The flow field behind spinning baseballs at two different seam orientations was investigated, and compared with a smooth sphere, to isolate effects of seams on the Magnus effect at Reynolds numbers of 5×104 and 1×105. The rotational speed of the three spheres varied from 0-2400 rpm, which are typical of spin rates imparted to a thrown baseball. These spin rates are represented non-dimensionally as a relative spin rate relating the surface tangential velocity to the freestream velocity, and varied between 0-0.94. Mean velocity profiles, streamline patterns, and power spectral density of the velocity signals were taken using hot-wire anemometry and/or stereoscopic particle image velocimetry in the wake region. The sphere wake orientation changed over a range of relative spin rates, indicating an inverse Magnus effect. Vortex shedding at a Strouhal number of 0.25 was present on the sphere at low relative spin rates. However, the seams on the baseball prevented any consequential change in wake orientation and, at most spin rates, suppressed the shedding frequency exhibited by the sphere. Instead, frequencies corresponding to the seam rotation rates were observed in the wake flow. It was concluded that the so-called inverse Magnus effect recorded by previous investigators at specific combinations of Reynolds number and relative spin rate on a sphere exists for a smooth sphere or an axisymmetrically dimpled sphere but not for a baseball near critical Reynolds numbers, where the wake flow pattern is strongly influenced by the raised seams.
The flowfield of a coaxial counter-rotating rotor in hover was measured using particle image velocimetry. The goal of the measurements was to investigate the flow features of coaxial rotors, including interaction between the rotors, and to measure inflow over the rotor radius and azimuth. The phase-resolved measurements were performed at several azimuthal index angles behind the rotor blades, with 500 instantaneous flow realizations per azimuth. Axial velocity profiles extracted from the phase-averaged flowfields exhibited the effect of bound circulation associated with blade passage, the trailed vortex sheet, and the effect of the blade tip vortex. Tip vortex characteristics were extracted from the measurements and were shown to compare well with semi-empirical models in most cases. The measured inflow was captured well by blade element momentum theory when the mutually induced velocities were accounted for. The lower rotor was found to behave more like an isolated single rotor, whereas tip vortices from the upper rotor convected faster radially inward and downstream than the lower rotor tip vortices. Upper and lower rotor tip vortices exhibited similar core radii ranging from 12 to 18% of the rotor blade chord, and they grew at a similar rate. However, this vortex growth rate was different from that of an isolated single rotor.
An experimental investigation into the flow field behind baseballs at two different seam orientations as well as a smooth sphere of the same diameter was undertaken at Reynolds numbers of 5 × 104 and 1 × 105. The rotational speed of the three spheres varied from 0 to 2400 rpm, with data collected in increments of 400 rpm which correspond to relative spin rates between 0 and 0.94. Mean velocity profiles, turbulence in intensity profiles, and power spectral density of the signals were taken using hot-wire anemometry. The smooth sphere wake was seen to change in orientation over a range of relative rotational speeds. The Strouhal number remained constant around 0.24 for relatively low spin rates. The seams on the baseball suppressed any measurable vortex shedding once rotation began, also eliminating any significant change in wake orientation as evidenced by the mean velocity deficit and turbulence intensity profiles. It was concluded that the so-called inverse Magnus effect recorded by previous investigators at a specific Reynolds number / relative rotational speed of a sphere exists only for a smooth sphere and not for a sphere where the boundary layer separation is governed by raised seams.
A hovering two-bladed, 2-m-diameter rigid rotor was used to investigate the effects of dynamic pitch inputs at multiple blade loading coefficients. Unsteady rotor loads and the flow field were measured using an internal load cell and time-resolved particle image velocimetry, allowing for inflow, tip vortex trajectories and strength to be measured. Two sets of measurements were performed with an image acquisition rate of 44/rev: constant pitch angle (CT/σ = 0.06, 0.08, 0.10), and measurements with dynamic pitch ramp inputs (Δθ0 = 1° amplitude change over four rotor revolutions) at CT/σ = 0.06 and 0.08. The measurements at constant pitch angle and with dynamic pitch inputs were performed over 670 rotor revolutions, in both cases yielding statistically converged averages. In addition, the experiment was simulated using a finite-volume CFD solver. The results were correlated to the experimental data to assess the accuracy of the flow simulations and to gain further insight into the flow phenomenology. Vortex trajectories and axial velocities (inflow and wake) correlated well, and the tip vortex strength was slightly underpredicted by the CFD. From measurements and predictions, it was found that (independent of the thrust setting) the axial velocity in the rotor plane steadily increased to the value after the pitch input. Furthermore, vortex trajectories were little affected by the increased thrust and inflow. The vortex strength revealed trends similar to the axial velocity and gradually increased to the values after the pitch ramp input.
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