Simultaneous Lateral Skewing in a Three-Dimensional Turbulent Boundary-Layer Flow

Abstract

The results of an experimental program are reported on, wherein the lateral flow in a low-speed, three-dimensional, turbulent, incompressible boundary layer inside a recurving duct was made to reverse itself completely. In such a reversal process there occurs a region of flow where the boundary layer experiences lateral flow in two different lateral directions simultaneously. The physical arguments which support the existence of such flow regions with simultaneous lateral skewing are discussed and supported by the experimental results. Several of the more recent velocity profile models which are intended for use in describing skewed turbulent boundary-layer flows are reviewed as to their applicability to a flow with such simultaneous lateral skewing.

An experimental investigation of a three-dimensional turbulent boundary layer in an ‘S’-shaped duct

“…Eichelbrenner (1963) and Eichelbrenner & Peube (1966) were the first to draw attention to cross-over profiles. Klinksiek & Pierce (1970) measured mean velocity profiles with two-sided lateral skewing in an 'S'-shaped channel of rectangular crosssection and Webster, DeGraaff & Eaton (1996) in a boundary layer over a swept bump. Recent measurements were performed by Schwarz & Bradshaw (1992, 1994 and by Compton & Eaton (1995) in a curved duct with unilaterally skewed velocity profiles and byÖlçmen & Simpson (1995b), in the flow of a wing-body junction.…”

Discussion: “A Family of Hodograph Models for the Cross Flow Velocity Component of Three-Dimensional Turbulent Boundary Layers” (Shanebrook, J. R., and Hatch, D. E., 1972, ASME J. Basic Eng., 94, pp. 321–329)

“…The question of a collateral near-wall region of flow in threedimensional turbulent layers is still open. The work of Francis and Pierce [36], 4 Klinksiek and Pierce [37], Gardow [38], Johnston [39], Hornung and Joubert [40], M. Smith [41], P. D. Smith [42], Lewkowicz [43], and Prahlad [44], all show from two up to seven experimentally determined points which suggest a collateral near-wall region of flow when w/U is plotted against u/U in a velocity polar (or hodograph) figure. In all cases the velocity polars referred to above were characterized by lateral flow in only one direction so that these polars can be put into a single class of flows.…”

Discussion: “An Explicit Scheme for the Calculation of Three-Dimensional Turbulent Boundary Layers” (Nash, J. F., 1972, ASME J. Basic Eng., 94, pp. 131–138)

“…In closing, it is suggested that the question of defining a limiting wall streamline in a three-dimensional turbulent boundary la3 r er flow must be approached with caution, since the existence of a collateral near-wall region of flow is open. The experimental work of Francis and Pierce [9], e Klinksiek and Pierce [10], Gardow [11], Johnston [12], Hornung and Joubert [13], M. Smith [14], P. D. Smith [15], Lewkowicz [16], Prahlad [17] 6 Numbers in brackets designate Additional References at end of Discussion.…”