This article summarizes our present understanding of the physical behavior of two-dimensional turbulent separated flows, which occur due to adverse pressure gradients around streamlined and bluff bodies. The physical behavior of turbulence is flow dependent, so detailed experimental infor­ mation is needed for understanding such flows and modeling their physics for calculation methods. An earlier review (Simpson 1 985) discussed in much detail prior experimental and computational work, and this was followed by an updated review of calculation methods only (Simpson 1 987). Here additional recent references are added to those cited in the two other works. By separation, we mean the entire process of departure or breakaway, or the breakdown of boundary-layer flow. An abrupt thickening of the rotational-flow region next to a wall and significant values of the normal­ to-wall velocity component must accompany breakaway, or otherwise this region would not have any significant interaction with the free-stream flow. This unwanted interaction causes a reduction in the performance of the flow device of interest (e.g. a loss of lift on an airfoil or a loss of pressure rise in a diffuser). It is too narrow a view to use vanishing surface shearing stress or flow reversal as the criterion for separation. Only in steady two-dimensional flow do these conditions usually accompany separation. In unsteady two­ dimensional flow the surface shear stress can change sign with flow reversal without the occurrence of breakaway_ Conversely, the breakdown of the boundary-layer concept can occur before any flow reversal is encountered. In three-dimensional flow the rotational layer can depart without the

/pdf/turbulent-boundary-layer-separation-u84v5eocej.pdf

Turbulent Boundary-Layer Separation

A new turbulence closure model designed specifically to treat two-dimensional, turbulent boundary layers with strong adverse pressure gradients and attendant separation is presented The influence of history effects are modelled by using an ordinary differential equation derived from the turbulent kinetic energy equation to describe the stream wise development of the maximum Reynolds shear stress in conjunction with an assumed eddy viscosity distribution that has as its velocity scale the maximum Reynolds shear stress In the outer part of the boundary layer, the eddy viscosity is treated as a free parameter which is adjusted in order to satisfy the ODE for the maximum shear stress Because of this, the model is not simply an eddy viscosity model, but contains features of a Reynolds stress model Comparisons with experiment are presented that clearly show the proposed model to be superior to the Cebeci-Smith one in treating strongly retarded and separated flows In contrast to two-equation, eddy viscosity models, it requires only slightly more computational effort than simple models such as the Cebeci-Smith

A mathematically simple turbulence closure model for attached and separated turbulent boundary layers

The problem of turbulent-boundary-layer separation due to an adverse pressure gradient is an old but still important problem in many fluid flow devices. Until recent years little quantitative experimental information was available on the flow structure downstream of separation because of the lack of proper instrumentation. The directionally sensitive laser anemometer provides the ability to measure the instantaneous flow direction and magnitude accurately. The experimental results described here are concerned with a nominally two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation. Upstream of separation single and cross-wire hot-wire anemometer measurements are also presented. Measurements in the separated zone with a directionally sensitive laser-anemometer system were obtained for U, V , $\overline{u^2}, \overline{v^2}, - \overline{uv}$ , the fraction of time that the flow moves downstream, and the fraction of time that the flow moves away from the wall. In addition to confirming the earlier conclusions of Simpson, Strickland & Barr (1977) regarding a separating airfoil-type turbulent boundary layer, much new information about the separated region has been gathered. (1) The backflow mean velocity profile scales on the maximum negative mean velocity U N and its distance from the wall N . A U + vs. y + law-of-the-wall velocity profile is not consistent with this result. (2) The turbulent velocities are comparable with the mean velocity in the backflow, although low turbulent shearing stresses are present. (3) Mixing length and eddy viscosity models are physically meaningless in the backflow and have reduced values in the outer region of the separated flow. Downstream of fully developed separation, the mean backflow appears to be divided into three layers: a viscous layer nearest the wall that is dominated by the turbulent flow unsteadiness but with little Reynolds shearing stress effects; a rather flat intermediate layer that seems to act as an overlap region between the viscous wall and outer regions; and the outer backflow region that is really part of the large-scaled outer region flow. The Reynolds shearing stress must be modelled by relating it to the turbulence structure and not to local mean velocity gradients. The mean velocities in the backflow are the results of time averaging the large turbulent fluctuations and are not related to the source of the turbulence.

/pdf/the-structure-of-a-separating-turbulent-boundary-layer-part-528e3f5nlp.pdf

The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses

Direct numerical simulation of two turbulent boundary layer flows has been performed. The boundary layers are both subject to a strong adverse pressure gradient. In one case a separation bubble is created while in the other the boundary layer is everywhere attached. The data from the simulations are used to investigate scaling laws near the wall, a crucial concept in turbulence models. Theoretical work concerning the inner region in a boundary layer under an adverse pressure gradient is reviewed and extended to the case of separation. Excellent agreement between theory and data from the direct numerical simulation is found in the viscous sub-layer, while a qualitative agreement is obtained for the overlap region.

/pdf/direct-numerical-simulation-of-a-separated-turbulent-l3rhvbfwll.pdf

Direct numerical simulation of a separated turbulent boundary layer

Aspects of turbulent boundary-layer separation

A universal velocity defect law for turbulent boundary layers developing in adverse pressure gradients is proposed. The velocity scale for this law is independent of the wall shear but related instead to the local maximum in the Reynolds stress profile. The proposal and its implications are checked against a very large body of experimental results and a partial connection between the mean velocity field and the shear stress field is established. A comparison between the present theory and the mixing length theory is presented. The experimental data do not appear to support many of the assumptions nor the predictions of the mixing length theory. The distinction between equilibrium and nonequilibrium layers made by Clauser is shown to be unnecessary as all classes of layers appear to conform to the new universal velocity defect law proposed, provided that the maximum shear stress is sufficiently larger than the wall shear stress.

Mean velocity and shear stress distributions in turbulent boundary layers

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Mean velocity and shear stress distributions in turbulent boundary layers