Number Of Vortex Filaments Research Articles

Accuracy of the Induced Velocity from Helicoidal Wake Vortices Using Straight-Line Segmentation

The accuracy of a straight-line segmentation approximation to a series of helicoidal vortices is considered. The problem is examined for different values of the helical pitch, the number of wake turns, and the wake skew angle. Results documenting both the accuracy and the relative errors of the discretized helical vortex and a vortex ring are compared. It is found that with sufficiently small segments, straight-line segmentation of both the vortex ring and of the helical vortex give at least a second-order accurate reconstruction of the induced velocity field. It is shown that the vortex ring can be viewed as a special case of a helical vortex as its pitch tends to zero. Based on the magnitude of the errors found for the two cases, a vortex ring is shown to be a more stringent test case than a helical vortex when the straight-line segmentation approach is used. The accuracy of the induced velocity field when a skewed helix is represented by straight-line segmentation is shown to be second-order accurate for various combinations of helical pitch and wake skew angle. A comparison with the unskewed helical vortex reveals that the errors in the induced velocity field are almost the same in the two cases. Nomenclature a = empirical constant for wake expansion E =L egendre’s elliptic integral of the second kind K =L egendre’s elliptic integral of the first kind L 2 norm = second norm of the error vector M = number of divisions per revolution of helical wake N = number of turns in the helix N f = number of vortex filaments in the helix p = helical pitch (distance between adjacent filaments normalized by radius) R = rotor radius or radius of vortex ring, m

A Study of Swirling Backflow and Vortex Structure at the Inlet of an Inducer.

This paper describes a vortex structure at the inlet of an inducer which appears on the boundary of backflow region. The vortex structure was visualized by the cavitation voids found by operating at cavitation number of σ=0.050 and recorded by a high speed video. It was measured quantitatively by two laser displacement sensors. The passing frequency and the shape of vortex filaments were determined from the outputs of the laser displacement sensors which respond to the passage of the vortex cavitation. The results show that the number of vortex filaments, their propagation angular velocity and radial location depend on the steady velocity profile at the inlet.

Rotor free-wake modeling using a pseudoimplicit relaxation algorithm

A pseudoimplicit predictor-cor rector relaxation algorithm with five-point central differencing in space has been developed for the solution of the governing differential equations of the helicopter rotor free-wake problem. This new approach is compared and contrasted with more conventional explicit-type free-wake algorithms. A convergence analysis shows that the new algorithm provides for much more rapid convergence characteristics compared to explicit methods, with improvements in numerical efficiency and predictive accuracy. Nomenclature be = spatial boundary condition vector CT = rotor thrust coefficient, Tlp7rR2([lR)2 c = blade chord, m E — shift operator i,/, k = unit vectors in the x, y, and z directions, respectively L = spatial discretization operator / = length of discretized vortex element, m Nh = number of blades N.t. = number of vortex filaments P = iteration scheme operator R = rotor radius, m r(. = vortex core radius, m r, = spanwise location from which vortex filaments are trailed, m r = position vector of a point on a vortex filament, m S = source vector T = rotor thrust, N / = time, s V.,_ — freestream velocity, m/s V = time invariant flowfield velocity, m/s Vind = induced velocity, m/s Vloc = local velocity at a point in space, m/s VH = tangential velocity, m/s Cartesian coordinate system, origin at hub center rotor shaft angle (negative forward), deg )3() = blade coning angle, deg r = circulation, m2/s Ar = nth iteration position-vector correction f = distance along trailed wake filament (wake age), rad A.- = uniform-induced inflow ratio

CI.On the analogy between the electromagnetic field and a fluid containing a large number of vortex filaments

CI.<i>On the analogy between the electromagnetic field and a fluid containing a large number of vortex filaments</i>