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 One-Dimensional Propagation

2020 ◽  
pp. 453-512
Author(s):  
Steven L. Garrett
Keyword(s):  
Sound Propagation ◽  
Impedance Matching ◽  
Low Frequency ◽  
Absolute Calibration ◽  
Sound Waves ◽  
Quality Factors ◽  
Electrical Measurements ◽  
One Dimensional ◽  
The One ◽  
The Waves

Abstract Having already invested in understanding both the equation of state and the hydrodynamic equations, only straightforward algebraic manipulations will be required to derive the wave equation, justify its solutions, calculate the speed of sound in fluids, and derive the expressions for acoustic intensity and the acoustic kinetic and potential energy densities of sound waves. The “machinery” developed to describe waves on strings will be sufficient to describe one-dimensional sound propagation in fluids, even though the waves on the string were transverse and the one-dimensional waves in fluids are longitudinal. These results are combined with the thermal and viscous penetration depths to calculate the frequencies and quality factors in standing wave resonators. The coupling of those resonators to loudspeakers will be examined. The introduction of reciprocal transducers that are linear, passive, and reversible will allow absolute calibration of transducers using only electrical measurements (i.e., currents and voltages) by the reciprocity method, if the acoustic impedance that couples the source and receiver is calculable. Reflection and transmission at junctions between multiple ducts and other networks will be calculated and applied to the design of filters. The behavior of waves propagating through horns will provide useful impedance matching but introduce a low-frequency cut-off.

Effect of non-parallel mean flow on the Green’s function for predicting the low-frequency sound from turbulent air jets

2012 ◽  
Vol 695 ◽  
pp. 199-234 ◽  
Author(s):  
M. E. Goldstein ◽  
Adrian Sescu ◽  
M. Z. Afsar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Low Frequency ◽  
Source Location ◽  
Parallel Flow ◽  
Numerical Calculations ◽  
Mean Flow ◽  
Frequency Sound ◽  
The Mean ◽  
Radiated Sound

AbstractIt is now well-known that there is an exact formula relating the far-field jet noise spectrum to the convolution product of a propagator (that accounts for the mean flow interactions) and a generalized Reynolds stress autocovariance tensor (that accounts for the turbulence fluctuations). The propagator depends only on the mean flow and an adjoint vector Green’s function for a particular form of the linearized Euler equations. Recent numerical calculations of Karabasov, Bogey & Hynes (AIAA Paper 2011-2929) for a Mach 0.9 jet show use of the true non-parallel flow Green’s function rather than the more conventional locally parallel flow result leads to a significant increase in the predicted low-frequency sound radiation at observation angles close to the downstream jet axis. But the non-parallel flow appears to have little effect on the sound radiated at $9{0}^{\ensuremath{\circ} } $ to the downstream axis. The present paper is concerned with the effects of non-parallel mean flows on the adjoint vector Green’s function. We obtain a low-frequency asymptotic solution for that function by solving a very simple second-order hyperbolic equation for a composite dependent variable (which is directly proportional to a pressure-like component of this Green’s function and roughly corresponds to the strength of a monopole source within the jet). Our numerical calculations show that this quantity remains fairly close to the corresponding parallel flow result at low Mach numbers and that, as expected, it converges to that result when an appropriately scaled frequency parameter is increased. But the convergence occurs at progressively higher frequencies as the Mach number increases and the supersonic solution never actually converges to the parallel flow result in the vicinity of a critical- layer singularity that occurs in that solution. The dominant contribution to the propagator comes from the radial derivative of a certain component of the adjoint vector Green’s function. The non-parallel flow has a large effect on this quantity, causing it (and, therefore, the radiated sound) to increase at subsonic speeds and decrease at supersonic speeds. The effects of acoustic source location can be visualized by plotting the magnitude of this quantity, as function of position. These ‘altitude plots’ (which represent the intensity of the radiated sound as a function of source location) show that while the parallel flow solutions exhibit a single peak at subsonic speeds (when the source point is centred on the initial shear layer), the non-parallel solutions exhibit a double peak structure, with the second peak occurring about two potential core lengths downstream of the nozzle. These results are qualitatively consistent with the numerical calculations reported in Karabasov et al. (2011).

Scheduling Algorithms With Application to Parallel Computing of Aeroacoustics

2000 ◽  
Author(s):  
Alex Povitsky
Keyword(s):  
Energy Transfer ◽  
Sound Propagation ◽  
Scheduling Algorithm ◽  
Multiprocessor Systems ◽  
Scheduling Problem ◽  
Sound Waves ◽  
Mean Flow ◽  
Shop Scheduling ◽  
Special Case ◽  
Efficient Parallelization

Abstract In this study we consider one method of parallelization of implicit numerical schemes on multiprocessor systems. Then, the parallel high-order compact numerical algorithm is applied to physics of amplification of sound waves in a non-uniform mean flow. Due to the pipelined nature of this algorithm, its efficient parallelization is based on scheduling of processors for other computational tasks while otherwise the processors stay idle. In turn, the proposed scheduling algorithm is taken as a special case of the general shop scheduling problem and possible extentions and generalizations of the proposed scheduling methodology are discussed. Numerical results are discussed in terms of baroclinic generation of wave-associated vorticity that appear to be a key process in energy transfer between a non-uniform mean flow and a propagating disturbance. The discovered phenomenon leads to significant amplification of sound waves and controls the direction of sound propagation.

scholarly journals Estimation of peak discharges of historical floods

2014 ◽  
Vol 11 (5) ◽  
pp. 5463-5485 ◽  
Author(s):  
J. Herget ◽  
T. Roggenkamp ◽  
M. Krell
Keyword(s):  
Flood Frequency ◽  
River Channels ◽  
Sources Of Information ◽  
Mean Flow ◽  
General Outline ◽  
One Dimensional ◽  
Flood Level ◽  
Alternative Approaches ◽  
The Mean ◽  
Generalized Statement

Abstract. There is no doubt, that the hazard assessment of future floods especially under consideration of the recent environmental change can be significantly improved by the consideration of historic flood events. While flood frequency inventories on local, regional and even European scale are already developed and published, the estimation of their magnitudes indicated by discharges is still challenging. Such data are required due to significant human impact on river channels and floodplains though historic flood levels cannot be related to recent ones or recent discharges. Based on own experiences from single local key studies the general outline of an approach to estimate the discharge of the previous flood based on handed down flood level and topographic data is presented. The model for one-dimensional steady flow is based on the empirical Manning equation for the mean flow velocity. Background and potential sources of information, acceptable simplifications and data transformation for each element of the model-equation are explained and discussed. Preliminary experiences on the accuracy of ±10% are documented and potential approaches for the validation of individual estimations given. A brief discussion on benefits and limitations including a generalized statement on alternative approaches closes the review presentation of the approach.

Fluctuating boundary layer on a magnetized plate

1967 ◽  
Vol 63 (2) ◽  
pp. 513-525 ◽  
Author(s):  
Sahib Singh Chawla
Keyword(s):  
Boundary Layer ◽  
Low Frequency ◽  
Surface Current ◽  
Frequency Range ◽  
Mean Flow ◽  
Wave Type ◽  
High Frequencies ◽  
Phase Lead ◽  
The Mean ◽  
The Magnetic Field

The laminar boundary layer on a magnetized plate, when the magnetic field oscillates in magnitude about a constant non-zero mean, is analysed. For low-frequency fluctuations the solution is obtained by a series expansion in terms of a frequency parameter, while for high frequencies the flow pattern is of the ‘skin-wave’ type unaffected by the mean flow. In the low-frequency range, the phase lead and the amplitude of the skin-friction oscillations increase at first and then decrease to their respective ‘skin-wave’ values. On the other hand the phase angle of the surface current decreases from 90° to 45° and its amplitude increases with frequency.

Wall friction and velocity measurements in a double-frequency pulsating turbulent flow

2016 ◽  
Vol 788 ◽  
pp. 521-548 ◽  
Author(s):  
L. R. Joel Sundstrom ◽  
Berhanu G. Mulu ◽  
Michel J. Cervantes
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Low Frequency ◽  
Turbulent Pipe Flow ◽  
Oscillating Flow ◽  
Base Case ◽  
Mean Flow ◽  
Double Frequency ◽  
The Mean ◽  
Wall Shear

Wall shear stress measurements employing a hot-film sensor along with laser Doppler velocimetry measurements of the axial and tangential velocity and turbulence profiles in a pulsating turbulent pipe flow are presented. Time-mean and phase-averaged results are derived from measurements performed at pulsation frequencies ${\it\omega}^{+}={\it\omega}{\it\nu}/\bar{u}_{{\it\tau}}^{2}$ over the range of 0.003–0.03, covering the low-frequency, intermediate and quasi-laminar regimes. In addition to the base case of a single pulsation imposed on the mean flow, the study also investigates the flow response when two pulsations are superimposed simultaneously. The measurements from the base case show that, when the pulsation belongs to the quasi-laminar regime, the oscillating flow tends towards a laminar state in which the velocity approaches the purely viscous Stokes solution with a low level of turbulence. For ${\it\omega}^{+}<0.006$, the oscillating flow is turbulent and exhibits a region with a logarithmic velocity distribution and a collapse of the turbulence intensities, similar to the time-averaged counterparts. In the low-frequency regime, the oscillating wall shear stress is shown to be directly proportional to the Stokes length normalized in wall units $l_{s}^{+}~(=\sqrt{2/{\it\omega}^{+}})$, as predicted by quasi-steady theory. The base case measurements are used as a reference when evaluating the data from the double-frequency case and the oscillating quantities are shown to be close to superpositions from the base case. The previously established view that the time-averaged quantities are unaffected by the imposition of small-amplitude pulsed unsteadiness is shown to hold also when two pulsations are superposed on the mean flow.

scholarly journals Stability of the laminar boundary layer in a streamwise corner

1984 ◽  
Vol 393 (1804) ◽  
pp. 101-116 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Viscous Incompressible Flow ◽  
Boundary Layer Region ◽  
Dimensional Boundary ◽  
The Mean ◽  
Layer Region ◽  
The Stability ◽  
Infinite Boundary Value Problem ◽  
Layer Problem

This work examines the stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary-layer problem. The semi-infinite boundary value problem satisfied by small-amplitude disturbances in the ‘blending boundary layer’ region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid ‘first approximations’ to solutions of the governing differ­ential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two-dimensional boundary layer profiles.

Coherent structures and dominant frequencies in a turbulent three-dimensional diffuser

2012 ◽  
Vol 699 ◽  
pp. 320-351 ◽  
Author(s):  
Johan Malm ◽  
Philipp Schlatter ◽  
Dan S. Henningson
Keyword(s):  
Coherent Structures ◽  
Large Scale ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Low Frequency ◽  
Bulk Velocity ◽  
Time Signal ◽  
Mean Flow ◽  
The Mean ◽  
Dominant Frequencies

AbstractDominant frequencies and coherent structures are investigated in a turbulent, three-dimensional and separated diffuser flow at $\mathit{Re}= 10\hspace{0.167em} 000$ (based on bulk velocity and inflow-duct height), where mean flow characteristics were first studied experimentally by Cherry, Elkins and Eaton (Intl J. Heat Fluid Flow, vol. 29, 2008, pp. 803–811) and later numerically by Ohlsson et al. (J. Fluid Mech., vol. 650, 2010, pp. 307–318). Coherent structures are educed by proper orthogonal decomposition (POD) of the flow, which together with time probes located in the flow domain are used to extract frequency information. The present study shows that the flow contains multiple phenomena, well separated in frequency space. Dominant large-scale frequencies in a narrow band $\mathit{St}\equiv fh/ {u}_{b} \in [0. 0092, 0. 014] $ (where $h$ is the inflow-duct height and ${u}_{b} $ is the bulk velocity), yielding time periods ${T}^{\ensuremath{\ast} } = T{u}_{b} / h\in [70, 110] $, are deduced from the time signal probes in the upper separated part of the diffuser. The associated structures identified by the POD are large streaks arising from a sinusoidal oscillating motion in the diffuser. Their individual contributions to the total kinetic energy, dominated by the mean flow, are, however, small. The reason for the oscillating movement in this low-frequency range is concluded to be the confinement of the flow in this particular geometric set-up in combination with the high Reynolds number and the large separated zone on the top diffuser wall. Based on this analysis, it is shown that the bulk of the streamwise root mean square (r.m.s.) value arises due to large-scale motion, which in turn can explain the appearance of two or more peaks in the streamwise r.m.s. value. The weak secondary flow present in the inflow duct is shown to survive into the diffuser, where it experiences an imbalance with respect to the upper expanding corners, thereby giving rise to the asymmetry of the mean separated region in the diffuser.

The use of a fibre anemometer in turbulent flows

1963 ◽  
Vol 16 (2) ◽  
pp. 269-281 ◽  
Author(s):  
D. J. Tritton
Keyword(s):  
Velocity Field ◽  
Turbulent Flows ◽  
Theoretical Study ◽  
Low Frequency ◽  
Frequency Theory ◽  
Background Information ◽  
Approximate Representation ◽  
Practical Situation ◽  
Quartz Fibre ◽  
The Mean

Quartz fibre anemometers have been used (as described in subsequent papers) to survey the velocity field of turbulent free convective air flows. This paper discusses the reasons for the choice of this instrument and provides the background information for its use in this way. Some practical points concerning fibre anemometers are mentioned. The rest of the paper is a theoretical study of the response of a fibre to a turbulent flow. An approximate representation of the force on the fibre due to the velocity field and the equation for a bending beam, representing the response to this force, form the basis of a consideration of the mean and fluctuating displacement of the fibre. Emphasis is placed on the behaviour when the spectrum of the turbulence is largely in frequencies low enough for the fibre to respond effectively instantaneously (as this corresponds to the practical situation). Incomplete correlation of the turbulence along the length of the fibre is taken into account. Brief mention is made to the theory of the higher-frequency (resonant) response in the context of an experimental check on the applicability of the low-frequency theory.

scholarly journals The Contribution of Striations to the Eddy Energy Budget and Mixing: Diagnostic Frameworks and Results in a Quasigeostrophic Barotropic System with Mean Flow

2015 ◽  
Vol 45 (8) ◽  
pp. 2095-2113 ◽  
Author(s):  
Ru Chen ◽  
Glenn R. Flierl
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Ocean Model ◽  
Invariance Property ◽  
Mean Flow ◽  
Eddy Diffusivities ◽  
Energy Cascades ◽  
The Mean ◽  
Flow Theories ◽  
Noise Forcing

AbstractLow-frequency oceanic motions have banded structures termed “striations.” Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a β-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of β-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations’ contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

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