Turbulent flow on a planar moving belt and a rotating disk: modelling and comparisons

Abstract

Modelling of the fully turbulent flow produced on a moving belt and of that induced on a rotating disk is described, for each of which a more analytical approach is adopted than previously seen. The analysis for the two-dimensional moving belt indicates novel structures and these are found to carry over directly to the rotating disk flow which, ignoring the transitional regime, is three-componential but twodimensional due to axisymmetry. This is based on addressing the Reynolds-averaged Navier-Stokes equations together with an eddy viscosity model, with the flow structure being analysed for high Reynolds numbers. A classical (von Kármán) constant within the model plays an important and surprising role, indicating that each of the belt and the disk flows has quite a massive thickness. Comparisons made with previous work show varying degrees of agreement. The approach, including the new prediction of massive thicknesses independent of the Reynolds number, is expected to extend to flows induced by rotary blades, by related rotary devices and by other configurations of industrial interest.

Turbulent interactions for rotating blades and wakes

“…The simpler case of the turbulent boundary layer on a rotating disk was examined in [10] where it was found that the boundary layer is relatively massive, a result also reported in [11] concerning turbulent jets and [12] concerning marginal separation. In this paper we extend the work of [10] to include non-axisymmetry by considering the fully three-dimensional turbulent boundary layer (cf.…”

“…The fluid motion induced is usually turbulent in practice. For example, one motivation for the current theoretical work is from industry, where the possible application to rotor-blade flows represents a potentially significant area of research not least because of its use in the study of helicopter dynamics and the desire within industry to develop a theoretical understanding of such flows in the hope that this may lead to improvements in design [1][2][3][4][5][6][7][8][9][10]. The detailed link with the present work may be quite indirect throughout as our emphasis is on fundamental properties and asymptotic description; indeed, the apparent breaks of both symmetry and periodicity associated with forward movement (rather than hovering) of a helicopter and the resulting complex vortex streets are not addressed.…”

“…The detailed link with the present work may be quite indirect throughout as our emphasis is on fundamental properties and asymptotic description; indeed, the apparent breaks of both symmetry and periodicity associated with forward movement (rather than hovering) of a helicopter and the resulting complex vortex streets are not addressed. We note that other applications exist [7][8][9][10], but we should also remark here that there are many continuing concerns regarding helicopter design and there is a wealth of numerical simulations for rotor flows, Fig. 1 The cut-disk configuration, on which the study mostly focuses Fig.…”

“…In this paper we extend the work of [10] to include non-axisymmetry by considering the fully three-dimensional turbulent boundary layer (cf. [13] and others) on a rotating cut-disk or blade system.…”

“…With respect to the present investigation, issues and questions surround the role of the massive thickness of the boundary layer on an uncut disk [9,10], the azimuthal periodicity, the part played by the disk solidity (see below) and the self-consistency of the theory. In particular, two questions will be addressed; firstly, how does the nature of the flow vary within different regions of the flow field; and secondly, how does this three-dimensional boundary layer relate to the flow on a rotating disk and to that on an isolated blade.…”