scholarly journals Using Boundary Conditions to Account for Mean Flow Effects in a Zero Mach Number Acoustic Solver

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Emmanuel Motheau ◽  
Franck Nicoud ◽  
Thierry Poinsot
Keyword(s):  
Boundary Condition ◽  
Mach Number ◽  
Boundary Conditions ◽  
Acoustic Impedance ◽  
Low Frequency ◽  
Mean Flow ◽  
Pressure Equation ◽  
Fluctuating Pressure ◽  
Impedance Modeling ◽  
Flow Effects

The present study is devoted to the modeling of mean flow effects while computing thermoacoustic modes under the zero Mach number assumption. It is first recalled that the acoustic impedance modeling of a compressor or a turbine must be prescribed under an energetical form instead of the classical acoustic variables. Then we demonstrate the feasibility to take into account the coupling between acoustic and entropy waves in a zero Mach number framework to capture a family of low frequency entropic modes. The proposed approach relies on a new delayed entropy coupled boundary condition (DECBC) and proves able to capture a family of low frequency entropic mode even though no mean flow term is included in the fluctuating pressure equation.

scholarly journals Using Boundary Conditions to Account for Mean Flow Effects in a Zero Mach Number Acoustic Solver

2012 ◽  
Author(s):  
Emmanuel Motheau ◽  
Franck Nicoud ◽  
Thierry Poinsot
Keyword(s):  
Boundary Condition ◽  
Mach Number ◽  
Boundary Conditions ◽  
Acoustic Impedance ◽  
Low Frequency ◽  
Mean Flow ◽  
Pressure Equation ◽  
Fluctuating Pressure ◽  
Flow Effects

The present study is devoted to the modeling of mean flow effects while computing thermoacoustic modes under the zero Mach number assumption. It is first recalled that the acoustic impedance modelling a compressor or a turbine must be prescribed under an energetical form instead of the classical acoustic variables. Then we demonstrate the feasibility to take into account the coupling between acoustic and entropy waves in a zero Mach number framework to capture a family of low frequency entropic modes. The proposed approach relies on a new Delayed Entropy Coupled Boundary Condition (DECBC) and proves able to capture a family of Low frequency entropic mode even though no mean flow term is included into the fluctuating pressure equation.

Scattering and distortion of the unsteady motion on transversely sheared mean flows

1979 ◽  
Vol 91 (4) ◽  
pp. 601-632 ◽  
Author(s):  
M. E. Goldstein
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
Infinite Plate ◽  
Low Frequency ◽  
Unsteady Motion ◽  
Transverse Component ◽  
Mean Flow ◽  
Hydrodynamic Motion ◽  
Inhomogeneous Wave Equation ◽  
Derivatives Of

It is shown that the pressure and velocity fluctuations of the unsteady motion on a transversely sheared mean flow can be expressed entirely in terms of the derivatives of two potential functions. One of these is a convected quantity (i.e. it is frozen in the flow) that can be specified as a boundary condition and is related to a transverse component of the upstream velocity field. The other can be determined by solving an inhomogeneous wave equation whose source term is also a convected quantity that can be specified as a boundary condition in any given problem. The latter is related to the curl of the upstream vorticity field. The results are used to obtain an explicit representation of the three-dimensional gust-like or hydrodynamic motion on a transversely sheared mean flow. It is thereby shown that this motion is ‘driven’ entirely by the two convected quantities alluded to above.The general theory is used to study the interaction of an unsteady flow with a scmi-infinite plate embedded in a shear layer. The acoustic field produced by this interaction is calculated in the limits of low and high frequency. The results are compared with experimental one-third octave sound pressure level radiation patterns. The agreement is found to be excellent, especially in the low frequency range, where the mean-flow and convective effects are shown to have a strong influence on the directivity of the sound.

A Formulation for Mean Flow Effects on Sound Radiation from Rectangular Baffled Plates with Arbitrary Boundary Conditions

1995 ◽  
Vol 117 (1) ◽  
pp. 22-29 ◽  
Author(s):  
N. Atalla ◽  
J. Nicolas
Keyword(s):  
Boundary Conditions ◽  
Radiation Resistance ◽  
Sound Radiation ◽  
Added Mass ◽  
Mean Flow ◽  
Low Frequencies ◽  
Radiation Impedance ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Flow Effects

A general formulation of the sound radiation from fluid-loaded rectangular baffled plates with arbitrary boundary conditions has been developed by Berry et al. (JASA, Vol. 90, No. 4, Pt. 2, 1991). In this paper, an extension of this formulation to inviscid, uniform subsonic flow is considered. The analysis is based on a variational formulation for the transverse vibrations of the plate and the use of the extended, to uniformly moving media, form of the Helmholtz integral equation. The formulation shows explicitly the effect of the flow in terms of added mass, and radiation resistance. Furthermore, it avoids the difficult problem of integration in the complex domain, typical of the wavenumber transform approaches to fluid-loading problems. Comparison of the acoustic radiation impedance with existing studies supports the validity of the approach. The details of the formulation and its numerical implementation is exposed and a discussion of the flow effects on the radiation impedance of a rectangular piston is presented. It is shown that subsonic mean flow increases the modal radiation resistance at low frequencies and affects added mass more strongly than it affects radiation resistance.

scholarly journals Aeroacoustic Attenuation Performance of a Helmholtz Resonator with a Rigid Baffle Implemented in the Presence of a Grazing Flow

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Di Guan ◽  
Dan Zhao ◽  
Zhaoxin Ren
Keyword(s):  
Mach Number ◽  
Transmission Loss ◽  
Low Frequency ◽  
Helmholtz Resonator ◽  
Loss Peak ◽  
Mean Flow ◽  
Theoretical Formulation ◽  
Grazing Flow ◽  
Maximum Transmission ◽  
Rigid Baffle

To broaden its’ effective frequency range and to improve its transmission loss performance, a modified design of a Helmholtz resonator is proposed and evaluated by implementing a rigid baffle in its cavity. Comparison is then made between the proposed design and the conventional one by considering a rectangular duct with the resonator implemented in the presence of a mean grazing flow. For this, a linearized 2D Navier-Stokes model in frequency domain is developed. After validated by benchmarking with the available experimental data and our experimental measurements, the model is used to evaluate the effects of (1) the width Lp of the rigid baffle, (2) its implementation location/height Hg, (3) its implementation configurations (i.e., attached to the left sidewall or right sidewall), (4) the grazing mean flow Mu (Mach number), and (5) the neck shape on a noise damping effect. It is shown that as the rigid baffle is attached in the 2 different configurations, the resonant frequencies and the maximum transmission losses cannot be predicted by using the classical theoretical formulation ω2=c2S/VLeff, especially as the grazing Mach number Mu is greater than 0.07, i.e., Mu>0.07. In addition, there is an optimum grazing flow Mach number corresponding to the maximum transmission loss peak, as the width Lp is less than half of the cavity width Dr, i.e., Lp/Dr≤0.5. As the rigid plate width is increased to Lp/Dr=0.75, one additional transmission loss peak at approximately 400 Hz is produced. The generation of the 12 dB transmission loss peak at 400 Hz is shown to attribute to the sound and structure interaction. Finally, varying the neck shape from the conventional one to an arc one leads to the dominant resonant frequency being increased by approximately 20% and so the secondary transmission loss peak by 2-5 dB. The present work proposes and systematically studies an improved design of a Helmholtz resonator with an additional transmission loss peak at a high frequency, besides the dominant peak at a low frequency.

SOUND GENERATION BY ONE-CELL AND TWO-CELL VORTICES IN A NONUNIFORM FLOW

2006 ◽  
Vol 14 (03) ◽  
pp. 321-337 ◽  
Author(s):  
TING-HUI ZHENG ◽  
GEORGIOS H. VATISTAS ◽  
ALEX POVITSKY
Keyword(s):  
Mach Number ◽  
Acoustic Wave ◽  
Boundary Conditions ◽  
Radial Velocity ◽  
Acoustic Pressure ◽  
Tangential Velocity ◽  
Maximum Amplitude ◽  
Vortical Flow ◽  
Sound Generation ◽  
Mean Flow

Sound generation by vortical disturbance in a subsonic flow around a cylinder is investigated, using different vortex formulations, by solving both linearized and nonlinear Euler equations numerically. Numerical errors associated with the finite-difference discretization and boundary conditions are kept small using the high-order-accurate spatial differentiation and time marching schemes along with accurate nonreflecting boundary conditions and the sponge layer. If the radial velocity in vortex is assumed equal to zero, the intensity and directivity of acoustic wave patterns appear to be quite similar for all vortex models. If the radial velocity is taken into consideration, for single-cell vortex, there is no noticeable change happening to the acoustic wave; for two-cell vortex, although the radial velocity is still much smaller than the tangential velocity, the former plays an important role in generation and propagation of nonsymmetrical sound waves. If only initial tangential velocity or only initial radial velocity of the two-cell vortical flow disturbance is considered, the generated sound level would increase with the Mach number of mean flow while the angular distribution of sound directivity remains the same. If the two-cell vortex with both velocity components is considered, the Mach number of the background flow would change not only the amplitude of the acoustic pressure but also the directivity of sound. As the Mach number increases, the maximum amplitude of acoustic pressure will be shifted to the upper half-plane.

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

2017 ◽  
Vol 10 (2) ◽  
pp. 131-153 ◽  
Author(s):  
Jingxuan Li ◽  
Dong Yang ◽  
Aimee S Morgans
Keyword(s):  
Mach Number ◽  
Temperature Gradient ◽  
Euler Equations ◽  
Heating Element ◽  
Mean Flow ◽  
One Dimensional ◽  
Mean Temperature ◽  
The Mean ◽  
Theoretical And Numerical Analysis ◽  
Flow Effects

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].

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