Analytic Continuation of weighted q-Genocchi numbers and polynomials

In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function {\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n | {\alpha}) is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted q-Genocchi polynomials.Comment: 5 pages, submitte

Free vorticity field-boundary layer conversions: Effect of boundary configuration and scale

Progress was made on further flow visualization of vortex-leading edge interaction, in conjunction with characterization of the unsteady pressure field. The range of scale of an elliptical leading edge, relative to the incident primary vortex, was determined. The scale of the incident vortex was characterized in terms of mean shear layer parameters. An overview of the interaction mechanism for the range of thin to thick leading-edges is given. The interaction mechanism corresponding to the case where the incident vortex is above the leading-edge is given for hydrogen bubble wires well upstream of and at the tip of the leading edge. A sample of the instantaneous pressure distribution for the case where the incident vortex dives beneath the edge is presented. The effect of scale of the incident vortex relative to that of the leading-edge was examined. The circulation and length scale of the incident vortices in the street are being characterized

Flow control of tip/edge vortices

Location, strength, and structure of tip and edge vortices shed from wings and bodies can be manipulated by using flow control techniques. Flow physics of these approaches involve flow separation from the edge, roll-up into the vortex, wing flow regime, vortex instabilities, vortex–vortex interactions, and vortex–turbulence interactions. Actuators include continuous and unsteady blowing as well as suction, bleed, and control surfaces, which add momentum, vorticity, and turbulence into the vortices. It is noted that actuation may have effects on more than one aspect of the flow phenomena. A comparative review of the control of delta-wing vortices, tip vortices, and afterbody vortices is presented. The delay of vortex breakdown and the promotion of flow reattachment require different considerations for slender and nonslender delta wings and may not be possible at all. Tip vortices can be controlled to increase the effective span, to generate rolling moment, to attenuate wing rock, and to attenuate vortex–wing interactions. Although there are different approaches for each application, opportunities for future research on turbulence ingestion, bleed, and excitation of vortex instabilities exist. Recent research also indicates that active and passive flow control can be used to manipulate the afterbody vortices to reduce the drag.</p

Lift Alleviation in Travelling Vortical Gusts

Lift alleviation by a mini-spoiler on airfoils, unswept and swept wings encountering an isolated counter-clockwise vortical gust was investigated by means of force and velocity measurements. The flow separation region behind the spoiler remains little affected during the gust encounter. The maximum lift reduction is found for the static stall angle of attack. The change in the maximum lift during the gust encounter is approximately equal to that in steady freestream. The comparison with plunging airfoils reveals that, for the same maximum gust and plunge velocity, the effectiveness of the mini-spoiler is much better in travelling gusts. This reveals the importance of the streamwise length scale of the incident gust. For the unswept wing, there is some three-dimensionality of the flow separation induced by the mini-spoiler near the wing-tip. The magnitude of the lift reduction can be estimated using the airfoil data and by making an aspect ratio correction for the reduced effective angle of attack. For the swept wing, the mini-spoiler can disrupt the formation of a leading-edge vortex induced by the incident vortex on the clean wing and can still reduce the maximum lift

Lift Alleviation in Travelling Vortical Gusts

Lift alleviation by a mini-spoiler on airfoils, unswept and swept wings encountering an isolated counter-clockwise vortical gust was investigated by means of force and velocity measurements. The flow separation region behind the spoiler remains little affected during the gust encounter. The maximum lift reduction is found for the static stall angle of attack. The change in the maximum lift during the gust encounter is approximately equal to that in steady freestream. The comparison with plunging airfoils reveals that, for the same maximum gust and plunge velocity, the effectiveness of the mini-spoiler is much better in travelling gusts. This reveals the importance of the streamwise length scale of the incident gust. For the unswept wing, there is some three-dimensionality of the flow separation induced by the mini-spoiler near the wing-tip. The magnitude of the lift reduction can be estimated using the airfoil data and by making an aspect ratio correction for the reduced effective angle of attack. For the swept wing, the mini-spoiler can disrupt the formation of a leading-edge vortex induced by the incident vortex on the clean wing and can still reduce the maximum lift

Coherence of unsteady wake of periodically plunging airfoil

We present an experimental investigation of the flow structure in the near wake of a NACA0012 airfoil plunging sinusoidally at a chord Reynolds number of Re = 20 000 and for a wide range of reduced frequency k and Strouhal number based on peak-to-peak amplitude St. Estimated mean thrust coefficients using the mean and fluctuating velocity fields confirm the St2 dependence as well as a significant effect of the reduced frequency for k ≤ 1. Generally, time-averaged flow quantities are better correlated with St than k in the range tested (k ≤ 3.14 and St ≤ 0.24). Analysis of the streamwise flow and cross-flow in the near wake using two-point cross-correlations and proper orthogonal decomposition reveals that the unsteady characteristics are even better correlated with St than the mean flow quantities. The percentage energy of the fundamental wake modes of the streamwise flow and the flapping mode of the cross-flow increases with increasing St, but at different rates in the drag-producing and thrust-producing wakes. There are similarities to the wake synchronisation behind oscillating bodies. The spanwise-averaged cross-correlation coefficient in the measurement domain grows linearly for small St (in drag-producing wakes), and is nearly constant at a high value for larger St (in thrust-producing wakes). Results show that the Strouhal number is the most important parameter that determines the degree of two-dimensionality of the wake, and suggest that spanwise vortices are quasi-two-dimensional for St ≥ 0.05 and x/c ≤ 4. The implications for experimental gust generators using oscillating airfoils are discussed.</p

Aerodynamics of a wing in turbulent bluff body wakes

The aerodynamics of a stationary wing in a turbulent wake are investigated. Force and velocity measurements are used to describe the unsteady flow. Various wakes are studied with different dominant frequencies and length scales. In contrast to the pre-stall angles of attack, the time-averaged lift increases substantially at post-stall angles of attack as the wing interacts with the von Kármán vortex street and experiences temporal variations of the effective angle of attack. At an optimal offset distance from the wake centreline, the time-averaged lift becomes maximum despite of small amplitude oscillations in the effective angle of attack. The stall angle of attack can reach 20° and the maximum lift coefficient can reach 64 % higher than that in the freestream. Whereas large velocity fluctuations at the wake centreline cause excursions into the fully attached and separated flows during the cycle, small-amplitude oscillations at the optimal location result in periodic shedding of leading edge vortices. These vortices may produce large separation bubbles with reattachment near the trailing-edge. Vorticity roll-up, strength and size of the vortices increase with increasing wavelength and period of the von Kármán vortex street, which also coincides with an increase in the spanwise length scale of the incident wake, and all contribute to the remarkable increase in lift.</p

Dynamic Deployment of a Minitab for Aerodynamic Load Control

Load control is the reduction of extreme aerodynamic forces produced by gusts, maneuvers, and turbulence to enable lighter, more efficient aircraft. To design an effective control system, the actuator's response in terms of amplitude and phase lagmust be known. Current load control technologies are limited to low-frequency disturbances due to their large inertia. This paper evaluates a potential high-frequency alternative: The minitab using periodic and transient deployments on a NACA0012 airfoil in wind-tunnel experiments. Periodic deployment for reduced frequencies, k ≤ 0.79 exhibits a normalized lift response amplitude, which decays with increasing k comparable to Theodorsen's circulation function but with substantially higher lag. Transient deployment, at rates as low as τdeploy = U∞;tdeploy/c = 1, illustrates a delay in aerodynamic response. The delay is larger for outward minitab motion than inward; τ; ≈ 6 and4, respectively, forα = 0 degandincreases withα. Theflowfields showthat the delay in response and the reduction in effectiveness for dynamic minitab deployment are due to delayed growth of the separated region behind the minitab. The aerodynamic response due to minitab deployment is approximated as the response of a first-order system, which is pertinent to control system design. This simple characterization for amplitude reduction and delay in response makes it well suited to load control.<br/