Flow visualization of compressible vortex structures using density gradient techniques

Abstract

Mathematical results are derived for the schlieren and shadowgraph contrast variation due to the refraction of light rays passing through two-dimensional compressible vortices with viscous cores. Both standard and small-disturbance solutions are obtained. It is shown that schlieren and shadowgraph produce substantially different contrast profiles. Further, the shadowgraph contrast variation is shown to be very sensitive to the vortex velocity profile and is also dependent on the location of the peak peripheral velocity (viscous core radius). The computed results are compared to actual contrast measurements made for rotor tip vortices using the shadowgraph flow visualization technique. The work helps to clarify the relationships between the observed contrast and the structure of vortical structures in density gradient based flow visualization experiments. Nomenclature c f Cr I 1 nb p p~ r, 0, Z rc R o0 Y F~ 7o /r p p~o 17 f2 Unobstructed height of schlieren light source in cutoff plane, m Blade chord, m Focal length of schlieren focusing mirror, m Rotor thrust coefficient, T/(pTz~2R 4) Image screen illumination, Zm/m 2 Distance from vortex to shadowgraph screen, m Number of blades Pressure, N/m 2 Ambient pressure, N/m 2 Cylindrical coordinate system Vortex core radius, m Non-dimensional radial coordinate, (r/rc) Rotor radius, m Tangential velocity, m/s Specific heat ratio of air Circulation (strength of vortex), m2/s Non-dimensional quantity, ( F 2 p~/8n2~poor 2) Refractive index of fluid medium Refractive index of fluid medium at reference conditions Gladstone-Dale constant, ma/kg Density, kg/m a Density at ambient conditions, kg/m a Non-dimensional density,

The Aero-Optical Environment of a Helicopter in Forward Flight

“…Investigations into the dynamics of rotor wakes for the purpose of predicting nearfield aero-optic aberrations and farfield irradiance patterns are limited [3,11]. On the other hand, density gradient measurements in the wake have been used to determine the trajectories of the tip vortices, blade vortex sheets, and root vortices [2,12]; these results have consistently shown that density variations in the rotor wake appear primarily in the blade tip vortices. These density-variation measurements have also been used to back out important features related to the tip vortices, such as the core radius and tangential velocity profile.…”

“…3). Specifically, as the flow separates, it rolls up into coherent vortical structures where the local flow curvature in the vicinity of the vortices corresponds to a reduction in pressure [1][2][3]. These low-pressure cells result in a nonuniform density field that will impose severe aberrations on a beam of light that traverses the flow, especially at small wavelengths.…”

Enhancement of Free Vortex Filament Method for Aerodynamic Loads on Rotor Blades

“…Therefore, the modification of the potential angle of attack by coupling to the 2D airfoil data influences the load and power predictions. Figures (15), (16) and (17) Figures (18) shows the power curve for the 5MW NREL turbine. For the attached flow region (no pitch regulation), where the wind velocity is less than the 11m/s, the VLFW potential solution, predicts more power than the VLFW viscous solution, the VLFW dynamic stall solution and the BEM method.…”

“…(3) for n = 2 for the rotor tip vortices. Therefore, in order to take into account the effect of viscous vortex core, a factor of K v must be added to the Biot-Savart law as [16] …”

Benchmarking Particle Image Velocimetry with Laser Doppler Velocimetry for Rotor Wake Measurements

“…A considerable amount of experimental research has been conducted over the last several decades toward this objective [1][2][3][4][5][6]. These measurements have been made at different facilities, with different rotors at different rotor operating conditions, and using different measurement techniques [1,2,5,[7][8][9][10][11]. Therefore, it becomes imperative to understand the measurement uncertainties associated with each type of experiment if the goal is ultimately to understand accurately the rotor flow physics.…”