Performance and aerodynamic braking of a horizontal-axis wind turbine from small-scale wind tunnel tests

Wind tunnel tests of three 20" diameter, zero twist, zero pitch wind turbine rotor models were conducted in a 7' x 10' wind tunnel to determine the performance of such rotors with NACA 23024 and NACA 64 sub 3-621 airfoil sections. Aerodynamic braking characteristics of a 38% span, 30% chord, vented aileron configuration were measured on the NACA 23024 rotor. Surface flow patterns were observed using fluorescent mini-tufts attached to the suction side of the rotor blades. Experimental results with and without ailerons are compared to predictions using airfoil section data and a momentum performance code. Results of the performance studies show that the 64 sub 3-621 rotor produces higher peak power than the 23024 rotor for a given rotor speed. Analytical studies, however, indicate that the 23024 should produce higher power. Transition strip experiments show that the 23024 rotor is much more sensitive to roughness than the 64 sub 3-621 rotor. These trends agree with analytical predictions. Results of the aileron test show that this aileron, when deflected, produces a braking torque at all tip speed ratios. In free wheeling coastdowns the rotor blade stopped, then rotated backward at a tip speed ratio of -0.6

Analytical aerodynamic model of a high alpha research vehicle wind-tunnel model

A 6 DOF analytical aerodynamic model of a high alpha research vehicle is derived. The derivation is based on wind-tunnel model data valid in the altitude-Mach flight envelope centered at 15,000 ft altitude and 0.6 Mach number with Mach range between 0.3 and 0.9. The analytical models of the aerodynamics coefficients are nonlinear functions of alpha with all control variable and other states fixed. Interpolation is required between the parameterized nonlinear functions. The lift and pitching moment coefficients have unsteady flow parts due to the time range of change of angle-of-attack (alpha dot). The analytical models are plotted and compared with their corresponding wind-tunnel data. Piloted simulated maneuvers of the wind-tunnel model are used to evaluate the analytical model. The maneuvers considered are pitch-ups, 360 degree loaded and unloaded rolls, turn reversals, split S's, and level turns. The evaluation finds that (1) the analytical model is a good representation at Mach 0.6, (2) the longitudinal part is good for the Mach range 0.3 to 0.9, and (3) the lateral part is good for Mach numbers between 0.6 and 0.9. The computer simulations show that the storage requirement of the analytical model is about one tenth that of the wind-tunnel model and it runs twice as fast

On the isometric version of Whitney's strong embedding theorem

We prove a version of Whitney's strong embedding theorem for isometric embeddings within the general setting of the Nash-Kuiper h-principle. More precisely, we show that any $n$-dimensional smooth compact manifold admits infinitely many global isometric embeddings into $2n$-dimensional Euclidean space, of H\"older class $C^{1,\theta}$ with $\theta<1/3$ for $n=2$ and $\theta<(n+2)^{-1}$ for $n\geq3$. The proof is performed by Nash-Kuiper's convex integration construction and applying the gluing technique of the authors on short embeddings with small amplitude.Comment: 30 page

Global Nash-Kuiper theorem for compact manifolds

We obtain global extensions of the celebrated Nash-Kuiper theorem for $C^{1,\theta}$ isometric immersions of compact manifolds with optimal H\"older exponent. In particular for the Weyl problem of isometrically embedding a convex compact surface in 3-space, we show that the Nash-Kuiper non-rigidity prevails upto exponent $\theta<1/5$. This extends previous results on embedding 2-discs as well as higher dimensional analogues.Comment: 31 page

Decentralized Event-triggered Control with Asynchronous Updates

We propose taking event-triggered control actions to implement decentralized control over wireless sensor/actuator networks without requiring synchronized measurement updates. In comparison with the existing results on event-triggered decentralized control, the proposed implementation does not rely on weak coupling between subsystems, nor does it assume the synchronization of local clocks or the existence of a central broadcasting node, and is applicable to nonlinear systems. In addition, higher energy efficiency at the sensors is expected because of the great reduction of the listening times of the sensors. We prove that with asynchronous measurement updates, the event-triggered control actions can guarantee semiglobal practical stability for the sensor/actuator system of interest. We also show that the time between any two consecutive transmissions of measurements at each sensor is bounded from below by a positive constant. Furthermore, asymptotic stability can be achieved when more complicated triggering conditions are introduced. The theoretical analysis is validated by simulations

Rigidity of four-dimensional K\"ahler-Ricci solitons

In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a K\"ahler model. The first theorem could be considered as a rigidity result for the K\"ahler-Ricci soliton structure on $\mathbb{S}^2\times \mathbb{R}^2$ (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a K\"ahler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally K\"ahler