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TECHNICAL PAPERS

# Development of a Tip-Leakage Flow—Part 1: The Flow Over a Range of Reynolds Numbers

[+] Author and Article Information
Ghanem F. Oweis1

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2121

David Fry, Chris J. Chesnakas, Stuart D. Jessup

Naval Surface Warfare Center, Carderock Division, Code 5400, 9500 MacArthur Blvd., West Bethesda, MD 20817-5700

Steven L. Ceccio

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2121ceccio@engin.umich.edu

1

Current address: Mechanical Engineering Department, American University of Beirut, 3 Dag Hammarskjold Plz., New York, NY 10017.

J. Fluids Eng 128(4), 751-764 (Mar 02, 2006) (14 pages) doi:10.1115/1.2201616 History: Received January 15, 2004; Revised March 02, 2006

## Abstract

An extensive experimental investigation was carried out to examine the tip-leakage flow on ducted propulsors. The flow field around three-bladed, ducted rotors operating in uniform inflow was measured in detail with three-dimensional laser Doppler velocimetry and planar particle imaging velocimetry. Two geometrically similar, ducted rotors were tested over a Reynolds number range from $0.7×106$ to $9.2×106$ in order to determine how the tip-leakage flow varied with Reynolds number. An identification procedure was used to discern and quantify regions of concentrated vorticity in instantaneous flow fields. Multiple vortices were identified in the wake of the blade tip, with the largest vortex being associated with the tip-leakage flow, and the secondary vortices being associated with the trailing edge vortex and other blade-wake vortices. The evolution of identified vortex quantities with downstream distance is examined. It was found that the strength and core size of the vortices are weakly dependent on Reynolds number, but there are indications that they are affected by variations in the inflowing wall boundary layer on the duct. The core size of the tip-leakage vortex does not vary strongly with varying boundary layer thickness on the blades. Instead, its dimension is on the order of the tip clearance. There is significant flow variability for all Reynolds numbers and rotor configurations. Scaled velocity fluctuations near the axis of the primary vortex increase significantly with downstream distance, suggesting the presence of spatially uncorrelated fine scale secondary vortices and the possible existence of three-dimensional vortex-vortex interactions.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 3

Tangential (Ut∕U∞), and axial (Ux∕U∞) velocity profiles of the duct inflow for the small rotor running at 1200rpm (triangles), and for the large rotor running at 500rpm (solid line with no symbols)

Figure 4

A photograph of the blade trailing edge taken through a clear section of the duct. The pressure has been lowered, and developed vortex cavitation makes the tip leakage and trailing edge (TE) vortices visible. The cavitation number is σ=5.6.

Figure 5

Sample instantaneous PIV velocity vector fields with vorticity contours from the mini rotor at 1200rpm (top), and the big rotor at 438rpm (bottom) at the downstream location s∕c=0.041. The vorticity is normalized by (U∞∕RP).

Figure 2

(a) A diagram of the open-jet test section of the 36-in.-diameter water tunnel, showing the P5206 propeller duct, which is an extension of the tunnel conduit; (b) diagram of the open jet test section with the P5407 ducted propeller installed

Figure 1

(a) A plan view of the rotor with a depiction of the duct and the tip vortex emanating near the trailing edge of a blade. Also shown is the coordinate system used. δτ is the time separation from the PIV measurement location along the vortex core, to the blade trailing edge. The tunnel mean flow is out of the page. (b) A diagram of the open-jet test section of the David Taylor model basin 36in. variable pressure cavitation tunnel with the three-bladed, ducted rotor P5206 installed. (c) A close up view of the blade tip at the trailing edge (1), the emanating tip leakage vortex on the inside of the duct—the dark curved line (2), the laser light sheet passing through a window installed in a pocket in the duct (3), another window in the duct to provide optical access for the camera (4), the underwater camera housing (5), and the hub (6) (Chesnakas and Jessup (7)).

Figure 6

Average vorticity field development as a function of the distance downstream from the blade trailing edge along the pitch line, s∕c, which is noted on each frame. Shown are fields from the small rotor running at (a) 300rpm, and (b) 1800rpm; and from the large rotor running at (c) 313rpm, and (d) 500rpm. The closed contours indicate the core boundaries of the identified vortices. The axes coordinates are normalized by RP and the vorticity by (U∞∕RP).

Figure 7

The average number of identified vortices, N, in the instantaneous flow field as a function of the distance downstream from the blade trailing edge along the pitch line, s∕c for various Reynolds numbers. Closed symbols correspond to the small rotor, open symbols to the large rotor.

Figure 8

Average circulation of the instantaneous primary vortex (solid line), and the average sum of the circulation of the identified instantaneous vortices in the field (dashed line). Closed symbols correspond to the small rotor, open symbols to the large rotor.

Figure 9

Circulation, G, measured downstream of the large and small rotors at x∕RP=0.650

Figure 10

Average core radius of the instantaneous primary vortex as a function of the downstream distance s∕c. Closed symbols correspond to the small rotor, open symbols to the large rotor.

Figure 11

Average inferred pressure coefficient of the instantaneous primary vortex CP,1=ΔP1∕(12ρU∞2) as a function of s∕c for varying Reynolds numbers. Closed symbols correspond to the small rotor, open symbols to the large rotor.

Figure 12

Histograms of the instantaneous primary vortex circulation, ΓO,1∕(U∞RP), at varying downstream distance, s∕c. The small rotor running at (a) 300rpm, and (b) 1800rpm. The large rotor running at (c) 313rpm, and (d) 500rpm.

Figure 13

Histograms of the primary vortex core radius, a1∕RP. Conditions are the same as in Fig. 1.

Figure 14

Histograms of the primary vortex pressure coefficient, CP,1. Conditions are the same as in Fig. 1.

Figure 15

A plot of Γ0,1∕(U∞RP) versus a1∕RP for the conditions shown in Fig. 1

Figure 16

Scatter plot of the center location of: (a), (c) the primary vortex; (b), (d) the secondary vortices at 300rpm, and 1800rpm for the small rotor, as a function of the downstream location s∕c. The tip of the blade trailing edge location is noted in the first frame. The shroud is toward the top of the image. Refer to Fig. 5 for explanation of the coordinate system.

Figure 17

Scatter-plot of the center location of: (a), (c) the primary vortex; (b), (d) the secondary vortices at 313rpm, and 500rpm for the large rotor, as a function of the downstream location s∕c. The shroud is toward the top of the image. Refer to Fig. 5 for explanation of the coordinate system.

Figure 18

Scaled and shifted average vorticity ω contours, at various downstream locations, s∕c, for the small rotor running at: (a) 300rpm, and (b) 1800rpm; and for the large rotor running at: (c) 313rpm, and (d) 500rpm. The value of the vorticity contour at the center of the primary vortex marked by an (×) is noted below each frame. The tip location of the blade trailing edge is depicted in the first frame. The shroud is towards the top of the image. Refer to Fig. 5 for explanation of the coordinate system.

Figure 19

Velocity fluctuations u′2¯+v′2¯ for the small rotor as a function of downstream location, s∕c. Shown in (a) are the directly computed fluctuations, and in (b) the corresponding fluctuations after scaling and shifting of the instantaneous fields for the propeller speed of 300rpm. Plotted in (c) are the directly computed fluctuations, and in (d) the corresponding fluctuations after scaling and shifting, for the propeller speed of 1800rpm. The value of the contour at the center of the primary vortex marked by an (×) is noted below each frame. The tip location of the blade trailing edge is depicted in the first frame. The shroud is towards the top of the image. Refer to Fig. 5 for explanation of the coordinate system.

Figure 20

Velocity fluctuations u′2¯+v′2¯ for the large rotor as a function of downstream location, s∕c. Shown in (a) are the directly computed fluctuations, and in (b) the corresponding fluctuations after scaling and shifting of the instantaneous fields for the propeller speed of 313rpm. Plotted in (c) are the directly computed fluctuations, and in (d) the corresponding fluctuations after scaling and shifting, for the propeller speed of 500rpm. The value at the center of the primary vortex marked by an (×) is noted below each frame. The tip location of the blade trailing edge is depicted in the first frame. The shroud is towards the top of the image. Refer to Fig. 5 for explanation of the coordinate system.

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