Acoustic Perturbation Equations Research Articles

Numerical study of the pulsatile flow and aeroacoustics of straight and curved pipes

From an engineering point of view pulsatile pipe flows, which include the hydrodynamic and acoustic fluctuations, can cause many problems such as vibration, noise and structural fatigue etc. Knowledge of the characteristics of hydrodynamic fluctuations (pseudo sound) and acoustic waves inside pipes particularly those with bends make is crucial to pipeline vibration and noise reduction. Numerical simulation of the pulsatile pipe flows shows challenges especially in curved pipes with different flow modes compounded, and predicting the acoustic fluctuations is even tougher. In this work, the unsteady flows of a straight and curved pipe with a 90° elbow induced by a pulsatile pressure inlet were calculated by Detached Eddy Simulations (DES). The pipe acoustic fields are solved through an acoustic perturbation equation, which takes the time derivative of hydrodynamic pressure as the aeroacoustic source. The characteristics of the flow and sound fields are discussed detailly, and special attention is paid to the influence of the 90° elbow on the curved pipe flow. The results show that the amplitude of hydrodynamic pressure fluctuations decrease almost linearly along the straight pipe, and the 90° elbow has obvious local influence on the flow pressure and velocity especially in the downstream side. The acoustic field is of 1-D standing wave pattern because of the fundamental pulsation frequency lower than the pipe cutoff frequency, and the 90° elbow has only negligible effect on the acoustic field in the flow frequency range.

Simulation of the Thermoacoustic Response of an Aero-Engine Gas Turbine Fuel Injector Using a Hybrid CFD-CAA Method

Abstract Given the stringent emission regulations of aircraft engines, the trend in the aero industry is toward developing leaner combustion systems, which are prone to produce combustion instabilities. Hybrid methods of simultaneous acoustics and fluid dynamics simulations offer an elegant solution for the numerical prediction of these instabilities, taking advantage of the appropriate discretization of relevant scales. The presented work employed a hybrid simulation framework to identify the thermoacoustic response of a practically relevant configuration. The fluid dynamics were described using a computational fluid dynamics solver employing the low Mach formulation of the Navier–Stokes equations, while the acoustics were simulated using a computational aeroacoustics solver employing the acoustic perturbation equations. The coupling was implemented to exchange information between both solvers during runtime. The considered real-life configuration was designed to investigate the thermoacoustic behavior of realistic gas turbine injectors. It is acoustically excited to characterize the given injector via the flame transfer function approach under controlled operating conditions. The computational fluid dynamics simulation results were postprocessed to obtain the acoustic behavior of the combustor. The reacting scattering matrix was constructed and then compared to the experimental reference, both obtained using the multimicrophone method. Finally, two different postprocessing approaches were used to calculate the flame transfer function and discuss the applied hybrid computation method. This work demonstrated that the hybrid method can capture general features of the flame response of a complex three-dimensional combustion system.

Acoustic resonances in an automotive HVAC outlet

In order to better understand the noise generation mechanism of air outlets in an HVAC (Heating Ventilation Air Conditioning) system of a car, investigations were performed in a generic geometry representing a typical air outlet of an automotive car. A hybrid aeroacoustic simulation based on a Large-Eddy Simulation of the incompressible flow coupled with a solver for the acoustic perturbation equations is backed up by an experiment to study the interaction between a throttle valve (used to control the flow rate) and fins (used to guide the flow). Several sound generation mechanisms are identified, of which the so-called Parker-β mode is the most prominent in the sensible frequency range. Both the experimental and simulation results indicate a whistling noise at certain gap lengths between the throttle valve and fins at the frequency of the Parker-β mode. Two different levels of resonance are identified of which one leads to feedback from the acoustic mode to the flow field and one works without feedback. We demonstrate that the latter is established by an efficient excitation of the Parker-β mode by the vortex shedding from the throttle valve if the vortex shedding frequency is close enough to the acoustic frequency.

Acoustic characteristics of supersonic planar impinging jets

The present work aims to study the tonal and broadband noise associated with a supersonic planar jet, of Mach number 1.28 and Reynolds number 50000, impinging on a flat plate. Five different cases are considered corresponding to different plate distances and angles of impingement. The near-field noise is analyzed using Large Eddy Simulation (LES). For this, we employ a low dispersive and dissipative Finite Volume solver using AUSM for inviscid fluxes and third-order Runge–Kutta method for temporal discretization. The far-field noise is calculated using a hybrid approach in which the acoustic sources and mean flow are provided by the fluid solver while the far-field acoustic pressure is calculated by an acoustic solver. It solves Acoustic Perturbation Equations using a spectral/hp element method with a Discontinuous Galerkin projection. The present work highlights many important acoustics studies of impinging jets. Firstly, the far-field sound with the effect of non-uniform base fields is obtained which is important as the far-field acoustic pressure in most of the literature is reported either without any base fields or by the application of uniform base fields. Secondly, a correlation between the different modes of oscillations of the impinging jet and the production of impinging tones is studied using Modal Decomposition techniques. This analysis also sheds some light on the number of concurrent cycles for the different nozzle-to-plate distances. Lastly, the relation between the phase lag term and the distance between the plate and the nozzle exit is highlighted using a vortex tracking method. These observations can serve to provide a better understanding of the sound generation process.

An Efficient Hybrid Computational Process for Interior Noise Prediction in Aeroacoustic Vehicle Development

Numerical methodologies for aeroacoustic analyses are increasingly crucial for car manufacturers to optimize the effectiveness of vehicle development. In the present work, a hybrid numerical tool based on the combination of a delayed detached-eddy simulation and a finite element model, which relies on the Lighthill's acoustic analogy and the acoustic perturbation equations, is presented. The computational aeroacoustics is performed by the software OpenFOAM and Actran, concerning respectively the CFD and the FEM. The aeroacoustic behavior of the SUV Lamborghini Urus at a cruising speed of 140 km/h has been investigated. The main aerodynamic noise phenomena occurring in the side mirror region in a frequency range up to 5 kHz are discussed. The numerical simulations have been verified against the measurements performed in the aeroacoustic wind tunnel of the University of Stuttgart, operated by FKFS. The predicted exterior noise propagation into the far field has been validated by comparing the sound pressure level with the experimental data measured by exterior microphones, which were located outside the turbulent region beside the wake of the side mirror. Furthermore, the noise transmission into the cabin through the side window has been modeled. Simulation results have been validated by means of interior microphones installed on the driver seat. Both the exterior and the interior noise predictions show very good correlations with experiments. Lastly, a comprehensive investigation of the most critical aeroacoustic sources has been carried out. The numerical tool has been proven to be in good accordance with the microphone array with respect to the distribution of the sound pressure level in the proximity of the side mirror. Besides, the main vortex structures involved in the generation mechanisms of wind noise have been investigated by a CFD analysis. The entire CAA process has been proven to be accurate and suitable for combined analysis between the generation mechanisms of wind noise and the resulting transfer into the interior cabin to the driver's ear as well.

Airfoil trailing-edge noise prediction based on CFD/CAA coupled boundary method

Flow-induced noise hybrid prediction method based on sound wave boundary condition is an effective numerical method to deal with a flow-induced noise problems of complex configuration. This method can not only finely simulate the sound source, but also analyze the noise propagation characteristics. In this paper, numerical methods such as space-time discrete scheme and boundary conditions involved in discrete solution of acoustic perturbation equations(APE) are developed, and strategies such as adding buffer layer are proposed to improve divergence caused by numerical discontinuity at the junction of sound source region and propagation region, so as to establish a high-precision flow-induced noise hybrid method. In order to study the rationality of flow-induced noise hybrid method, the numerical simulation of acoustic radiation at the trailing edge of NACA0012 airfoil in BANC experiment was carried out. Compared with the results of sound field solved by large eddy simulation method, the analysis shows that the high-precision flow-induced noise hybrid method based on sound wave boundary conditions can predict the spatial sound field distribution with high precision and directly reflect the interaction between sound waves. Compared with the results of large eddy simulation, the error of sound pressure level is less than 2 dB, and the noise directional distribution trend is consistent.

Application of wavy geometries for the reduction of trailing edge instability noise

Trailing edge instability noise can occur in a wide range of applications, including wind turbines and small aerial vehicles. It can be characterised by a high amplitude tonal or narrowband sound resulting from instability waves in the boundary layer scattering as they are convected over the trailing edge. In this study, a hybrid aero-acoustic model is used to demonstrate how wavy geometries can be used to successfully reduce trailing edge instability noise. The hybrid model uses incompressible large eddy simulations to compute acoustic source terms, which are then mapped onto a larger domain using radial basis functions. The acoustic perturbation equations are then solved on this larger domain to obtain the 3-dimensional acoustic field. The study uses a modified NACA0012 wing, where the surface contains spanwise waves of different wavelengths. The results show that there is an optimal wavelength that produces the greatest noise reduction for a given flow speed and Reynolds number, and that this relates to wavelengths of the dominant structures within the boundary layer. This shows that by understanding the spectral character of the boundary layer, one can design optimal geometries for reducing this important source of fluid-induced noise.

A direct-hybrid CFD/CAA method based on lattice Boltzmann and acoustic perturbation equations

The accuracy of two direct coupled two-step CFD/CAA methods is discussed. For the flow field either a finite-volume (FV) method for the solution of the Navier–Stokes equations or a lattice Boltzmann (LB) method is coupled to a discontinuous Galerkin (DG) method for the solution of the acoustic perturbation equations. The coupling takes advantage of a joint Cartesian mesh allowing for the exchange of the acoustic sources without MPI communication. An immersed boundary treatment of the acoustic scattering from solid bodies by a novel solid wall formulation is implemented and validated in the DG method. Results for the case of a spinning vortex pair and the low Reynolds number unsteady flow around a circular cylinder show that a solution with comparable accuracy is obtained for the two direct-hybrid methods when using identical mesh resolution.

Numerical investigation of wall effects on combustion noise from a lean-premixed hydrogen/air low-swirl flame

A hybrid computational fluid dynamics (CFD)/computational aero-acoustics (CAA) approach, in which large-eddy simulation (LES) and APE-RF (solution of the acoustic perturbation equations for reacting flows) are employed for the CFD and CAA, respectively, calling it the hybrid LES/APE-RF approach, is used to analyze the influence of a wall on the combustion noise from a lean-premixed gaseous hydrogen/air low-swirl turbulent jet flame. The wall boundary conditions pertaining to the APE-RF system are formulated to account for acoustic reflection from the wall. The results show that the sound pressure level (SPL) spectrum obtained from the LES/APE-RF is in good agreement with that measured in the experiment. In the LES/APE-RF, the SPL spectrum of combustion noise with the wall plate explicitly changes compared to that without the wall plate. Specifically, the presence of the wall plate tends to ease the peaks that appeared in the case without the wall plate and create a nearly constant SPL within a specific frequency band. The analysis of the heat release rate fluctuation reveals that these phenomena are caused by the absence of a single periodic oscillation of heat release rate. The presence of the wall plate creates an asymmetric flow around the flame and distorts the flame structure, thereby altering the flame fluctuation phenomena.

A Hybrid, Runtime Coupled Incompressible CFD-CAA Method for Analysis of Thermoacoustic Instabilities

Abstract Thermoacoustic instabilities in gas turbine engines are of increasing interest for design of future low-emission technology combustors. Numerical methods used to predict thermoacoustic instabilities often employ either fully compressible resource-intense computational fluid dynamics (CFD) simulations, or two-step approaches where source terms extracted from CFD simulations are supplied to subsequent computational aeroacoustics (CAA) simulations. This work demonstrates an analysis of self-excited thermoacoustic instabilities using a hybrid method based on runtime coupling of incompressible CFD and CAA simulations. A prior implementation for the computation of combustion noise through one-way coupling of CFD and CAA solvers has been extended to a two-way coupling that allows acoustics to influence the flow field. The resulting hybrid method couples acoustic and convective physical phenomena by using mean flow field quantities and the thermoacoustic energy source term obtained from the solution of the Navier–Stokes equations in the low Mach number limit as an input for the acoustic perturbation equations (APEs). The fluctuating acoustic quantities pressure and velocity obtained from the solution of the APE are in turn included in the solution of the low Mach number Navier–Stokes equations, influencing the convective dynamics of the flow field. The suitability of the present implementation to capture thermoacoustic feedback is demonstrated through analysis of the well-known self-excited instability observed in a Rijke tube. The results are presented and discussed in comparison with a fully compressible reference solution.

Investigation of combustion noise generated by an open lean-premixed H[formula omitted]/air low-swirl flame using the hybrid LES/APE-RF framework

An open lean-premixed hydrogen/air low-swirl (LPHALS) turbulent flame exhibiting a pronounced peak in its combustion noise spectra, is investigated numerically using a hybrid Computational Fluid Dynamics/Computational Aero-Acoustics (CFD/CAA) framework. Under this framework, the reacting flow-field of the flame is computed via Large-Eddy Simulation (LES), while the direct combustion noise it produces is captured by solving the Acoustic Perturbation Equations for Reacting Flows (APE-RF). Flame configuration and simulation conditions correspond to those of an experimental study on an open lean-premixed H2/air flame stabilized using a Low-Swirl Burner (LSB). LES results are validated against experimental data. The CAA simulation is able to predict a pronounced sharp peak in the computed combustion noise spectra, similar to one of the two characteristic peaks observed in the measured combustion noise spectra. Frequency of this spectral peak predicted by the CAA simulation is 840 Hz, which is close to that of the higher frequency secondary spectral peak at 940 Hz measured in the experiment. Upon examining the hybrid LES/APE-RF results, the noise generation mechanism at 840 Hz is found to be the intense local heat release rate fluctuations, caused by strong interaction between the flame and the periodically generated vortical flow structures in the shear layers, downstream of the LSB exit. Additionally, analysis of the spectral content and directivity of the noise generated by different acoustic source terms is performed, in order to investigate their impact on the radiated acoustic field, and hence the characteristics of direct combustion noise produced by the open LPHALS flame.

Extension of the concept of Ffowcs-Williams and Hawkings type wave extrapolation to non-trivial flow effects and exterior surfaces

In appreciation of Ffowcs-Williams and Hawkings’ seminal contribution on describing the sound radiation from moving objects, this article discusses a concept of taking into account local non-trivial flow effects on the sound propagation. The approach is motivated by the fact that the numerical simulation of the sound propagation from complete full scale aircraft by means of volume-discretizing (CAA = Computational AeroAcoustics) methods is prohibitively expensive. In fact, a homogeneous use of such CAA approach would waste computational resources since for low speed conditions the sound propagation around the aircraft is subject to very mild flow effects almost everywhere and may be treated by more inexpensive methods. The part of the domain, where the sound propagation is subject to strong flow effects and thus requiring the use of CAA is quite restricted. These circumstances may be exploited given a consistent coupling of methods. The proposed concept is based on the strong (alternatively weak) coupling of a volume discretizing solver for the Acoustic Perturbation Equations (APE) and a modified Ffowcs-Williams and Hawkings (FW-H) type acoustic integral. The approach is established in the frequency domain and requires two basic ingredients, namely a) a volume discretizing solver for the APE, or for Möhring-Howe’s aeroacoustic analogy, to take into account strong non trivial flow effects like refraction at shear flows wherever necessary, and b) an aeroacoustic integral equation for the propagation part in areas where non-potential mean flow effects are negligible. The coupling of this aeroacoustic integral and the APE solver may be realized in a strong (i.e. two-ways) form in which both components feed back information into one another, or in a weak form (i.e. one-way), in which the sound field output data from the APE solver serves as given input for the integral equation. If an aircraft geometry has minor influence on the sound radiation to arbitrary observer positions, the aeroacoustic integrals may simply be evaluated explicitly. If on the other hand, the presence of the geometry has an important influence on the sound radiation, then the acoustic integral equation is implicit and requires some sort of numerical solution, in this case a Fast Multipole Boundary Element solver. While conceptually the weak coupling follows the spirit of the FW-H approach to describe sound propagation from aeroacoustic sources the underlying aeroacoustic integral is not based on Lighthill’s analogy, but the aeroacoustic analogy of Möhring-Howe. This is a consequence of the fact that in the two way-coupling the acoustic particle velocity in a moving medium needs to be determined, which is non-trivial based on an acoustic integral. As an important feature of the strong coupling the acoustic integral also provides practically perfect non-reflection boundary conditions even when the desireably small CAA domain does not extend into the far field. The validity of the presented computation approach is demonstrated in two example use cases.

Analysis and Optimization of Aerodynamic Noise in Vehicle Based on Acoustic Perturbation Equations and Statistical Energy Analysis

Analysis and Optimization of Aerodynamic Noise in Vehicle Based on Acoustic Perturbation Equations and Statistical Energy Analysis

Aerodynamic noise control of rearview mirror by steady and unsteady jets

Aerodynamic noise control of rearview mirror by steady and unsteady jets was investigated by combining numerical simulation and wind tunnel test. The maximum reduction of total turbulent pressure level for isolated rearview mirror is 1.2 dB when the jet ratio is 0.23. Whether it is an isolated or vehicle rearview mirror, numerical simulations without jet have obtained consistent results with experiments. Eight unsteady jets are quickly evaluated by subdomain method, where the turbulent pressure and sound pressure of the front side window were obtained by large eddy simulation and acoustic perturbation equations. The jet velocity ratio of 0.23, the best noise reduction effect, in the experiment was adopted, and the jet frequency of 78 Hz and phase were obtained by spectral proper orthogonal decomposition and phase analysis. The simulation results show that three jets have better noise reduction effect and the best jet2 can reduce the total sound pressure level by 0.7 dB. Sound pressure level at the frequencies from 200 Hz to 2000 Hz becomes small, and the maximum magnitude is about 1.5 dB.

On the convective wave equation for the investigation of combustor stability using FEM-methods

Solving the Helmholtz equation with spatially resolved finite element method (FEM) approaches is a well-established and cost-efficient methodology to numerically predict thermoacoustic instabilities. With the implied zero Mach number assumption all interaction mechanisms between acoustics and the mean flow velocity including the advection of acoustic waves are neglected. Incorporating these mechanisms requires higher-order approaches that come at massively increased computational cost. A tradeoff might be the convective wave equation in frequency domain, which covers the advection of waves and comes at equivalent cost as the Helmholtz equation. However, with this equation only being valid for uniform mean flow velocities it is normally not applicable to combustion processes. The present paper strives for analyzing the introduced errors when applying the convective wave equation to thermoacoustic stability analyses. Therefore, an acoustically consistent, inhomogeneous convective wave equation is derived first. Similar to Lighthill’s analogy, terms describing the interaction between acoustics and non-uniform mean flows are considered as sources. For the use with FEM approaches, a complete framework of the equation in weak formulation is provided. This includes suitable impedance boundary conditions and a transfer matrix coupling procedure. In a modal stability analysis of an industrial gas turbine combustion chamber, the homogeneous wave equation in frequency domain is subsequently compared to the Helmholtz equation and the consistent Acoustic Perturbation Equations (APE). The impact of selected source terms on the solution is investigated. Finally, a methodology using the convective wave equation in frequency domain with vanishing source terms in arbitrary mean flow fields is presented.

A hybrid computational aeroacoustic model with application to turbulent flows over foil and bluff bodies

In this study, a versatile and general three-dimensional hybrid aeroacoustic model is presented for low Mach number turbulent flows. A dual-domain approach is adopted, with the fluid and acoustic fields being solved simultaneously on separate, partially overlapping grids. By solving both parts at the same time, the need to store large data sets is removed, which improves the efficiency and usability of the model. Incompressible large eddy simulations are used to resolve the flow field and compute the source terms, which are interpolated onto the acoustic domain using radial basis functions. The acoustic perturbation equations are then solved using a finite-volume Riemann-based solver. The model is validated using a series of cases involving transitional and turbulent flows over foil and bluff bodies. Trailing edge instability noise and rod-foil interaction noise are modelled, with the results being compared to a range of experimental sources. Excellent agreement is seen, demonstrating the robustness and accuracy of the method. The trailing edge studies also provide additional insights into the origin of secondary tones in the acoustic spectra.

Zonal direct-hybrid aeroacoustic simulation of trailing edge noise using a high-order discontinuous Galerkin spectral element method

We present the extension of a discontinuous Galerkin framework to zonal direct-hybrid aeroacoustic simulations. This extension provides the ability to simultaneously perform a zonal large eddy simulation (LES), solving the compressible Navier–Stokes equations, and an acoustic propagation simulation, solving the acoustic perturbation equations. In doing so, the acoustic sources are exchanged without using the file system, and the bottleneck of I/O operations is avoided. This approach is well suited for large-scale simulations done in high-performance computing. The zonal LES uses the recently introduced recycling rescaling anisotropic linear forcing as a turbulent inflow method. We present a methodology to model the required Reynolds stresses based on the distribution of the turbulent kinetic energy obtained from solving the Reynolds-averaged Navier–Stokes equations. We show at the example of a turbulent flow over a flat plate and a NACA 64418 trailing edge simulation that the chosen model of the Reynolds stresses is valid. Direct-hybrid simulation results of a NACA 0012 airfoil, including tonal self-noise and a NACA 64418 trailing edge, demonstrate the presented approach’s applicability. This zonal direct-hybrid simulation approach shows great potential for efficient hybrid computational aeroacoustic simulations in high-performance computing.

Analysis of the sound sources of lean premixed methane–air flames

AbstractTwo investigations on the sound generation mechanisms of lean methane–air flames are reviewed and linked. A two‐step approach is used for the analysis. First, the compressible conservation equations are solved in a large‐eddy simulation formulation to compute the acoustic source terms of the reacting fluid. Second, the acoustic source terms are used in computational aeroacoustics simulations to determine the acoustic field by solving the acoustic perturbation equations. To identify the contributions of the different source terms to the overall sound emission of the flames different source term formulations are considered in the computational aeroacoustics simulations. The results of various flames of increasing complexity are shown: harmonically excited laminar flames, a turbulent jet flame, and an unconfined and a confined swirl flame. The results show that in general the heat release source alone does not determine the acoustic emission of the flame. Only the acoustic emission of the unconfined swirl flame could be computed by the heat release source. To accurately predict the phase and the amplitude of the sound emission of the other flames the acceleration of density gradients occurring at the flame front must be included in the considered set of source terms.

Comparison of hydrodynamic and acoustic pressure on automotive front side window

The unsteady flow in the front side window region of the vehicle can generate hydrodynamic and acoustic pressure on the front side window, which can influence the interior sound field. The hydrodynamic pressure on the front side window was achieved by the incompressible wall-modeled large-scale eddy simulation (WMLES) or improved delayed detached eddy simulation (IDDES), and the hybrid computational aeroacoustics (CAA) method based on acoustic perturbation equations (APE) was employed to achieve the acoustic pressure on the front side window. The numerical results of both hydrodynamic and acoustic pressure ware validated by the wind tunnel experiment, especially the corrected force analysis technique (CFAT) is employed to validate the acoustic pressure. The comparison of hydrodynamic and acoustic pressure on the front side window was performed by the Dynamic Mode Decomposition (DMD). Results show that the hydrodynamic pressure regionally distributes on the front side window and most energy concentrates on area interacted with the side mirror wake, while the acoustic pressure distributes uniformly on the front side window acting as a diffusion field and the energy disperses in frequency region.

Study on flow field and aerodynamic noise of electric vehicle rearview mirror

With the development of new energy and intelligent vehicles, aerodynamic noise problem of pure electric vehicles at high speed has become increasingly prominent. The characteristics of the flow field and aerodynamic noise of the rearview mirror region were investigated by large eddy simulation, acoustic perturbation equations and reduction order analysis. By comparing the pressure coefficients of the coarse, medium and dense grids with wind tunnel test results, the pressure distribution, and numerical accuracy of the medium grid on the body are clarified. It is shown from the flow field proper orthogonal decomposition of the mid-section that the sum of the energy of the first three modes accounts for more than 16%. Based on spectral proper orthogonal decomposition, the peak frequencies of the first-order mode are 19 and 97 Hz. As for the turbulent pressure of side window, the first mode accounts for approximately 11.3% of the total energy, and its peak appears at 39 and 117 Hz. While the first mode of sound pressure accounts for about 41.7%, and the energy peaks occur at 410 and 546 Hz. Compared with traditional vehicle, less total turbulent pressure level and total sound pressure level are found at current electric vehicle because of the limited interaction between the rearview mirror and A-pillar.