exhibit both longitudinal and circumferential modeshapes, the latter across different circumferential wave numbers. For linear acoustic disturbances downstream of the flame, the presence of HRs leads to modal coupling and mode shape shifts, which makes design and placement of multiple HRs very complicated. A procedure which ensures that the design and placement of the HRs can be optimised for good acoustic damping performance would be very valuable, and such a procedure is presented in this work. A simplified linear, low-dimensional model for the acoustic behaviour in a hot annular duct sustaining a mean flow is extended to account for the attachment of multiple HRs. The HRs are assumed to sustain a cooling mean bias flow through them, towards the combustor, such that they can be modelled using linear, lumped element Rayleigh conductivity models. An optimisation method based on the gradient derived from adjoint sensitivity analysis is then applied to the low order network acoustic modelling framework for hot annular ducts incorporating HR models, for the first time. It is used to optimise over multiple HR geometry and placement parameters, to obtain optimum acoustic damping over all acoustic modes in a given frequency range. These optimisation procedures are validated via multi-dimensional parameter sweep results. Thus a novel and efficient tool for HR optimisation for thin annular ducts is presented. [ABSTRACT FROM AUTHOR]

The sound generated or absorbed by short circular holes with a mean flow passing through them is relevant in many practical applications. Analytical models for their acoustic response often ignore the fact that such holes open to a confined or finite space either side, or account for this effect simply by adding an end mass inertial correction. The vortex–sound interaction within a short hole has been recently shown to strongly affect the acoustic response at low frequencies (D. Yang, A.S. Morgans, J. Sound Vib. 384 (2016) 294–311 [ 19] ). The present study considers a semi-analytical model based on Green's function method to investigate how the expansion ratios either side of a short hole affect the vortex–sound interaction within it. After accounting for expansions to confined spaces using a cylinder Green's function method, the model is substantially simplified by applying a half-space Green's function for expansions to large spaces. The effect of both the up- and downstream expansion ratios on the acoustics of the hole is investigated. These hole models are then incorporated into a Helmholtz resonator model, allowing a systematic investigation into the effect of neck-to-cavity expansion ratio and neck length. Both of these are found to affect the resonator damping. [ABSTRACT FROM AUTHOR]

This study is concerned with the theoretical modelling and experimental verification of the coupled vibrations of building and elevator ropes. The elevator ropes consist of a main rope which supports the cage and the compensation rope which is connected to the compensation sheave. The elevator rope is a flexible wire with a low damping, so it is prone to vibrations. In the case of a high-rise building, the rope length also increases significantly, so that the fundamental frequency of the elevator rope approaches the fundamental frequency of the building thus increasing the possibility of resonance. In this study, the dynamic model for the analysis of coupled vibrations of building and elevator ropes was derived by using Hamilton's principle, where the cage motion was also considered. An experimental testbed was built to validate the proposed dynamic model. It was found that the experimental results are in good agreement with the theoretical predictions thus validating the proposed dynamic model. The proposed model was then used to predict the vibrations of real building and elevator ropes. [ABSTRACT FROM AUTHOR]

The acoustic response of a circular hole with mean flow passing through it is highly relevant to Helmholtz resonators, fuel injectors, perforated plates, screens, liners and many other engineering applications. A widely used analytical model [M.S. Howe. “Onthe theory of unsteady high Reynolds number flow through a circular aperture”, Proc. of the Royal Soc. A. 366, 1725 (1979), 205‐223] which assumes an infinitesimally short hole was recently shown to be insufficient for predicting the impedance of holes with a finite length. In the present work, an analytical model based on Green׳s function method is developed to take the hole length into consideration for “short” holes. The importance of capturing the modified vortex noise accurately is shown. The vortices shed at the hole inlet edge are convected to the hole outlet and further downstream to form a vortex sheet. This couples with the acoustic waves and this coupling has the potential to generate as well as absorb acoustic energy in the low frequency region. The impedance predicted by this model shows the importance of capturing the path of the shed vortex. When the vortex path is captured accurately, the impedance predictions agree well with previous experimental and CFD results, for example predicting the potential for generation of acoustic energy at higher frequencies. For “long” holes, a simplified model which combines Howe׳s model with plane acoustic waves within the hole is developed. It is shown that the most important effect in this case is the acoustic non-compactness of the hole. [ABSTRACT FROM AUTHOR]

In this work, we investigate both numerically and theoretically the sound generated by entropy waves passing through sudden area expansions. This is a canonical configuration representing internal flows with flow separation and stagnation pressure losses. The numerical approach is based on a triple decomposition of the flow variables into a steady mean, a small-amplitude coherent part, and a stochastic turbulent part. The coherent part contains acoustic, vortical, and entropy waves. The mean flow is obtained as the solution of the Reynolds-Averaged Navier–Stokes (RANS) equations. The equations governing the coherent perturbations are linearised and solved in the frequency domain. To account for the effect of turbulence on the coherent perturbations, a frozen eddy viscosity model is employed. When entropy fluctuations pass through the area expansion, the generated entropy noise behaves as a low-pass filter. The numerical predictions of the noise at low frequencies are compared to the predictions of compact, quasi-one-dimensional, and isentropic theory and large discrepancies are observed. An alternative model for the generated entropy noise tailored for area expansions is then proposed. Such model is based on the conservation of mass, momentum, and energy written in integral form. The model assumes zero frequency and the one-dimensionality of the flow variables far upstream and downstream of the expansion. The predictions of this model agree well with the numerical simulations across a range of finite subsonic Mach numbers including low, intermediate, and high Mach numbers. The contributions of this work are both numerical and theoretical. Numerically, a triple decomposition adapted to high-Mach-number, compressible flows is introduced for the first time in the context of acoustic simulations. From a theoretical point of view, the quasi-steady model proposed here correctly captures the low-frequency entropy noise generated at sudden area expansions, including at high subsonic Mach numbers. • Isentropic, quasi-1D theory overpredicts the entropy noise at sudden area expansions • We propose a numerical approach based on a triple decomposition for compressible flows. • We propose an alternative compact analytical model tailored to area expansions. [ABSTRACT FROM AUTHOR]

The structural health monitoring (SHM) involves the sampled operational vibration measurements over time so that the structural features can be extracted accordingly. The recurrence plot (RP) and corresponding recurrence quantification analysis (RQA) have become a useful tool in various fields due to its efficiency. The threshold selection is one of key issues to make sure that the constructed recurrence plot contains enough recurrence points. Different signals have in nature different threshold values. This paper is aiming at presenting an approach to determine the optimal threshold for the operational vibration measurements of civil engineering structures. The surrogate technique and Taguchi loss function are proposed to generate reliable data and to achieve the optimal discrimination power point where the threshold is optimum. The impact of selecting recurrence thresholds on different signals is discussed. It is demonstrated that the proposed method to identify the optimal threshold is applicable to the operational vibration measurements. The proposed method provides a way to find the optimal threshold for the best RP construction of structural vibration measurements under operational conditions. [ABSTRACT FROM AUTHOR]

Helmholtz resonators with sound absorption materials filling the neck may have an improved sound absorption capacity. In this work, parallel perforated ceramics with different perforation diameters were installed into the neck of a Helmholtz resonator to improve its acoustic impedance to simultaneously achieve a better acoustic absorption coefficient and a wider absorption bandwidth. An experimental system was built to investigate the effect of the perforation diameters on the sound absorption performance of the resonator. It is found that nonlinear effects near the resonance frequency affect the resonator׳s neck mouth impedance and further its sound absorption performance significantly. For frequency range 50–500 Hz, a model of the neck mouth impedance is developed based on a revised Forchheimer relationship. The experimental results are in good agreement with the theoretical model. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the suppression of vibrations and radiated sound of a ring-stiffened circular cylindrical shell in contact with unbounded external fluid by means of piezoelectric sensors and actuators. The dynamic model of a circular cylindrical shell based on the Sanders shell theory was considered together with a ring stiffener model. The mass and stiffness matrices for a ring stiffener were newly derived in this study and added to the mass and stiffness matrices of the cylindrical shell, respectively. The fluid-added mass matrix, which was derived by using the baffled shell theory, was also added to the mass matrix. Finally, the equations representing the piezoelectric sensor measurement and piezoelectric actuation complete the theoretical model for the addressed problem. The natural vibration characteristics of the ring-stiffened cylindrical shell both in air and in water were investigated both theoretically and experimentally. The theoretical predictions were in good agreement with the experimental results. An active vibration controller which can cope with a harmonic disturbance was designed by considering the modified higher harmonic control, which is, in fact, a band rejection filter. An active vibration control experiment on the submerged cylindrical shell was carried out in a water tank and the digital control system was used. The experimental results showed that both vibrations and radiation sound of the submerged cylindrical shell were suppressed by a pair of piezoelectric sensor and actuator. [Copyright &y& Elsevier]

Traditional bridge health monitoring is both expensive and time-consuming because of the need for installing a large quantity of sensors on the bridge. The indirect monitoring method as a feasible alternative has become popular over the last decade, as useful information can be gathered from moving vehicles installed with sensors by considering vehicle-bridge interaction. This paper describes an indirect time-varying modal parameter identification method for bridges under a moving test vehicle. A novel reference-driven S-transform is proposed for the parametric modal identification of time-varying structural systems with non-stationary characteristics based on a multisensory arrangement, comprising a fixed reference sensor installed on the bridge and another movable sensor installed on a moving test vehicle. By the phase-preservation property of S-transform and the multisensory time-frequency analysis, the proposed iterative reference-driven S-transform can be used to extract the time-varying modal parameters of the vehicle-bridge system when the vehicle moves on the bridge. Based on the coherence between measurements from the sensors mounted on the bridge and vehicle, one can track the time-varying characteristics by combining the spatial and time-frequency information obtained by the multisensory array. The efficiency of the proposed reference-driven S-transform method is validated by numerical simulations and laboratory experiments using a simply supported beam with a moving vehicle. The effects of the vehicle property, driving speed, road roughness and measurement noise are discussed. The numerical and experimental results have demonstrated that the proposed method is useful for time-varying parameter extraction with a multisensory system. This will be useful to structural condition monitoring of bridges. [ABSTRACT FROM AUTHOR]

The acoustic characteristics of bluff-body burners play a critical role in the combustion stability for combustors using this type of burners. The acoustic modelling of an axisymmetric bluff-body burner entails properly capturing the sound-vortex interaction for the flow through the annular aperture of the burner. Such a problem pertaining to annular apertures can also be of relevance to other engineering applications, such as acoustic dampers or turbofan duct systems. The methodology of combining suitable acoustic Green's functions with a vortex sheet model has been applied extensively in previous theoretical studies of the acoustic response of a short circular orifice with a mean flow passing through it. In this work, the Green's function and vortex sheet model theory is generalised in order to efficiently predict the acoustic characteristics of thin annular apertures sustaining a mean flow, which effectively emulate the typical axisymmetric bluff-body burner configurations in realistic combustors. This requires the incorporation of multiple Kutta conditions for modelling the vortex shedding and multiple vortex sheets for modelling the interaction of the shed vorticity and the acoustics. A high-resolution compressible Large Eddy Simulation (LES) of a simplified representative geometry is performed for validation; the analytical prediction and numerical findings show very good agreement, and the LES further provides key insights into the speed with which vortical disturbances convect downstream. [ABSTRACT FROM AUTHOR]

The acoustic inertia of the canonical configuration of inclined circular aperture(s) in a finite-thickness plate at the low frequency limit is investigated under the inviscid still-air condition. A hybrid approach combining modal expansion and boundary element method is applied to calculate the effective length of the aperture as a quantitative characterisation of its acoustic inertia. These calculations, covering different inclination angles up to 75°, are performed for a single isolated aperture with a selected range of plate thickness and the periodic aperture arrays of aligned and staggered arrangements with a selected range of aperture spacing respectively. The results are validated by the simulations carried out with the commercial software COMSOL. The parametric studies of geometric dimensions included in this work provide representative results for typical acoustic related engineering applications of finite-length inclined apertures. A link for access to the MATLAB programmes implementing the calculations is provided for interested readers. As an example of application, the hybrid method described in this work is used for the acoustic modelling of a representative multi-perforated liner studied in the literature for the problem of thermo-acoustic instability. The results compared well against those obtained from the Computational Fluid Dynamics simulations reported in the literature. • An efficient method to compute acoustic inertia of inclined apertures is developed. • Inviscid acoustic inertia of inclined apertures in still air is studied. • Application of acoustic inertia calculation to a representative case is demonstrated. [ABSTRACT FROM AUTHOR]

One of the most important parameters influencing the acoustic response of holes that sustain a low-Mach-number bias flow is their length-to-diameter ratio. For sufficiently short holes, the bias flow is detached within the hole's length, while in long holes the bias flow reattaches. The acoustic behaviour of each class is different and separate modelling approaches exist in the literature. For many technical applications, however, the length-to-diameter ratio falls in the range 1. 5 < L h / D h < 3. 0 , where is not clear if the holes behave acoustically as short or long holes. In this work, the acoustics of such medium holes are explored numerically and analytically. The numerical approach is based on the linearisation of the compressible Navier–Stokes equations (LNSE) around a Reynolds-averaged mean flow. Medium holes are shown to whistle at higher Strouhal numbers than short holes although the mean flow reattaches within them. The underlying physics are further investigated by incorporating selected flow features of the LNSE results into a semi-analytical model accounting for vortex-sound interaction. It is shown that the perturbation field is determined by the three-way coupling of the two vortex sheets shed from the inlet and outlet edges of the hole with the acoustic field. Furthermore, the modelling of the growth of vorticity inside the hole is shown to be crucial to enable whistling in the semi-analytical model. • Short holes with reattached bias flow generate acoustic energy (whistle). • Whistling frequency significantly higher than for holes with detached bias flow. • New semi-analytical model captures the acoustics of medium holes. • Two vortex sheets shed from the hole edges couple with the acoustic field. • Shear layer instability within the hole is crucial for whistling to occur. [ABSTRACT FROM AUTHOR]

• Developing a new form of inversion matrix (ITDM) for moving force identification. • The two sources of error in the formation of the inversion matrix are analyzed, one is the load compression error and the other is the unit impulse response dispersion error. • The ITDM eliminates the influence of the discrete error of the unit impulse response on the load solution. • All the results have demonstrated the effectiveness of the ITDM. This paper presents a new form of inversion matrix, which aims to obtain more accurate moving force identification results from the responses of a simply supported bridge deck to vehicles passing over it. The load identification process of the modal superposition method discretizes the time-domain integral equation of the load response, obtains the load inversion matrix, and converts the load identification problem into a linear equation solving problem. The inversion matrix formation process of this traditional time domain method (TDM) can introduce the load compression error and the discretization error of the unit impulse response function, which affect the load solution. To reduce the source of error and maintain the stability of the solution, the discretized unit impulse response function is replaced by an integral form, thereby eliminating the discretization error. This method is called the integral time domain method (ITDM). A supported beam subjected to a single force and two forces is illustrated as a numerical example. Through numerical analysis, the effects of the two methods in single time-varying force identification are analyzed. Using two moving forces analysis, when noise is included, the influence of discretization error on the load solution is analyzed. Numerical results show that the discretization error has a greater impact on the load inversion using the acceleration response than the bending moment and displacement response inversion, and the ITDM should be used to avoid the interference of discrete error. [ABSTRACT FROM AUTHOR]

Heat exchanger tube rows can influence the thermoacoustic instability behaviour of combustion systems since they act as both acoustic scatterers and unsteady heat sinks. Therefore, with careful tuning of their thermoacoustic properties, heat exchangers have the potential to act as passive control devices. In this work, we focus on (only) the acoustic scattering behaviour of heat exchanger tubes. We present a comparison of existing acoustic models for tube rows and slits, models for the latter having the advantage of incorporating frequency dependence. We then propose a new model that enables the adaptation of slit models for tube rows. This model is validated against experiments and Linearised Navier–Stokes Equations (LNSE) predictions for the transmission and reflection coefficients, including phase information. The model predictions show very good agreement with the experimental and numerical validations, especially for low frequencies (Strouhal number < 0. 5 , based on tube radius and excitation frequency), with mean differences less than 2% for the transmission coefficients (the reflection coefficient errors are somewhat larger since their magnitudes are very close to zero). [ABSTRACT FROM AUTHOR]

Abstract: We propose a novel non-parametric method to identify generalized frequency response functions (GFRFs) for multi-input multi-output (MIMO) nonlinear systems in this paper. Firstly, the formula to calculate GFRFs is derived in terms of the corresponding output frequency properties of GFRFs of the MIMO nonlinear system excited by a single-tone signal. Secondly, to improve the efficiency of the non-parametric identification method, we utilize the multitone excitation to drive the MIMO nonlinear system, and propose a searching algorithm of the frequency base of multitone excitation. Finally, the general procedure of identifying GFRFs of MIMO nonlinear system excited by the multitone excitation is summarized. The proposed non-parametric identification method is suitable for application as it only depends on input–output data of the MIMO nonlinear system and avoids time-consuming study of its complicated physical mechanisms. Moreover, the proposed non-parametric identification method is proved to be effective by the precisely identifying GFRFs of a two-input two-output nonlinear system. [Copyright &y& Elsevier]