Effect Of Mean Flow Research Articles

Bandgap characteristics of a duct embedded with multiple membrane-cavity resonators in the presence of mean flow

Bandgap characteristics of periodic structures can be investigated by the effective material properties via reflection and transmission coefficients. In this paper, for the first time, corresponding effective properties such as mass density, relative impendence and refractive index are presented for a duct embedded with membrane-cavity resonators in its sidewalls. Around the membrane or cavity resonant frequencies, the effective density varies drastically with the negative values, implying that its acceleration has opposite phase with the dynamic pressure load, within which almost a total sound pressure reflection can be obtained. Moreover, the presence of flow will cause a significant decrease in both the amplitude of relative impedance and refractive index, especially for the resonant peaks. Mean flow effect on bandgap characteristics of periodic resonant cells is conducted in the last part. Significant decrease and slight shift can be observed in the Bragg reflection and locally resonant bandgaps, and their dispersion curve (phase change per cell) cannot reach zero or ±π within these bandgaps. It implies that the presence of flow in duct is similar to the damping effect which leads to the dispersion branch that cannot cover the entire Brillouin zone.

An analytical correction to Amiet’s solution of airfoil leading-edge noise in non-uniform mean flows

Gust/turbulence–leading edge interaction is a significant source of airfoil broadband noise. An approach often used to predict the sound is based on Amiet’s flat-plate solution. Analytical studies have been conducted to investigate the influences of airfoil geometries, non-uniform mean flows and turbulence statistics, which, however, were often too convoluted. In this work, the problem is revisited by proposing simple corrections to the standard flat-plate solution to account for the effect of non-uniform mean flows of real airfoils. A key step in the method is to use a new space–time transformation that is analogous to the Prandtl–Glauert transformation to simplify the sound governing equation with spatially varying coefficients to a classical wave equation, which is then solved using the Schwarzschild technique as in Amiet’s solution. The impacts of Mach number, wavenumber and airfoil geometry on the prediction accuracy are investigated for both single-frequency and broadband cases, and the results are compared against high-fidelity simulations. It predicts the sound reduction by the airfoil thickness, and reveals that the reduction is caused by the non-uniform streamwise velocity. The limitations of the model are discussed and the approximation errors are estimated. In general, the prediction error increases with the airfoil thickness, the sound frequency and the flow Mach number. Nevertheless, in all cases studied in this work, the proposed correction can effectively improve the prediction accuracy of the flat-plate solution much more efficiently compared to numerical solutions of the Euler equations using computational aeroacoustics.

On the numerical eigenmode analysis of acoustically lined ducts with uniform mean flow

The present work concerns the numerical eigenmode analysis of acoustically lined ducts of any constant cross-sectional shape in the presence of mean flow. The duct is lined with bulk-reactive porous material, which is separated from the flow channel by a perforated panel. A combined wave and finite element (WFE) method is introduced to investigate the effects of uniform mean flow on the eigenmodes and eigenvalues of the lined ducts. The proposed method is validated against analytical solutions for a simple case. A convergence rate of Se4 for eigenvalues can be reached for Mach number up to 0.8, with Se being the mesh size. In this study, the eigenmodes of a lined duct are divided into air-borne modes and lining-borne modes. The air-borne modes propagate mostly in the air domain, while the lining-borne modes can propagate in both air domain and porous domain. The effect of Mach number on the axial wavenumbers and mode shapes are analysed. It is found that, for air-borne modes, Mach number will strongly affect their wavenumbers, while its effect on the mode shape is marginal. On the contrary, for the lining-borne modes, Mach number has small effect on the wavenumber, but its effect on the mode shape is significant. Specifically, even the mode properties can be changed from a lining-borne mode to an air-borne mode for some left-travelling lining-borne mode. The transmission loss (TL) of a lined duct with three typical Mach numbers is calculated by the mode matching method. It is found that up-flow will generally increase TL of lined duct, compared with the case of no flow; while down-flow will generally decrease TL. In both situations, the peak frequency does not show significant change.

Phase Dynamics of the Dysthe Equation and the Bifurcation of Plane Waves

The bifurcation of plane waves to localised structures is investigated in the Dysthe equation, which incorporates the effects of mean flow and wave steepening. Through the use of phase modulation techniques, it is demonstrated that such occurrences may be described using a Korteweg–de Vries equation. The solitary wave solutions of this system form a qualitative prototype for the bifurcating dynamics, and the role of mean flow and steepening is then made clear through how they enter the amplitude and width of these solitary waves. In addition, higher order phase dynamics are investigated, leading to increased nonlinear regimes which in turn have a more profound impact on how the plane waves transform under defects in the phase.

Effect of non-parallel mean flow on the acoustic spectrum of heated supersonic jets: Explanation of “jet quietening”

Noise measurements of heated axisymmetric jets at a fixed supersonic acoustic Mach number indicate that the acoustic spectrum reduces when the temperature ratio increases. The “spectral quietening” effect has been observed both experimentally and computationally using large Eddy simulations. It was explained by Afsar, Goldstein, and Fagan [AIAA J. 49, 2522 (2011)] through the cancellation introduced by the enthalpy flux/momentum flux coupling term using the generalized acoustic analogy formulation. But the parallel flow assumption is known to give inaccurate predictions at high jet speeds. In this paper, we therefore extend the nonparallel flow asymptotic theory of Goldstein, Sescu, and Afsar [J. Fluid Mech. 695, 199 (2012)] for the vector Green’s function of the adjoint linearized Euler equations in the analogy. Using the steady Reynolds averaged Navier Stokes calculation for the jet mean flow, we find that the coupling term propagator is positive-definite and asymptotically subdominant at low frequencies corresponding to the peak jet noise when nonparallel flow effects are taken into account and self-consistent approximations for the turbulence structure are made. We then assess the validity of the non-parallel flow-based acoustic analogy model by computing the overall sound pressure level (OASPL) at various observation angles. Interpretation of the latter allows a more rational explanation of the quietening effect. In general, our noise predictions are in very good agreement with acoustic data beyond the peak frequency.

Effects of Mean Flow, Temperature Ratio and Area Ratio on Combustion Instability of a Dump Combustor

ABSTRACT This paper studies the effect of mean flow, temperature ratio and area ratio of a dump combustor on combustion instability. From an explicit transfer function representation of combustor acoustics, it is shown that mean flow has an effect of scaling reflection coefficients and that combustion instability can be determined from roots of a scalar equation having two key parameters; temperature and area ratios. As a special case, we present a general condition for the occurrence of intrinsic thermo-acoustic modes for a non-zero mean flow. Our theoretical findings are validated with experimental data in literature.

Latitudinal dependence of the dry air effect on tropical cyclone development

The impacts of dry air on tropical cyclone (TC) development at different latitudes with no mean flows are investigated with idealized simulations. It is found that the effective radius of the dry air is sensitive to its vertical distribution and the background earth rotation. The effect of low-level dry-air layer in inhibiting TC development decreases with increasing latitude. At lower latitudes, the greater boundary layer gradient wind imbalance results in a strong low-level inflow, and the dry air can easily penetrate into the TC inner-core region. The intruding dry air inhibits the inner-core deep convection and leads to marked asymmetric convective structure, which significantly suppresses TC development. In contrast, at higher latitudes, the dry air gets moistened before reaching the TC inner-core region due to a weaker radial inflow but can suppress the development of the outer spiral rainbands. The suppressed outer spiral rainbands lead to a weaker barrier effect to the boundary layer inflow and help TC development. Furthermore, the lower the altitude of dry-air layer resides, the greater the impact on TC intensification. The low-level pathway associated with the boundary layer inflow plays an important role on how dry-air layer acts on a TC without considering the mean flow effects. Through examining the climatological distribution of the moisture field, we expect that the intrusion of dry air can be more frequent in the North Atlantic area and therefore has more effects on TC development than in the western North Pacific.

Effect of background mean flow on PSI of internal wave beams

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

Numerical Assessment of Open-Rotor Noise Shielding with a Coupled Approach

In this work, scattering and shielding of the tonal noise from contrarotating open rotors by surrounding parts are investigated. The computational tool chain is based on unsteady Reynolds-averaged Navier–Stokes simulations providing permeable integration surface data for a Ffowcs Williams and Hawkings-type evaluation (“Sound Generated by Turbulence and Surfaces in Arbitrary Motion,” Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 264, No. 1151, 1969, pp. 321–342), which is coupled with a fast multipole boundary-element method to account for shielding by the airframe. The effect of a background mean flow is taken into account by applying a Lorentz transform to the boundary-element problem and using the Möhring analogy instead of the Ffowcs Williams and Hawkings formulation to obtain the incident acoustic field. Validation of the Möhring/boundary-element coupling method is shown on the basis of a model contrarotating open rotor with shielding geometries and a mounting pylon. The tool chain is then applied to a full-scale open-rotor engine installed in different aircraft tail configurations (T tail, L tail, and U tail) to assess their influence on flyover and lateral noise in takeoff conditions.

Effect of mean flow on mutual radiation resistances of a rectangular plate

Very few investigations have considered the effects of fluid convection on the mutual- radiation resistance, which could be important in stationary fluids. In this work, we quantified the effects of a convected fluid on the radiation resistances including self- and mutual radiation resistances. We derived the non-dimensional modal impedance in the presence of mean flow based on an expansion in the panel mode of a simply supported plate. Then we compared the self-radiation resistances with the previous reports and analyzed the effects of flow on mutual radiation resistances. The results show that the radiation efficiency increases with the flow velocity, which compare very well with the previous reports. The flow introduces a strong coupling between modes that weakly coupled in no-flow case and with the increase of flow velocity. This coupling effect increases until Mach number (M) reaches 0.5 and then decreases. For the modes with the same parity indices, the flow shifts coupling lobes toward lower frequency with the increase of flow velocity due to the shift of critical frequency of higher mode radiation resistance, and the degree of coupling change is consistent with the change of critical frequency of the higher mode self-radiation resistance.

Space-time characteristics of aero-optical effect around conformal turrets

This study simulated the aero-optical effect of beams with different projection directions around conformal turrets with different radii(400 mm and 2 000 mm). The Mach number was fixed, and the Reynolds number remained similar in all cases. The space-time characteristic of beam quality factor and beam tilt angle caused by the aero-optical effect was comprehensively studied. The aero-optical effect was mainly determined based on the mean flow effect, and the characteristic frequency of the mean flow effect was determined based on that of the flow around the turret. The spatial characteristic of the aero-optical effect was accurately reproduced in the reduced-scale experiments; however, the temporal characteristic was poorly simulated. It is pointed out that the wavefront distortion statistics and fluctuation values caused by aero-optical effect aero-optical effect appear to be minimized at a projection direction of 40° zenith in the forward direction, and the increase of projection radius can result in fast increaseing of the mean flow effect while maintaining the turbulent effect almost constant.

Interactions of azimuthal acoustic modes with an unsteady heat source in an annular duct.

The interactions of azimuthal acoustic modes with an unsteady heat source in an annular duct is studied in the present paper. Based on a linear analysis, two methods are given. One is the untruncated low order method in which the linear equations with full terms are solved. Another is the truncated low order method in which terms of order O(M) or higher are neglected, where M denotes the mean flow Mach number. From investigations, the quantities of disturbances, including reflected, transmitted acoustic waves, generated entropy waves, and vorticity waves are calculated. Results show that the amplitudes of reflected and transmitted acoustic waves dramatically depend on the temperature ratio across the heat source and the non-dimensional frequencies of incident acoustic waves. Furthermore, mean flow effects are investigated. The flow Mach number has significant effects on flow disturbances, especially on vorticity waves. Based on analytical results, the energy fluxes of disturbances are investigated. It is found that the energy flux contributed from an entropy fluctuation is much higher than the acoustic energy flux. The energy flux associated with a vortical mode becomes comparable with the acoustic energy flux only when the flow Mach number is large.

Linear Acoustic Analysis of Main Combustion Chamber of an Oxidizer-Rich Staged Combustion Engine

A comprehensive linear acoustic analysis of the main combustion chamber of an oxidizer-rich staged combustion engine is presented. The theoretical basis is an acoustic wave equation derived from the conservation equations that characterize unsteady flow motions in the chamber. The physical model mimics the RD-170 main combustion chamber and includes all the geometric details, including the upstream flow distributor, oxidizer plenum, injector assembly, and main chamber. Damping effects associated with the flow distributor plate and injectors are accounted for by means of impedance boundary conditions. Acoustic communication between the main chamber and oxidizer manifold via the injector assembly is found to be significant. Acoustic waves excited in the main chamber propagate upstream and interact with the oxidizer dome, where they are partially damped by the flow distributor. The influence of baffle injectors on the chamber acoustic behavior is also studied. It is found that the largest contributor to damping is increased transport of acoustic energy out of the domain due to advective mean flow effects.

Effects of Low-Level Flow Orientation and Vertical Shear on the Structure and Intensity of Tropical Cyclones

Abstract This article explores the simultaneous effect of vertical wind shear (VWS) and low-level mean flow (LMF) on tropical cyclone (TC) structure evolution. The structural evolution of 180 western North Pacific TCs from 2002 to 2014 was measured by a new parameter, the RV ratio, which is defined as the ratio of a TC’s radius of 34-kt (17.5 m s−1) wind to its maximum wind speed at the ending point of the intensification period. Whereas TCs with RV ratios in the lowest quartile of all 180 samples favored intensification over expansion, and 82% of these TCs experienced rapid intensification, TCs with RV ratios in the topmost quartile favored size expansion over intensification. A novel result of this study is that TC RV ratios were found to correlate with the LMF orientation relative to the deep-layer VWS vector. Specifically, whereas an LMF directed toward the left-of-shear orientation favors TC intensification, a right-of-shear LMF favors TC size expansion. This study further analyzed the TC rainfall asymmetry and asymmetric surface flow using satellite observations. Results show that for a TC affected by an LMF with right-of-shear orientation, the positive surface flux anomaly in the upshear outer region promotes convection in the downshear rainband region. On the other hand, a left-of-shear LMF induces a positive surface flux anomaly in the downshear outer region, thus promoting convection in the upshear inner core. Enhancement of the symmetric inner-core convection favors intensification, whereas enhancement of the downshear rainband favors expansion.

An analytical study of the effect of flame response to simultaneous axial and transverse perturbations on azimuthal thermoacoustic modes in annular combustors

Transverse mean flows and transverse acoustic perturbations are factors that may influence the flame response, and thus change the frequency, growth rate and mode nature (standing, spinning or mixed) of the azimuthal thermoacoustic modes in annular combustors. Previous analytical and low-order network models for annular combustors usually consider only axial flame response. This work identifies the linear response of an asymmetric planar Bunsen flame under simultaneous axial and transverse perturbations. A linearized analytical method for studying the response of an inclined flame under perturbations using G-equation is applied. The relation between the flame responses under a 2-D perturbation and separate axial/transverse perturbations is studied to identify a linear 2-D flame response superposition, with the response under simultaneous perturbations being equal to the sum of two responses under each single perturbation. The effect of this linear 2-D flame response on the azimuthal thermoacoustic modes is then investigated by incorporating it into a linear low-order network methodology [19]. An annular combustor both with and without mixing burners and transverse mean flows is studied. The results are verified by comparing with FEM (Helmholtz solver) simulations. It is found that even though the transverse flame response is usually much smaller than the axial flame response, it may strongly affect the spin ratio of the azimuthal thermoacoustic modes. The asymmetries (e.g. due to burner difference) in both the transverse and axial flame response, and the effect of transverse mean flow on the acoustic propagation may all significantly change the spin ratio of the azimuthal modes, and thus need to be considered simultaneously.

Application of acoustic oscillations in quenching of gas burner flame

This paper concerns the flame extinguishing with the use of acoustic waves. A small laboratory stand allowing to generate acoustic waves in the horizontal direction was used for that purpose. The speaker extinction power and the acoustic extinction pressure were selected to quantify the process. Varying frequencies (30–50 Hz) burner powers (3.45-11.72 kW) and distances between the acoustic source and the flame (0.02–0.06 m) were investigated. It was shown that the lower the frequency is it is easier to extinguish the flame. It was also found that the fuel load has a minor impact on the extinction pressure. The results are supplemented with the visualisation of the flame behaviour under the influence of acoustic waves performed with the use of Schlieren apparatus. It was shown that the extinction is a result of cumulative effect of acoustic mean flow and oscillatory perturbations.

Vibroacoustic behavior of orthotropic aerospace composite structure in the subsonic flow considering the Third order Shear Deformation Theory

An analytical model is performed across the aerospace composite structure to interpret acoustic transmission of the infinitely long doubly curved shell considering the effect of mean flow with the aid of Higher-order Shear Deformation Theory (HSDT). Accordingly, the displacements are extended up to cubic order of thickness coordinate based on Third-order Shear Deformation Theory (TSDT) known as HSDT including no effect of shear correction factor. Consequently, in order to present the Sound Transmission Loss (STL) of the present model, the excitation of the structure with an oblique plane sound wave is set in order. However, the acoustic transmission is performed by incorporating the both of shell equations and acoustic wave equations, simultaneously. In the next step, the accuracy as well as the reliability of the present model is provided by comparing the achieved results with those available in literature. Moreover, the present results illustrate the importance of investigating TSDT due to clarifying the more precise outcomes. Finally, the importance of the present model is cleared as a result of improving the mechanical and sound insulation properties particularly in low frequency zone by illustrating the STL comparison between the current structure and those structures without any curvature.

The effect of an axial mean temperature gradient on communication between one-dimensional acoustic and entropy waves

This work performs a theoretical and numerical analysis of the communication between one-dimensional acoustic and entropy waves in a duct with a mean temperature gradient. Such a situation is highly relevant to combustor flows where the mean temperature drops axially due to heat losses. A duct containing a compact heating element followed by an axial temperature gradient and choked end is considered. The proposed jump conditions linking acoustic and entropy waves on either side of the flame show that the generated entropy wave is generally proportional to the mean temperature ratio across the flame and the ratio [Formula: see text], where [Formula: see text] is the flame transfer function. It is inversely proportional to the Mach number immediately downstream of the flame M2. The acoustic and entropy fields in the region of axial mean temperature gradient are calculated using four approaches: (1) using the full three linearised Euler equations as the reference; (2) using two linearised Euler equations in which the acoustic and entropy waves are assumed independent (thus allowing the extent of communication between the acoustic and entropy wave to be evaluated); (3) using a Helmholtz solver which neglects mean flow effects and (4) using a recently developed analytical solution. It is found that the communication between the acoustic and entropy waves is small at low Mach numbers; it rises with increasing Mach number and cannot be neglected when the mean Mach number downstream of the heating element exceeds 0.1. Predictions from the analytical method generally match those from the full three linearised Euler equations, and the Helmholtz solver accurately determines the acoustic field when [Formula: see text].

Control-Oriented Methods for Turbomachinery Noise Simulation

This paper presents an innovative stability analysis and design approach for time-domain impedance boundary conditions to simulate noise propagation and radiation from a lined turbomachinery duct in the presence of a mean flow. A control-oriented model is developed for the stability analysis of the impedance boundary condition by using generalized function at the lining surface. The mean flow effect and sound propagation are considered in the model as well. Then, the numerical stability issue is analyzed by using the Bode plots before stabilized accordingly by employing the phase lead compensator method, which results in a rational transfer function. Finally, the corresponding time-domain implementation is achieved by using the so-called controllable canonical form rather than an inconvenient convolution operation. The performance of the current proposed approach is first validated in an in-duct propagation case by comparing to analytical solutions obtained by employing the Wiener–Hopf method and then demonstrated in a couple of duct acoustic problems with representative turbomachinery setups. The innovative cross-disciplinary nature of the current proposed approach can shed light on impedance problems and is very useful to time-domain acoustic simulations for turbomachinery applications.

Quantifying Residual, Eddy, and Mean Flow Effects on Mixing in an Idealized Circumpolar Current

AbstractMeridional diffusivity is assessed for a baroclinically unstable jet in a high-latitude idealized circumpolar current (ICC) using the Model for Prediction across Scales Ocean (MPAS-O) and the online Lagrangian in Situ Global High-Performance Particle Tracking (LIGHT) diagnostic via space–time dispersion of particle clusters over 120 monthly realizations of O(106) particles on 11 potential density surfaces. Diffusivity in the jet reaches values of O(6000) m2 s−1 and is largest near the critical layer supporting mixing suppression and critical layer theory. Values in the vicinity of the shelf break are suppressed to O(100) m2 s−1 because of the presence of westward slope front currents. Diffusivity attenuates less rapidly with depth in the jet than both eddy velocity and kinetic energy scalings would suggest. Removal of the mean flow via high-pass filtering shifts the nonlinear parameter (ratio of the eddy velocity to eddy phase speed) into the linear wave regime by increasing the eddy phase speed via the depth-mean flow. Low-pass filtering, in contrast, quantifies the effect of mean shear. Diffusivity is decomposed into mean flow shear, linear waves, and the residual nonhomogeneous turbulence components, where turbulence dominates and eddy-produced filamentation strained by background mean shear enhances mixing, accounting for ≥80% of the total diffusivity relative to mean shear [O(100) m2 s−1], linear waves [O(1000) m2 s−1], and undecomposed full diffusivity [O(6000) m2 s−1]. Diffusivity parameterizations accounting for both the nonhomogeneous turbulence residual and depth variability are needed.