Thermoacoustic Instabilities Research Articles

Fuel blend combustion for decarbonization

The utilization of fossil fuels is currently transforming to low-carbon or zero-carbon fuels, which is one of the solutions to global warming. Hydrogen and ammonia are regarded as promising zero-carbon fuels in power supply and transportation scenarios but the availability of hydrogen and their distinctly different chemical activity constrain their large-scale direct utilizations. Fuel blends with physical and chemical complementary are considered as the effective approaches in the utilization of hydrogen and ammonia because no significant modification to the existing end-user infrastructures is needed. This paper reports recent progress in the fundamental combustion behaviors of fuel blends, focusing on hydrogen-hydrocarbon blends and ammonia-hydrocarbon blends. Firstly, laminar flame behaviors, auto- and forced-ignition characteristics, and pollutant emissions of binary fuels containing hydrogen are reviewed, all of which are supplemented with a discussion on the governing hydrogen-enriched combustion chemistry. Subsequently, the hydrogen-enriched flame responses to the flow conditions are discussed, including the turbulent burning velocity and statistical structures, the flashback swirl flames, thermoacoustic instabilities, and the jet ignition characteristics; Furthermore, with the increasing concern over ammonia as a zero carbon fuel and its extremely weak reactivity, recent progress on combustion of fuel blends containing ammonia are also reviewed. The fundamental combustion chemistry studies including laminar burning velocity, the ignition delay times data collection, as well as the attempts for chemical kinetic modeling development for fuel blend with ammonia are presented. The literature reported ammonia containing blends of turbulent flame characteristics are presented. Finally, from an engineering point of view, examples using hydrogen blends in practical internal combustion engines and in gas turbines are introduced, including the topic of engine efficiency performance and pollutant emissions and different combustors for gas turbines. It is suggested that fuel blends with hydrogen or ammonia that potentially monitors the overall reactivity will be one realistic solution to de-carbonization, on the basis of current transportation and power generation systems.

Determination method of Markstein number based on wavenumber measurement of cellular flames at the onset of parametric instability of downward propagating flames

This work proposes a new method to estimate the Markstein number by investigating the thermoacoustic parametric instability of laminar premixed flames propagating downwards in an open-closed tube. Methane-air flames were propagated in a combustion tube to capture the flame evolution in transition to parametric instability. By synchronized high-speed imaging filming both lateral and longitudinal views of flame propagation, cellular flame wavenumbers are measured from the clear transition of flat flames to cellular flames visualized in the present approach. The Markstein number is indirectly determined from wavenumber measurements at the onset of parametric instability by employing a laminar flame model under acoustic excitation treating the Markstein number as a free parameter. Acoustic velocity fluctuation amplitudes obtained from pressure fluctuation measurements were determined to further evaluate the validity of wavenumber-derived Markstein numbers. Markstein numbers obtained in the present work are compared with Markstein numbers relative to fresh gases in the literature from indirect and computational methods.

Flame transfer function analysis of hydrogen diffusion swirl flames

This paper investigates the first Flame Transfer Functions (FTFs) of hydrogen diffusion swirl flames, which are crucial for predicting and mitigating thermoacoustic instabilities. Given the need to develop new combustion technologies for hydrogen, it is therefore essential to accurately measure and analyze these FTFs. Employing acoustic and optical methods, we obtained the FTFs over a wide frequency range from 50 to 1000 Hz. Using the acoustic method, the FTFs are deduced from the flame transfer matrices. The FTFs exhibit a low-pass filter behavior with gains decreasing significantly above 150 Hz. Strouhal number normalization effectively collapses the FTFs across various thermal powers, bulk mass flow rates and global equivalence ratios. This result suggests that a generic flame response to acoustic perturbations exists and that the FTF can be interpolated over a range of operating conditions. This study identifies two dominant combustion modes in these hydrogen diffusion swirl flames: a diffusion-mode thin reaction layer near the nozzle and a partially premixed thicker reaction layer downstream. Phase-averaged OH* and OH-PLIF imaging revealed non-uniform transversal oscillations of the reaction zone, offering key insights into the complex swirling flow and the convective wavelength of the coherent heat release rate oscillations along these turbulent hydrogen diffusion swirl flames.

Investigation of longitudinal self-excited combustion instability in a micromix hydrogen combustor

The increasing emphasis on low-carbon energy has heightened investigations into hydrogen combustion. This study focuses on the critical yet underexplored topic of thermoacoustic instabilities in micromix hydrogen combustors. We employ a newly designed micromix burner to explore the intricate relationships among acoustic modes, flame dynamics, and flow-vortex interactions. High-speed particle image velocimetry (PIV) and OH* chemiluminescence, supplemented by dynamic pressure measurements, are employed to capture dynamic behaviors and instability modes of the flame. Through thermoacoustic network analysis, we can identify two primary self-excited modes: a dominant low-frequency mode oscillating between 520 Hz and 565 Hz, and a secondary high-frequency mode surpassing 4400 Hz, originating from the hydrodynamic instability of the nozzle's jet flow. The low-frequency mode significantly influences the flame dynamics, generating a distinct longitudinal flame oscillation behavior. In particular, the inner premixed flame exhibits a periodic pattern of lifting and re-attachment phenomena. The outer diffusion flame, however, dynamically interacts with the outer shear layer (OSL) and the shed outer vortex rings (OVRs), which gives rise to notable deformations in the flame surface, manifesting as neck and swell structures propagating downstream with the OVRs. Furthermore, the dynamics of the OSL and OVRs are attributed to the fluctuations in the bulk flow velocity and local equivalence ratio at the nozzle exit, which are sustained by pressure oscillations induced by thermoacoustics. This presents important insights into the interplay between hydrodynamics and thermoacoustics in the formation of combustion instability in the micromix hydrogen combustor.

Mitigating thermoacoustic instabilities in premixed hydrogen flames using axial staging

In this paper we demonstrate how axial staging can be utilised to mitigate thermoacoustic instabilities in a combustion system by flame redistribution. This is achieved by moving flow to a second stage flame while keeping the combined thermal power and total flow fixed. The stability of the system was first characterised for premixed H2-CH4-air flames operated with hydrogen volume fraction in the range 80%–100%. As observed in recent work, increasing the hydrogen concentration led to the onset of strong self-excited instabilities. Increasing the flow velocity for a fixed hydrogen concentration was shown to have the same effect. Both of these are linked to a decrease in the convective time scale — causing the flame to become more convectively compact and responsive to higher frequencies. We then show that these instabilities could be reduced for all conditions, by distributing flow to the secondary flame. Two main driving mechanisms causing suppression were observed and analysed. Firstly, a reduction in the flow rate provided to the first stage flame, leading to a corresponding change in the flame structure. This leads to an increase in the convective time scale. This effect is quantified by a reduced gain at higher frequencies, and a change in the time delay of the flame transfer function. Secondly, introducing a second flame with a different convective time scale results in interference between the two flames. This acts to suppress or enhance the global fluctuations in heat release rate and hence, the amplitude of the pressure oscillations in the system.

Погодно-климатический аспект стратегии устойчивого развития экосистем горных территорий

Introduction. The results of an analysis of information about threats to the development of civilization from the consequences of global warming and the effectiveness of projects presented to society to prevent it are presented. Research methods and materials. The method of inductive-deductive content analysis of scientific publications on the problems of global warming and the effectiveness of known methods for adjusting the heat balance of the planet was used. Research results. The high sensitivity of the thermal balance of the earth’s shell to cloud albedo and the complex dependence of cloud albedo on combinations of different types of clouds and on the frequency of cyclone formation have been established. Discussion of research results. Projects presented by various initiative groups to prevent global warming are assessed as unpromising. Conclusions on the article. An alternative method for adjusting cloud albedo is presented based on the use of thermoacoustic instability of atmospheric moisture. The method uses not a material substrate, but a phase of acoustic vibrations to influence the atmosphere. As a result, the use of the method is not accompanied by an increase in the entropy of the terrestrial ecosystem. Suggestions for practical applications and directions for future research. The application of the acoustic method is carried out in the form of remote initiation in the atmosphere of direct and reverse thermoacoustic effects using narrowly directed acoustic radiation from a ground-based installation and is characterized by high scalability, constant readiness for use and the absence of supporting infrastructure.

Acoustic characteristics and performance analysis of a solid-state thermoacoustic oscillator

Thermoacoustic instability in solids paves the way for the development of solid-state thermoacoustic (SSTA) engines with superior reliability. Acoustic characteristics with respect to the performance of SSTA oscillators are investigated, where growth ratio is taken as a performance metric. Numerical analyses show that the acoustic characteristics not only determine the temperature gradient direction for strengthening the oscillation, but also affect the maximum growth ratio. A high growth ratio is obtained at a low angular frequency and an acoustic field around 1/8 wavelength from the strain antinode. To realize appropriate acoustic characteristics, the angular frequencies and acoustic fields under different boundary conditions are studied, based on which the method to adjust the acoustic characteristics is discussed. This work aims to reveal the relationship between the acoustic characteristics and the performance of SSTA oscillators, and to provide new insights on adjusting the acoustic characteristics for improving SSTA oscillators.

Longitudinal and azimuthal thermo-acoustic instabilities in an industrial gas turbine combustor operating at elevated pressure

This work numerically investigates longitudinal and azimuthal thermo-acoustic instabilities in the swirl-stabilised can-type industrial SGT-100 gas turbine combustor operated at elevated pressures of 3 and 6 bar. Previous experiments have shown that the combustor is susceptible to self-excited flame oscillations sustained by a thermo-acoustic feedback loop at specific operating conditions. In order to gain a better understanding of this feedback loop, a fully compressible large eddy simulation method is applied. The unknown sub-grid scale turbulence-chemistry interactions are modelled via a transported probability density function approach solved by the Eulerian stochastic fields method. First, the reaction zones and global flame topology at both operating pressures are analysed and compared to experimental images providing good qualitative agreement. Radial profiles of time-averaged and root-mean-square quantities furthermore demonstrate good quantitative agreement with the available measurement data. The applied simulation approach is capable of successfully reproducing self-excited thermo-acoustic instabilities in the longitudinal direction. The fundamental frequency of the predicted limit-cycle oscillation matches the experimentally measured frequency with high accuracy. Similar to the experimental observations, the fluctuation amplitudes of the pressure and global heat release rate increase significantly upon increasing the mean operating pressure from 3 to 6 bar. In addition to the dominant longitudinal mode, a high-frequency, low-amplitude azimuthal mode is also identified at both pressures. This azimuthal mode is periodically amplified and attenuated by the superposed longitudinal mode and induces small asymmetric (around the burner circumference) fluctuations of the local fuel and total mixture mass flow rates entering the flame region.

The Structure and Stability of Premixed CH4, H2, and NH3/H2 Flames in an Axially Staged Can Combustor

Abstract An experimental investigation of flame structure, stability, and emissions performance was conducted in a two-stage lab-scale generic combustor design operated with CH4, H2, and NH3/H2 fuel blends. The main flame zone features a premixed bluff body stabilized flame, with a secondary flame zone initiated downstream by injecting premixed air and fuel using two opposing radial jets. The total power and air flowrate are kept constant between the different fueling cases, while the air split between stages and equivalence ratios are varied to explore conditions relevant to gas turbine operation. Given the relative novelty of the configuration, special emphasis is given to analyzing the structure of the opposing jet flames in the secondary stage. In contrast to previous literature on reacting jets in cross flow, these interact significantly due to their proximity, leading to a merged flame zone at the impingement location in the center of the combustion chamber, and some flame propagation upstream of the jet location. As the jet-to-crossflow momentum ratio increases, the merged flame zone changes shape, reaching close to the walls for the methane cases but remaining very compact when operating with almost pure hydrogen. For the hydrogen flames, diverting more air to the second stage allows higher total thermal power conditions to be reached, while avoiding flashback, and eliminates thermoacoustic instabilities. For ammonia-hydrogen flames, air is diverted to the second stage, while a constant fuel flow is sent to the primary stage, resulting in some locally rich conditions in the primary flame. A local minima in terms of NOX occurs when the primary flame is operated at an equivalence ratio of 1.15. Analysis of the flame structure suggests that this state corresponds to almost complete combustion or pyrolysis of NH3 in the main flame, with the remaining hydrogen burned in an inverse diffusion flame in the secondary zone.

Large eddy simulation of effects of oxidizer inlet temperatures on the transition routes before and after thermoacoustic instability in a subcritical hydrogen peroxide/kerosene liquid rocket engine

This paper presents the first numerical evidence of the intermittency routes that exist before and after the occurrence of thermoacoustic instability in a subcritical single-element liquid rocket engine burning liquid kerosene and decomposed hydrogen peroxide with increasing oxidizer inlet temperatures (T). Three-dimensional compressible large eddy simulation algorithms, combined with Euler–Lagrangian frameworks, are employed to model the spray turbulent combustion process in a high-pressure rocket combustor where a one-equation eddy viscosity sub-grid turbulence model and a PaSR sub-grid combustion model are used based on OpenFOAM. After verifying the numerical framework and achieving grid independence, we focus on (i) dynamical transition routes before and after the thermoacoustic regime, (ii) frequency-locking phenomena between acoustic perturbations, vortex dynamics, and combustion heat release, and (iii) the underlying physical mechanisms associated with different dynamical states. The results show that as we increase the oxidizer inlet temperature (700 K ≤ T ≤ 900 K), the system dynamics undergo a transition from a state of combustion noise to a period-1 limit cycle via intermittency. Furthermore, by further increasing the oxidizer inlet temperature (950 K ≤ T ≤ 1450 K), a second bifurcation occurs, causing a transition from a limit cycle state back to a combustion noise state also via intermittency. These bifurcation phenomena are attributed to frequency-locking interactions among pressure fluctuations, combustion heat release, and vortex dynamics. Evidence from combustion flow subsystems including mixture fraction, burning modes, and flame-induced vorticity sources provides additional insights into the complex instability mechanism.

Boundary proportional control of thermoacoustic instability in a Rijke tube

Thermoacoustic instability has always been a critical concern of low pollution combustion chambers and combustion components of ground gas turbines. It is also a severe challenge for dynamic system design. In order to reveal the thermoacoustic instability, a typical Rijke tube based on partial differential equations (PDEs) cascaded with the Heckl heat release is studied. A boundary proportional feedback control to stabilize the thermoacoustic instability in the Rijke tube is proposed. First of all, one-dimensional gas dynamic equations coupled with the Heckl heat release are presented to describe the thermoacoustic unstable dynamic system in the Rijke tube. Then by using the small deviation linearization and characteristic coordinate transformation, the thermoacoustic coupling inside the domain is transferred into a group of 4 × 4 PDEs with the boundary coupling. Next, a boundary proportional feedback control, characterized by its practical implementation feasibility, is proposed to ensure the exponential stabilization of the thermoacoustic unstable system. A solvability condition is also provided to theoretically design the boundary proportional controller. Furthermore, the optimal control parameters are given by solving the nonlinear programming problem to achieve the fastest convergence rate of the system. Finally, the effectiveness of the boundary proportional feedback control is verified by simulations, and its robustness to the uncertain time delay and the nonlinearity of the heat release is also discussed.

Effect of CO2 Opposing Multiple Jets on Thermoacoustic Instability and NOx Emissions in a Lean-Premixed Model Combustor

Effect of CO2 Opposing Multiple Jets on Thermoacoustic Instability and NOx Emissions in a Lean-Premixed Model Combustor

Theoretical model of azimuthal combustion instability subject to non-trivial boundary conditions

The problem of evaluating the sensitivity of non-trivial boundary conditions to the onset of azimuthal combustion instability is a longstanding challenge in the development process of modern gas turbines. The difficulty lies in how to describe three-dimensional in- and outlet boundary conditions in an artificial computational domain. To date, the existing analytical models have still failed to quantitatively explain why the features of the azimuthal combustion instability of a combustor in laboratory environment are quite different from that in a real gas turbine, making the stability control devices developed in laboratory generally lose the effectiveness in practical applications. To overcome this limitation, we provide a novel theoretical framework to directly include the effect of non-trivial boundary conditions on the azimuthal combustion instability. A key step is to take the non-trivial boundary conditions as equivalent distributed sources so as to uniformly describe the physical characteristics of the inner surface in an annular enclosure along with different in- and outlet configurations. Meanwhile, a dispersion relation equation is established by the application of three-dimensional Green’s function approach and generalized impedance concept. Results show that the effects of the generalized modal reflection coefficients on azimuthal unstable modes are extremely prominent, and even prompt the transition from stable to unstable mode, thus reasonably explaining why the thermoacoustic instability phenomena in a real gas turbine are difficult to observe in an isolated combustion chamber. Overall, this work provides an effective tool for analysis of the azimuthal combustion instability including various complicated boundary conditions.

Numerical investigation of combustion instability in a liquid rocket engine: Interaction effect between hydrodynamics and acoustic mode

In this paper, we present the numerical evidence of multiple bifurcations in thermoacoustic instability as we decrease the equivalence ratio (ϕ) from fuel-rich (ϕ = 1.5) to fuel-lean (ϕ =0.59) within a single-element coaxial liquid rocket engine burning hydrogen peroxide and methane. An axisymmetric compressible Large Eddy Simulation solver in an open-source platform OpenFOAM combined with a global methane chemical kinetical mechanism was used to model the turbulent mixing and combustion process. After the validation of grid independence and simulation results, the synchronization phenomenon between hydrodynamic instability, acoustics and combustion is the main focus of this paper. The results here first revealed that in a direction of decreasing equivalence ratios, the first transition to limit cycle state from combustion noise state was observed via intermittency. A second bifurcation was also observed, leading to quasi-period thermoacoustic instability from the limit cycle state. Intrinsic vorticity modes and natural acoustic modes could be regarded as oscillators. The competition and cooperation between the two modes led to a phenomenon beyond limit cycle states. The vortex dynamics of thermoacoustic systems are dominated by the interaction of intrinsic vorticity modes and natural acoustic modes and exhibit an adjustment of vortex shedding frequencies, resulting in different stability regions. Herein, the flame index was performed in more detail to distinguish between the premixed flame and diffusion flame. Results indicated that the burning mode was an important driver in promoting instability whilst it also served as a medium for competition and cooperation between the natural acoustic modes and intrinsic vorticity modes.

Combustion dynamics analysis of a pressurized airblast swirl burner using proper orthogonal decomposition

Jet fuel-fired combustors in aero gas turbine engines have switched to lean burn to decrease nitric oxide emissions in recent years as a result of strict emission regulations. Lean operating conditions, however, exhibit a heightened sensitivity to thermoacoustic instabilities and such burners require careful consideration in design and operation. Similar to natural gas-fired combustors, they exhibit thermoacoustic instabilities, but the characteristics are more complex and less well-studied. This paper presents a numerical investigation of an airblast jet fuel swirl burner operating with preheated air at lean pressurized conditions. In order to understand the acoustic characteristics of the in-house designed burner (Magister UT burner), detached eddy simulations are performed at relevant aero engine conditions. Simulation results are then analyzed by means of our internally developed parallel modal analysis package, PARAMOUNT, to perform proper orthogonal decomposition (POD) on large datasets. The resulting modes are inspected to highlight flow features of interest and their associated acoustic frequencies at unforced conditions. Single frequency acoustic forcing is employed to study the acoustic response of the burner to perturbations at similar frequencies to its precessing vortex core. We show that parallel computation of POD modes is a viable tool to investigate the main flow features of swirl burners and is suitable for highlighting the important acoustic frequencies without the need to employ fully compressible computational fluid dynamics solvers. Additionally, the analysis method reveals the ways in which various flow structures correlate with each other and how external perturbations modify them.

Effects of Hydrogen Enrichment on Thermoacoustic and Helical Instabilities in Swirl Stabilised Partially Premixed Flames

The effects of hydrogen enrichment on flame and flow dynamics of a swirl-stabilised partially premixed methane-air flame are studied using large eddy simulation. The sub-grid reaction rate is modelled using unstrained premixed flamelets and a presumed joint probability density function approach. Two cases undergoing thermoacoustic oscillations at ambient conditions are studied. The addition of hydrogen modifies both thermoacoustic and fluid dynamical characteristics. The amplitude of the fundamental thermoacoustic mode increases with the addition of 20% hydrogen by volume. A second pressure mode associated with the chamber mode is also excited with the hydrogen addition. Intermittent single, double and triple helical instabilities are observed in the pure methane case, but are suppressed substantially with hydrogen addition. The results are analysed in detail to shed light on these observations. The feedback loop responsible for the thermoacoustic instability is driven by mixture fraction perturbations resulting from the unequal impedances of the fuel and air channels. It is shown that hydrogen addition increases the flame’s sensitivity to these perturbations, resulting in an increase in amplitude. This higher amplitude thermoacoustic oscillation, along with a higher local heat release rate in the presence of hydrogen, is shown to considerably modify the flow structures, leading to a suppression of the helical instabilities.

Effects of temperature ratio on combustion instability in a non-premixed hydrogen-rich ram combustor

The effects of the burnt-to-unburnt temperature ratio (Tb/Tu) (reciprocal density ratio) on thermoacoustic combustion instability were investigated in a hydrogen-rich ram combustor by controlling the inlet air temperature under cruising conditions. Steady and unsteady combustion dynamics were investigated with the simultaneous measurement of combustion pressure and near-infrared (NIR) emissions. Time-resolved NIR images were analyzed using dynamic mode decomposition (DMD) to extract modes of the combustion instability, which show two oscillation modes: longitudinal (500 Hz) and flame-vortex interaction modes (2000 Hz) with a Strouhal number of approximately 0.5. The thermoacoustic combustion instability was not excited at Tb/Tu = 3.3, but was excited at Tb/Tu= 2.6 and 2.9. The DMD modes show that the structure of the vortex mode is similar to that of the fourth longitudinal mode at Tb/Tu = 2.6 and 2.9, indicating that the coupling of the vortex and the fourth longitudinal modes excited the thermoacoustic combustion instability.

Compressible Large Eddy Simulation of Thermoacoustic Instabilities in the PRECCINSTA Combustor Using Flamelet Generated Manifolds With Dynamic Thickened Flame Model

Abstract The fully compressible, density-based CFD-solver TRACE has been extended for simulations of turbulent reacting flows in aero engine gas turbine combustors. The flamelet generated manifolds combustion model is utilized to account for detailed chemical kinetics and combined with the dynamically thickened flame model to resolve the flame front on the large eddy simulation (LES) mesh. The chemistry tabulation is coupled with the LES solver by inversion of the transported energy equation using tabulated mixture averaged NASA polynomial coefficients. LES of the PRECCINSTA test case, a lean, partially premixed swirl combustor are performed and the two distinctive regimes are correctly predicted: a stable regime with a “quite” stable flame and an unstable regime with an oscillating flame driven by self-excited thermoacoustic instabilities. Statistics collected from the simulations, mean, and root-mean-square values are in good agreement with the experimental reference data for both operating conditions. The dominant frequency of the unstable flame deviates from the measurement by about 100 Hz and requires further investigation. The results demonstrate the general suitability of the simulation framework for reacting flow simulations in gas turbine combustion systems and the prediction of self-excited thermoacoustic oscillations.

Numerical investigation of combustion instability in a single-element liquid rocket engine: Intermittency routes before and after thermoacoustic instability

This paper provides the first numerical proof of intermittency routes existing before and after thermoacoustic instability, as we increase the oxidizer inlet temperature under fuel-lean (ϕ=0.91) and fuel-rich (ϕ=1.25) conditions in coaxial liquid rocket engine utilizing methane and hydrogen peroxide as propellant. Axisymmetric compressible Large Eddy Simulation algorithms combined with global chemical reaction mechanisms are used to simulate the non-premixed turbulent combustion process in high-pressure flows, where the one-equation eddy sub-grid turbulence model and the PaSR sub-grid combustion model are employed based on OpenFOAM. After verification of the grid independence as well as the global chemical mechanism against experimental measurements and existing simulations, the multi-bifurcation process of the system dynamics and the corresponding lock-in phenomenon are the main focus of this paper. The results suggest that with an increase in oxidizer inlet temperatures, the system dynamics at ϕ=0.91 conditions experience an initial shift from states of combustion noise to states of thermoacoustic instability through intermittent oscillation. A further rise in oxidizer inlet temperature leads to a second bifurcation from thermoacoustic instability states back to combustion noise states via intermittency, which is the first observation in the liquid rocket engine. Such an intermittency route before and after thermoacoustic instability is preserved at ϕ=1.25 conditions. Furthermore, a decrease in the equivalence ratio accelerates the initial bifurcation point for the onset of thermoacoustic instability. Flame index analysis is also employed to distinguish between diffusion and premixed flames, providing further insight into the underlying physical mechanism of the frequency-locking phenomenon between the pressure and combustion flow subsystems both in fuel-lean and fuel-rich conditions. Other details of the combustion flow fields also include the migration of the flame anchor point towards the injector with an increase in oxidizer inlet temperature.

Low-frequency still-air acoustic inertia of inclined circular aperture in an infinite flat plate of finite thickness

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.