Showing papers on "Strouhal number published in 1971"

Orderly Structure in Jet Turbulence

Abstract: Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

The spacing, position and strength of vortices in the wake of slender cylindrical bodies at large incidence

Abstract: Extensive schlieren studies and yawmeter traverses of the wake behind slender cone-cylinders at large angles of incidence have shown that the flow pattern is generally steady. Under certain flow conditions, however, the wake exhibits an instability which is not understood. For cross-flow Reynolds numbers in the subcritical region the wake can be described in terms of a cross-flow Strouhal number which has a constant value of 0·2 for cross-flow Mach number components (Mc) up to 0·7 and then increases steadily to a value of 0·6 at Mc = 1·6. The strength of the wake vortices varies substantially with Mc, increasing to a maximum at Mc ≈ 0·7 and then decreasing rapidly for higher values of Mc. Schlieren photographs of the wake have been analysed by means of the impulse flow analogy and also by considering the vortices to be part of a yawed infinite vortex street. The impulse flow analogy is shown to be of use in determining the cross-flow Strouhal number but estimates of vortex strength are too high. The Karman vortex street theory combined with the sweepback principle leads to reliable estimates of vortex strength up to Mc = 1·0.Information is given on the spacing, path and strength of the vortices shed from the body for flow conditions varying from incompressible speeds up to Mc = 1·0. Finally this information is used to determine the vortex drag of a two-dimensional circular cylinder below Mc = 1·0.

Vortex shedding from circular cylinders at low Reynolds numbers

Abstract: Experiments on slightly tapered models of circular cross-section have shown that the vortex wake structure exists in a number of discrete cells having different shedding frequencies. Within each cell shedding is regular and periodic, the frequency being somewhat lower than that from a parallel cylinder of the same diameter. A similar type of wake behaviour has also been observed on a parallel model in a non-uniform mean flow. These results suggest that the discontinuities in the shedding law observed by Tritton could arise through non-uniformities in the flow.

The near field within the potential cone of subsonic cold jets

Abstract: This investigation describes a detailed study of the near pressure field within the potential cone of a subsonic circular turbulent jet.The components of the near pressure field in the potential cone in which the potential flow condition exists within the fist four and a half diameter downstream appear to be moving with a phase velocity equal to the local speed of sound. The direction of propagation is roughly normal to the shear layer surrounding the cone. Some components of the hot-wire signal can be associated with the jet structure as a simple complex source, while others are related to the local characteristics of turbulence. Differences in the characteristics of the pressure field within the potential cone exist between the vortex generated noise at very low jet velocity and the eddy generated noise at higher velocity.The power spectra obtained in the potential cone show the peak which is due to the pressure fluctuations and the flat portion due to the turbulence. The frequencies of the dominant components, in terms of the Strouhal number, are functions of both the axial and radial positions.Microphone measurements were made in the near field outside for detailed comparison with the potential cone results.

Vortex shedding from a turbulent jet in a cross-wind

Abstract: Measurements in the wake behind turbulent jets exhausting from a solid surface into a cross-wind indicate that vortex shedding occurs as in the case of flow past solid bluff bodies. The Strouhal numbers for flow past a circular and a blunt jet are in qualitative agreement with those for corresponding solid bodies, provided that the width of the spreading jet some distance from the surface is used rather than the jet exit plane dimension.

Experimental Stability Studies in Wakes of Two-Dimensional Slender Bodies at Hypersonic Speeds

Abstract: Experimental stability studies were conducted in the transition region from laminar to turbulent flow in wakes of slender wedges and a flat plate at Mach number 6. As in low-speed flat plate wakes, transition from laminar to turbulent flow may be divided into a linear and a nonlinear instability region. Inviscid linear stability theory predicts well the growth of fluctuations and amplitude distribution in the linear region. In the nonlinear region similarities with low-speed wakes exist. Characteristic persisting peaks in the power spectra are observed. Based on these peak frequencies a nearly universal Strouhal number of fb_0/u∞ = 0.3 was found for both incompressible and hypersonic wake flows. A theoretical approach to predict the development of mean flow and flow fluctuations in the nonlinear region as employed by Ko, Kubota, and Lees in slender body low-speed wakes appears equally applicable for hypersonic wakes.

Comparison of theory and experiment for ion collection by spherical and cylindrical probes in a collisional plasma

Abstract: Roshko for vortex shedding in steady flow. Our data points in general are lower than the Roshko curve, however, they do show a definite correlation between the instantaneous Strouhal and Reynolds numbers. These results suggest the following conclusions: 1) In an oscillatory freestream of 3 Hz and Reynolds number up to 4 X 10, the vortex shedding from a circular cylinder responds instantaneously to the freestream variations. 2) In the instantaneous Reynolds number range of 500 to 4 X 10, the instantaneous Strouhal number stays sensibly constant at 0.20, ±0.01. 3) With a limited set of data points in the instantaneous Reynolds number range of 3 to 8 X 10, the results show no systematic variation when the frequency is increased from 3 to 6 Hz.

On the Vibration of Cylinders Caused by Karman Vortex

Abstract: As bridges becomes larger in size, the members become slenderer and a severe vibration sometimes occurs in the cylinder members because of a Karman vortex caused by gentle winds. A lot of studies have already been conducted on this phenomenon, but there are still many unknown factors left about the behaviors of cylinders, qualititatively and quantitatively. In this study we carried out a few wind tunnel tests in the subcritical range and investigated the vibrating characteristics of the cylinder and the aerodynamic force working on the vibrating cylinder. The following facts were made clear. (1) The vibration of cylinders caused by Karman vortex is self-excited and the range of self-excited vibration is effected by the damping factor of the system. (2) Strouhal's number at the resonant condition reduces to 0.17 as vibrating amplitude increases. (3) Life coefficient at the resonant condition is effected by vibrating amplitude. In the case of the large amplitude, it can be arranged from the view-point of the forced vibration to some extent.

Propeller Noise at Low Tip Speeds

Abstract: : The study comprises an analytical and experimental investigation of the vortex noise generated by low-tip speed propellers. intially, the treatment of the subject is focussed on an examination of the origins of broadband noise and the methods by which these can be analytically represented. Subsequent noise measurements on simple-design propellers indicate how the typical spectra in the Strouhal frequency range are significantly influenced by an extensive range of high order harmonics of the blade passage frequency, and a treatment of this harmonic content is included in this study report. The broadband and harmonic components of noise data, obtained from propellers with blade number and blade angle variations, have been analyzed in detail and noise prediction methods have been derived for each. It is postulated that the noise source mechanisms may be associated with unstable laminar flow separation (or transition) at the blade surfaces. The report also includes a set of graphical procedures by which both harmonic and random spectral details of the radiated noise can be calculated by tip Mach numbers in the range 0.2 to 0.6.

On the Vibration of Cylinders Caused by Karman Vortex

Abstract: As bridges becomes larger in size, the members become slenderer and a severe vibration sometimes occurs in the cylinder members because of a Karman vortex caused by gentle winds. A lot of studies have already been conducted on this phenomenon, but there are still many unknown factors left about the behaviors of cylinders, qualititatively and quantitatively. In this study we carried out a few wind tunnel tests in the subcritical range and investigated the vibrating characteristics of the cylinder and the aerodynamic force working on the vibrating cylinder. The following facts were made clear. (1) The vibration of cylinders caused by Karman vortex is self-excited and the range of self-excited vibration is effected by the damping factor of the system. (2) Strouhal's number at the resonant condition reduces to 0.17 as vibrating amplitude increases. (3) Life coefficient at the resonant condition is effected by vibrating amplitude. In the case of the large amplitude, it can be arranged from the view-point of the forced vibration to some extent.

The Behaviour of Orifice and Venturi-Nozzle Meters in Pulsating Flow.

Abstract: The conventional quasi-steady theory for the behaviour of meters in pulsating flow is that at any instant the differential pressure is only dependent on the acceleration of the flow due to the contraction and is given by the steady flow relationship. The analysis presented in this thesis is based on a quasi-steady theory modified to take into account the additional instantaneous differential pressure due to the temporal acceleration of the flow. Relationships are derived for metering errors in terms of the r.m.s. amplitude of the differential pressure pulsation and a Strouhal Number dependent on the waveform of the velocity pulsation. To test the validity of the derived theoretical relationships the behaviour of square edge orifice plates with corner tappings and of venturi nozzles were investigated in pulsating air flows. A piston pulsator was built on which the stroke can be varied to obtain a required pulsation amplitude while the machine is running at frequencies up to 50 Hz. The results of the tests showed that, although there were some discrepancies, the theoretical relationships were basically sound. It was found that it was possible to define when pulsations were significant in terms of the r.m.s. amplitude of the differential pressure fluctuation. It was also possible to determine an effective Strouhal Number when temporal inertia effects became significant. No basic differences in the behaviour of the two types of meter were detected but certain predictable effects due to compressibility were observed in tests on the venturi nozzles. The techniques for reducing metering errors due to pulsations are reviewed in the light of the analysis and experimental results. Criteria by which the pulsation conditions can be properly assessed and appropriate courses of action for reducing metering error are suggested.

Laminar flows past a flat plate at various angles of attack

Abstract: Numerical solutions are obtained by means of a stream function-vorticity formulation for laminar incompressible fluid flows past a flat plate at the angles of attack α = 0°, 45°, and 90° with Reynolds numbers Re = 30, 50, and 200. The cross-section of the plate is elliptic and the flow is assumed to be two-dimensional and time-dependent. Potential flow is selected as the initial condition. Asymptotic steady-state solutions have been obtained for the symmetric configurations α= 0° and 90°, whereas the 45°-inclined plate always caused vortex shedding, even for Re as low as 30. The development of a Karman vortex street for Re = 200, α= 45° is presented in detail.

Vortex Shedding Noise of an Isolated Airfoil.

Abstract: : The purpose of the study was to determine the vortex shedding noise characteristics of isolated airfoils in a Reynolds number range applicable to full-scale helicopter rotors. Measurements of far-field noise, airfoil surface pressure fluctuations, and correlation coefficients were obtained for three airfoils. Two models of differing thickness were tested as two-dimensional models (NACA 0012 and 0018 airfoils) and the third has a span of half the tunnel width (NACA 0012 airfoil). Airfoil vortex shedding noise was found to be discrete rather than broadband. The frequency dependence of this noise on velocity and chord was found to be well predicted by a constant Strouhal number near 0.2 referenced to laminar wake thickness at the airfoil trailing edge. The presence of a laminar boundary layer on the pressure surface of the airfoils was found to be critical to the presence of vortex shedding noise. (Author)

Analyses of Propeller Vortex Noise

Abstract: A detailed experimental program of noise measurements was conducted on a low‐speed 4‐ft diam propeller with variations in blade number, tip shape, tip speed, and blade angle. Narrow‐band analyses of the noise data indicated blade passage harmonics of up to the 60‐mB order are present and dominate the frequency regime usually associated with broad‐band “vortex” noise. Additionally, a high‐frequency component, in the region of seven times the Strouhal frequency, is extremely apparent in the data. This component is sensitive to tip shape and tip angle of attack and in some cases dominates the over‐all sound‐pressure level near the propeller axis. A similar phenomenon has been previously observed in helicopter noise spectra, but neglected owing to its apparent insignificance relative to the rotational noise. An interpretation of these findings and semi‐empirical approaches to the prediction of their component levels are presented.

Jet Noise Contribution to Wind Noise in Vehicles

Abstract: A source of “wind noise” in a vehicle with a slightly opened window has been modeled as a slit jet issuing from a plenum (idealized vehicle). The nondimensional power spectra measured inside and outside were quite similar; the curves collapsed together well when plotted against Strouhal number fD/U (f=frequency, D=slit width, U=jet nozzle velocity). The higher frequency sources of the jet noise, being closer to the slit, subtend a larger angle and would be expected to transmit more noise into the plenum. This expectation was confirmed, with inward transmission increasing with both frequency and slit width; at 10 000 Hz and 1.5‐in. slit width (maxima for these experiments, with 80‐fps jet velocity) the jet noise power transmitted inward through the slit reached 68% of the power emitted externally in the 13‐oct band. These were exploratory tests, and there was no external wind. [Work supported by Air Force Office of Scientific Research.]

Theoretical predictions of supersonic jet noise

Abstract: Analytical predictions of supersonic jet noise, considering acoustic intensity, directivity, refraction, convection and peak Strouhal number

Intensification of heat and mass transport in a free jet with the aid of a mechanical turbulator

Abstract: In the development of published data on the dynamic problem (IAN SSSR, MZhG [Fluid Dynamics], no. 6, 1966) results are presented from experiments on the discharge of a nonisothermal jet, which characterize the possibility of intensification of the momentum, heat, and mass transfer in the free jet with the aid of a mechanical turbulator. The experiments were conducted with discharge into air of subsonic jets of slightly heated air (~30–35° C) and to a small extent of helium and burning propane-butane jets. We find from the experimental results that the intensity of the heat and mass transport, and momentum as well, increases markedly with operation of the turbulator. At the same time the possibility is confirmed of the generalization of the experimental results with the aid of the Strouhal number.