On the flow instabilities in the end-wall region of a surface mounted obstacle

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Abstract

Visualization of flow in the around a surface mounted obstacle revealed that the pressure gradients imposed on the boundary layer amplified the formation of turbulent spots in the end-wall region. It was observed that the juncture vortices exhibited Λ waveform instability even during the stretching phase that was followed by a rapid amplification and formation of a turbulent spot. The turbulent spot spread laterally as it convected past the attachment and corner region of the end-wall flow. At the Reynolds number used in this investigation the instabilities were always initiated in the region where the primary singular point is located.

Introduction

During an experimental investigation of vorticity dynamics in the end-wall region of a surface mounted obstacle [1], intermittent but fairly large eruptions of the hydrogen bubbles were observed from an otherwise uniform horizontal sheet of bubbles from a wire that was positioned only a few mm above the flat plate and upstream of a surface mounted streamlined cylinder. The unsteady “packet” of bubbles traversed the entire length of the cylinder and the flow later restored to the original state. With increasing Reynolds number the frequency of eruptions increased until the flow became completely turbulent. When the near wall flow was visualized with the help of dye that was injected on the flat plate, it became abundantly clear that the eruptions were due to the formation and passage of turbulent spots. Far upstream of the obstacle these turbulent spots resembled classical flow visualization photographs [2] but appeared profoundly different as they approached the end-wall region and interacted with the local flow.

Turbulent spots play crucial role in transition to turbulence in wall bounded flows. Both naturally occurring and artificially generated have been a subject of investigation ever since they were first reported by Emmons [3] as streaky structures on a free surface water table. Turbulent spots have been investigated by a number of researchers. Early research has focused on the evolution of the turbulent spot and identification of its salient features in laminar boundary layers [4], [5], [6]. However a large body of work on the structure, characteristics and hair pin vortices, growth and convection is based on artificially generated turbulent spots in zero pressure gradients [7], [8], [9].

In the end-wall region, several distinct regimes of flow are encountered simultaneously such as the axial and cross-stream pressure gradients, streamline curvature and associated inflectional velocity profiles that are inherently unstable, and regions of separated flow. There is however only a limited amount of experimental work on turbulent spots that include the effects of lateral divergence and pressure gradients in addition to the high freestream or wall bounded turbulence. For example, Amini and Lespinard [9] found the turbulent spot to be highly evolutionary in transitional boundary layer; Jahanmiri et al. [10] explored the effects of lateral divergence on the structure of turbulent spot in the absence of pressure gradient; flow visualization results of Zhong et al. [11] focused on geometric spread of turbulent spot in adverse pressure gradient, and recently Yaras [12] reported that the spanwise meandering of streaks in a turbulent spot decreased in accelerating flow.

An obstacle placed in the path of a two dimensional boundary layer induces axial and cross-stream pressure gradients that result in the formation of secondary flows in the end-wall region for both the laminar and turbulent approaching boundary layers [13], [14]. An axial pressure gradient in the plane of symmetry of the obstacle results in boundary layer to separate upstream of it and the vorticity in the separated boundary layer rolls up to form the classical horseshoe vortex, necklace vortex or juncture vortex and has been a subject of investigation as early as 1947 [15]. Additional details of the vorticity dynamics in this region can be found in a review article by Simpson [16]. The cross-stream pressure gradient displaces the streamlines and the resulting curvature introduces transverse flow in the near wall region while the outer flow retains its streamwise direction. This results in an inflectional cross-flow boundary layer profile [17] that produces skew-induced vorticity and is inherently unstable. The primary objective of the present experiments was to investigate the influence of extra rates of strain due to end-wall flow on the formation and amplification of instabilities in this region.

Section snippets

Experimental setup

Tests were conducted in a 45 cm × 45 cm cross-section test section water tunnel on a flat plate. The 2.5 m long, 25 mm thick and 45 cm wide acrylic flat plate had a 1:8 fineness ratio elliptical leading edge and a tapered trailing edge. The plate was sanded flat and polished to minimize surface imperfections and was equipped with a dye reservoir machined in the underside. The dye reservoir was fitted with a porous ceramic strip to ensure uniform distribution of dye during injection. Fluorescent dye

Results and discussion

A plane of symmetry view of the end-wall flow in Fig. 2 shows the juncture vortex system made visible with hydrogen bubbles from three platinum wires. The system of vortices was spatially static and was similar to the low Reynolds number Mode-I behavior described by Khan et al. [19] and Khan and Ahmed [20]. Fig. 3 shows the trajectory of limiting streamlines made visible with a thin layer of dye. Just upstream of the leading edge of the cylinder, dye is completely scrapped off due to the

Conclusions

Flow visualization tests were conducted in a water tunnel to investigate the onset of instabilities in a laminar boundary layer due to the presence of an obstacle. Results show that the instabilities originate in the vicinity of the primary singular point and are amplified rapidly downstream due to a combination of streamlines curvature, axial and cross-stream pressure gradients. Formation of turbulent spots in the juncture region also conforms to the observations of Elder [5] whose

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