scholarly journals Low-frequency sound radiated by a nonlinearly modulated wavepacket of helical modes on a subsonic circular jet

2009 ◽  
Vol 637 ◽  
pp. 173-211 ◽  
Author(s):  
XUESONG WU ◽  
PATRICK HUERRE
Keyword(s):  
Acoustic Field ◽  
Low Frequency ◽  
Base Flow ◽  
Matched Asymptotic Expansion ◽  
Sound Waves ◽  
Mean Flow ◽  
Flow Distortion ◽  
Experimental Conditions ◽  
Modulation Equation ◽  
Instability Modes

A possible fundamental physical mechanism by which instability modes generate sound waves in subsonic jets is presented in the present paper. It involves a wavepacket of a pair of helical instability modes with nearly the same frequencies but opposite azimuthal wavenumbers. As the wavepacket undergoes simultaneous spatial–temporal development in a circular jet, the mutual interaction between the helical modes generates a strong three-dimensional, slowly modulating ‘mean-flow distortion’. It is demonstrated that this ‘mean field’ radiates sound waves to the far field. The emitted sound is of very low frequency, with characteristic time and length scales being comparable with those of the envelope of the wavepacket, which acts as a non-compact source. A matched-asymptotic-expansion approach is used to determine, in a self-consistent manner, the acoustic field in terms of the envelope of the wavepacket and a transfer factor characterizing the refraction effect of the background base flow. For realistic jet spreading rates, the nonlinear development of the wavepacket is found to be influenced simultaneously by non-parallelism and non-equilibrium effects, and so a composite modulation equation including both effects is constructed in order to describe the entire growth–attenuation–decay cycle. Parametric studies pertaining to relevant experimental conditions indicate that the acoustic field is characterized by a single-lobed directivity pattern beamed at an angle about 45°–60° to the jet axis and a broadband spectrum centred at a Strouhal number St ≈ 0.07–0.2. As the nonlinear effect increases, the radiation becomes more efficient and the noise spectrum broadens, but the gross features of the acoustic field remain robust, and are broadly in agreement with experimental observations.

scholarly journals Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011 ◽  
Vol 681 ◽  
pp. 116-153 ◽  
Author(s):  
NICHOLAS J. VAUGHAN ◽  
TAMER A. ZAKI
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Low Frequency ◽  
Finite Amplitude ◽  
Base Flow ◽  
Streamwise Vorticity ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Tollmien Schlichting

The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the Tollmien–Schlichting (T–S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

Origin of the peak-valley wave structure leading to wall turbulence

1989 ◽  
Vol 208 ◽  
pp. 1-23 ◽  
Author(s):  
Masahito Asai ◽  
Michio Nishioka
Keyword(s):  
Three Dimensional ◽  
Wave Structure ◽  
Wall Turbulence ◽  
Generation Process ◽  
Two Dimensional ◽  
Mean Flow ◽  
S Wave ◽  
Flow Distortion ◽  
Experimental Conditions ◽  
Dimensional Wave

A generation process for the three-dimensional wave which dominates the transition preceded by a Tollmien-Schlichting (T-S) wave is studied both experimentally and numerically in plane Poiseuille flow at a subcritical Reynolds number of 5000. In order to identify the origin of the three-dimensional wave in Nishioka et al.'s laboratory experiment, the corresponding spanwise mean-flow distortion and two-dimensional T-S wave modes are introduced into a parabolic flow as the initial disturbance conditions for a numerical simulation of temporally growing type. Through reproducing the actual wave development into the peak-valley structure, the simulation pinpoints the origin to be the slight spanwise mean-flow distortion in the experimental basic flow. Furthermore, the simulation clearly shows that the growth of the three-dimensional wave requires the vortex stretching effect due to the streamwise vortices, which appear under the experimental conditions only when the amplitude of the two-dimensional T-S wave is above the observed threshold.

Noise generation by high-frequency gusts interacting with an airfoil in transonic flow

2000 ◽  
Vol 411 ◽  
pp. 91-130 ◽  
Author(s):  
I. EVERS ◽  
N. PEAKE
Keyword(s):  
Steady Flow ◽  
Acoustic Field ◽  
Transonic Flow ◽  
High Frequency ◽  
Power Series Expansion ◽  
Outer Region ◽  
Leading Edge ◽  
Mean Flow ◽  
Flow Distortion ◽  
The Mean

The method of matched asymptotic expansions is used to describe the sound generated by the interaction between a short-wavelength gust (reduced frequency k, with k [Gt ] 1) and an airfoil with small but non-zero thickness, camber and angle of attack (which are all assumed to be of typical size O(δ), with δ [Lt ] 1) in transonic flow. The mean-flow Mach number is taken to differ from unity by O(δ2/3), so that the steady flow past the airfoil is determined using the transonic small-disturbance equation. The unsteady analysis is based on a linearization of the Euler equations about the mean flow. High-frequency incident vortical and entropic disturbances are considered, and analogous to the subsonic counterpart of this problem, asymptotic regions around the airfoil highlight the mechanisms that produce sound. Notably, the inner region round the leading edge is of size O(k−1), and describes the interaction between the mean-flow gradients and the incident gust and the resulting acoustic waves. We consider the preferred limit in which kδ2/3 = O(1), and calculate the first two terms in the phase of the far-field radiation, while for the directivity we determine the first term (δ = 0), together with all higher-order terms which are at most O(δ2/3) smaller – in fact, this involves no fewer than ten terms, due to the slowly-decaying form of the power series expansion of the steady flow about the leading edge. Particular to transonic flow is the locally subsonic or supersonic region that accounts for the transition between the acoustic field downstream of a source and the possible acoustic field upstream of the source. In the outer region the sound propagation has a geometric-acoustics form and the primary influence of the mean-flow distortion appears in our preferred limit as an O(1) phase term, which is particularly significant in view of the complicated interference between leading- and trailing-edge fields. It is argued that weak mean- flow shocks have an influence on the sound generation that is small relative to the effects of the leading-edge singularity.

The pre-transitional Klebanoff modes and other boundary-layer disturbances induced by small-wavelength free-stream vorticity

2009 ◽  
Vol 638 ◽  
pp. 267-303 ◽  
Author(s):  
PIERRE RICCO
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Streamwise Velocity ◽  
Matched Asymptotic Expansion ◽  
Two Dimensional ◽  
Mean Flow ◽  
Flow Distortion ◽  
The Mean

The response of the Blasius boundary layer to free-stream vortical disturbances of the convected gust type is studied. The vorticity signature of the boundary layer is computed through the boundary-region equations, which are the rigorous asymptotic limit of the Navier–Stokes equations for low-frequency disturbances. The method of matched asymptotic expansion is employed to obtain the initial and outer boundary conditions. For the case of forcing by a two-dimensional gust, the effect of a wall-normal wavelength comparable with the boundary-layer thickness is taken into account. The gust viscous dissipation and upward displacement due to the mean boundary layer produce significant changes on the fluctuations within the viscous region. The same analysis also proves useful for computing to second-order accuracy the boundary-layer response induced by a three-dimensional gust with spanwise wavelength comparable with the boundary-layer thickness. It also follows that the boundary-layer fluctuations of the streamwise velocity match the corresponding free-stream velocity component. The velocity profiles are compared with experimental data, and good agreement is attained.The generation of Tollmien–Schlichting waves by the nonlinear mixing between the two-dimensional unsteady vorticity fluctuations and the mean flow distortion induced by localized wall roughness and suction is also investigated. Gusts with small wall-normal wavelengths generate significantly different amplitudes of the instability waves for a selected range of forcing frequencies. This is primarily due to the disparity between the streamwise velocity fluctuations in the free stream and within the boundary layer.

scholarly journals First-principle description of acoustic radiation of shear flows

2019 ◽  
Vol 377 (2159) ◽  
pp. 20190077 ◽  
Author(s):  
Xuesong Wu ◽  
Zhongyu Zhang
Keyword(s):  
Acoustic Waves ◽  
Shear Flows ◽  
Acoustic Radiation ◽  
Higher Order ◽  
Far Field ◽  
Sound Waves ◽  
Leading Order ◽  
Mean Flow ◽  
Asymptotic Approach ◽  
Flow Distortion

As a methodology complementary to acoustic analogy, the asymptotic approach to aeroacoustics seeks to predict aerodynamical noise on the basis of first principles by probing into the physical processes of acoustic radiation. The present paper highlights the principal ideas and recent developments of this approach, which have shed light on some of the fundamental issues in sound generation in shear flows. The theoretical work on sound wave emission by nonlinearly modulated wavepackets of supersonic and subsonic instability modes in free shear flows identifies the respective physical sources or emitters. A wavepacket of supersonic modes is itself an efficient emitter, radiating directly intensive sound in the form of a Mach wave beam, the frequencies of which are in the same band as those of the modes in the packet. By contrast, a wavepacket of subsonic modes radiates very weak sound directly. However, the nonlinear self-interaction of such a wavepacket generates a slowly modulated mean-flow distortion, which then emits sound waves with low frequencies and long wavelengths on the scale of the wavepacket envelope. In both cases, the acoustic waves emitted to the far field are explicitly expressed in terms of the amplitude function of the wavepacket. The asymptotic approach has also been applied to analyse generation of sound waves in wall-bounded shear flows on the triple-deck scale. Several subtleties have been found. The near-field approximation has to be worked out to a sufficiently higher order in order just to calculate the far-field sound at leading order. The back action of the radiated sound on the flow in the viscous sublayer and the main shear layer is accounted for by an impedance coefficient. This effect is of higher order in the subsonic regime, but becomes a leading order in the transonic and supersonic regimes. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

On the disturbance evolution downstream of a cylindrical roughness element

2014 ◽  
Vol 758 ◽  
pp. 238-286 ◽  
Author(s):  
B. Plogmann ◽  
W. Würz ◽  
E. Krämer
Keyword(s):  
Boundary Layer ◽  
Roughness Element ◽  
Low Frequency ◽  
Initial Growth ◽  
Mean Flow ◽  
Flow Distortion ◽  
Near Wake ◽  
Local Boundary ◽  
Displacement Thickness ◽  
The Mean

AbstractRoughness-induced transition is one of the main parameters contributing to performance loss of airfoils. Within this paper, the disturbance evolution downstream of a single, cylindrical roughness element, which is placed in a laminar boundary layer in an airfoil leading edge region, is investigated. The experiments focus on medium height roughness elements with respect to the local boundary layer displacement thickness. Hence, transition is not directly tripped at the roughness element. The roughness diameter is comparable to the streamwise wavelength of the most amplified (linear) disturbance eigenmodes. The vortical structures observed downstream of the roughness are in agreement with previous findings in the literature. In the near roughness wake, a distinct growth of high-frequency (fundamental) modes, that is modes with a high $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$-factor at the roughness location, is observed. In the far roughness wake, these fundamental modes recover linear stability characteristics due to a possible relaxation of the mean flow. However, an interaction of particularly two-dimensional fundamental modes and by the roughness interference excited oblique fundamental modes results in an excitation of subharmonic type, low-frequency combination modes, which are associated with a phase-locked interaction mechanism. Depending on the initial growth of the fundamental modes in the near wake, the low-frequency modes can experience a nonlinear growth in the far roughness wake and, thereby, trip turbulence. The fundamental mode growth rate in the near wake in turn is a weak function of the disturbance frequency and of the pressure gradient, whereas it is decisively increasing with the roughness height, that is with the mean flow distortion caused by the roughness.

scholarly journals An optimal path to transition in a duct

2008 ◽  
Vol 367 (1888) ◽  
pp. 529-544 ◽  
Author(s):  
Damien Biau ◽  
Alessandro Bottaro
Keyword(s):  
Travelling Waves ◽  
Optimal Path ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Travelling Wave ◽  
Base Flow ◽  
Mean Flow ◽  
Flow Distortion ◽  
Optimal Perturbation ◽  
Optimal Disturbances

This paper is concerned with the transition of the laminar flow in a duct of square cross section. As in the similar case of pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the ‘bypass’ path to turbulence. It has already been shown that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an ‘optimal’ path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the optimal travelling wave associated with its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called ‘minimal defect’, for the same parameters. Finally, numerical simulations of an ‘edge state’ are conducted, to identify an unstable solution that mediates laminar–turbulent transition and relate it to results of the optimization procedure.

Mach number effects on the global mixing modes induced by ramp injectors in supersonic flows

2014 ◽  
Vol 757 ◽  
pp. 403-431 ◽  
Author(s):  
Luca Massa
Keyword(s):  
Mach Number ◽  
Free Stream ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Base Flow ◽  
Recirculation Region ◽  
Mean Flow ◽  
Mixing Rate ◽  
Flow Distortion ◽  
The Mean

AbstractModern injectors for supersonic combustors (hypermixers) augment the fuel–air mixing rate by energizing the perturbation in the mixing layer. From an instability point of view, the increased perturbation growth is linked to the increased complexity of the equilibrium base flow when compared to the axisymmetric mixing layer. Common added features are streamwise vortex streaks, oblique recompression shocks and Prandtl–Meyer expansions. One of the main effects of such distortions of the mean flow is to transform the instability responsible for the creation of fine scales from a local amplified mode to a global self-sustained fluctuation. The focus of the present research is on the flow distortion induced by flushed ramps for free-stream Mach numbers in the range 2.5–3.5. The principal mean flow features are the recirculation region due to the recompression of the flow after the ramp, the shear layer over the recirculation region and the vortex streaks propagating from the ramp corners. A global three-dimensional stability analysis and three-dimensional direct numerical simulations of small perturbations of the mean flow are performed. The growth and energy distribution of the dominant and subdominant fluctuations supported by the three-dimensional steady laminar base flow are computed. The main results are the growth rates of the self-sustained varicose and sinuous modes and their correlation to the variation in the free-stream Mach number. The complex three-dimensional wavemaker is investigated by evaluating the three-dimensional eigenfunctions of the direct and adjoint modes, and the effects of the axial vorticity generated by the ramp corners are discussed.

Low-frequency sound propagation in a quasi-one-dimensional flow

1981 ◽  
Vol 104 ◽  
pp. 81-92 ◽  
Author(s):  
R. Mani
Keyword(s):  
Sound Propagation ◽  
Low Frequency ◽  
Frequency Theory ◽  
Sound Waves ◽  
Mean Flow ◽  
One Dimensional ◽  
Boundary Layer Region ◽  
Mach Number Distribution ◽  
The Mean ◽  
Layer Region

A systematic low-frequency theory is developed for the propagation of one-dimensional sound waves in a variable-area duct. The mean flow in the duct is assumed to be isentropic, compressible, and one-dimensional. Two applications are made of the theory. One concerns the reflexion coefficient from a pipe-nozzle combination, in which case comparisons are also made with some experimental data. In the second application, we consider the case of a sonic throat separating subsonic and supersonic flow. In this case, if the mean Mach number distribution in addition to being unity at the throat is also stationary at the throat, there is an axial ‘boundary-layer’ region in which the impedance of the sound wave changes from a fundamentally unsteady (reflexion-free) value at the sonic throat to the quasi-steady value away from the throat.

scholarly journals Interaction of oblique instability waves with weak streamwise vortices

1995 ◽  
Vol 284 ◽  
pp. 377-407 ◽  
Author(s):  
M. E. Goldstein ◽  
David W. Wundrow
Keyword(s):  
Streamwise Vortices ◽  
Rayleigh Instability ◽  
Mean Flow ◽  
Flow Distortion ◽  
Instability Waves ◽  
Instability Modes ◽  
Blasius Boundary Layer ◽  
The Common ◽  
Tollmien Schlichting ◽  
Streamwise Distance

This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even relatively weak distortions can cause certain oblique Rayleigh instability waves to grow much faster than the usual two-dimensional Tollmien–Schlichting waves that would be the dominant instability modes in the absence of the distortion. The oblique instability waves can then become large enough to interact nonlinearly within a common critical layer. It is shown that the common amplitude of the interacting oblique waves is governed by the amplitude evolution equation derived in Goldstein & Choi (1989). The implications of these results for Klebanoff-type transition are discussed.

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