Showing papers on "Strouhal number published in 1974"

Vortex shedding from spheres

Abstract: Vortex shedding from spheres has been studied in the Reynolds number range 400 < Re < 5 × 106. At low Reynolds numbers, i.e. up to Re = 3 × 103, the values of the Strouhal number as a function of Reynolds number measured by Moller (1938) have been confirmed using water flow. The lower critical Reynolds number, first reported by Cometta (1957), was found to be Re = 6 × 103. Here a discontinuity in the relationship between the Strouhal and Reynolds numbers is obvious. From Re = 6 × 103 to Re = 3 × 105 strong periodic fluctuations in the wake flow were observed. Beyond the upper critical Reynolds number (Re = 3.7 × 105) periodic vortex shedding could not be detected by the present measurement techniques.The hot-wire measurements indicate that the signals recorded simultaneously at different positions on the 75° circle (normal to the flow) show a phase shift. Thus it appears that the vortex separation point rotates around the sphere. An attempt is made to interpret this experimental evidence.

The effects of surface roughness and tunnel blockage on the flow past spheres

Abstract: The effect of surface roughness on the flow past spheres has been investigated over the Reynolds number range 5 × 104 < Re < 6 × 106. The drag coefficient has been determined as a function of the Reynolds number for five surface roughnesses. With increasing roughness parameter the critical Reynolds number decreases. At the same time the transcritical drag coefficient rises, having a maximum value of 0·4.The vortex shedding frequency has been measured under subcritical flow conditions. It was found that the Strouhal number for each of the various roughness conditions was equal to its value for a smooth sphere. Beyond the critical Reynolds number no prevailing shedding frequency could be detected by the measurement techniques employed.The drag coefficient of a sphere under the blockage conditions 0·5 < ds/dt < 0·92 has been determined over the Reynolds number range 3 × 104 < Re < 2 × 106. Increasing blockage causes an increase in both the drag coefficient and the critical Reynolds number. The characteristic quantities were referred to the flow conditions in the smallest cross-section between sphere and tube. In addition the effect of the turbulence level on the flow past a sphere under various blockage conditions was studied.

The vortex-street wakes of vibrating cylinders

Abstract: The strength (initial circulation) and spacing of vortices in the wake of a circular cylinder have been obtained for conditions under which the body undergoes lateral vibrations. The vibrations of the cylinder were at all times synchronized with those in the wake, thereby suppressing the natural Strouhal frequency in favour of a common synchronized or ‘locked-in’ frequency for the body-wake system. All experiments were performed at a Reynolds number of 144 or 190. An inverse relation between the initial circulation K and the length lF of the vortex formation region was obtained for cylinder oscillations of up to 50% of a diameter, at vibration frequencies both above and below the Strouhal shedding frequency. The initial circulation K of the vortices was increased by as much as 65%, at lF = 1·6 diameters, from the stationary-cylinder value of K corresponding to lF = 3·2d. An increase in the rate A of vorticity generation of 80% from the stationary-cylinder wake value was obtained with the cylinder vibrating at 30% of a diameter and 110% of the Strouhal frequency. Both flow-visualization and hot-wire results show that the lateral spacing of the vortex street decreases as the vibration amplitude of the cylinder is increased, but that the longitudinal vortex spacing is independent of changes in amplitude. The longitudinal spacing, however, varies inversely with the vibration frequency. The street approaches a single line of vortices of alternating sign as the amplitude of vibration approaches values near a full cylinder diameter, and secondary vortex formation at these large amplitudes is associated with the vanishing lateral spacing of the street. Observation of the wake has elucidated the mechanism of vortex formation; the entrainment processes in the formation region have been observed at small intervals over a cycle of the cylinder's motion.

Spatial waves in turbulent jets

Abstract: Measurements of the spatial development of disturbance pressure waves in a low‐speed axisymmetric turbulent free jet have been carried out. The results show that the wavenumbers of the pressure waves increase monotonically, while the phase velocities decrease as the Strouhal number of the jet increases. The pressure disturbance grows to a maximum at some distance downstream from the nozzle and then decays. The distributions of the amplitude of the pressure waves along the jet are similar if the data are plotted against a normalized distance St x/D. The most amplified mode is at a Strouhal number of 0.5 for the shear layer and 0.35 for the center line. The wave characteristics follow closely the linear stability theory of an inviscid diverged shear flow.

Angular motions of freely falling spheroidal hailstone models

Abstract: The free fall behavior of rotating oblate spheroids with Reynolds numbers of 4 × 104 to 4 × 105 is studied by solving semiempirical Eulerian equations of motion which use a quasistatic approximation for aerodynamic forces and torques. The angular motions are classified in terms of solutions to the restricted set of equations in which the center of mass falls uniformly. One class of solutions, named symmetric gyration, is relevant for studies of the symmetric growth of hailstones because symmetrically equivalent points on the surface of a spheroid are equally exposed to the flow. For large hailstones with horizontal total angular momentum, critical frequencies sufficient for symmetric gyration are in the range of 2‐6 Hz (Strouhal numbers 0.005 to 0.01), they increase with increasing axis ratio, decrease with size, and are independent of the density ratio spheroid/air. Solutions to the full equations of motion show that the rotational energy of a symmetrically gyrating spheroid increases with time. This results in an increase in nutational amplitude which depends on the spheroid, its spin rate and its nutation amplitude. Such an effect occurs because the horizontal velocity, which tends to align with the horizontal major axis, causes the aerodynamic torque to have an oscillating vertical component in phase with the oscillating angular velocity about the vertical. A similar interaction prevents a steady helical motion.

Experimental Study of Structure of Gas Flow in Tube Banks with Tube Axes Normal to Flow Part II ; On the Structure of Gas Flow in Single-Column, Single-Row, and Double-Rows Tube Banks

Abstract: This second report describes the experimental results about the gas flow between tubes arranged in single column, single row, and double rows. The word "column" indicates a line of tubes in the direction of the gas flow, and "row" indicates a line of tubes perpendicular to the direction of the gas flow. Visual observations disclose that the vortex formation region and the Coanda effect have dominant effects on the structure of the gas flow in the three types of tube banks. The variation of the Strouhal number with the tube spacing is strongly dependent on the size of the vortex formation region. The gap flow between adjacent tubes normal to the flow behaves as a two-dimensional jet. It was found that in some tube spacings, the jets coalesced with each other due to the Coanda effect, and in an extreme case, non-uniformity was observed in the bulk flow.

Thin film gauges for fluctuating velocity measurements in blood

Abstract: The frequency response has been determined for two probe designs used for cardiovascular measurements: one conical, the other cylindrical. The frequency range was 1-1000 Hz using an oscillatory velocity component superimposed on a mean flow; the test fluid was water. The amplitude response to the fluctuating component was found to depend on the Strouhal number (a normalized frequency) and was almost independent of the amplitude of oscillation. At small Strouhal numbers the behaviour is quasi-steady; at higher values the sensitivity progressively diminishes, but for the cylindrical probe there is an intermediate region of increased sensitivity. The oscillatory component had no effect upon the conical probe sensitivity to the mean velocity, whereas the cylindrical probe showed an increasing apparent mean velocity for some conditions. Fluctuating velocity values were inferred from steady flow calibration data and, therefore, a detailed comparison was made between such calibrations in blood and water.

The Orbital Movement and the Damping of the Fluidelastic Vibration of Tube Banks Due to Vortex Formation: Part 3—Damping Capability of the Tube Bank Against Vortex-Excited Sonic Vibration in the Fluid Column

Abstract: The damping criterion previously proposed by Chen 1964/1968 is evaluated with respect to a series of existing units using various fuels. The critical value of this criterion, which was given by Chen as 600 for the ideal case with uniform velocity distribution, has been found to be about 2000 for the tube bank heat exchangers in boiler units. The reason for this difference appears to lie in the degree of uniformity of the velocity distribution over the streaming section. Since the velocity distribution in the boiler units cannot be uniform at all, the vortex streets formed in the tube bank will disturb each other. A large damping will thus arise. The damping criterion can thus be employed to design a sonic vibration-free tube bank through proper consideration of tube spacings, Reynolds number, and Strouhal number.

Aerodynamic torques on rotating oblate spheroids

Abstract: Aerodynamic torques about the vertical major axis of each of three rotating oblate spheroids (axis ratios 0.50, 0.67, and 0.79) with smooth surfaces were measured in a horizontal wind tunnel as a function of Reynolds number (4 × 104 < Re < 3 × 105) and rotation rate. Rotations were either about the vertical axis or the minor axis which was held inclined to the mean air flow at several fixed angles. Spin about a minor axis only shifted critical Reynolds numbers to lower values. Spin rates corresponding to Strouhal numbers less than 0.1 at Reynolds numbers less than 1.5 × 105 had no effect on the aerodynamic restoring torque. Each of the three spheroids autorotated at frequencies with Strouhal numbers of approximately 0.15. For rotations at Strouhal numbers less than 0.04, the average nonconservative torque was less than 10% of the maximum static torque. Hence, these experiments establish the range of applicability of a quasistatic approximation for the aerodynamic torques on smooth oblate spheroids. They a...

Heat transfer to a resonant pulsating air stream in a pipe

Abstract: The effect on convective heat transfer of resonant, longitudinal oscillations superimposed on a turbulent mean flow in a pipe has been investigated relative to the equivalent steady flow. Theoretically it is shown that the effect of acoustic streaming velocities is negligible for the range of pulsation parameters, but that the oscillating velocity can generate changes in the time-mean flow diffusivity - the change in mean diffusivity can only be predicted if quasi-steady pulsations are assumed. Heat transfer coefficients for the mean flow are evaluated from the Energy equation, for fully established conditions, assuming quasi-steady oscillations. It is proposed that a frequency factor can be derived to relate experimental heat transfer to the quasi-steady predictions, and that the factor would be a function of Strouhal number only. Local heat transfer coefficients were measured for a constant heat flux supply to an oscillating air flow in a pipe. The pulsations were generated by a siren. It was shown that the centre-line velocity amplitudes could be predicted from inviscid flow theory using a mean velocity of sound. The range of the major parameters was: Diraensionless pulsation velocity 0.3 < B < 5 Strouhal number 0.5 < S < 10 Reynolds number 14,300 < Red < 31,250. For fully developed flow, the experimental results were related to the corresponding quasi-steady predictions by a function of Strouhal number. It was shown that the changes in heat transfer were due to changes in the mean diffusivity generated by the acoustic velocity. For a defined range of pulsation parameters, it is possible to predict local heat transfer coefficients under fully established conditions for a pulsating flow from the empirical frequency correction factor applied to the theoretical quasi-steady predictions.

Comment on "The Lift Force Due to von Karman's Vortex Wake"

Abstract: where S is the Strouhal number, I the longitudinal vortex spacing, d the width of the body, and CD the drag coefficient. The Strouhal number, as calculated from Eq. (46), is plotted in Fig. 1 together with experimental values collected from Refs. 2 and 3, as function of the wedge angle. It can be seen that the agreement between theory and experiment is very good. It may be pointed out that in the work by Page and Jo-

On a Test of the Resonance Hypothesis

Abstract: This note presents results of an experimental test of van der Hegge Zijnen’s resonance hypothesis. Near wake turbulence spectra obtained over a range of stream turbulence intensities and integral scales revealed no preferential amplification of turbulent fluctuations at or near the Strouhal frequency thus invalidating predictions of the resonance hypothesis.

Variation of aerodynamic damping of vibrations of a plane grid of compressor-blade models, with angle of attack

Abstract: This art icle examines some resul ts of an experimental study of the a i r -damping of the vibrations of compres so r blades set at var ious angles of attack. In order to verify the assumed variation of the a i r damping effect with the Strouhal Number and the l inear model scale, the investigation was ca r r i ed out using wide and independent variat ions of the flow velocity, vibration frequency, the chord, and other dimensions of the profile.

The transverse distribution of velocity in estuary flow

Abstract: Homogeneous estuary flows and tidal models of estuaries are known to exhibit a phase shift effect. The velocity versus time curves from various positions in the transverse, z, direction (perpendicular to the long axis) may be shifted relative to one another by times of as much as 1 hour. An explanation of this phase shift is presented in terms of the magnitude of the relevant forces. A Strouhal number, proportional to fu 0 T/d, where f is the friction factor, u 0 is the longitudinal velocity, T is the tidal period and d is the depth of flow, is shown to be important in describing the amount of phase shift. Two situations which result in horizontal phase differences are analysed, and laboratory measurements of both cases are presented. In one case the phase difference results from a slow variation of depth with position z, and in the second case the phase shift results from the influence of very large sidewall roughness in a deep channel.