Turbulence models and their applications to the prediction of internal flows: a review

This paper documents the results of an experimental study of the mean flow and turbulence characteristics of a turbulent free jet of air issuing, into still air surroundings, from a sharp‐edged elliptical slot of aspect ratio 5. The measured quantities, which were obtained with hot‐wire anemometry as a flow diagnostic tool, include the mean streamwise velocity, the turbulence intensities, the Reynolds shear stress, the transport of some of the Reynolds stresses, and the flatness and skewness of the distributions of the streamwise velocity fluctuations. Two switches of the major and minor axes were observed and it was found that the jet attains an axisymmetric shape at about 30 equivalent slot diameters downstream of the exit plane. Also, the jet, compared to a turbulent free jet from a sharp‐edged round slot of the same exit area, was found to entrain ambient fluid faster both in the near and far flow fields.

On mixing in an elliptic turbulent free jet

Utilisation de la theorie de distorsion rapide pour le calcul de la reponse de la turbulence a des deformations appliquees

Recent Developments in Rapid-Distortion Theory

In continuation to an earlier publication, experiments have been made in the turbulent flow through a conduit of rectangular cross-section with large aspect ratio. One of the long walls has been made rough, except for a strip, located centrally. As shown in the earlier paper, secondary currents will occur in the regions of transition from smooth to rough wall-condition. The main purpose of the investigation was to check the admissibility of the simplifying assumptions made to the mechanical-energy balance equation. The results of the measurements indeed justified the neglect of unimportant terms of this equation, leading to the following rule. When in a localized region the production is much greater (smaller) than the viscous dissipation, there must be a secondary current that transports turbulence-poor fluid into (outwards) this region and turbulence-rich fluid outwards (into) the region.

Experimental investigation on secondary currents in the turbulent flow through a straight conduit

Parametric studies have been made of devices introduced into the outer region of a low-Reynolds-number turbulent boundary layer (Reθ = 1000-3500) with a view to understanding the manner in which such ‘manipulators’ reduce the surface drag. The devices considered were single flat plates, a cylinder with the same drag as one of these, and two plates stacked, staggered, and in tandem, with chord Reynolds numbers Rec in the range 1000-100000. Direct measurements of local skin friction using a floating-plate drag balance are reported together with the results of laser- sheet smoke flow visualization. The skin-friction results are in good agreement with other floating-element data while the visual and photographic studies in both stationary and convected frames completely support the hairpin description of the boundary-layer structure, and reveal that the wake of the device may play a more important role than has previously been suggested. A picture is presented of the interaction of the devices and their wakes with the hairpin eddy structure which could explain the magnitudes and shapes of the skin-friction distributions observed downstream; their dependence on the height, thickness, and if appropriate, length and spacing of the device(s); the optimum values for these parameters; and the existence of a preferred, tandem plate configuration. The results suggest that such plates do not act primarily as large-eddy break-up systems (LEBUs). Instead several ‘active’ mechanisms are identified which supplement the ‘passive’ effect of the imposed momentum defect. The suppression of large-scale motions is one of these, but, a t least for our relatively thick devices, it would appear that it is an interaction between the vortices, introduced into the layer via the wake, and the near-wall structure that provides the principal mechanism for reducing the skin friction. The observation that the maximum skin-friction reduction always occurred close to the position where these vortices reached the sublayer provides strong evidence for such a view.

Manipulation of turbulent boundary layers by outer-layer devices: skin-friction and flow-visualization results

An explanation is given for a phenomenon observed e.g. in a wall jet in a small region near the maximum velocity. The turbulence shear stress is expressed as the sum of two terms, proportional to the first and the second derivative of the mean velocity, respectively. Use is made of the nonsymmetric flow pattern around the maximum velocity, and of the nonuniform distribution of the intensity of the lateral turbulence velocity component. The coefficient of the second derivative of the mean velocity is shown to contain the first derivative of this turbulence velocity component. Since the second derivative of the mean velocity is negative around its maximum, a positive turbulence intensity gradient as observed in the region concerned in the wall jet, results in a negative contribution to the shear stress. Hence, in this region the shear stress can have a sign opposite to the positive — though very small — gradient of the mean velocity. Consequences with respect to the mechanical energy balance of the mean flow and of the turbulence are discussed.

J. O. Hinze

Papers

Turbulent flow regions with shear stress and mean velocity gradient of opposite sign