Prediction of Viscous Trailing Vortex Structure from Basic Loading Parameters

Rule, John A.; Bliss, Donald B.

doi:10.2514/2.7503

Cited by 15 publications

(1 citation statement)

References 26 publications

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“…Perhaps the Gordian Knot of all vortex models is strapped around their tendencies to over-predict the peak swirl velocity in their core regions [68,111]. The resulting overshoot may be attributed to a variety of factors including, but not limited to, the inability to determine with sufficient precision neither the effective viscosity in different segments of the domain, nor the effects of vortex wandering and diffusion.…”

Section: B Maximum Swirl Velocity Overshoot and Effective Kinematic mentioning

confidence: 92%

Unified Framework for Modeling Swirl Dominated Helical Motions

Majdalani¹

2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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In this article, the fundamental characteristics of swirl dominated motions are examined in the context of both external and internal flows, single and two-cell vortices, as well as unidirectional and multidirectional configurations. Our coverage begins with the single cell Rankine, Lamb-Oseen, and Burgers-Rott solutions, evolves into the two-cell vortices by Sullivan and Kuo, and then transitions into the family of multidirectional motions in both conically and cylindrically confined cyclonic chambers. In the process, a judicious renormalization of variables enables us to recast the modest selection of models in question into a selfsimilar, universal form that is mainly dependent on an Ekman-like, off-swirl parameter. This is achieved by rescaling external vortices by their peak tangential velocity and core radius, which is the distance from the axis of rotation to the point of maximum swirl. For internal vortices, the renormalization is based on the average tangential injection speed and characteristic chamber radius. By providing a basic correction to Kuo's two-cell motion, straightforward reconciliation with traditional models is attained, and this includes the ability to bring into perspective Kuo's strong similarity with Sullivan's vortex, a property that stands in fulfilment of the Prandtl-Bradshaw analogy between temperature-induced buoyancy and curvature-based rotation. Furthermore, by providing a subtle correction to the Bloor-Ingham vortex, an exact solution for conical cyclones is made possible. This is followed by a novel extension to the matched-asymptotic, viscous layer analysis of wall-bounded cyclonic flowfields. Our work thus culminates in the presentation of a generic, uniformly valid viscous approximation, which is applicable to the special class of bidirectional vortices that arise in the context of a right-cylindrical Vortex Combustion Cold-Wall Chamber (VCCWC), a prototypical thrust chamber that is well known in the propulsion community. The ensuing discussion encompasses mutually complementary sets of helical profiles of the complex lamellar, linear Beltramian, and nonlinear Beltramian types. Our viscous analysis also extends to a generalized Beltramian formulation that can assimilate a variable endwall injection pattern. At the outset, several dimensionless parameters are derived from first principles and compared to traditional analogues that are conjectured via guesswork, scaling, or rationalization. These include a modified form of the swirl number that remains configuration-independent, and unique forms of the vortex Reynolds number that incorporate the effects of swirl, finite chamber length, and tangential injection patterns at entry. After identifying commonalities in vortex patterns, such as the composite structure of the swirl velocity and its containment of forced, free, and transitional vortex layers, the fundamental features of the aforementioned models are expressed as a function of dimensionless parameters and then briefly described. These include the core and wall boundary ...

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Section: B Maximum Swirl Velocity Overshoot and Effective Kinematic mentioning

confidence: 92%

Unified Framework for Modeling Swirl Dominated Helical Motions

Majdalani¹

2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

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Challenges in modelling the unsteady aerodynamics of wind turbines

2002

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Many of the aerodynamic phenomena contributing to the observed effects on wind turbines are now known, but the details of the flow are still poorly understood and are challenging to predict accurately. This article emphasizes two key areas that need continued serious consideration for wind turbine predictive analyses: the modelling of the rotor wake and the modelling of the unsteady aerodynamics of the blade sections. Issues discussed herein include the modelling of the induced velocity field produced by the vortical wake behind the turbine, the various unsteady aerodynamic issues associated with the blade sections, and the non-linear intricacies of dynamic stall. Fundamental limits exist in the capabilities of all models, and ambiguities can also arise in how these models should be properly applied. A challenge for analysts of the future is to use complementary experimental measurements and modelling techniques to better understand the aerodynamic problems found on wind turbines, and to develop more rigorous models with wider ranges of application.The aerodynamic modelling of wind turbines has spanned the gamut from parsimonious models based on simple momentum and blade element momentum (BEM) theories, through 'engineering models' based on blade element and dynamic inflow or vortex wake methods, to computational fluid dynamics (CFD) methods that solve numerically the Euler or Navier-Stokes equations. In this article, the focus will be on the use of engineering methods, which represent a majority of the methods currently being used to design wind turbines. While the other approaches using BEM theory, and perhaps even CFD, can play a useful role in the design * Only for k < O 0Ð01 can the flow be assumed steady or quasi-steady.

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