Eigenmodes of lined flow ducts with rigid splices

This paper presents an analytic expression for the acoustic eigenmodes of a cylindrical lined duct with rigid axially running splices in the presence of flow. The cylindrical duct is considered to be uniformly lined except for two symmetrically positioned axially running rigid liner splices. An exact analytic expression for the acoustic pressure eigenmodes is given in terms of an azimuthal Fourier sum, with the Fourier coefficients given by a recurrence relation. Since this expression is derived using a Greens function method, the completeness of the expansion is guaranteed. A numerical procedure is described for solving this recurrence relation, which is found to converge exponentially with respect to number of Fourier terms used and is in practice quick to compute; this is then used to give several numerical examples for both uniform and sheared mean flow. An asymptotic expression is derived to directly calculate the pressure eigenmodes for thin splices. This asymptotic expression is shown to be quantitatively accurate for ducts with very thin splices of less than 1 % unlined area and qualitatively helpful for thicker splices of the order of 6 % unlined area. A thin splice is in some cases shown to increase the damping of certain acoustic modes. The influences of thin splices and thin boundary layers are compared and found to be of comparable magnitude for the parameters considered. Trapped modes at the splices are also identified and investigated. © 2011 Cambridge University Press.

Measurements of triggering and transient growth in a model lean-premixed gas turbine combustor

Instability triggering and transient growth of thermoacoustic oscillations were experimentally investigated in combination with linear/nonlinear flame transfer function (FTF) methodology in a model lean-premixed gas turbine combustor operated with CH 4 and air at atmospheric pressure. A fully premixed flame with 10kW thermal power and an equivalence ratio of 0.60 was chosen for detailed characterization of the nonlinear transient behaviors. Flame transfer functions were experimentally determined by simultaneous measurements of inlet velocity fluctuations and heat release rate oscillations using a constant temperature anemometer and OH */CH * chemiluminescence emissions, respectively. The phase-resolved variation of the local flame structure at a limit cycle was measured by planar laser-induced fluorescence of OH. Simultaneous measurements of inlet velocity, OH */CH * emission, and acoustic pressure were performed to investigate the temporal evolution of the system from a stable to a limit cycle operation. This measurement allows us to describe an unsteady instability triggering event in terms of several distinct stages: (i) initiation of a small perturbation, (ii) exponential amplification, (iii) saturation, (iv) nonlinear evolution of the perturbations towards a new unstable periodic state, (v) quasi-steady low-amplitude periodic oscillation, and (vi) fully-developed high-amplitude limit cycle oscillation. Phase-plane portraits of instantaneous inlet velocity and heat release rate clearly show the presence of two different attractors. Depending on its initial position in phase space at infinitesimally small amplitude, the system evolves towards either a high-amplitude oscillatory state or a low-amplitude oscillatory state. This transient phenomenon was analyzed using frequency- and amplitude-dependent damping mechanisms, and compared to subcritical and supercritical bifurcation theories. The results presented in this paper experimentally demonstrate the hypothesis proposed by Preetham et al. based on analytical and computational solutions of the nonlinear G-equation [J. Propul. Power 24 (2008) 1390-1402]. Good quantitative agreement was obtained between measurements and predictions in terms of the conditions for the onset of triggering and the amplitude of triggered combustion instabilities. © 2011 The Combustion Institute.

Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.

Experimental investigation of dynamic response of acoustically forced turbulent premixed CH4/CO2/air flames

Increasing demand for energy and continuing increase in environmental as well as financial cost of use of fossil fuels drive the need for utilization of fuels from sustainable sources for power generation. Development of fuel-flexible combustion systems is vital in enabling the use of sustainable fuels. It is also important that these sustainable combustion systems meet the strict governmental emission legislations. Biogas is considered as one of the viable sustainable fuels that can be used to power modern gas turbines: However, the change in chemical, thermal and transport properties as well as change in Wobbe index due to the variation of the fuel constituents can have a significant effect on the performance of the combustor. It is known that the fuel properties have strong influence on the dynamic flame response; however there is a lack of detailed information regarding the effect of fuel compositions on the sensitivity of the flames subjected to flow perturbations. In this study, we describe an experimental effort investigating the response of premixed biogas-air turbulent flames with varying proportions of CH4 and CO2 to velocity perturbations. The flame was stabilized using a centrally placed conical bluff body. Acoustic perturbations were imposed to the flow using loud speakers. The flame dynamics and the local heat release rate of these acoustically excited biogas flames were studied using simultaneous measurements of OH and H2CO planar laser induced fluorescence. OH* chemiluminescence along with acoustic pressure measurements were also recorded to estimate the total flame heat release modulation and the velocity fluctuations. The measurements were carried out by keeping the theoretical laminar flame speed constant while varying the bulk velocity and the fuel composition. The results indicate that the flame sensitivity to perturbations increased with increased dilution of CH4 by CO2 at low amplitude forcing, while at high amplitude forcing conditions the magnitude of the flame response was independent of dilution.

Nonlinear phenomena in thermoacoustic systems with premixed flames

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies, amplitudes and stability of limit cycles. Limit cycles in thermoacoustic systems are reached when the energy input from driving processes and energy losses from damping processes balance each other over a cycle of the oscillation. In this paper an integral relation for the rate of change of energy of a thermoacoustic system is derived. This relation is analogous to the well-known Rayleigh criterion in thermoacoustics, but can be used to calculate the amplitudes of limit cycles, as well as their stability. The relation is applied to a thermoacoustic system of a ducted slot-stabilized 2-D premixed flame. The flame is modelled using a nonlinear kinematic model based on the G-equation, while the acoustics of planar waves in the tube are governed by linearised momentum and energy equations. Using open-loop forced simulations, the flame describing function (FDF) is calculated. The gain and phase information from the FDF is used with the integral relation to construct a cyclic integral rate of change of energy (CIRCE) diagram that indicates the amplitude and stability of limit cycles. This diagram is also used to identify the types of bifurcation the system exhibits and to find the minimum amplitude of excitation needed to reach a stable limit cycle from another linearly stable state, for single- mode thermoacoustic systems. Furthermore, this diagram shows precisely how the choice of velocity model and the amplitudedependence of the gain and the phase of the FDF influence the nonlinear dynamics of the system. Time domain simulations of the coupled thermoacoustic system are performed with a Galerkin discretization for acoustic pressure and velocity. Limit cycle calculations using a single mode, as well as twenty modes, are compared against predictions from the CIRCE diagram. For the single mode system, the time domain calculations agree well with the frequency domain predictions. The heat release rate is highly nonlinear but, because there is only a single acoustic mode, this does not affect the limit cycle amplitude. For the twenty-mode system, however, the higher harmonics of the heat release rate and acoustic velocity interact resulting in a larger limit cycle amplitude. Multimode simulations show that in some situations the contribution from higher harmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Copyright © 2012 by ASME.

The absorption of sound by helmholtz resonators with and without flow

Helmholtz resonators are commonly used as absorbers of incident acoustic power. Theoretical and experimental investigations have been performed in the four cases of no mean flow, grazing mean flow, bias mean flow and a combination of grazing and bias mean flows. In the absence of a mean flow, the absorption coefficient (deflned as the proportion of incident energy absorbed) is a non-linear function of the acoustic pressure and high incident acoustic pressures are required before the absorption becomes signiflcant. In contrast, when there is a mean flow present, either grazing or bias, the absorption is linear and thus absorption coefficient is independent of the magnitude of the acoustic pressure, and absorption is obtained over a wider range of frequencies. Non-linear effects are only discernible very close to resonance and at very-high amplitude. With grazing mean flow, there is the undesirable effect that sound can be generated over a range of frequencies due to the interaction between the unsteadily shed vorticity waves and the downstream edge of the aperture. This production is not observed when there is a bias flow because here the vorticity is shed all around the rim of the aperture and swept away by the mean flow. When there is both a grazing mean flow and a mean bias flow, we flnd that only a small amount of bias mean flow, compared with grazing mean flow, is required to destroy the production of acoustic energy. © 2002 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc.

Film bulk acoustic resonator pressure sensor with self temperature reference

A novel film bulk acoustic resonator (FBAR) with two resonant frequencies which have opposite reactions to temperature changes has been designed. The two resonant modes respond differently to changes in temperature and pressure, with the frequency shift being linearly correlated with temperature and pressure changes. By utilizing the FBAR's sealed back trench as a cavity, an on-chip single FBAR sensor suitable for measuring pressure and temperature simultaneously is proposed and demonstrated. The experimental results show that the pressure coefficient of frequency for the lower frequency peak of the FBAR sensors is approximately -17.4 ppm kPa-1, while that for the second peak is approximately -6.1 ppm kPa-1, both of them being much more sensitive than other existing pressure sensors. This dual mode on-chip pressure sensor is simple in structure and operation, can be fabricated at very low cost, and yet requires no specific package, therefore has great potential for applications. © 2012 IOP Publishing Ltd.

Ultrasensitive mass balance based on a bulk acoustic mode single-crystal silicon resonator

A single-crystal silicon resonant bulk acoustic mass sensor with a measured resolution of 125 pg cm2 is presented. The mass sensor comprises a micromachined silicon plate that is excited in the square-extensional bulk acoustic resonant mode at a frequency of 2.182 MHz, with a quality factor exceeding 106. The mass sensor has a measured mass to frequency shift sensitivity of 132 Hz cm2 μg. The resonator element is embedded in a feedback loop of an electronic amplifier to implement an oscillator with a short term frequency stability of better than 7 ppb at an operating pressure of 3.8 mTorr. © 2007 American Institute of Physics.

Thin film monitoring with silicon bulk acoustic resonators

Abstract-This paper reports a single-crystal silicon mass sensor based on a square-plate resonant structure excited in the wine glass bulk acoustic mode at a resonant frequency of 2.065 MHz and an impressive quality factor of 4 million at 12 mtorr pressure. Mass loading on the resonator results in a linear downshift in the resonant frequency of this device, wherein the measured sensitivity is found to be 175 Hz cm2/μg. The silicon resonator is embedded in an oscillator feedback loop, which has a short-term frequency stability of 3 mHz (approximately 1.5 ppb) at an operating pressure of 3.2 mtorr, corresponding to an equivalent mass noise floor of 17 pg/cm2. Possible applications of this device include thin film monitoring and gas sensing, with the potential added benefits of scalability and integration with CMOS technology. © 2008 IEEE.

Spray visualisation and acoustic analysis in a gas-turbine type burner

This paper presents the characterisation of self-excited oscillations in a kerosene burner. The combustion instability exhibits two different modes and frequencies depending on the air flow rate. Experimental results reveal the influence of the spray to shift between these two modes. Pressure and heat release fluctuations have been measured simultaneously and the flame transfer function has been calculated from these measurements. The Mie scattering technique has been used to record spray fluctuations in reacting conditions with a high speed camera. Innovative image processing has enabled us to obtain fluctuations of the Mie scattered light from the spray as a temporal signal acquired simultaneously with pressure fluctuations. This has been used to determine a transfer function relating the image intensity and hence the spray fluctuations to changes in air velocity. This function has identified the different role the spray plays in the two modes of instability. At low air flow rates, the spray responds to an unsteady air flow rate and the time varying spray characteristics lead to unsteady combustion. At higher air flow rates, effective evaporation means that the spray dynamics are less important, leading to a different flame transfer function and frequency of self-excited oscillation. In conclusion, the combustion instabilities observed are closely related with the fluctuations of the spray motion and evaporation.

The calculation of acoustic shielding of engine noise by the Silent Aircraft Airframe

The Silent Aircraft airframe has a flying wing design with a large wing planform and a propulsion system embedded in the rear of the airframe with intake on the upper surface of the wing. In the present paper, boundary element calculations are presented to evaluate acoustic shielding at low frequencies. Besides the three-dimensional geometry of the Silent Aircraft airframe, a few two-dimensional problems are considered that provide some physical insight into the shielding calculations. Mean flow refraction effects due to forward flight motion are accounted for by a simple time transformation that decouples the mean-flow and acoustic-field calculations. It is shown that significant amount of shielding can be obtained in the shadow region where there is no direct line of sight between the source and observer. The boundary element solutions are restricted to low frequencies. We have used a simple physically-based model to extend the solution to higher frequencies. Based on this model, using a monopole acoustic source, we predict at least an 18 dBA reduction in the overall sound pressure level of forward-propagating fan noise because of shielding.

Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere.

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.

The nonlinear heat release response of stratified lean-premixed flames to acoustic velocity oscillations

This paper analyzes the forced response of swirl-stabilized lean-premixed flames to high-amplitude acoustic forcing in a laboratory-scale stratified burner operated with CH4 and air at atmospheric pressure. The double-swirler, double-channel annular burner was specially designed to generate high-amplitude acoustic velocity oscillations and a radial equivalence ratio gradient at the inlet of the combustion chamber. Temporal oscillations of equivalence ratio along the axial direction are dissipated over a long distance, and therefore the effects of time-varying fuel/air ratio on the response are not considered in the present investigation. Simultaneous measurements of inlet velocity and heat release rate oscillations were made using a constant temperature anemometer and photomultiplier tubes with narrow-band OH*/CH* interference filters. Time-averaged and phase-synchronized CH* chemiluminescence intensities were measured using an intensified CCD camera. The measurements show that flame stabilization mechanisms vary depending on equivalence ratio gradients for a constant global equivalence ratio (φg=0.60). Under uniformly premixed conditions, an enveloped M-shaped flame is observed. In contrast, under stratified conditions, a dihedral V-flame and a toroidal detached flame develop in the outer stream and inner stream fuel enrichment cases, respectively. The modification of the stabilization mechanism has a significant impact on the nonlinear response of stratified flames to high-amplitude acoustic forcing (u'/U∼0.45 and f=60, 160Hz). Outer stream enrichment tends to improve the flame's stiffness with respect to incident acoustic/vortical disturbances, whereas inner stream stratification tends to enhance the nonlinear flame dynamics, as manifested by the complex interaction between the swirl flame and large-scale coherent vortices with different length scales and shedding points. It was found that the behavior of the measured flame describing functions (FDF), which depend on radial fuel stratification, are well correlated with previous measurements of the intensity of self-excited combustion instabilities in the stratified swirl burner. The results presented in this paper provide insight into the impact of nonuniform reactant stoichiometry on combustion instabilities, its effect on flame location and the interaction with unsteady flow structures. © 2011 The Combustion Institute.

Film bulk acoustic resonator nanosensors for multi-task sensing

This paper shows that film bulk acoustic resonator (FBAR) arrays can be very useful sensors either to detect physical parameters such as temperature and pressure directly or to detect bio-chemicals with extremely high sensitivities by incorporating a chemisorption layer or bio-probe molecules. Furthermore, it also shows that surface acoustic wave devices can be integrated with a FBAR sensor array on the same piezoelectric substrate as the microfluidics systems to perform transportation and mixing of biosamples etc. demonstrating the possibility to fabricate integrated lab-on-a-chip detection systems, in which all the actuators and sensors are operated by acoustic wave devices. This makes the detection system simple, low cost and easy to operate and hence has great commercial potential. © 2011 Inderscience Enterprises Ltd.