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TECHNICAL PAPERS

# Movement of Deposited Water on Turbomachinery Rotor Blade Surfaces

[+] Author and Article Information
John Williams

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK and Whittle Laboratory, Cambridge University Engineering Department, Cambridge University, Cambridge CB2 1PZ, UKjohn.williams@eng.ox.ac.uk

John B. Young

Hopkinson Laboratory, Cambridge University Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UKjby@eng.cam.ac.uk

J. Turbomach 129(2), 394-403 (Jun 16, 2006) (10 pages) doi:10.1115/1.2437780 History: Received May 29, 2006; Revised June 16, 2006

## Abstract

A theoretical approach for calculating the movement of liquid water following deposition onto a turbomachine rotor blade is described. Such a situation can occur during operation of an aero-engine in rain. The equation of motion of the deposited water is developed on an arbitrarily oriented plane triangular surface facet. By dividing the blade surface into a large number of facets and calculating the water trajectory over each one crossed in turn, the overall trajectory can be constructed. Apart from the centrifugal and Coriolis inertia effects, the forces acting on the water arise from the blade surface friction, and the aerodynamic shear and pressure gradient. Nondimensionalization of the equations of motion provides considerable insight and a detailed study of water flow on a flat rotating plate set at different stagger angles demonstrates the paramount importance of blade surface friction. The extreme cases of low and high blade friction are examined and it is concluded that the latter (which allows considerable mathematical generalization) is the most likely in practice. It is also shown that the aerodynamic shear force, but not the pressure force, may influence the water motion. Calculations of water movement on a low-speed compressor blade and the fan blade of a high bypass ratio aero-engine suggest that in low rotational speed situations most of the deposited water is centrifuged rapidly to the blade tip region.

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## Figures

Figure 1

Representation of a rotor blade surface as a collection of triangular facets (2D meridional view)

Figure 2

Definition of coordinate system local to facet: (a) 3D representation; and (b) view along line D‐E (2D representation with facet omitted)

Figure 3

Relationship between Fig. 2 and turbo-machinery rotor blade sections

Figure 4

Water packet trajectories on a rotating flat plate set at various stagger angles β. Zero friction (K=0), zero lean angle, and zero aerodynamic forces. Initial velocity is: (a) Ẋ0=0, Ẏ0=0; (b) Ẋ0=0.1, Ẏ0=0; and (c) Ẋ0=0, Ẏ0=0.1.

Figure 5

Water packet trajectories on a rotating flat plate set at various stagger angles β. High friction (K=20), zero lean angle and zero aerodynamic forces. Initial velocity is: (a) Ẋ0=0, Ẏ0=0; (b) Ẋ0=0.1, Ẏ0=0; and (c) Ẋ0=0, Ẏ0=0.1.

Figure 6

Contours of constant trajectory angle ϕ from Eq. 14 with K=20, β=−40deg, α=0deg, and zero aerodynamic forces

Figure 7

Laminar film flow on a rotating plate: variation of K with Refilm for various values of Recent from Eq. 16

Figure 8

Droplet moving on the surface of a horizontal flat disk rotating about a vertical axis: comparison of experimentally measured trajectory with calculation

Figure 9

Water packet trajectories on a rotating flat plate set at β=−40deg and various lean angles α: zero blade friction (K=0), zero aerodynamic forces, and zero initial velocity

Figure 10

Water movement on a model compressor rotor blade pressure surface (200,000 100‐μm-diameter droplets tracked with uniform inlet distribution, water-to-air mass flowrate ratio=0.1, ϕ=0.54). Contours of: (a) deposition rate (g∕cm2∕s); (b) dimensionless friction factor K; and (c) blade skin friction coefficient cf.

Figure 11

Droplet trajectories on model compressor rotor blade pressure surface (baseline conditions: K=12.0, cf=0.008, ϕ=0.54)

Figure 12

Water movement on an aero-engine fan blade pressure surface (200,000 100μm-diameter droplets tracked with uniform inlet distribution, water-to-air mass flowrate ratio=0.1, engine close to design point). Contours of: (a) deposition rate (g∕cm2∕s); (b) dimensionless friction factor K; (c) blade skin friction coefficient cf.

Figure 13

Droplet trajectories on an aero-engine fan blade pressure surface (baseline conditions: K=2.75, cf=0.004, engine close to design point)

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