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RESEARCH PAPERS

Prediction of Leading-Edge Sheet Cavitation Inception on Hydrofoils at Low to Moderate Reynolds Number Flows

[+] Author and Article Information
Zvi Rusak, Wallace J. Morris, Yoav Peles

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180-3590

J. Fluids Eng 129(12), 1540-1546 (Jun 27, 2007) (7 pages) doi:10.1115/1.2801350 History: Received May 16, 2006; Revised June 27, 2007

The inception of leading-edge sheet cavitation on two-dimensional smooth thin hydrofoils at low to moderately high Reynolds number flows is investigated by an asymptotic approach and numerical simulations. The asymptotic theory is based on the work of Rusak (1994, “Subsonic Flow Around Leading Edge of a Thin Aerofoil With a Parabolic Nose  ,” Eur. J. Appl. Mech., 5, pp. 283–311) and demonstrates that the flow about a thin hydrofoil can be described in terms of an outer region, around most of the hydrofoil chord, and an inner region, around the nose, which asymptotically match each other. The flow in the outer region is dominated by the classical thin hydrofoil theory. Scaled (magnified) coordinates and a modified (smaller) Reynolds number (ReM ) are used to correctly account for the nonlinear behavior and extreme velocity changes in the inner region, where both the near-stagnation and high suction areas occur. It results in a model (simplified) problem of a uniform flow past a semi-infinite smooth parabola with a far-field circulation governed by a parameter à that is related to the hydrofoil’s angle of attack, nose radius of curvature, and camber. The model parabola problem consists of a viscous flow that is solved numerically for various values of à and ReM to determine the minimum pressure coefficient and the cavitation number for the inception of leading-edge cavitation as function of the hydrofoil’s geometry, flow Reynolds number, and fluid thermodynamic properties. The predictions according to this approach show good agreement with results from available experimental data. This simplified approach provides a universal criterion to determine the onset of leading-edge (sheet) cavitation on hydrofoils with a parabolic nose in terms of the similarity parameters à and ReM and the effect of hydrofoil’s thickness ratio, nose radius of curvature, camber, and flow Reynolds number on the onset.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) The distribution of the pressure coefficient along the parabola upper surface at various values of Ã. Here, ReM=720. (b) The distribution of the pressure coefficient along the parabola upper surface at various values of Ã. Here, ReM=7200.

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Figure 2

σi as function of à for various values of ReM

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Figure 3

σi as function of à for various values of ReM for the range of attached flow 0.4<Ã<1.45. Experimental data from Kjeldsen (8).

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Figure 4

σi as function of ReM for various values of Ã

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Figure 5

(a) σi as function of Re for a NACA 16-012 at various fixed values of angle of attack α. Experimental results from Van der Meulen (5). (b) σi as function of Re for a NACA 4412 at various fixed values of angle of attack α. Experimental results from Van der Meulen (5).

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