Bias Flow Velocity Research Articles

Experimental study of a slit in the presence of a bias flow under medium- and high-level acoustic excitations

This work presents an experimental investigation of the acoustic properties of a slit in the presence of a bias flow under moderate- and high-acoustic excitations. Impedance tube experiments are discussed for a geometry inspired by deep punching resulting in a cut in the plate. The acoustic transfer impedance of the plate is discussed for several bias flow velocities, acoustic excitation, and different frequencies. In the range considered for this study, a bias flow appears to have two main effects, globally enhancing the sound absorption of the plate and creating a protective layer downstream of the plate due to the interaction between the slits. A maximum of the enhancement factor is found at a specific ratio between the acoustic velocity and the bias flow velocity. Two simple asymptotic behaviors are found, dominated by the flow or by the acoustic excitation, respectively. The behavior of the inertance is complex. Globally the inertance decreases with decreasing flow Strouhal number while its dependency on the amplitude of the acoustic velocity is less obvious.

流速と音圧と角部形状による共鳴器開口部の音響抵抗の変化

Acoustic resistance of the rectangular orifice of a resonator attached on a duct was measured. Four types of resonator orifices with different corner shapes were used. To express acoustic resistance as a linear sum of bias flow velocity, grazing flow velocity, and particle velocity in the neck of the resonator, we classified the measured resistance data in two regions dominated by sound pressure and grazing flow velocity, respectively. The acoustic resistance is approximated by the larger value of the linear sum in good agreement with experimental results. The dependence of the acoustic resistance on the Strouhal number was also examined. The variation in acoustic resistance due to vortex shedding at similar orifice corner shape shown by Moers was clearly reproduced.

Effect of nonlinear flame response on the design of perforated liners in suppression of combustion instability

This paper aims at investigating how to suppress combustion instability using perforated liners under nonlinear flame response. A theoretical model is thus presented to describe the interaction between the unsteady heat release, acoustics, and fluid fields, which takes both perforated liner and flame nonlinearity into account. To establish an eigenvalue problem to evaluate combustion instability, appropriate matching and boundary conditions are set up by applying conservation laws across the interfaces, consequently deriving the dispersion relation equation in the form of a matrix. In view of the nonlinearity of flame response function, it is found that the control strategy of combustion instability should be devoted to the reduction of the limit cycle amplitude to an acceptable level rather than the complete elimination of its onset. Based on the present model, we have studied the first longitudinal mode of a Rijke tube equipped with perforated liners. It is noted that the change of combustion instability evolution is sensitive to the design parameters of perforated liners, including cavity depth, installation position, and bias flow velocity. On the one hand, it is indeed possible to suppress the onset of combustion instability with elaborately designed parameters of the perforated liners. On the other hand, the limit cycle amplitude can be reduced as small as possible under various design restrictions of perforated liners in practice. Therefore, this study presents an alternative design criteria of perforated liners for the control of combustion instability.

Application of the Perforated Plate in Passive Control of the Nonpremixed Swirl Combustion Instability Under Acoustic Excitation

Perforated plates are widely used to attenuate noise emission and as acoustic liners in combustion chambers. In this study, the damping performance of the perforated plate located in the combustor inlet section is experimentally and numerically studied. The primary response of nonpremixed swirl flame under 30–400 Hz acoustic excitation with a 445 mm inlet length occurs at 134 Hz and 210 Hz modes. The perforated plate designed for 210 Hz sound absorption with a 328 mm cavity length and an 8.04% porosity is compared to plates with various cavity lengths and different orifice patterns. The acoustic absorption capability of perforated plates is evaluated by the Luong model and tested in an impedance tube. The acoustic measurements show that the sound absorption performance of each plate is strongly affected by the bias flow velocity and cavity length. The combustion results indicate that the installation of perforated plates at the inlet section has two effects: sound attenuation and redistribution of the pressure mode of the combustor. The acoustic mode analysis further demonstrated that, for damping the nonpremixed flame when the combustion instability is caused by the inlet pressure fluctuation, modification of the inlet acoustic mode shape is more efficient than the sound attenuation.

Low-frequency sound absorptive properties of dual perforated plates under bias flow

The low-frequency sound absorptive properties of dual perforated plates with fixed cavity lengths under bias flow is investigated in this paper. The modulus and phase of the reflection coefficient are predicted by the Luong model in the wide range of Strouhal number (0.01–12). The high-pressure amplitude effect is described by the Impedance Describing Function (IDF) nonlinear model. The porosity of the plate varies from 0.15 to 1.23%. The frequency range is 40–400 Hz. The bias flow greatly influences the sound absorptive performance of dual perforated plates both in the linear and nonlinear regime. The comparison between model predictions and measurements show a good agreement. The matching between the bias flow velocity of two plates is the key parameter to determine the sound absorptive performance of dual perforated plates configuration under bias flow. To extend the low-frequency absorption capability by dual perforated plates configuration when lower porosity plate installed with short cavity length, the ratio limit between the two bias flow velocities is given by 0.25–4. Beyond the limitation, the dual perforated plates only work on each absorption frequency with each cavity length. The expressions derived in this study can be used to improve the design of dual perforated plates acoustic dampers.

Design of Acoustic Liner in Small Gas Turbine Combustor Using One-Dimensional Impedance Models

The side-wall cooling liner in a gas turbine combustor serves main purposes—heat transfer and emission control. Additionally, it functions as a passive damper to attenuate thermoacoustic instabilities. The perforations in the liner mainly convert acoustic energy into kinetic energy through vortex shedding at the orifice rims. In the previous decades, several analytical and semi-empirical models have been proposed to predict the acoustic damping of the perforated liner. In the current study, a few of the models are considered to embody the transfer matrix method (TMM) for analyzing the acoustic dissipation in a concentric tube resonator with a perforated element and validated against experimental data in the literature. All models are shown to quantitatively appropriately predict the acoustic behavior under high bias flow velocity conditions. Then, the models are applied to maximize the damping performance in a realistic gas turbine combustor, which is under development. It is found that the ratio of the bias flow Mach number to the porosity can be used as a design guideline in choosing the optimal combination of the number and diameter of perforations in terms of acoustic damping.

Acoustic quasi-steady response of thin walled perforated liners with bias and grazing flows

This paper considers the acoustic performance of a passive damper in which acoustic energy is absorbed by orifices located within a thin plate (i.e. a perforated liner). The perforated liner, which incorporates orifices of length to diameter ratios of ∼0.2, is supplied with flow from a passage. This enables the liner to be subject to a flow that grazes the upstream side of each liner orifice. Flow can also pass through each orifice to create a bias flow. Hence the liner can be subjected to a range of grazing and bias flow combinations. Two types of liners were investigated which incorporated either simple plain or ‘skewed’ orifices. For the mean flow field, data is presented which shows that the mean discharge coefficient of each liner is determined by the grazing to bias flow velocity ratio. In addition, measurements of the unsteady flow field through each liner were also undertaken and mainly presented in terms of the measured admittance. For a given liner geometry, the admittance values were found to be comparable for a given Strouhal number (with the exception of the lowest bias to grazing flow velocity ratio tested) which has also been noted by other authors. The paper shows that this is consistent with the unsteady orifice flow being associated with variations in both the velocity and the area of the vena contracta downstream of each orifice. These same basic characteristics were observed for both of the liner geometries tested. This provides a relatively simple means of predicting the acoustic liner characteristics over the specified operating range.

Passive instability control by a heat exchanger in a combustor with nonuniform temperature

Thermoacoustic instabilities, caused by the feedback between unsteady heat release and acoustic pressure perturbations, are characterised by large-amplitude pressure oscillations. These oscillations, if uncontrolled, pose a threat to the integrity of combustion systems. One strategy to mitigate them is by installing cavity-backed perforated plates with bias flow into the combustion chamber. In this study, we consider a generic combustor configuration: a one-dimentional tube (with open and/or closed ends) containing a compact heat source and a heat exchanger tube row. The idea is to use the heat exchanger tube row as a device (analogously to a cavity-backed perforated plate) to manipulate the downstream end condition. We simulate the row of heat exchanger tubes by a slit-plate with bias flow. We derive the characteristic equation for the complex eigenfrequencies of this set-up. From the growth rates (imaginary parts of the eigenfrequencies), we construct stability maps for various system parameter combinations. The results, obtained for the first two modes of the system, show that by varying the cavity length or the bias flow velocity through the slits, we can stabilise a previously unstable combustion system.

Optimal and off-design operations of acoustic dampers using perforated plates backed by a cavity

The frequency of thermo-acoustic instabilities may vary during operation of combustors, a feature that must be included in the design of robust acoustic dampers tuned to damp specific unstable modes. This problem is tackled here by using perforated plates traversed by a bias flow and backed by a resonant cavity in the absence of grazing flow. A methodology is proposed to find the optimal dimensionless products maximizing absorption in two limit regimes. In these two asymptotic regimes, the optimal bias flow velocity is only controlled by the plate porosity while the size of the back cavity fixes the peak absorption frequency. The present analysis also includes effects of the plate thickness. A Helmholtz resonance and a narrow absorption peak in the frequency space characterize the first absorption regime reached at high Strouhal numbers. Conversely, the second absorption regime reached at low Strouhal numbers operates with a quarter-wave resonance type. This regime requires larger cavity depths but offers a wider absorption bandwidth around the peak absorption frequency. In both cases, total absorption is achieved at the nominal conditions identified. The way the absorption coefficient is reduced when variations of the bias flow velocity around the optimal value are considered is then investigated. Theoretical predictions are validated by measurements in the two nominal regimes identified and at off-design operation. The expressions derived in this study can be used to improve the design of robust acoustic dampers.

A comparison of the damping properties of perforated plates backed by a cavity operating at low and high Strouhal numbers

Liners backed by a resonant cavity and traversed by a bias flow are widely used for acoustic damping in aeronautical engines. Their design relies on a relatively complex optimization procedure with a large number of parameters to examine. It is shown in this study how to reduce this number by maximizing absorption in two limit regimes where the choice of the optimal bias flow velocity and size of the back cavity can be decoupled. These developments apply for perforated plates of different porosity and thickness in the absence of grazing flow. In these regimes, the optimal bias flow velocity is only controlled by the plate porosity while the size of the back cavity fixes the peak absorption frequency. The first absorption regime reached at high Strouhal numbers is characterized by a Helmholtz resonance (He≪1) and a narrow frequency absorption bandwidth. The Mach number associated to the optimal bias flow velocity is then given by Mc=(2/π)σ, where σ is the plate porosity. This regime minimizes the size of the resonant back cavity, but the absorption bandwidth narrows also with the Strouhal number. The second absorption regime reached at low Strouhal numbers operates with a quarter-wave resonator (He≃π/2) and a bias flow velocity fixed by Mc=σ/2. This regime offers a wide absorption bandwidth around the peak absorption frequency well suited for low frequency dampers when the bias flow velocity may vary within the system. Theoretical expressions derived in this study are validated against experimental data in the two regimes identified. They may be used to ease the design of robust dampers to hinder self-sustained thermo-acoustic instabilities when the instability frequency varies.

Modeling the damping properties of perforated screens traversed by a bias flow and backed by a cavity at low Strouhal number

Acoustic absorption properties of perforated screens traversed by a bias flow and backed by a resonant cavity are examined at a new absorption regime. The reflection coefficient of these dampers can be canceled at specific frequencies for low Strouhal numbers St ⪡ 1 and Helmholtz numbers of order unity He ∼ 1 . This regime differs from the classical one where resonance is sought at low Helmholtz numbers He ⪡ 1 and large Strouhal numbers St ⪢ 1 . A theoretical analysis is carried out and analytical expressions are derived to determine conditions for optimal absorption in this regime. It is shown that the optimal bias flow velocity and back cavity length can be fixed separately. The former is determined by the plate porosity and the latter controls the peak absorption frequency. This operating regime at low Strouhal numbers enables to increase sound absorption at low frequencies over a larger frequency bandwidth around the peak absorption frequency than the one obtained with a damping system working at high Strouhal numbers. This is confirmed by experiments carried out on a set of dampers in the frequency range 100–1000 Hz. Predictions of the reflection coefficient, including effects of bias flow velocity and cavity depth, show good agreement with experimental data for small pressure perturbation levels. These elements can contribute to the development of robust dampers to control low frequency thermoacoustic instabilities in gas turbines and jet engines.

On the Rayleigh conductivity of a bias-flow aperture

Abstract An analysis is made of the attenuation of sound by vorticity production in a bias flow aperture. A modified form of the Cummings equation describing unsteady flow through a small aperture is used to extend the linear theory of the bias flow conductivity of a circular aperture in a thin wall of Howe (1979. On the theory of unsteady high Reynolds number flow through a circular aperture. Proceedings of the Royal Society of London A 366, 205–233) to a wall of arbitrary thickness and to examine the influence acoustic nonlinearity within the aperture. Numerical results are compared with existing analytic predictions of linear theory. It is shown that attenuations predicted by both linear and nonlinear theories agree over a wide range of incident acoustic pressures, approaching in amplitude that required to maintain the steady mean flow through the aperture. The dominant nonlinear effect is a small reduction (less than about 5%) in the mean bias flow velocity. Application of the Cummings equation in the linear regime leads to a new, simple formula for the bias flow conductivity for a screen of finite thickness.

Numerical and Experimental Study of Acoustic Damping Generated by Perforated Screens.

A model is presented to compute the acoustic impedance of perforated screens with bias flow. Different incompressible submodels are combined to simulate the bias flow regimes ranging from the nonlinear one (no bias flow) to the linear one (bias flow velocity larger than acoustic velocity). Experimental fits are employed to express the orifice end correction as a function of both acoustic and bias flow velocity. The validation of the model is performed for low bias flow Mach numbers and low orifice radius Helmholtz numbers by varying perforated screen geometry, bias flow velocity, and acoustic pressure amplitude.