Rankine Vortex Model Research Articles

Wind turbine response to parameter variation of analytic inflow vortices

AbstractAs larger wind turbines are placed on taller towers, rotors frequently operate in atmospheric conditions that support organized, coherent turbulent structures. It is hypothesized that these structures have a detrimental impact on the blade fatigue life experienced by the wind turbine. These structures are extremely difficult to identify with sophisticated anemometry such as ultrasonic anemometers. This study was performed to identify the vortex characteristics that contribute to high‐amplitude cyclic blade loads, assuming that these vortices exist under certain atmospheric conditions. This study does not attempt to demonstrate the existence of these coherent turbulent structures. In order to ascertain the idealized worst‐case scenario for vortical inflow structures impinging on a wind turbine rotor, we created a simple, analytic vortex model. The Rankine vortex model assumes that the vortex core undergoes solid body rotation to avoid a singularity at the vortex centre and is surrounded by a two‐dimensional potential flow field. Using the wind turbine as a sensor and the FAST wind turbine dynamics code with limited degrees of freedom, we determined the aerodynamic loads imparted to the wind turbine by the vortex structure. We varied the size, strength, rotational direction, plane of rotation, and location of the vortex over a wide range of operating parameters. We identified the vortex conformation with the most significant effect on the blade root bending moment cyclic amplitude. Vortices with radii on the scale of the rotor diameter or smaller caused blade root bending moment cyclic amplitudes that contribute to high damage density. The rotational orientation, clockwise or counter‐clockwise, produces little difference in the bending moment response. Vortices in the XZ plane produce bending moment amplitudes significantly greater than vortices in the YZ plane. Published in 2005 by John Wiley & Sons, Ltd.

Variability of the Outer Wind Profiles of Western North Pacific Typhoons: Classifications and Techniques for Analysis and Forecasting

The hazard posed by tropical cyclones (TCs) is often quantified in terms of the minimum central pressure (MCP) or maximum wind speed. While significant, these qualities must be balanced against considerations for the strength and spatial extent of the outer-core circulation, which also significantly determines the total peril posed by these storms. To this end, the results of recent studies on the time evolution of the outer wind structure of western North Pacific typhoons are presented. The results include a technique for diagnosing the azimuthally averaged wind profile from a combination of regional synoptic data and estimates of MCP. Aircraft reconnaissance data, augmented with available synoptic and scatterometer data, are used to determine the radial extent of 15 (R15), 25 (R25), and 33 (R33) m s−1 winds for 50 typhoons. Thirty-five of these typhoons were designated as the developmental dataset and 15 were reserved for use as independent data. Using the developmental data, concurrent time series were constructed for outer wind radii and MCP values for TCs whose life cycles were unperturbed by proximity to land. Analysis of these time series revealed a distinct type of TC with very large R15 and weak intensity values. These “gyre” systems were examined as a special TC class. The remaining TCs were divided according to the size of their outer circulations into groups termed small, medium, and large. Observations stratified for these size categories revealed that for about 40% of the TCs, significant increases of R15 [greater than 50 km day−1] occurred during the 1.5-day period before maximum intensity. Composite analyses revealed that mature large (small) TCs develop as larger (smaller) TCs early in their life cycle. Composite analysis of the gyre systems showed several unusual characteristics including very large initial R15 values (much larger than even large TCs) and weak intensities. Spatial analyses indicate that the gyre and larger TCs tend to attain maximum R15 values in locations west of 135°E whereas the smaller TCs tend to maximize farther east. Analyses of surface pressure showed that the gyres are associated with broad areas of comparatively low pressure (versus other TCs), in agreement with previous studies. Statistical associations between R15 values and an array of environmental parameters revealed that although area coverage of intense convection was poorly correlated with R15, the radial extent of the 1004-hPa isobar (ER04) enveloping the systems was well correlated with R15. Whereas the overall relationship between MCP and R15 is weak, it is noted that when data for the gyre TCs are removed (14% of the observations), the total variance explained between MCP and R15 is more than doubled. Consequently, a regression equation using both MCP and ER04 was developed and used in conjunction with a Rankine vortex model to successfully estimate values for R15 and R25. The independent data were used to evaluate this analysis technique versus a procedure used by the Joint Typhoon Warning Center (the Huntley method) for estimating the radius of 17 m s−1 winds (R17). The new ER04/MCP-based technique created in this study suffered no loss of skill when applied to the independent data and both methods appear to be quite useful for estimating the properties of symmetric outer wind profiles of northwest Pacific typhoons.

Cylinder wakes in flowing soap films

We present an experimental characterization of cylinder wakes in flowing soap films. From instantaneous velocity and thickness fields, we find the vortex-shedding frequency, mean-flow velocity, and mean-film thickness. Using the empirical relationship between the Reynolds and Strouhal numbers obtained for cylinder wakes in three dimensions, we estimate the effective soap-film viscosity and its dependence on film thickness. We also compare the decay of vorticity with that in a simple Rankine vortex model with a dissipative term to account for air drag.

Simulation of typhoon's anomalous track (I)—Rankine vortex model

This paper proposes a method for simulating symmetric and asymmetric typhoon by using Rankine vortex model. Considering similarity between tropical cyclone and the Rankine vortex, the paper has qualitatively discussed the feasibility of the methods. In order to decide quantitatively Rankine vortex's parameters to simulate typhoon's structure, the paper has dealt with TCM data for Yancy Typhoon (9012) as initial fields. These results are considered as a foundation for further studying typhoon motion by CD approach.

An experimental investigation of turbulent shear flow cavitation

Cavitation inception in a turbulent shear layer was studied at Reynolds numbers up to 2 × 106. Flash photography, high-speed motion pictures and holography were used to study the relation of cavitation inception to the shear-layer turbulent structure. Both spanwise and streamwise vortices were clearly visualized by the cavitation. Cavitation inception consistently occurred in the streamwise vortices and more fully developed cavitation was visible in both structures, with the streamwise cavities typically confined to the braid regions between adjacent spanwise vortices. The strength of the streamwise vortices was estimated using a Rankine vortex model, which showed that their strength was always less than 10% of that of the spanwise vortices. Measurements of fluctuating pressures were made by holographically monitoring the size of air bubbles injected into the non-cavitating shear flow. The measured pressure fluctuations had positive and negative peaks as high as 3 times the free-stream dynamic pressure, sufficient to explain cavitation inception at high values of the inception index. The occurrence of inception in the streamwise vortices of the shear layer, combined with previous reports of velocity dependence of the streamwise vortex strength, may explain the commonly observed Reynolds-number scaling of the cavitation inception index in shear flows.

Free‐Surface Air Core Vortex

A Rankine vortex model is used as the basis for an equation for critical submergence of intakes. The equation relates critical submergence to Froude number, circulation number, Reynolds number, and Weber number. The Froude and circulation numbers are the major controlling parameters. The model accounts for the effect of eddy viscosity on vortex-core characteristics. The equation for critical submergence is in agreement with experimental results. Criteria for neglect of surface tension and kinematic viscosity are established.

Aircraft Vortex Studies in Forest Aerial Spraying

ABSTRACT FIELD tests were conducted to reproduce the con-ditions of spruce budworm spraying carried out in Eastern Canada. For a Grumman TBM aircraft, generating droplets with a VMD of 60 M, the finer spray droplets were found to be caught in vortices generated by the aircraft. The trajectories of the vortices were followed photographically. The descent rate of the vortices, above tree-top, was reduced by atmospheric instability. The in-itially high vortex descent rates were found to approach the theoretically predicted values from the Rankine vortex model using elliptic wing loading.