Linearized Navier-Stokes Equations Research Articles

Boundary-layer instability on a highly swept fin on a cone at Mach 6

The growth and characteristics of linear, oblique instabilities on a highly swept fin on a straight cone in Mach 6 flow are examined. Large streamwise pressure gradients cause doubly inflected cross-flow profiles and reversed flow near the wall, which necessitates using the harmonic linearized Navier–Stokes equations. The cross-flow instability is responsible for the most-amplified disturbances, however, not all disturbances show typical cross-flow characteristics. Distinct differences in perturbation structure are shown between small ( $\sim$ 3–5 mm) and large ( $\sim$ 10 mm) wavelength disturbances at the unit Reynolds number $Re' = 11 \times 10^6$ m $^{-1}$ . As a result, amplification measurements based solely on wall quantities bias a most-amplified disturbance assessment towards larger wavelengths and lower frequencies than would otherwise be determined by an off-wall total-energy approach. A spatial-amplification energy-budget analysis demonstrates (i) that wall-normal Reynolds-flux terms dictate the local growth rate, despite other terms having a locally larger magnitude and (ii) that the Reynolds-stress terms are responsible for large-wavelength disturbances propagating closer to the wall compared with small-wavelength disturbances. Additionally, the effect of free-stream unit Reynolds number and small yaw angles on the perturbation amplification and energy budget is considered. At a higher Reynolds number ( $Re' = 22 \times 10^6$ m $^{-1}$ ), the most-amplified wavelength shrinks. Perturbations do not behave self-similarly in the thinner boundary layer, and the shift in most-amplified wavelength is due to decreased dissipation relative to the lower-Reynolds-number case. Small yaw angles produce a streamwise shift in the boundary layer and disturbance amplification. The yaw results quantify a potential uncertainty source in experiments and flight.

Flow–acoustic resonance mechanism in tandem deep cavities coupled with acoustic eigenmodes in turbulent shear layers

This study presents the interplay of flow and acoustics within tandem deep cavities, focusing on the resonance mechanism occurring between turbulent shear layers and acoustic eigenmodes. The arrangement inside the tandem deep cavities includes both close and remote configurations. A combined fully coupled and decoupled aeroacoustic simulation strategy was devised. Employing an advanced high-order spectral/hp element method in conjunction with implicit large eddy simulation, the nonlinear compressible Navier–Stokes equations were solved to acquire internal flow–acoustic resonant field. In parallel, the linearized Navier–Stokes equations were tackled to determine coherent shear layer perturbations with external acoustic forcing. Based on acoustic measurements, the mainstream Reynolds number approaches approximately $R{e_{in}} = {O}({10^5})$ , where we identified the presence of frequency lock-in and a resonance range. Aeroacoustic noise sources were examined by implementing spectral proper orthogonal decomposition to decompose the pressure fields into hydrodynamic and acoustic components. As feedback intensified, the flow characteristics by the acoustic forcing effect and the flow-interactive effect were categorized according to the development of concurrent turbulent shear layers. Subsequently, the alternating and synchronous behaviours of concurrent shear layers resonated with the out-of-phase and in-phase acoustic eigenmodes were identified, and the corresponding large-scale counter-rotating vortex pairs and co-rotating vortex structures at the cavity entrances were extracted. The acoustic power generated by the Coriolis force was calculated using Howe's vortex-sound analogy, and the aeroacoustic energy transfer mechanism between large-scale shear layer vortices with acoustic eigenmodes was further explored. Finally, a linear response of coherent perturbations of the concurrent shear layers by external acoustic forcing was established. The amplification of flow in the streamwise direction toward the main duct led to the formation of coherent vortex structures, accompanied by separation bubbles into the main duct.

Numerical investigation on acoustic damping characteristics of dual Helmholtz resonators in presence of a grazing flow

In this study, the acoustic damping performances of the dual Helmholtz resonators were numerically evaluated using a 3D model. The grazing flow passes tangentially through the resonator neck, with a Mach number range of 0 ≤ Ma ≤ 0.1. The numerical model operates by solving the linearized Navier–Stokes equations. The current model is validated through a comparison with experimental data. The model is then utilized to explore the effects of the dual Helmholtz resonators on acoustic transmission loss performance in the presence of a grazing flow. Three key parameters are examined: 1) different implementation configurations of the dual Helmholtz resonators (including Models (b), (c), and (d)), 2) the mean temperature of the grazing flow, and 3) the axial distance between the dual Helmholtz resonators. For comparison, the acoustic damping performance of these dual Helmholtz resonators is compared to the single Helmholtz resonator case (Model (a)). The maximum transmission loss of Model (c) is significantly higher, recording values of 91%, 89.4%, and 92.5% than those observed for Model (a) at Ma = 0, Ma = 0.05, and Ma = 0.1, respectively. It is observed that the dual Helmholtz resonators dramatically increase the transmission loss. Model (c) is demonstrated to be associated with the most significant damping on the acoustic plane waves in comparison with that of Model (a). Additionally, the maximum transmission loss of Model (c) is 23.23 dB, 30.32 dB, and 34.58 dB at mean temperatures of 300 K, 600 K, and 900 K, respectively. Therefore, increasing the mean temperature is shown to be beneficial to enhance transmission losses in the presence of the grazing flow. Furthermore, under Ma = 0.1, the resonant frequency of Model (c) is 127 Hz, 152 Hz, and 172 Hz, corresponding to mean temperatures of 300 K, 600 K, and 900 K. It can be concluded that increasing the temperature has the effect of broadening the resonant frequency, especially at a high grazing flow Mach number. However, increasing the mean temperature results in a reduction of transmission loss in the absence of the grazing flow. In the case of Model (c), a 32 cm axial distance results in a 5.6% larger transmission loss at Ma = 0 and a 26.4% larger loss at Ma = 0.1 compared to a 16 cm axial distance. This indicates that increasing the axial distance between the dual Helmholtz resonators improves transmission loss.

Synchrotron X-ray phase-contrast imaging of ultrasonic drop atomization

Ultrasonic atomization is employed to generate size-controllable droplets for a variety of applications. Here, we minimize the number of parameters dictating the process by studying the atomization of a single drop pending from an ultrasonic horn. Spatiotemporally resolved X-ray phase-contrast imaging measurements show that the number-median sizes of the ejected droplets can be predicted by the linear Navier–Stokes equations, signifying that the size distribution is controlled by the fluid properties and the driving frequency. Experiments with larger pendant water drops indicate that the fluid–structure interaction plays a pivotal role in determining the ejection onset of the pendant drop. The atomization of viscoelastic drops is dictated by extended ligament formation, entrainment of air, and ejection of drop-encapsulated bubbles. Existing scaling laws are used to explain the required higher input amplitudes for the complete atomization of viscoelastic drops as compared to inviscid drops. Finally, we elucidate the differences between capillary wave-based and cavitation-based atomization and show that inducing cavitation and strong bubble oscillations quickens the onset of daughter drop ejection but impedes their size control.

The harmonic linearized Navier–Stokes equations for transition prediction in three-dimensional flows

The conventional method to predict the onset of laminar-turbulent transition in convectively unstable boundary-layer flows is based on the logarithmic amplification ratio, the N-factor, of the linear instability waves. To calculate the N-factor, the flow variables are decomposed into a laminar basic state solution and the linear disturbances, which are assumed to be harmonic in time. The most commonly used linear stability analysis approaches include the locally parallel linear stability theory (LST) and the nonlocal, weakly nonparallel parabolized stability equations (PSE). However, these methods do not account for strong streamwise gradients that are encountered in several configurations of interest, such as those in the vicinity of roughness elements, steps, gaps, or corners. To compute the linear evolution of disturbances along such strongly nonparallel regions, the harmonic linearized Navier–Stokes equations (HLNSE) need to be solved. The discretization of the HLNSE for spanwise/azimuthally inhomogeneous laminar basic states yields a linear system of complex arithmetic with a leading dimension of the order of 107 to 108 even in relatively simple flows. A combined multithread and multiprocessor algorithm is implemented for the direct solution of such linear systems. Results for a supersonic boundary layer over a three-dimensional roughness patch show good agreement with experimental measurements when the evolution of the instability waves over the roughness patch is included via the HLNSE. Additionally, inflow-resolvent analysis based on the HLNSE for discrete-roughness-induced disturbances in the nose tip of a blunt cone at Mach 6 demonstrates the importance of including the disturbance amplification along the near vicinity of the roughness element and separation region.

Resolvent-based motion-to-wake modelling of wind turbine wakes under dynamic rotor motion

We propose a linearized deterministic model for predicting coherent structures in the wake of a floating offshore wind turbine subject to platform motions. The model's motion-to-wake predictive capability is achieved through two building blocks: a motion-to-forcing (M2F) part and a forcing-to-wake (F2W) part. The M2F model provides a unified framework to parameterize the effects of arbitrary floating wind turbine motions as unsteady loads of a fixed actuator disk, requiring only the radial distribution of the aerodynamics force coefficient on the blade as input. The F2W model is derived based on a bi-global resolvent model obtained from the linearized Navier–Stokes equations, using the time-averaged wake of a fixed wind turbine as input. In addition to its capability of predicting sensitive frequency ranges, the model excels linear stability analysis by providing spatial modes of the wake response in a motion-specific and phase-resolved manner. The model successfully predicts the wake pulsing mode induced by surge, as well as the similarity and difference of the wake meandering modes caused by sway and yaw. Large-eddy simulations under different inflow turbulence intensities (TIs) and length scales are further conducted to analyse the wake meandering triggered by the simultaneous excitation of free-stream turbulence and sway motion. The results show distinct frequency signatures for the wake dynamics induced by ambient turbulence and sway motion. The inflow TI is found to have a stabilizing effect on the wake, reducing the motion-induced wake responses. Such a stabilizing effect is captured satisfactorily with the proposed model, provided that the effective viscosity is calibrated properly using the data from the fixed turbine wake under the corresponding turbulent inflow.

Enhanced dissipation and transition threshold for the Poiseuille-Couette flow

In this paper, we consider the hydrodynamic stability of the 2D Navier-Stokes equations on T×R around Poiseuille-Couette flow V=(y2,0)+a(y,0) with a∈(0,1). By means of the hypocoercivity method with time dependent weights and introducing a new estimate on the energy functional, we establish the enhanced dissipation estimates for the linearized Navier-Stokes equations. More precisely, for a⩽10−3ν14, we obtain a decay rate proportional to ν12, which is consistent with the Poiseuille flow. For a=10−3νs with s∈[0,14], the decay rate is proportional to ν1−2s. As an application of the linear estimates, we obtain the result of nonlinear stability transition threshold.

Acoustic attenuation prediction and analysis of perforated hybrid mufflers with non-uniform flow based on frequency domain linearized Navier-Stokes equations

The three-dimensional frequency-domain linearized Navier-Stokes equations (LNSEs) with consideration of eddy viscosity are developed to evaluate the acoustic attenuation performance of perforated hybrid mufflers in the presence of non-uniform flow. The computations are performed in two steps: time averaged flow variables are acquired by using steady-state computational fluid dynamics (CFD) method and then mapped into the acoustic mesh, and the acoustic perturbation variables are obtained by solving frequency-domain LNSEs, where the sound-absorbing material is treated as an equivalent fluid with complex sound speed and density. The predictions of transmission losses of the two-pass perforated hybrid mufflers in the presence of non-uniform flow are in good consistencies with the measurements, which verifies the correctness of LNSEs. The effect of Mach numbers on acoustic attenuation performance of the mufflers with different filling densities and perforated components is investigated in detail. The transmission loss of the mufflers with various filling densities are increased by complex airflow in the lower frequency range. For the mufflers where not all components have been perforated, the flow lowers low-frequency resonance peak. The influence of complex airflow on acoustic attenuation performance of all configurations is weakened at higher frequencies.

Receptivity of the rotating disk boundary layer to traveling disturbances

An adjoint approach is developed to undertake a receptivity study of the rotating disk boundary layer. The adjoint linearized Navier–Stokes equations are first derived in cylindrical coordinates. A receptivity formula is then formulated that specifies the response of stationary and traveling linear perturbations to an external force, including sources of momenta and mass and unsteady wall motion. Using the parallel flow approximation, in which the radial dependence of the undisturbed flow is ignored, receptivity characteristics are computed for a broad range of temporal frequencies, radial wavenumbers, azimuthal mode numbers, and Reynolds numbers. The type-I crossflow instability attains a maximum amplitude for external forces fixed near the wall-normal location of the critical layer (i.e., α¯rF+βG=ω), and the type-II Coriolis instability achieves larger amplitudes when external forces are located in the vicinity of a vanishing effective shear stress (i.e., α¯rF′+βG′=0). Sources of radial momenta fixed about these wall-normal locations establish larger-sized disturbances than equivalent-sized sources of azimuthal momenta, wall-normal momenta, and mass. At the disk surface, motion along the wall-normal direction induces a stronger receptivity response than wall motions acting along the radial and azimuthal directions. In general, the crossflow instability achieves larger-sized amplitudes than the Coriolis instability, with the peak response realized for Reynolds numbers near the critical conditions for linear instability.

Numerical prediction of the whistling potentiality of a turbulent channel flow with corrugated walls

This study explores the turbulent flow-induced whistling phenomena in a channel with corrugated wall surfaces, which is crucial for mitigating the acoustic fatigue problem in the aerospace field. By solving a compressible linearized Navier–Stokes equation in the frequency domain, the interference between the turbulent flow field along the corrugated wall and the incident acoustic field is studied, including the acoustic wave scattering phenomenon caused by turbulence and the fluid perturbation induced by acoustic waves. In conjunction with this, the acoustic two-ports method is utilized to investigate the transfer-function model and predict the whistling potentiality of the turbulent flow along corrugated walls. Experimental validations through the literature results confirm the numerical accuracy of this aeroacoustic simulation strategy. Subsequently, the investigation extends to different cavity configurations with different cavity profiles and numbers, and the two-port scattering matrix is applied to quantify the acoustic transmission and damping coefficients caused by the background flow field and turbulent eddy viscosity. The acoustic power conversion mechanism between the turbulent flow field and the incident acoustic field is established, allowing for quick prediction and effective analysis of the generation frequency range of the whistling phenomenon. Furthermore, the modulation effect of sound waves on the fluid is studied by analyzing the response of the incident sound wave frequency to the phase interference momentum and shear layer of different configurations of corrugated cavities. The results show that compared with the right-edge configuration, the rounded-edge configuration produces whistling at a lower frequency due to the turbulence effect, and the number of cavities adjusts the intensity, not the frequency, of the sound power generated. In addition, the oscillation of the shear layer caused by sound waves is related to the cavity configuration and the sound wave frequency.

Data assimilation finite element method for the linearized Navier-Stokes equations with higher order polynomial approximation

In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier–Stokes equation. We derive quantitative local error estimates for the velocity, which account for noise level and polynomial degree, using the stability of the continuous problem in the form of a conditional stability estimate. Numerical examples illustrate the performances of the method with respect to the polynomial order and perturbations in the data. We observe that the higher order polynomials may be efficient for ill-posed problems, but are also more sensitive for problems with poor stability due to the ill-conditioning of the system.

Acoustic Attenuation Prediction of Perforated Reactive and Dissipative Mufflers With Flow by Using Frequency-Domain Linearized Navier-Stokes Equations

To comprehensively consider the impact of complex airflow on sound propagation, a numerical approach by solving the three-dimensional (3-D) frequency-domain linearized Navier-Stokes equations (LNSEs) is proposed to accurately predict the transmission losses of perforated tube reactive and dissipative mufflers in the presence of complex airflow. The numerical computations are performed in two steps: (1) solve the time averaged flow by steady-state computational fluid dynamics (CFD) simulation and then map the results into acoustic mesh; (2) treat sound-absorbing material as an equivalent fluid and obtain acoustic perturbation variables by solving the frequency-domain LNSEs. The transmission losses of perforated tube reactive and dissipative mufflers are measured in the presence of flow and compared with the numerical predictions. The excellent consistencies between predictions and measurements validate the present approach. The influence of Mach number on acoustic attenuation performance of perforated tube reactive and dissipative mufflers is then investigated. With Mach number increases, the transmission loss of perforated tube reactive muffler increases somewhat, while the transmission loss of dissipative mufflers decreases obviously in the lower frequency range and change is limited at higher frequencies.

Transition control of the blasius boundary layer using linear robust control theory

AbstractThe paper considers control system design for linearized three-dimensional perturbations about a nominal laminar boundary layer over a flat plate (the Blasius profile). The objective is prevention of the laminar to turbulent transition using appropriate inputs, outputs, and feedback controllers. They are synthesized with a view to reducing transient energy growth, a known precursor to important transition scenarios. The linearized Navier–Stokes equations are reduced to the Orr–Sommerfeld and Squire equations with wall-normal velocity actuation entering through the boundary conditions on the wall. The sensor output is taken to be the wall-normal derivative of the wall-normal vorticity measured on the plate. Several multivariable output controllers are examined, including simple constant gain output feedback, loop transfer recovery, and $$H_{\infty }$$ H ∞ loop shaping. Reduced order compensators are developed using balanced truncation and analyzed for robustness using the gap metric between reduced order models and full order models. It is demonstrated that the level of minimum transient energy growth that can be achieved is similar for these diverse controller methodologies but falls short of that which can be achieved using optimal state feedback.

Aeroacoustic simulation of transient vortex dynamics inside double-degree-of-freedom orifice-cavity structure subjected to high-intensity acoustic waves

As a noise reduction device commonly used for aero-engines at present, the double-degree-of-freedom acoustic liner has the advantage of broadband noise elimination, which is related to the energy transformation during the process of vortex generation and shedding from its dual orifice-cavity unit when subjected to high-intensity acoustic waves. Based on the compressible linear Navier-Stokes equations with the influence of nonlinear thermo-viscous acoustics, this study simulated the three-dimensional acoustic-vortex coupling field of dual orifice-cavity structures with different orifices' distances under high-intensity acoustic waves with different frequencies. The first and second resonance frequencies of the structures were found by the transmission loss coefficient. Then, through the vortex dynamics analysis, the interference behavior of the vortex shedding with fusion and shifting was observed under the first resonance frequency when the orifices' distance was close. By establishing an energy transfer model, it was found that the energy transfer was concentrated at the upper orifice under the second resonance frequency, and the interference effect increased the vortex kinetic energy and viscous dissipation energy here under the first resonance frequency. The relevant research results provide a theoretical basis for the structural optimization of aerodynamic noise control devices of modern aircraft.

Global stability analysis of axisymmetric boundary layer on a rotating circular cylinder

In this manuscript, we comprehensively investigated the global stability of the incompressible axisymmetric boundary layer (ABL) developed on a rotating circular cylinder. A finite length of a rotating cylinder was considered in an axial stream of incompressible fluid. The rotation of a cylinder produces centrifugal force in the radial direction, which produces a pressure gradient (PG) in the radial direction. The axial flow (U∞) develops shear in the BL which has a stabilization effect on the BL. Thus, the Reynolds number (Re) and rotation rate (S) are two important control parameters of the BL and they are calculated based on a cylinder radius. The spectral collocation method has been used to discretize the linearized Navier–Stokes equations (LNS) and Arnold’s iterative algorithm for the numerical solution of the 2D eigenvalues problem. The computations were performed for Reynolds numbers Re=2600, 5200, and 20,800, rotation rates S=0.5, 1.0, and 2.0 for azimuthal wave-numbers N=0, 1, 2, and 3. Thus, the effects of S, Re, and N were studied on the stability of the rotating ABL. The temporal and spatial properties of the small disturbances were studied to understand the effect of shear and centrifugal force by varying S and Re. The increased rotation of a cylinder makes the BL unstable while increased axial flow stabilizes the ABL. The small disturbances are found globally unstable for N=1 at a small Re with an even small S.

Algebraic growth of 2D optimal perturbation of a plane Poiseuille flow in a Brinkman porous medium

The impact of various factors on the stability of a plane porous Poiseuille flow is investigated in detail. Both modal and non-modal linear stability analyses are used to study the effects of the porosity of the porous media and the ratio of effective viscosity to the fluid viscosity. The present analysis includes solving the linearized Navier-Stokes equation in the form of the Orr-Sommerfeld (O-S) type equation by applying the 2D perturbation to the basic mean flow. The Chebyshev collocation method is used to solve the Orr-Sommerfeld equation numerically. Through modal analysis, the accurate values of the critical triplets (αc,Rc,cc), the eigen-spectrum, the growth rate curves, and the marginal stability curves are studied. Then, by using non-modal analysis, the transient energy growth G(t) of two-dimensional optimal perturbations, the ε-pseudospectrum of the non-normal O-S operator (L), and the regions of stability, instability, and potential instability of the fluid flow system are investigated in detail. The collective results of both modal and non-modal analysis show that the porous parameter and the ratio of effective viscosity to the fluid viscosity have stabilizing effects on the fluid system due to the postponement of the onset of stability.

Dispersion of axisymmetric longitudinal waves propagating in an inhomogeneous prestressed hollow cylinder immersed in an inviscid compressible fluid

The paper investigates the dispersion of axisymmetric waves in a cylinder with inhomogeneous initial stresses caused by the hydrostatic pressure of the compressible inviscid fluid in which this cylinder is immersed. In the context of this study, the motion of the cylinder is described by the three-dimensional linearized equations for elastic waves in bodies with initial stresses, but the flow of the fluid is described by the linearized Navier-Stokes equations for compressible (barotropic) inviscid fluids. The initial stresses in the cylinder, due to the action of hydrostatic pressure on the outer surface of the cylinder, are determined according to the well-known Lame formulas of classical linear elasticity theory. The corresponding eigenvalue problem for the dispersion of axisymmetric waves propagating in the hydro-elastic system under consideration is solved using the discrete-analytic method. The dispersion equation is obtained and solved numerically. Concrete numerical investigations are carried out for three pairs of materials: Soft Rubber + Glycerin, Lucite + Water and Steel + Water. The dispersion curves obtained for these pairs of materials are presented and discussed for different values of the intensity of the external pressure. In particular, it is found that the inhomogeneous initial stresses in the cylinder cause zero group velocity (ZGV) points to appear on the dispersion curves of the lowest modes. However, the ZGV points (or modes) appear on the dispersion curves of the higher modes as a result of the contact of the hollow cylinder with the fluid.

Numerical study of the behavior of rectangular acoustic black holes for sound absorption in air

In this work, the behavior of acoustic black holes (ABHs) serving as an anechoic termination of air-filled waveguides with a rectangular cross-section is numerically studied. These ABHs consist of a set of rigid ribs separated by narrow slits, whose height smoothly varies along the structure and whose aim is to slow-down the impinging acoustic wave and cause its absorption. For the purpose of this study, a 2D mathematical model based on linearized Navier–Stokes equations and employing the finite element method has been proposed, which allows for an accurate capturing the thermoviscous losses in the acoustic boundary layer adjacent to the solid–fluid interfaces, as well as the effects connected with geometrical details of the ABHs’ inner structure. The numerical results show that in rectangular ABHs with a fine internal structure, the acoustic wave slow-down plays a significant role and that absorption properties are strongly dependent on their inner structure details. Simplified 1D mathematical models of rectangular ABHs based on the Riccati equation or transfer matrix method have also been proposed. These simplified models are computationally highly efficient, as it has been demonstrated, they provide accurate results, especially in the case of ABHs with a fine internal structure, which feature superior acoustic energy absorbing properties.

Stochastic Dynamical Modeling of Wind Farm Turbulence

Low-fidelity engineering wake models are often combined with linear superposition laws to predict wake velocities across wind farms under steady atmospheric conditions. While convenient for wind farm planning and long-term performance evaluation, such models are unable to capture the time-varying nature of the waked velocity field, as they are agnostic to the complex aerodynamic interactions among wind turbines and the effects of atmospheric boundary layer turbulence. To account for such effects while remaining amenable to conventional system-theoretic tools for flow estimation and control, we propose a new class of data-enhanced physics-based models for the dynamics of wind farm flow fluctuations. Our approach relies on the predictive capability of the stochastically forced linearized Navier–Stokes equations around static base flow profiles provided by conventional engineering wake models. We identify the stochastic forcing into the linearized dynamics via convex optimization to ensure statistical consistency with higher-fidelity models or experimental measurements while preserving model parsimony. We demonstrate the utility of our approach in completing the statistical signature of wake turbulence in accordance with large-eddy simulations of turbulent flow over a cascade of yawed wind turbines. Our numerical experiments provide insight into the significance of spatially distributed field measurements in recovering the statistical signature of wind farm turbulence and training stochastic linear models for short-term wind forecasting.

Acoustic attenuation analysis of expansion chamber mufflers with non-uniform cold and hot flow

In the presence of flow, the acoustic field and the flow field inside mufflers will interact with each other. In order to capture this phenomenon, the frequency-domain linearized Navier–Stokes equations (LNSEs) are employed to investigate the vortex-sound interaction inside expansion chamber mufflers. The calculations are performed in three steps: (1) to obtain the background mean flow variables by using the steady-state CFD simulation, (2) to map CFD results to acoustic meshes, and (3) to calculate the acoustic perturbation by using the finite element method based on LNSEs. Primarily, the transmission loss of single expansion chamber with inlet/outlet extensions is predicted in the presence of cold flow and the numerical predictions of LNSEs showed consistent agreements with measurements published in the literature. With the increase of inlet flow velocity, transmission loss in the low frequency range is obviously influenced by the vortex-sound interaction, which is attributed to the energy transfer between the fluidic and acoustic scales inside the muffler. Further, the acoustic attenuation performance of dual-chamber mufflers with flow is investigated numerically and experimentally, and the LNSEs predictions agree well with measurements. In the presence of cold flow, the transmission loss curves of the mufflers in the low frequency range is disturbed by the acoustic dissipation and amplification, while the effect of hot flow on the acoustic attenuation behavior of the mufflers is almost the same as that of cold flow, except that the non-coaxial mufflers with side-inlet is remarkably influenced by temperature. The studies demonstrated that the background mean velocity gradient is the most important impact factor for acoustic attenuation performance of the dual-chamber mufflers in low frequency range, whether in the presence of cold or hot flow.