Turbulent interactions for rotating blades and wakes

Abstract

Modelling and asymptotic analysis of the fully turbulent flow produced on a rotating blade system or cut-disk are described, the cut-disk being a thin disk with a significant amount of solidity removed. This is based on addressing the Reynolds-averaged Navier-Stokes equations in three-dimensional boundary-layer form together with an eddy-viscosity model, with the flow structure being analyzed for high Reynolds numbers. Interaction between blades and wakes plays a substantial part. The relationship between the present three-dimensional flow and the two-dimensional or axisymmetric flow over an isolated blade and a rotating disk is considered and leads to the finding that for the most part the flow on a cut-disk is, to leading order, the same as that on a rotating disk. A physical parameter, the disk solidity, plays an important role linking these two flows. The limiting case of low disk solidity yields the flow past an isolated blade locally, with global wake effects acting to provide the necessary azimuthal periodicity. This low-solidity limit also permits more analytical solutions which show agreement with numerical findings.

On turbulent separation

“…The current approach, including the prediction of massive thickness independent of the Reynolds number, extends to flows induced by rotary blades, by related rotary devices and by other configurations of industrial interest as in [21] which in turn reveals newer structures of interest. The theoretical rotating-disk flow is also an attractive one concerning practical applications because it forms a convenient starting point for the context of complete rotor blade flow prediction by means of the cut-disk model.…”

“…The results for the displacement thickness are less so as they suggest that this measure of the flow thickness grows more rapidly than is seen in the scenarios of [6,22], a difference which may well arise due to the quasi-similarity solution employed here. The relatively massive thickness of the flow overall, nonetheless, seems to be undeniable whether for the disk or the belt or, indeed, the rotor-blade and similar three-dimensional non-axisymmetric flow configurations [21].…”

Turbulent viscosity variability in self-propelled body wake model

“…Study the behavior of long-lived turbulent wakes behind moving bodies is not only important from a scientific [2,3,13] but also practical point of view [4,7,10]. On the one hand the evolution of such wakes can affect the operation of airports, and on the other -mixing processes in the surface layer of the sea or ocean.…”

“…One of the most important models of the turbulent wakes behavior, from a practical point of view, is the model of self-propelled body wake [2,5,6,7,9], and the main characteristic of this wake is turbulent viscosity,ν t . Analytical approaches so far assumed a constant viscosity ν t = const , which leads to the wake width at the distance x equal to W (x) ∼ x α (where α = 1/5 for an axisymmetric wake and for α = 1/4 a plane one).…”

Preface to the fifth special issue on practical asymptotics

“…The present issue is concerned with body motion in a two-layer fluid [6], interaction of water waves with a porous plate [7], displacement of one fluid by another in a porous medium [8], liquid-film flows over a step topography with external electric field [9], turbulent flows produced on rotating blades [10], a water-impact problem [11], the Maslov canonical operator for shallow-water equations with localized initial data [12], internal gravity waves over a bottom topography [13], a reaction-diffusion model for concrete corrosion in sewer pipes [14] and convection in a two-layer fluid with external high-frequency vibration [15]. Different methods of asymptotic analysis such as the homogenization method, the Maslov canonical operator, the method of matched asymptotic expansions, generalized methods from geometric optics, and their combinations with numerical methods are used to demonstrate their practical importance in the analysis of practical problems.…”