When modeling a droplet impingement, it is reasonable to assume a surface is flat when the radius of curvature of the surface is significantly larger than the droplet radius. In other contexts where water droplet erosion (WDE) has been investigated, the typical droplet size has either been sufficiently small, or the radius of curvature of the surface sufficiently large, that it has been sensible to make this assumption. The equations describing the kinematics of an impinging water droplet on a flat surface were reformulated for a curved surface. The results suggest the relatively similar radii of curvature, of the leading-edge of a fan blade and the impinging water droplet, will significantly affect the application of the initial high-pressures, along with the onset of lateral outflow jetting. Jetting is predicted to commence substantially sooner and not in unison along the contact periphery, leading to an asymmetric flow stage. This is likely to have significant implications for the WDE that occurs, and thus, the engineering approaches to minimize the WDE of fan blades.

References

1.
Brunton
,
J. H.
, and
Rochester
,
M. C.
,
1979
, “
Erosion of Solid Surfaces by the Impact of Liquid Drops
,”
Erosion
(Treatise on Materials Science and Technology, Vol. 16),
C. M.
Preece
, ed., 1st ed.,
Academic Press
,
New York
, pp.
185
244
.
2.
Keegan
,
M. H.
,
Nash
,
D. H.
, and
Stack
,
M. M.
,
2013
, “
On Erosion Issues Associated With the Leading Edge of Wind Turbine Blades
,”
J. Phys. D: Appl. Phys.
,
46
(
38
), p. 383001.
3.
Engel
,
O. G.
,
1973
, “
Damage Produced by High-Speed Liquid-Drop Impacts
,”
J. Appl. Phys.
,
44
(
2
), pp.
692
704
.
4.
Sayma
,
A. I.
,
Kim
,
M.
, and
Smith
,
N. H. S.
,
2003
, “
Leading-Edge Shape and Aeroengine Fan Blade Performance
,”
J. Propul. Power
,
19
(
3
), pp.
517
520
.
5.
Field
,
J. E.
,
2009
, “
Elsi Conference: Invited Lecture. liquid Impact: Theory, Experiment, Applications
,”
Wear
,
233–235
, pp.
1
12
.
6.
Heymann
,
F. J.
,
1992
, “
Liquid Impingement Erosion
,”
Friction, Lubrication, and Wear Technology
(ASM Handbook, Vol. 18),
P. J.
Blau
, ed., 1st ed.,
ASM International
,
Materials Park, OH
, pp.
221
231
.
7.
Cook
,
S. S.
,
1928
, “
Erosion by Water-Hammer
,”
Proc. R. Soc. London, Ser. A
,
119
(
783
), pp.
481
488
.
8.
Bowden
,
F. P.
, and
Field
,
J. E.
,
1964
, “
The Brittle Fracture of Solids by Liquid Impact, by Solid Impact, and by Shock
,”
Proc. R. Soc. London. Ser. A
,
282
(
1390
), pp.
331
352
.
9.
Field
,
J. E.
,
Dear
,
J. P.
, and
Ogren
,
J. E.
,
1989
, “
The Effects of Target Compliance on Liquid Drop Impact
,”
J. Appl. Phys.
,
65
(
2
), pp.
533
540
.
10.
Adler
,
W. F.
,
1979
, “
The Mechanics of Liquid Impact
,”
Erosion
(Treatise on Materials Science and Technology, Vol. 16),
C. M.
Preece
, ed., 1st ed.,
Academic Press
,
New York
, pp.
127
178
.
11.
Thomas
,
G. P.
, and
Brunton
,
J. H.
,
1970
, “
Drop Impingement Erosion of Metals
,”
Proc. R. Soc. London. Ser. A
,
314
(
1519
), pp.
549
565
.
12.
Bourne
,
N. K.
,
Obara
,
T.
, and
Field
,
J. E.
,
1997
, “
High-Speed Photography and Stress Gauge Studies of Jet Impact Upon Surfaces
,”
Philos. Trans. R. Soc. London. Ser. A
,
355
(
1724
), pp.
607
623
.
13.
Meyers
,
M. A.
,
1994
,
Dynamic Behavior of Materials
,
Wiley
,
New York
.
14.
Adler
,
W. F.
, and
Vyhnal
,
R. F.
,
1974
, “
Rain Erosion of Ti-6al-4v
,”
Fourth International Conference on Rain Erosion and Associated Phenomena
, Meersburg, Germany, May 8–10, pp.
539
569
.
15.
Zhou
,
Q.
,
Li
,
N.
,
Chen
,
X.
,
Xu
,
T.
,
Hui
,
S.
, and
Zhang
,
D.
,
2009
, “
Analysis of Water Drop Erosion on Turbine Blades Based on a Nonlinear Liquid-Solid Impact Model
,”
Int. J. Impact Eng.
,
36
(
9
), pp.
1156
1171
.
16.
Hand
,
R. J.
,
Field
,
J. E.
, and
Townsend
,
D.
,
1991
, “
The Use of Liquid Jets to Simulate Angled Drop Impact
,”
J. Appl. Phys.
,
70
(
11
), pp.
7111
7118
.
17.
Field
,
J. E.
,
1967
, “
The Importance of Surface Topography on Erosion Damage
,”
Second International Conference on Rain Erosion and Allied Phenomena
, Meersburg, Germany, Aug. 16–18, pp.
593
603
.
18.
Springer
,
G. S.
,
1976
,
Erosion by Liquid Impact
,
Scripta Publishing
, Washington, DC.
19.
Ahmad
,
M.
,
Casey
,
M.
, and
Sürken
,
N.
,
2009
, “
Experimental Assessment of Droplet Impact Erosion Resistance of Steam Turbine Blade Materials
,”
Wear
,
267
(
9–10
), pp.
1605
1618
.
20.
European Aviation Safety Agency
,
2015
, “
Certification Specifications for Engines CS-E, Amendment 4, Airworthiness Code 1
,” European Aviation Safety Agency, Cologne, Germany.
21.
Lesser
,
M. B.
, and
Field
,
J. E.
,
1983
, “
The Impact of Compressible Liquids
,”
Annu. Rev. Fluid Mech.
,
15
(
1
), pp.
97
122
.
22.
Heymann
,
F. J.
,
1968
, “
On the Shock Wave Velocity and Impact Pressure in High-Speed Liquid-Solid Impact
,”
ASME J. Basic Eng.
,
90
(
3
), pp.
400
402
.
23.
de Haller
,
P.
,
1933
, “
Untersuchungen Ber Die Durch Kavitation Hervorgerufenen Korrosionen
,”
Schweiz. Bauztg.
,
101
, pp. 243–
260
.
24.
Blowers
,
R. M.
,
1969
, “
On the Response of an Elastic Solid to Droplet Impact
,”
IMA J. Appl. Math.
,
5
(
2
), pp.
167
193
.
25.
deBotton
,
G.
,
1998
, “
The Interaction of a Coated Target and an Impinging Waterdrop
,”
Wear
,
219
(
1
), pp.
60
72
.
26.
Heymann
,
F. J.
,
1969
, “
High-Speed Impact Between a Liquid Drop and a Solid Surface
,”
J. Appl. Phys.
,
40
(
13
), pp.
5113
5122
.
27.
Lesser
,
M. B.
,
1981
, “
Analytic Solutions of Liquid-Drop Impact Problems
,”
Proc. R. Soc. London. Ser. A
,
377
(
1770
), pp.
289
308
.
28.
Rochester
,
M. C.
, and
Brunton
,
J. H.
,
1974
, “
Surface Pressure Distribution During Drop Impingement
,”
Fourth International Conference on Rain Erosion and Associated Phenomena
, Meersburg, Germany, May 8–10, pp.
371
393
.
29.
Adler
,
W. F.
,
1995
, “
Waterdrop Impact Modeling
,”
Wear
,
186–187
(
2
), pp.
341
351
.
30.
Lesser
,
M.
,
1995
, “
Thirty Years of Liquid Impact Research: A Tutorial Review
,”
Wear
,
186–187
(
1
), pp.
28
34
.
31.
Field
,
J. E.
,
Camus
,
J. J.
,
Tinguely
,
M.
,
Obreschkow
,
D.
, and
Farhat
,
M.
,
2012
, “
Cavitation in Impacted Drops and Jets and the Effect on Erosion Damage Thresholds
,”
Wear
,
290–291
, pp.
154
160
.
32.
Momber
,
A. W.
,
1997
, “
The Response of Geo-Materials to High-Speed Liquid Drop Impact
,”
Int. J. Impact Eng.
,
89
(
1724
), pp.
83
101
.
33.
Fyall
,
A. A.
,
1965
, “
Meteorological Parameters Relevant to the Phenomenon of Rain Erosion
,”
First International Conference on Rain Erosion and Associated Phenomena
, pp.
30
42
.
34.
Tasdelen
,
V.
,
Hertel
,
J.
,
Fiola
,
R.
, and
Staudacher
,
S.
,
2014
, “
A Numerical Investigation on Ingested Water Separation in Modern Turbofan Engines
,”
Deutscher Luft- Und Faumfahrtkongress,
Lilienthal-Oberth eV, Bonn, Germany.
35.
EASA
,
2016
, “
Type-Certificate Data Sheet E.036 Issue 7: Rolls-Royce Plc Trent 1000 Series Engines, Data Sheet 1
,” European Aviation Safety Agency, Cologne, Germany.
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