Showing papers on "Strouhal number published in 1977"

The role of shear-layer instability waves in jet exhaust noise

Abstract: Large-scale structures in the form of instability waves are an inherent part of a shearlayer mixing process. Such structures are shown to be present in an acoustically and aerodynamically well behaved jet even at high Mach numbers. They do not directly radiate significant acoustic power in a subsonic jet, but do govern the production of the turbulent fluctuations which radiate broad-band jet noise. Over the whole subsonic Mach number range, a significant increase in jet noise can be produced by exciting the shear layer with a fluctuating pressure at the nozzle of only 0·08 % of the jet dynamic head but with the correct Strouhal number. Such excitation by internal acoustic, aerodynamic or thermal fluctuations could explain the variability of jet noise measurements between different rigs and could also be responsible for some components of ‘excess’ noise.

Wall shear stress caused by small amplitude perturbations of turbulent boundary-layer flow: an experimental investigation

Abstract: The oscillation of the wall shear stress caused by imposing sound on a turbulent boundary-layer flow constitutes a boundary condition for the solution of the acoustic wave equation. The no-slip condition at the wall requires the excitation of a shear wave which is superimposed on the sound wave. The shear wave propagates into the turbulent medium. The wall impedance (shear stress/velocity) of streamwise polarized shear waves has been measured in two different ways, namely (a) by evaluating the phase velocity and the attenuation of a plane sound, wave which propagates in turbulent pipe flow, and (b) by evaluating the resonance frequency and the quality factor of a longitudinally vibrating glass pipe which carries turbulent flow. The results, which were obtained over a wide range of Strouhal numbers, exhibit very good agreement between the two measuring methods. The wall shear stress impedance is strongly affected by the turbulence. This indicates that the turbulent shear stress is modulated by the shear wave. At all measuring conditions, the propagation of the shear wave was confined essentially to the inner portion of the turbulent boundary layer. In principle, two different Strouhal numbers, based on inner and outer variables respectively, describe the dynamics of the Reynolds stress, even in the inner layer (Laufer & Badri Narayanan 1971). However, it turns out that the outer Strouhal number (based on the diameter and the centre-line velocity) has no noticeable effect on the wall shear stress impedance. The dependence of the impedance on the inner Strouhal number (based on the friction velocity and the viscosity) reveals that the shear wave is strongly reflected at the edge of the viscous sublayer. It is concluded that the stress-to-strain ratio at the edge of the viscous sublayer corresponds either to a viscoelastic medium or even to a medium with negative viscosity.

Reynolds Number Dependence in Supersonic Jet Noise

Abstract: An experimental study of the noise production by high speed jets over a wide range of Reynolds numbers has been performed. Two jets of nominal Mach numbers 1.5 and 2.3 were run over a Reynolds number range from 5300 to 107,000. Microphone measurements of the radiated noise and hot-wire measurements of the flow fluctuations demonstrate that at low Reynolds numbers coherent flow instabilities produce a dominant portion of the noise. In the nominal Mach number 2.3 jet these instability waves convect downstream supersonically with respect to the ambient air. In the nominal Mach number 1.5 jet the instabilities convect downstream subsonically. In both cases however, sound pressure level amplitude contours show that the low Reynolds number jets radiate noise comparable to intermediate and high Reynolds number jets. These measurements constitute substantial evidence that a flow instability model of the dominant noise generators may be appropriate for conventional high Reynolds number supersonic jets. a0 C D d M m n r Re St u U Nomenclature speed of sound outside jet wavespeed in the downstream direction diameter of the jet effective diameter of the jet Mach number of the jet at the exit normalized mass velocity fluctuations = azimuthal mode number = radial distance from jet centerline = Reynolds number = p Ud/n. = Strouhal number =fd/ (/(/is frequency) = local velocity =mean centerline velocity of the jet at the nozzle exit

Fluid mechanics of the edgetone

Abstract: A model is proposed to explain the means by which an edgetone transforms the energy of a fully developed plane jet into energy which is radiated as sound. The edgetone configuration considered consists of a flat plate located in the medial plane of a fully developed two‐dimensional jet. The flow is modeled as follows. A periodic disturbance at the jet origin leads to the formation of an asymmetric vortex street which propagates downstream with a fixed convection velocity and wavelength. The vortex strength, convection velocity, and wavelength are determined as functions of the Strouhal number by applying conservation laws and kinematic relationships. A potential flow analysis of the interaction of the vortices with the edge is used to estimate the nearfield oscillating flow at the jet exit which, in turn, is used to calculate the phase of the feedback mechanism. The phase then determines the operating frequency as a function of jet velocity and edge stand‐off distance. It is shown that the proposed model is capable of predicting the major observed features of edgetone operation. The frequency predictions of the theory are compared with experiments for a wide range of jet parameters in both air and water. The comparison indicates that the frequency predictions are as good or better than previous empirical or semiempirical formulas.

The Scattering of Sound by a Simple Shear Layer

Abstract: A fixed line source, oscillating harmonically in time, produces sound waves which fall on a two dimensional shear layer in which the velocity increases linearly over a finite distance and then remains constant. The linearized theory of sound allows a multiplicity of solutions. The ambiguity is resolved by an application of the principle of causality. As a result it is found that, for Strouhal numbers below a certain critical level, Helmholtz instability is evident but not if the Strouhal number is above critical. The instability wave fans out from a negligibly small region as the Strouhal number drops from critical until it occupies a wedge of 45 degrees when the layer simplifies to a vortex sheet. The limit is the same as that derived by direct analysis of the vortex sheet but no ultra-distributions are necessary if the layer is not infinitesimally thin. Various other aspects of thin and thick layers are also discussed.

MHD Oscillatory Flow past a Semi-Infinite Plate

Abstract: Theme L IGHTHILL studied effects of small amplitude oscillations and Lin studied effects of finite amplitude oscillations on the boundary-layer flow. Lighthill's results were experimentally confirmed by Hill and Stenning. They assumed the freestream to consist of a constant mean velocity over which is superimposed a purely time-dependent oscillatory flow. Kestin et al. and Patel studied the effects of oscillatory progressive wave type of freestream on the boundary-layer flow. In the energy equation, the viscous dissipation effects were neglected by Kestin et al. So taking into account viscous dissipative heat, Kestin's problem was solved again by Takhar and Soundalgekar. We now consider the effects of a transverse magnetic field on the flow past a semi-infinite plate, taking into account the progressive wave type of disturbance in the freestream. By assuming the disturbance in the form (/oo(0 =U0(1 + te), a similar problem was solved by Evans. Evans solved it by assuming a series in powers of two parameters s(wx/w0), the Strouhal number, and \(oByx/pU0 = Ha//Re), the magnetic field parameter. We have solved the problem by assuming a series in powers of Vs only and x > 1 • The induced magnetic field is assumed to be negligible (Cowling) which is true when magnetic Reynolds numer is small.

An inviscid numerical simulation of vortex shedding from an inclined flat plate in shear flow

Abstract: Two-dimensional vortex shedding behind an inclined flat plate in uniform shear flow is numerically investigated by means of an inviscid discrete-vortex approximation. The points of appearance of the vortices are fixed in the plane of the plate at a short distance downstream of the edges of the plate. The strengths of the vortices are determined from the Kutta condition. On the assumption that the steadily periodic flow patterns are independent of initial conditions, the numerical calculations are performed for an inclined flat plate immersed in an incompressible fluid which is set in motion impulsively from rest with the velocity profile of uniform shear flow. The results of analysis show that the Strouhal number of vortex shedding and the time-averaged values of other hydrodynamic characteristics of the flow such as the outer-edge velocity of the separated shear layers, the convective velocity of the shear layers and the drag force exerted on the plate vary closely linearly with the shear parameter of the approaching shear flow. A linear relation between the Strouhal number and the shear parameter is confirmed by an air-tunnel experiment. The effects of the shear parameter on the calculated vortex patterns in the wake are also presented.

Nonsteady supersonic flow over spiked bodies

Abstract: In longitudinal supersonic flow over spiked cylinders nonsteady regimes can occur in which a separation zone is periodically generated at the spike, grows vigorously in size, and then vanishes. Several authors [1–6] have investigated the physical pattern of flow with separation zone fluctuations (using shadowgraphs) and have determined the boundaries of existence of the nonsteady regime as a function of the ratio between the spike length and diameter of the cylinder. The authors, however, did not systematically study the dependence of the pulsation frequency on the freestream Mach and Reynolds numbers or on the relative diameter and tip angle of the spike. We have undertaken such an investigation. We are concerned primarily with the influence of the dimensionless parameters on the Strouhal number Sh of the separation zone pulsations at a spike attached to the front of a flat-ended cylinder. Earlier investigations [4–6] have been carried out using motion pictures with film speeds up to 32·103 frames/sec. In the present study we used high-speed motion pictures with a speed of 6.25· 105 frames/sec. This speed allowed us to determine the precise sequence of phases of the pulsations and their relative durations, as well as the speed at which the boundaries of the separation zone move.

Constrained Flow Past Cavitating Bluff Bodies

Abstract: An experimental program has been carried out to determine the effects of wall interference on the drag and vortex shedding characteristics of cavitating two-dimensional triangular prisms and circular cylinders. The former shapes were chosen to eliminate effects of Reynolds number in interpreting the results. Direct pressure measurements were made to estimate the drag force. The vortex shedding frequency of the cavitating bodies was recorded with the help of a pressure transducer. The gap velocity u1 and the jet contraction velocity uj are shown to be the proper velocity scales to form the drag coefficients and Strouhal numbers for the bluff shapes tested. The drag coefficient was found to increase due to wall interference effects when partial cavitation conditions prevailed. The trend of the drag coefficient data indicated that wall interference effects are relatively small at very low cavitation numbers (σ → σch ) which correspond to choking conditions. As choking conditions are reached, the vortex shedding from the cavitating source becomes intermittent and finally vortex shedding ceases.

Modelling techniques for jet impingement

Abstract: A technique for testing scale models for the determination of fluctuating pressure loads due to jet impingement has been investigated using a quarter-scale model of a boilerplate test facility in which a JT-15D engine with a rectangular outer nozzle blows over a small curved airfoil representing the upper-surface of a wing When model and full-scale spectra of fluctuating surface pressures are reduced to plots of pressure coefficient power-spectral density vs Strouhal number, moderate agreement is obtained, but a shift of spectral peaks is noted However, when a correction for the ratio of average jet to ambient temperature is applied, the spectral peaks agree

A far field analysis of the propagation of sound waves from various point sources through a linear shear layer

Abstract: 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in "sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again beginning below the first row and continuing on until complete.

Effects of geometry and jet velocity on noise associated with an upper-surface-blowing model

Abstract: The noise characteristics associated with various upper surface blowing configurations were investigated using a small model consisting of a plate and flap assembly (simulated wing with flap) attached to a rectangular nozzle. Nozzle aspect ratio, flow-run length, and flap-deflection angle were the experimental parameters studied. Three nozzle-exit velocities were used. The normalized noise spectra obtained for different nozzle aspect ratios proved to be similar in terms of Strouhal number based on jet velocity and flow-run length. Consequently, the need for knowing local flow velocity and length scales (for example, at the flap trailing edge) as required in some of the existing noise prediction schemes is eliminated. Data are compared with results computed from three different noise prediction schemes, and the validity of each scheme is assessed. A simple method is proposed to evaluate the frequency dependence of acoustic shielding obtained with the simulated wing flap.

Noise reduction evaluation of grids in a supersonic air stream with application to Space Shuttle

Abstract: Near field acoustic measurements were obtained for a model supersonic air jet perturbed by a screen. Noise reduction potential in the vicinity of the space shuttle vehicle during ground launch when the rocket exhaust flow is perturbed by a grid was determined. Both 10 and 12 mesh screens were utilized for this experiment, and each exhibited a noise reduction only at very low frequencies in the near field forward arc. A power spectrum analysis revealed that a modest reduction of from 3 to 5 decibels exists below a Strouhal number S sub t = 0.11. Above S sub t = 0.11 screen harmonics increased the observed sound pressure level. The favorable noise reductions obtained with screens for S sub t 0.11 may be of substantial interest for the space shuttle at ground launch.

Determination of strouhal characteristics and power spectrum for elastically restrained h-shape sections

Abstract: This document provides results of experimental investigation of Strouhal numbers and power spectral density of H-shaped members. The aspect ratios of the cross-sections of the members examined were approximately 1:1, 3:4 and 1:2, respectively. The specimens were sharp-cornered and mounted on adjustable springs at the ends. The tests were conducted in a wind tunnel having minimum upstream turbulence. The Reynolds number ranged from 1 x 10 to the 5th power to 1.7 x 10 to the 6th power. The results showed that the Strouhal number was 0.12 for sections having a high aspect ratio, but indicated a markedly decreasing trend for those having lower aspect ratios. The power spectra had narrow-bands indicating that subcritical flow prevailed during the tests. There was no evidence of a transition zone which would indicate a random shedding regime. This document is the second in a series of reports discussing the structural dynamics of long slender members of contemporary cross-section shapes. The first report entitled: "Response of Bridge Structural Members Under Wind-Induced Excitation" presents a state-of-the-art discussion and an extensive bibliography of this subject area. /FHWA/

Acoustic conditions in the vicinity of an orifice that depends on grazing flow boundary layers. An experimental investigation

Abstract: The reflection factor at a tube which ends at a plate over which a flow is forming was determined as a function of the Strouhal number, formed from the flow velocity, the aperture radius, and the acoustic frequency. Several adjacent openings were investigated to determine the interactions between several openings.