CI, -J o U. o O
I
-J z o CI) z w O o u. O CI, w.Q
I
Q z o w o z z o I->Del
NAVAL SNIP RESEARCH AND DEVELOPMENT CENTERBethesda, Maryland 20034
by
Daniel T. Valentine
THE EFFECT OF NOSE RADIUS ON THE CAVITATION-INCEPTION CHARACTERISTICS OF
TWO-DIMENSIONAL HYDROFOILS
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
SHIP PERFORMANCE DEPARTMENT RESEARCH AND DEVELOPMENT REPORT
A flCL1V
The Naval Ship Research and Development Center is a U. S. Navy center for laboratory effort directed at achieving improved sea and air vehicles. lt was formed in March 1967 by merging the David Taylor Model Basin at Carderock. Maryland with the Manne Engineering
Laboratory at Annapolis, Maryland.
Naval Ship Research and Development Center Bethesda, Md. 20034
* REPORT ORIGINATOR
MAJOR NSRDC ORGANIZATIONAL COMPONENTS
[_FFICERINCKARGE CAR DE ROCK 05
*
SHIP PERFORMANCE DEPARTMENT 15 STRUCTURES DEPARTMENT 17 SHIP ACOUSTICS DEPARTMENT 19 MATERIALS DEPARTMENT 28 N SR D C COMMANDER 00 TECHNICAL DIRECTOR I OFFICER-IN-CHARGE ANNAPOLIS 04 AVIATION AND SURFACE EFFECTS DEPARTMENT COMPUTATION AND MATHEMATICS DEPARTMENT 18 PROPULSION AND AUXILIARY SYSTEMS DE PAR TM EN T 27 CENTRAL INSTRUMENTATION DEPARTMENT 29 NDVH\SRDC3960/44 (REV. S/71) CPO 9t7-872 SYSTEMS DEVELOPMENT DEPARTMENT 11SECURITY CLASSIFICATION OF TI4IS PAGE (W7i., 0.1. nt.r.d)
DD I JAN 73FORM EDITION OF NOV68 IS OBSOLETE
S/N 0102-014-6601 UNCLASSI FI ED
SECUITV CLASSIFICATION OF TWIS PAGE (WI.n Data Int.r.d)
REPORT DOCUMENTATION PAGE BEFOREDCTNpSoRM
L REPORT NUMBER 3813
2. GOVT ACCESSION WO. 3. RECIPIENTS CATALOG NUMBER
4. TITLE (id Subtltl.)
THE EFFECT OF NOSE RADIUS ON THE CAVITATION-INCEPTION CHARACTERISTICS OF
TWO-DIMENSIONAL HYDROFOILS
3. TYPE OF REPORT & PERIOD COVERED
6. PERFORMING ODO. REPORT NUMBER
7. AUTP4OR(a)
Daniel T. Valentine
9. CONTRACT OR GRANT NuMBER(.)
9. PERFORMING ORGANIZATION NAME AND ADDRESS Naval Ship Research and Development Center
Bethesda. Maryland 20034
¶0. PROGRAM ELEMENT. PROJECT, TASK AREA & WORK UNIT NUMBERS
Task 12231
Program Element 63508N
Work Unit 1-1544-005
II. CONTROLLING OFFICE NAME ANO ADDRESS Naval Ship Systems Command
Washington. D. C. 20360
12. REPORT DATE July 1974 13. NUMBER OF PAGES
52
14, MONITORING AGENCY NAME & AODRESS(il diff.r.nt fron, Controllln Ottica) IS. SECURITY CLASS. (of this r.perl) UNCLASSI FlED
IS.. DECLASSIFICATION/DOWNGRADING SCN E DU L E
16. DISTRIBUTION STATEMENT (of (hi. Raport)
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
¶7. DISTRIBUTION STATEMENT (of h. ab.tract .nt.r.d in Block 20, it diff.r.i,l froi R.port)
19. SUPPLEMENTARY NOTES
IS. KEY WORDS (Continu. on rayar., aid. il n.caa.ary ,d id.ntify by block nmib.r)
Hydrofoils
Cavitation Inception Pressure Distribution
20 ABSTRACT (Continu. on r.v.,.. aid. If n.c.a.a?, wd fd.ntlty. by block nun,b.r)
Results of an analytical investigation of the cavitation-inception characteristics of modified marine propeller-type hydrofoils are presented. In particular, dependence of the critical cavita-tion number and the cavitacavita-tion-free, angle-of-incidence range on changes in the leading-edge thickness is determined. It is shown that within a narrow range of changes of leading-edge thickness, a delay in inception is possible. depending on the design problem under consideration. An increase in critical inception speed, accompanied by a sacrifice in some of the cavitation-free.
.LLJTV CLASSIFICATION OF THIS PAGE(W?.(. Data nt.r.d)
(Block 20 continued)
angle-of-incidence range occurs for a small increase in the leading-edge thickness. A range ot thickness changes exists for which beneficial results can he obtained.
UNCLASSI FlED
UNCLASSI FlED
Page ABSTRACT i ADMINISTRATIVE INFORMATION j INTRODUCTION PROBLEM LITERATURE REVIEW 2 INVESTIGATION PROCEDURE 11 HYDROFOIL SECTIONS II CAVITATION-INCEPTION CHARACTERISTICS 13 RESULTS 17 DISCUSSION 31 DESIGN EXAMPLES 35 CONCLUSIONS 38
RECOMMENDATIONS FOR FURTHER INVESTIGATION 39
REFERENCES 40
LIST OF FIGURES
I Minimum Pressure Envelopes for BUSHIPS Type I and
Type Ii Sections with Zero Camber 4
2 - Minimum Pressure Envelopes for BUSHIPS Type I and Type II Sections Having a Maximum Camber Ratio of 0.02
3 - Minimum Pressure Envelopes for BUSHIPS Type I and Type II Sections Having a Maximum Camber Ratio of
0.04 6
4 Minimum Pressure Envelopes for NACA 66 (TMB Modified)
Sections with Zero Camber 7
5 - Minimum Pressure Envelopes for NACA 66 (1MB Modified)
Sections Having a Maximum Camber Ratio of 0.02 8
6 - Minimum Pressure Envelopes for NACA 66 (TMB Modified)
Sections Having a Maximum Camber Ratio of 0.04 9
7 Minimum Pressure Envelope for a Propeller-Type Basic
iv
Page
8 - Influence of Nose Radius on the Minimum Pressure
Coefficient for NACA 4-Digit Foils at Zero Angle
of Attack 1 2
9 - Pressure Distribution on NACA 66 (TMB Modified
and BUSHIPS Type 11 lliickness Forms 1 8
10 - Minimum Pressure Envelopes for BUSHIPS Type Il,
N = 1 .05 Sections with Zero Camber 20
11 - Minimum Pressure Envelopes for BUSHIPS Type 11,
N 1 .1 Sections with Zero Camber 21
1 2 - Minimum Pressure Envelopes for BUSHIPS Type Il. N = 1.1 Sections Having a Camber Ratio of 0.02 13 - Minimum Pressure Envelopes for BUSHIPS Type 11.
N I I Sections Having a Camber Ratio of 0.04
14 - Minimuni Pressure Envelopes for NACA 66 (TMB
Modified) N 1.1 Sections with Zero Camber
1 5 - Minimum Pressure Envelopes for NACA 66 (TMB
Modified) N 1 .3 Sections with Zero Camber 25
16 - Minimum Pressure Envelopes for NACA 66 (TMB
Modified) N-Modified Sections: N 1 .0.
r = 0.23 with Zero Camber 26
17 - Minimum Pressure Envelopes for NACA 66 (TMB Modified) N-Modified Sections: N 1.0,
r = 0.23 with Zero Camber 27
18 - Minimum Pressure Envelopes for NACA 66 (TMB Modified) N-Modified Sections: Range of N.
r = 0.23. = 0.18 28
19 Minimum Pressure Envelopes for BUSHIPS Type Il.
e Modified Sections with Zero Camber 30
20 Comparison of Cavitation Characteristics of BUSHIPS Type Il. N-Modified and c Modified Hydrofoils with
r = 0.18 and Zero Camber 32
21 - Comparison of the Outer Boundary of the Minimum
Pressure Envelopes of the NACA 66 (TMB Modified)
N-Modified Sections with Zero Camber 33
22 - Comparison of the Outer Boundary of the Minimum
Pressure Envelopes of BUSHIPS Type II. N-Modified
and e Modified Sections with Zero Camber 34
11
23
y
Page - N-Modified Foil Geometries of NACA 66 (TMB
MoiIit'icd) at Conventional Stations 14
2 - N-Modified BUSHIPS Foil Geometries at Conventional
Stations I S
3 Leading-Edge Radii for NACA 66 (TMB Modified) and BUSHIPS Type li N- and c Modified
Hydrofoils 16
4 Comparison of Thickening Methods 37
S Hydrofoil Design Problem. Comparing Different
NOTATION
CL Lift coefficient CL = LIFT/[(l/2)p U2 c]
CN Nose radius constant CN PLE/T2
C
Pressure coefficient C = (p - p)/[(l/2)p U2]
c Chord length
Maximum camber ratio = camber/chord
N Thickness parameter defined by Equation (I)
p Local static pressure on section Vapor pressure on the liquid p Free-stream static pressure
U Velocity of section
x Fraction of chord. measured from leading edge Thickness ordinate, divided by chord length Camber line ordinate, divided by chord length
Angle of attack
Thickness parameter defined by Equation (6)
p Fluid mass density
LE Nondirnensional leading-edge radius = CN r2
u Cavitation number u = (p
-- Pv'112P
U2 "Critical" cavitation number, defined in Figure 7Ud Cavitation number defined in Figure 7
r
Thickness ratio, twice maximum thickness ordinateRelative divergence of inception curve, defined in Figure 7
Results of an analytical investigation of the cavitation-inception charac-teristics of modified marine propeller-type hydrofoils are presented. In
par-ticular. dependence of the critical cavitation number and the cavitation-free,
angle-of-incidence range on changes in the leading-edge thickness is determined. lt is shown that within a narrow range of changes of leading-edge thickness, a delay in inception is possible, depending on the design problem under
consid-eration. An increase in critical inception speed, accompanied by a sacrifice
in some of the cavitation-free, angle-of-incidence range occurs for a small increase in the leading-edge thickness. A range of thickness changes exists for which beneficial results can be obtained.
ADMINISTRATIVE INFORMATION
The project was authorized and funded by the Naval Ship Systems Command under
Task, 12231 and Program Element 63508N; Work Unit l-1544-005. INTRODUCTION
PROBLEM
Prediction of cavitation inception on propeller blades, struts, appendages and other ship
and submarine control surfaces is important since even small amounts of cavitation can lead to erosion and noise problems. Knowledge of the cavitation-inception characteristics of two-dimensional hydrofoil sections is useful in choosing the appropriate section for a particular
design application.1'2 In this report modifications of the hydrofoil sections used in the design
of modern marine propellers are investigated theoretically, albeit the results are applicable to any hydrofoil design problem.
The investigation was undertaken with the objective of determining the effect of increas-ing the leadincreas-ing-edge thickness on cavitation performance of marine propellers. Impetus for the investigation was the necessity to sometimes change the leading- and/or trailing-edge
thicknesses in order to satisfy various design requirements. An increase in thickness at the trailing edge may be required by strength considerations. An increase in thickness at the
Brockett, T., "Steady Two-Dimensional Pressure Distributions on Arbitrary Profiles," David Taylor Model Basin Report 1821 (1965). A complete listing of references is given on pages 40 and 41.
2Brockett, T., "Minimum Pressure Envelopes for Modified NACA-66 Sections with NACA a = 0.8 Camber and BUSHIPS Type I and Il Sections," David Taylor Model Basin Report 1780 (1966).
leading edge may be required to provide space for air ducts in the propeller blade in the vicinity of the leading edge. Assessment of these design modifications on the cavitation-inception characteristics of the hydrofoils is needed and, consequently, is the purpose of the
investigation.
The approach taken in investigating the change in hydrofoil leading-edge shape was to
determine the effect on the cavitation-inception characteristics of varying the nose radius by
varying the leading-edge thickness of propeller-type hydrofoils. A transformation was used to
vary the leading-edge thickness so that no change would occur either in the position of the
leading edge and midchord or in the maximum thickness of the modified hydrofoils. In
addi-tion. the effect was determined of a typical foil-modification method used by the Naval Ship
Engineering Center on the cavitation-inception characteristics of the hydrofoils used in a recent propeller design. Both modification methods are described in detail in the appropriate
sections of this report. as well as a comparison of their cavitation-inception characteristics.
The results presented in this report concern the effect of the leading edge or nose radius
on the cavitation-inception characteristics of the parent NACA 66 (TMB modified) and BUSHIPS Hydrofoils. These hydrofoils were chosen because of their use in the design of marine propellers. Results are presented on the effect of nose thickening on the cavitation-inception characteristics of symmetric and cambered hydrofoils. A comparison of the parent and modified hydrofoils is given. The effect of the leading-edge shape as an independent foil
parameter such as thickness, camber. and chord is discussed. Such knowledge is useful in
design problems where the given design constraints restrict the choice of the foil shape so that
the parent foils are inadequate. In this case, if only small modifications are necessary, the procedure and results presented should prove useful.
LITERATURE REVIEW
The cavitation-inception characteristics of the hydrofoils investigated have been reported by Eckhardt and Morgan.3 Milam and Morgan.4 Caster,5 and Brockett.2 Brockett2 showed that the NACA 66 (TMB modified) thickness form and an a 0.8 mean line exhibited very nearly the same cavitation-inception characteristics in comparison to the BUSHIPS type sections (NACA 1 6 thickness form and NACA 65 parabolic mean line). For most propeller-design problems both sections can be considered good from the point of view of propeller-blade cavitation.
3Eckhardt. M. K. and W. B. Morgan, "A Propeller Design Method." Society of Naval Architects and Marine Engineers Transactions, Vol. 63. pp. 325-374 (1955).
4MiJam, A. and W. B. Morgan, "Section Moduli and Incipient Cavitation Diagrams for a Number of NACA Sections," David Taylor Model Basin Report 1177 (1957).
5Castcr, E., "Incipient Cavitation Diagrams for BUSHJPS Type I and II Sections," David Taylor Model Basin Report 1643 (1962).
the cavitation-inception characteristics as presented by Brockett.2 Figures 1 through 6 are
examples taken from the Brockett report of the cavitation-inception curves which apply to the parent hydrofoils considered in this report. The curves show the effect of incidence angle
on the minimum pressure coefficient for a particular hydrofoil section. The curves are plotted for different thickness and camber ratios, illustrating the effect of thickness and camber on cavitation-inception characteristics. As the thickness ratio increases, the cavitation-inception speed at the shock-free incidence angle decreases, and the cavitation-free angle of attack range
increases. The effect of increasing camber for a constant thickness-to-chord ratio is to decrease the shock-free, attack angle inception speed and to increase the fluctuation range of cavitation-free angle of attack.
Mandel7 in 1953 plotted the minimum pressure coefficient versus the nose radius for 58 NACA symmetrical airfoil sections for several attack angles. This composite plot showed
that for a given attack angle there existed an optimum nose radius, i.e., a nose radius at which
the minimum pressure versus nose radius curve exhibited a maximum. Optimum nose radius increased with increasing attack angle.
Alef8 studied analytically, relatively sharp-nosed (0.36 <PLEIr2 < 0.72) symmetrical
airfoil shapes at small attack angles of less than 6 degrees. The term PLEIT equal to 0.5 corresponds to an elliptical nose shape for the polynomial defined foils investigated by Alef.
For "great values" of the nose radius (PLE/T2 near 0.72) Alef found that a suction peak occurred near the leading edge. As the nose radius decreased this suction peak decreased.
Also, the chordwise extent of the suction decreased with decreasing nose radius. Looking at
a hypothetical inception curve (Figure 7) Alef found that the relative divergence of the
cavi-tation inception diagram increased with increasing nose radius while the design-point angle of attack variation 5 decreased.
Breslin and Landweber9 reviewed the cavitation inception literature to 1961. They
presented results which showed that for a series of foil shapes at zero angle of attack with a nose thickness parameter, the ratio of the nondimensional nose radius to the thickness ratio
6Morgan, W. B. and J. P. Lichtman, "Cavitation Effects on Marine Devices," Cavitation State of Knowledge published by American Society of Mechanical Engineers (Jun 1969).
7Mandel, P., "Some Hydrodynamic Aspects of Appendage Design," Society of Naval Architects and Marine Engineers Transactions, Vol. 61, pp. 464-515 (1953).
8Alef, W. E., "Propeller Sections to be Used in a Non-Homogeneous Wake," Hamburg Model Basin Report 11 87 (Jun
1959).
9Breslin, J. P. and L. Landweber, "A Manual for Calcuiation of Inception of Cavitation on Two and Three Dimensional Forms," Society of Naval Architects and Marine Engineers T & R Bulletin 1-21 (Oct 1961).
±8 ±7 ±6 +5
(D w
±4 ±3 ±2 ±1
BUSHIPS BASI C C1 = 0.1097
---FOILS
THICK N ESS FOAMS
(1 - 0.617) a
BUSHIPS TYPE I (NACA 16 WITH PARABOLIC
TAIL)
BUSHIPS TYPE II (NACA 16)
u.
ash
T = 0.20 0.18 0.15
o.i5
U
0.10ia
rn:
zII!iii.r
ijllø
r -i 0.06 0.2 j 02 0.4 0.6 08 1.0 12 1.4 1.6 1.8 2.0 22 2.4 2.6 2.8 30c
"MI NFigure 1 - Minimum Pressure Envelopes
for BUSHIPS Type I and Type II Sections with
Zero Camber
6 5 4 3 2
i
2
3
4
5
Figure 2 - Minimum Pressure Enve opes
for BUSHIPS Type I and Type II Sections
Having a Maximum Camber Ratio of
0.02
C
L
n IN
BUSHIPS PARABOLIC CAMBE
= 0.1097 DEGREES R RATIO ± FOILS (1
-IUIUI
CAMBER 0.61 0.02 (NACA 65 CAMBER r)( + 2.13) LINE) -O.20P 0.18 ________________ 0124
-008TMiila::fE
0.02 -0.2 0.8 1.0 1.2 1.4 18 2.0 2.2 24 26 2.8I ,ikiit Ii' 'iii RtÑrc rice 2)
M
:,':::
JHHHUM
I
6 5 4 3 2
i
2 34
5
Figure 3 - Minimum Pressure Envelopes
for BUSE) PS Type I a id Type II Sections
Having a Maximum Camber Ratio of 0.04
=
CL a IN
iBUSHIPS PARABOLIC CAMBER
VC = 0.1097 DEGREES ± FOILS RATIO (1 -CAMBER = 0.04 0.61r) (NACA (a 65 + 4.26) CAM
RLiN4JjØ
iì::i:
aamua
u.u.gf7j,u..uu
fl
iIiiE
iHhIIfr*r_i.._
1 4u
UI__alu
au__au
O 1.6 1 8i...'
________ 2 2 2.4 2.6 2.8 3.1îaa
P11!ii:m
(Taken1:1111
alus..'
from Reference 2) BUSH BUSHIPS PS TYPE TYPEI THICKNE II THICKN ESS
1
Q w±8 ±7 ±3 ±2 ±1
luIuIuus-016iauivau
_I .Iu_aI___
IflhNIIP1!I!g.
L
BASIC THICKNESS FORMS CL = 0.1097 (1 - 0.83r) a a IN DEGREES
0.02 0 0.2 0.4 06 08 10 12 1.4 16 1.8 20 22 24 26 -C MIN
Figure 4 - Minimum Pressure Envelopes for NACA 66
(TMB Modified) Sections with Zero Camber
(Taken from Reference 2)
r = 0.20
0.18
NACA 66 (TMB MOD NOSE AND TAIL)
±6
- +5
o LU±4
6 5 4 3 2
i
oi
2
3
4
5Figure 5 - Minimum Pressure Envelopes
l'or NACA 66 (TMB Moi! fied) Sections
Having a Maximum Camber Ratio of 0.02
NACA NACA CAMBER THICKNESS CL a IN
a = 0.1097 66 DEGREES = 0.8 (TMB RATIO PE RPE (1 -CAMBER MOD = 0.02 0.83r) NOI NOSE AND LINE CULA R TO (a + 2.35) TAIL)
r = 0.2044
-_u
-I0.04
i4iuuì
002 02 2)Ii.îir'__
tiitqjuumpjJ!.
II1Ii1iiIIi=!
_
TT
_
28 3 I L I Referenceu.
(Taken from6 5 4 3 2
1
2
3
-4
5Figure 6 - Minimum Pressure Envelopes for NACA 66 (TM B Moilified) Sections
I laying a Maximum Camber Ratio of 0.04
NACA NACA CL c IN CAMBER THICKNESS a = 0.1097 66 DEGREES = 0.8 (TMB RATIO (1 -CAMBER MOD = 0.04 O.83r) PERPENDICULAR NOSE ( LINE AND TAIL) TO CAMBE + 4.70) T = 0.10 I
I
I#î1Ji..irnm
___rn_i
W!IßwIu...Irn _
i_ii
020.4
iii
uuulului
.uu.uuuui.
ii
ANGLE OF ATTACK
CAVITATION FREE ZONE CAVITATION
ZON E
0c 0d
u, CAVITATION INDEX
Figure 7 - Minimum Pressure Envelope for a Propeller-Type Basic Thickness Form
one conclusion is that, if choosing a foil to operate at or near its shock-free entry angle ot attack, the foil should be nearly elliptical with a nose radius parameter, ranging from 0.5 to 0.8 see Figure 8, taken from Reference 9. The data leading to this conclusion was first
presented by Berggren and Graham.10
Spurred by the work of Mandel7 and Alef,8 Collins and Evans1 1 investigated the effects of severa! foil parameters on the cavitation characteristics of several foil shapes ut large angles
of attack. i.e., greater than ô degrees. The foils considered were the polynomial shapes
devel-oped by Alef. All the cases considered were for symmetric shapes. Confirmation of the existence of an optimum nose radius for each angle of attack was found.
The optimum nose radius for a given attack angle depends on the position of maximum thickness and is effectively independent of thickness-to-chord ratio and other section
param-eters. For practical considerations. it is well to note that the minimum pressure coefficient.
or critical cavitation index, does not appreciably vary in the region of the optimum nose
radius.
The fact that an increase in the leading-edge radius may increase the resistance to
cavita-tion near the design cavitacavita-tion index was also found by Moeckel in l96ó.' 2 By increasing the leading-edge radius of a NACA 16-X08 cambered foil, X = 0.390, Moeckel calculated a
reduction in the inception velocity in the attack angle range of --2 degrees < < + I derce.
Beyond tuis range of attack angles. an increase in the inception velocity was calculated.
The present investigation is an extension of the work of Brockett. Evans and Col!in.
Alef, and Breslin and Landwebcr. which is to investigate the effect of changes in leading-ede thickness on the cavitation-inception characteristics of symmetric and cambered marine-propeller-type hydrofoils not reported before.
INVESTIGATION PROCEDURE HYDROFOIL SECTIONS
The NACA 66 (TMB modified) and BUSHIPS Type Il hydrofoil sections were chosen for this investigation because of their use in the design of marine propellers. Tile NACA 66
10Berggrcn, R. i,. and D. J. Graham. "Effects of Leading Edge Radius and Maximum Thickness-Chord Ratio on the Variation with Macli Number of the Aerodynamic Characteristics of Several NACA Airfoil Sections." National Advisory Committee for Aeronautics TN 3172(1954).
Collins. I. F. and A. M. Evans. "Theoretical Study of the Cavitation Resistance of Aerofoil Sections at incidence." Admiralty Research Laboratory Report ARL/R4/G/AE/2/5 (Nov 1965).
Mocckcl. G. P., "The 1-lIcei il 1)istortion of Suhcavitating Foil Contours on Cavitation-Inception Velocity, Journal ot Ship Research, pp. 253-262 (Dcc 1966).
Figurc 8 - Influcuce of Nose Radius on the Miiìiiìnun Pressure Coeft'icient tor
NACA 4-Digit FoiL at Zero Angle of Attack
(taken from Reference
); sec
13
modified by Brockett2 to obtain a smooth, flat, pressure-distribution curve, based on the program Brockett developed. Using these sections as the starting point, the modifications
consisted of effectively changing the leading-edge radius.
The leading-edge radius was varied by shifting the contour of the thickness form in the
y-direction from the leading edge to the point of maximum thickness. The transformation
equation used is
(YT/r)N = (l/2)[2(YT/r)Io]1' (1)
where (YT/r)lo thickness-form offsets of parent foil section being considered
(YT/r)N = modified thickness-form offsets from leading edge to point of
maximum thickness
This method of modification was chosen to ensure that no change in the foil-section chord
length and maximum thickness occurred. Values of N greater than unity correspond to leading-edge radii greater than tile radius of the parent section. The parent thickness-form offsets, the camber-line offsets, and the modified thickness-form offsets for tile modified leading-edge radius sections are given in Tables 1 and 2 for the NACA 66 (TMB modified) and BUSHIPS type sections, respectively.
For the given foil shapes, the leading-edge radius is proportional to the maximum thickness squared. i.e.
LE = CN r2 leading-edge radius/chord length (2)
The constant CN depends on tile thickness distribution, or foil geometry, in the vicinity of the leading edge. Tile nose radius can be found from the change in slope near the leading
edge, which is given in the computer output of the symmetric foil.1 Tile constants for tile
modified foils are given in Table 3.
CAVITATION-INCEPTION CHARACTERISTICS
The pressure distribution at various angles of attack was calculated, using the two-dimensional, pressure-distribution program developed at the Center.' The method used was an arbitrary conformal mapping approach with viscous corrections. The method required the
lift curve slope r and the zero lift angle of attack oe' These experimentally determined parameters yielded the lift coefficient as follows
TABLE 1 - N-MODIFIED FOIL GEOMETRIES OF NACA 66 (TMB MODIFIED) AT CONVENTIONAL STATIONS
Station x
Thickness Ordinate {YT/r)N for N Equal
NACA a 0.8 Camber Line Camber Ordinate Camber Slope
(dYc/dX)/f 1 3 1.1 1 05 1.0 0.95 0.9 0.8 o o o o û o o o o
-0.005 0.10593 007989 0 07321 0.0665 0.05980 0.05315 0.04016 0.0423 7.149 0.0075 0.12352 009579 0.08854 0.0812 0.07379 0.06635 0.05155 0.0595 6.617 o 0125 0 14986 0.12038 0.11249 0.1044 0.09614 0.08772 0.07057 0.0907 5.944 0.025 0.19458 0 16390 0 15542 0,1466 0.13743 0.12792 0.10788 0.1586 5.023 005 0.25334 022389 0.21548 02066 019721 0.18728 016564 0.2712 4.083 0.075 0.29562 0.26868 0.26085 0.2525 0.24358 0.23404 0.21285 0.3657 3.515 0.1 0 32946 0.30539 0.29831 0.2907 0.28252 0.27370 0.25384 0.4482 3 100 0 15 038178 0.36351 0.35803 0.3521 0.34566 0.3386.4 0.32254 0.5869 2.488 0 2 0.42114 0.40820 040427 04000 0.39533 0.39020 0.37830 06993 2.023 025 045024 0,44174 043914 0.4363 0.43318 0.42974 0.42974 0.7905 1.635 03 0,47184 0.46689 0.46537 0.4637 0.46186 0.45983 0.45504 0.8635 1.292 035 0.48703 0.48470 048399 0.4832 0.48233 0.48127 0.47909 0.9202 0.933 0.4 0.49630 0.49563 0.49543 0.4952 0.49495 0.49467 0.49401 0.9615 0.678 045 0 50 0 50 0.50 0 5000 0.50 0$0 0.50 0.9881 0.385 0.5 04962 1.0 0.091 055 0.4846 0,9971 -0.211 0 6 04653 0.9786 -0.532 0 65 04383 0.9434 -0.885 0.7 0 4035 0.8892 -1.295 075 0.3612 0.8121 -1.813 08 0.3110 0.7027 -2.712 0.85 0.2532 0.5425 -3.523 0.9 0.1877 0.3586 -3.768 0.95 0.1143 0.1713 -3.668 0.975 0.0748 0.0823 -3.441 1.0 0.0333 0.0 -3.00315
Station
Type li Thickness Type I Thickness NACA 65
Mean Line Ordinate Yc/f N = 1.1 (''T'T)1.i N = 1.05 'T'1.O5 N = 1.0 (YTIT)lo N = 1.0 TIT)1 o ICr = 0.05277 i (YTIT) O O O O O 0 o 0.005 0.08232 0.07554 0.06873 0.06873 0.11425 0.0199 0.0075 0.09864 0.09130 0.08386 0.08386 0.12778 0.029775 0.0125 0.12371 0.11575 0.10758 0.10758 0.14900 0.049375 0.025 0.16775 0.15924 0.15039 15039 0.18729 0.0975 0.05 0.22633 0.21794 0.20908 0.20908 0.23978 0.19 0.075 0.26872 0.26089 0.25254 0.25254 0.27866 0.2775 0.1 0.30281 0.29577 0.28800 0.28800 0.31037 0.36 0.15 0.35641 0.35071 0.34455 0.34455 0.36096 0.51 0.2 0.39760 0.39328 0.38859 0.38859 0.40035 0.64 0.25 0.43013 0.42705 0.42370 0.42370 0.43175 0.75 0.3 0.45566 0.45365 0.45145 0.45145 0.45657 0.84 0.35 0.47516 0.47401 0.47275 0.47275 0.47563 0.91 0.4 0.48895 0.48853 0.48786 0.48786 0.48914 0.96 0.45 0.49723 0.49709 0.49695 0.49695 0.49727 0.99 0.5 0.5 0.5 0.5 0.5 0.5 1.0 0.55 0.49674 0.495 0.49625 0.99 0.6 0.48624 0.48 0.48502 0.96 0.65 0.46740 0.455 0.46629 0.91 0.7 0.43912 0.42 0.44008 0.84 0.75 0.40031 0.375 0.40637 0.75 0.8 0.34988 0.32 0.36518 0.64 0.85 0.28673 0.255 0.31 649 0.51 0.9 0.20976 0.18 0.26023 0.36 0.95 0.11788 0.095 0.1620 0.19 0.975 0.06601 0.04875 0.0890 0.0975 1.0 0.01 0.0 0.0 0
NOTE; For N-thickness forms only the leading portion is varied; trailing edge for all foils is the same as for N = 1.0.
TABLE 3 - LEADING-EDGE RADII FOR NACA 66 (TMB MODIFIED) AND BUSHIPS TYPE II N- AND e MODIFIED HYDROFOILS
16 Hydrofoil N e1Icr CN NACA 66 (1MB modified) 1.3
-
1.272 1.1-
0.674 1.05-
0.556 1.0-
0.448 0.95 .- 0.355 0.9-
0.272 NACA 66 )TMB modified) 0.8-
0.144 BUSHIPS II 1.1-
0.751 BUSHIPS II 1.05-
0.607 BUSHIPS I and I 1.0-
0.48889 BUSHIPS I-
0.05277 1.459LE = CN r2 = LEADINGEDGE RADIUS/CHORD LENGTH Refer to Equation (6) in text.
For high Reynolds number, aoe and ri are independent and can be determined by the
following approximate formulas,2 i.e., the lift coefficient for NACA 66 (TMB modified) sections with an NACA a = 0.8 camber line becomes
CL = 2ir(l - 0.83r)(a + 2.05f)
(4)For the BUSHIPS section
CL = 2ir(l - 0.61r)(cx + 186f) (5)
For the modified section shapes the experimental lift data are not available: therefore. the assumption has been made that aoe and values do not change significantly with small
modifications in the thickness distribution. Pinkerton13 found experimentally that the slope of the lift curve and the zero lift angles of attack were independent of small changes in the
leading-edge radius and of small changes in the thickness distribution.
From the pressure distribution at a given attack angle. the minimum pressure is deter-mined. Cavitation characteristics are shown as a plot of the attack angle a versus the mini-mum pressure coefficient C . The cavitation criterion assumed is that the inception
mm
of cavitation occurs when Ute minimum pressure coefficient corresponds to the vapor pressure
of the fluid in which the foil shape is moving. RESULTS
The pressure distributions for the two parent foils are relatively fiat: see Figure 9.
Increasing the leading-edge radius while keeping the maximum thickness r and the chord
length c constant results in the development of a suction peak in the vicinity of the leading
edge. In this case the suction peak at approximately midchord decreases. The optimum.
shock-free incidence, airfoil shape would be the shape with equal suction near the leading
edge and midchord at the ideal angle of attack. However, this would lead to a
cavitation-inception characteristic with a cavitation-free angle of attack variation of zero at the
cavita-tion index see Figure 7. Whether or not this is desirable depends on the design problem.
3inierton. R. M., "Effects of Nose Shapeon the Characteristics of Symmetrical Airfoils." National Advisory Committee
for Aeronautics TN 386 (August 1931).
BUSHIPS TYPE I
(NACA 16 NOSE.
PARABOLIC TA(L)
N
Figure 9a - Theoretical Pressure Distribution at Ct = O Degree on BUSHIPS Foils
of 10-Percent Thickness and Zero Camber
Figure 9b - Theoretical Pressure Distribution at Ct O Degree on the
NACA 66-010 (TMB Modified Nose and Tail)
Figure 9 - Pressure Distribution on NACA 66 (TMB Modified) and
BUSHIPS Type II Thickness Forms (Taken from Reference 2)
18 -0.3 -0.2 -0.1 Cp 0.1 0.2 0.3 BUSHIPS TYPE II (NACA 16) ZERO CAMBER 10% THICKNESS ZERO INCIDENCE I L.E. 0.1 0.2 0.3 0.4 0.5 0.6 FRACTION OF CHORD L 0.7 0.8 0. 1.0 T.E.
\
-0.3 -0.2NACA 66 TMB MODIFIED NOSE ANDTAIL)
ZERO CAMBER -0.1 10% THICK ZERO INCIDENCE CP 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FRACTION OF CHORD 0.1 0.2 0.3
increases while the leading-edge suction decreases. These results as well as the following
results of the nose radius effects on the cavitation-inception characteristicsassumes small changes in the leading-edge shape.
Figures I O through I 8 present the cavitation-inception characteristics of the modified
19
Figures 10 through 15 show that within the range of leading-edge variations considered. the inception characteristics are similar in shape, although the width of the cavitation-free region changes; the changes will be discussed later. Figures 1 6 through 18 illustrate the effect of nose radius change on the cavitation-inception curve for a fixed thickness and camber.
The NACA 66 (TMB modified) and BUSHIPS hydrofoils in use today are finer than ari
ellipse at the leading edge. i.e., CN equals 0.448 and 0.489. respectively, as compared to 0.5
for ellipse. Therefore, increasing the nose radius should improve the critical, shock-free, inception speed. However, as shown in Figure 8 and in Figure 1 5 as compared to Figure 4. there is a limit to the increase in bluntness which will give an improved critical inception
speed. From the data presented in this report, this limit is reached between an N of I-i and
1.3 for the propeller hydrofoils considered, which corresponds to (pE/r2) of the order of
0.7. This is consistent with the results of Berggren and Graham10 as shown in Figure 8. The increase in critical inception speed is obtained at the sacrifice of cavitation-free.
angle-of-incidence range as shown in Figures 16 through 18. On the other hand. decreasing
the nose radius is shown to increase the cavitation-free incidence range with a small sacrifice
in the critical inception cavita..ion index. This beneficial effect of decreasing nose radius has also been found to have a limit. For the propeller-type hydrofoils a range of N exists in which benefits of either critical shock free inception speed, or increase in cavitation-free.
hydrofoils as listed.
F gu re N Corn me nl
10 1 .05 0.0 Varied N-Modified, BUSH IPS Type Hydrofoil
li
1.1 0.0 Varied N-Modified, BUSHIPS Type Hydrofoil12 1.1 0.02 Varied N-Modified, BUSHIPS Type Hydrofoil
13 1.1 0.04 Varied N-Modified, BUSHIPS Type Hydrofoil
14 1.1 0.00 Varied N-Modified, NACA 66 (1MB modified) Hydrofoil
15 1.3 0.00 Varied N-Modified, NACA 66 (TMB modified) Hydrofoil
16 Varied 0.00 0.23 N-Modified, NACA 66 (TMB modified) Hydrofoil
17 Varied 0.00 0.23 N-Modified, NACA 66 )TMB modified) Hydrofoil
o 0.0
02
0.406
08
1.0-c
inFigure lO - Minimum Fressure Envelopes tor
I3USIIIPS Type II, N = 1.05 Sections with Zero
Camber 1.2
14
16
18
2.0BUSHIPS N = 1.05 BASIC THICKNESS FORMS CL =
0.1097(1 -0.61r)a
a
IN DEGREES0
O.O6P5g
-O.O2 ±6 ±5 ±4a ±3
±2 ±1BUSHIPS N = 1.1 BASIC THICKNESS FORMS
CL = 0.1097(1 O.61r)
IN DEGREES -o.O200
0.2 0406
0.8 10 1.2 14 1.6 18-c
minFigurc Il - Minimum Pressure Envelopes for BUSIIIPS Type Il. N
I .1 Sections with Zero Camber
4 3 2
i
o -2-3
BUSHIPS NACA 65 CAMBER
-
=±
CL =0.1097(1
c IN
N = 1.1 HYDROFOILS CAMBERLINE RATIO = 0.02 DEGREES
-0.61r)(a+2
. 13)11111
o.o8 0.06 0.04 0.02tif
0.02h___
0.0400
02
0.4 0.608-C
10 12 1.4 16 18 2.0 minFigure 12 - Minimum Pressure Envelopes for BUSIIIPS Type Il. N =
I
I
4 3 2
i
o 2-3
BUSH IPS NACA 65 CAMBER
- Y = Y. ±
CL =0.1097
c IN
N = 1.1 HYDROFOILS CAMBERLINE RATIO = 0.04 D EG R E ES
(1 -061r)(a+426}
r=O.18giglI
0.02¡:11111
0.02 0.04 0 0 0.2 0.4 0.6O 8 -c
1 0 1 2 1 4 1 6 1 8 minFigure 13 -- Minimum Pressure Envelopes for BUSHIPS Type Il, N
O 0.0
02
0.4 0.6 0.810
1.2 1.4 1.6 1.8 2.0 NACA 66 (TMB MODIFIED)BASIC THICKNESS FORMS CL =
0.1097 (1 - 0.83r)cx IN DEGREESa o p-. o
_____
___
o.O44drAt
.
III
_0.02
-c
Pmu n Figure 4Minimum Pressure Envelopes tor
NACA 66 (TM B Modilied) N
1 .1 Sections with Zero Camber
±6 ±5 ±4
a ±3
±5 ±4 ±3 ±2 ±1 o 0.0
1.0
-C
pnhin
Figure
1 5 - Minimum Pressure Envelopes for NACA 66 (TM 13 Modified) N =
1 .3 Sections with Zero Camber
NACA 66 (TMB MODIFIED) BASIC THICKNESS FORM CL=O.lO97(l-O.83r)OE
c IN DEGREES
A
p,p
0 02_
0.204
06
0.8 1.214
16
1.8±6 ±5 ±4 ±3 ±2 ±1 0
00
NACA 66 (TMB MODIFIED) BASIC THICKNESS FORMS
rO.23; N1.0
'z
3________________-z
/
J
i
I
II
1/
I/
/7/
i'!
III II ¡02
0406
08
10 1.2 1.4 16 18 20-c
minFigure 16 - Minimum Pressure
Envelopes for NACA 66 (TMB Modified) N-Modified Sections:
N
1
0, r = 0.23 with
±6 ±5 ±4
c
±3 ±2 ±1 O
NACA 66 (TMB MODIFIED) BASIC THICKNESS FORM
r0.23; N1.0
/
#
/
/
'7
/
¶/
i
ftii
00
02
04
0.6 0.8 1.0 1.2 1.4 -C mi nFigure 17 - Minimum Pressure Envelopes t'or NACA 66 (TMB Modified) N-Modified Seetions:
N
NACA NACAa=0.BCAMBERLINE 66 (TMB MODIFIED) M = 0.18
-r0.23;
-141
I
00
02
04
0.6 0.8 1.012
1.4 1.6 1.8 2.0-c
nFigure 18 - Minimum Pressure Envelopes for NACA óô
(TMB Modified) N-Modified Sections
Range of N. r = 0.23,
M
= 0.18
7 6 5 4 3 2 2
0.8 <N < 1.3.
The maximum N is between 1.1 and 1.3 as mentioned previously, and the minimum N is between 0.8 and 0.9.Figure 19 shows the inception characteristics for an e modified method* combined with the BUSHIPS Type I hydrofoil. The e parameters chosen were typical of several recently designed Navy propellers. The transformation equation for this modification is:
(YT/r)E = [(1/2) - (cj/rc)12(YT/r)E_o + (e1/rc) (6)
where i = I, 2 corresponds to the leading and trailing edges, respectively. The formulas results in an additional thickness of 2e1 at the leading edge and an additional thickness of 2e2 at the trailing edge. The maximum thickness and chord remain identical to the thickness and chord of the parent section, which in this example is the BUSHIPS Type I hydrofoil.
an NACA 16 with a parabolic tail. The leading-edge radius for the foil (in this investigation)
was determined by the computer-fairing technique in the vicinity of the leading edge as
described in Brockett.1 In this example the e modified basic thickness form is defined as follows EI = 0.05277 TC E, = 0.12550 rc
Therefore, from the leading edge to the midchord
fT
t -)
= 0.89446 + 0.05277\ TIE
\ Tand from the midchord to the trailing edge
fT\
t-)
=0.7490t-\TI
\T
= 2 E 29 + 0.12550* Naval Ship Systems Command. "Propeller Blade Section Design Coefficients for Type I Sections...BUSHIPS Drawing
±4 ±3 c ±2 ±1 O
00
02
04
0.6 0.8 1.0-c
Pm! n 1.2 14 16Figure 19 - Minimum Pressure Envelopes for I3USE-IIPS Type
ii,
Modified Sections with Zero Camber
1.8
2.0
BUSHIPS c-MODIFIED BASIC THICKNESS FORMS CL = 0.1097(1- 0.61 r)o
cINDEGREES t O
.
/rc = 0.052770'
O0!
O .06 0.02at zero angle of attack is given by
PLE = 1 .459 r2
From the previously described equations, the e modified basic thickness form given in Table 2 was determined.
The data given in Figure 20 show that this design is not within the range of N's which
gives beneficial effects. In fact, by comparing CN for the e modified design with CN for the
N-modified designs you would expect this to be the case: see Table 3. DISUSSION
To begin the discussion of nose radius effects on the cavitation characteristics of
hydro-foils, one should first consider the inception characteristics of the parent hydrofoils predicted by Brockett see Figures 1 through 6. His results show that as the nose radius increases with
thickness ratio, the range of cavitation-free angle of attack increases. However, a decrease in shock-free inception speed must be accepted. By considering small modifications of the
thick-ness distribution as a means of varying the nose radius, one might expect the same trends in the changes in the cavitation-inception curves of the hydrofoil. However, the present investi-gation lias shown that this was not the case.
Figure 7 is a sketch of the cavitation inception characteristic for a typical basic thickness distribution of a propeller-type hydrofoil. The cavitation index Ud and the critical cavitation
index are not significantly different. For a given design cavitation index there is a unique
thickness ratio for a given hydrofoil which gives the maximum cavitation-free angle of attack
range & A plot of
yields an outer envelope which for a given hydrofoil separates two zones.the cavitation zone in which cavitation is inevitable and the cavitation free zone in which a judicious choice of thickness ratio for a given camber and foil shape leads to a design that
will not cavitate. For the foils considered in this investigation, the outer envelopes of the
cavitation-free zone are compared in Figures 21 and 22. For small increases in iiose radius. the range of cavitation-free angles of attack decreases, while for small decreases in nose radius.
the range of cavitation-free angles of attack increases. This is opposite to the effect of increas-ing the thickness of the hydrofoil and is due to the different effects of each modification on
the pressure distribution.
Increasing the thickness-to-chord ratio increases the suction in the vicinity of the rnidchord
relative to the suction at the leading edge. Also, increasing the thickness-to-chord ratio increases
the total suction for a given chordwise thickness distribution. These effects can be observed
o
00
02
04
0.6 0.8-c
1.0 1.2 1416
PminFigure 20 - Comparison of Cavitation Characteristics of BUSHEPS Type II, N-Moditied
and e Modified Hydrofoils with r
0.18 and Zero Camber
1.8
2.0
BUSHIPS II N-MODIFIED& c-MODIFIED HYDROFOILS
r0.18;
M
=0.0
.-\O
--,,
-S-,,
/7
,,
,-/
7
7
oo'11
J
±6 ±5 ±4a ±3
±2 ±1± 5.0 ±4.0 ± 3.0 ±2.0 ±1.0 0 0.0 I I I
I
NACA 66 (1MB MODIFIED) N=0.90-BASIC THICKNESS FORMS PLOTS OF THE OUTER ENVELOPES OF
0.95
THE CAVITATION INCEPTION CURVES
Ø 1.0 0.80 1.1 1.05 CAVITATION ZONE
1.3 CAVITATION FREE ZONE
Figure 21 - Comparison of the Outer Boundary of the Minimum Pressure Envelopes of
the NACA 66 (TMB Modified) N-Modified Sections with Zero Camber
0.2 0.4 0.6 0.8 1.0 -C Pm i n
±4.0 ± 3.0
a ±2.0
±1.0
O
00
BUSHIPS N-MODIFIED BASIC THICKNESS FORMS PLOTS OF THE OUTER ENVELOPES
OF
THE CAVITATION INCEPTION CURVES
0.6 -C Pm s n N=1.0 CAVITATION ZONE
-1.05 1.1 BUSHIPS MODIFIED FOILS e1 /rc = 0.05277CAVITATION FREE ZONE
Figure 22 - Comparison of the Outer
Boundary of the Minimum Pressure Envelopes of
BUSHIPS Type II, N-Modified and
e
Modified Sections with Zero Camber
0.2
0.4
0.8
1.0
were consistent with the inception curves presented by Brockett.2 The total increase in the
suction for an increase in thickness-to-chord ratio explains the decrease in critical inception speed. i.e.. the increase in critical see Figures 1 through ô. Also, the decrease in
leading-edge suction due to increasing thickness-to-chord ratio explains the increase in the range of
cavitation-free angle of attack. This is because suction at the midchord increases at a slower rate than suction at the leading edge when angle of attack is increased.
Changing the nose radius while keeping the thickness-to-chord ratio constant, i.e.,
chang-ing the leadchang-ing-edge shape of the hydrofoil, has the opposite effect on the pressure
distribu-tion. Increasing the nose radius increases leading-edge suction while it decreases the midchord
suction. This results in the increase in critical inception speed with a sacrifice of some of
the range of cavitation-free angle of attack. The reverse occurs with decreases in the nose
radius. These results are for small changes in nose radius about the parent hydrofoil geometry.
Also, as pointed out before, only a small range of leading-edge changes results in beneficial
effects on the cavitation-inception curves. The range of the leading-edge parameter N for which beneficial effects occur is within 0.8 < N < 1 .3 for the foil shapes considered.
DESIGN EXAMPLES
Tl1ree examples are presented to illustrate the usefulness of the results of this
investiga-tion. The first example illustrates a rational approach to the problem of increasing the
thick-ness of the leading edge of a hydrofoil. A required increase in the leading-edge thickthick-ness has
resulted in at least one design problem to date, viz., the introduction of air ducts in the
vicin-ity of the leading edge of propeller-blade hydrofoils to emit air into the low-pressure region. The second example illustrates the improvement in cavitation inception gained by using a blunter hydrofoil, depending on the design criteria chosen, and assuming that small changes
in the leading-edge geometry do not affect the hydrofoil lift curve slope and angle of zero
lift. The third example illustrates the application of modifying the leading edge after
cavita-tion experiments are conducted, and early incepcavita-tion of blade-surface cavitacavita-tion seems to be a
problem.
For the first example, consider the following situation. The decision has been made to
use an air-emission system to introduce air at the low-pressure region of the leading edge of a propeller blade to minimize the effects of cavitation-associated problems. Assume the
oper-ating range of attack angle for the 0.7-radius blade element is 1/2 <a < 1/2. If the
BUSHIPS Type Il hydrofoil with zero camber is chosen as the hydrofoil for this blade
14Abbott, 1. H. and A. E. Von Doenhoff, "Theory of Wing Sections.," Dover Publications. Inc., New York (1959).
element, to obtain the maximum cavitation-free range of operating pressure coefficients, the required thickness-to-chord ratio r is O.O7 see Figure 1. Consequently. the
cavitation-inception index for this design is approximately 0.20. However, assume that this foil is not blunt enough and that an e lcr = 0.05277 is required to accommodate the air ducts. From
Figure 1 9, the c type modification results in a cavitation-inception index of 0.63 for a
r = 0.07. A second method for increasing thickness at the leading edge is to use the N = I .1
modified hydrofoil data given in Figure II. For 1/2 <a <
1/2 and for the maximumcavitation-free range of minimum pressure coefficient, the thickness-to-chord ratio is 0.08
with a cavitation-inception index of 0.30. Table 4 gives these data along with giving the
differences in the thickness at the 5-percent-chord location for a 36-inch chord. The table
shows that if the BUSHIPS foil is inadequate because of size limitations, a better method for obtaining a thicker foil is to use the N-modified-foil data. The N = I .I modified hydrofoil
yields a foil with more than adequate thickness in the vicinity of the leading edge, as well as a sacrifice of only 0.1 in the cavitation-inception index as opposed to a sacrifice of 0.43
in the cavitation-inception index for a sufficient increase in leading-edge thickness, using the
e modification method. Even if r = 0.07 was used for the BUSHIPS N = I.I foil, better cavitation performance as well as adequate thickness would be realized.
The second example is a design that requires a camber ratio of 0.02 for a BUSHIPS Type II hydrofoil. Suppose the maximum angle of attack a for this hydrofoil is +1 degree.
For maximum cavitation-free speed. the N 1 .0 design requires a thickness-to-chord ratio
of 0.06. which leads to a 0.38, and the greatest minimum cavitation-free angle of attack a_max at o = 0.38 is 0.6 degree; see Figure 2. For the maximum cavitation-free speed
range. the N = 1.1 design requires r = 0.08. which leads to o = 0.4 and a_max = 0.55
degree: see Figure 1 2. Utilizing a blunter foil to maximize the cavitation-free speed range
leads to detrimental effects. However, suppose the operating cavitation index a is 0.3. and that the avoidance of back bubble cavitation is desired. For the N = 1 .0 case, r = 0.04 and
a1 = 0.63: for the N = 1.1 case. r = 0.05 and u 0.5; Table 5 gives the results. This example
illustrates that when the avoidance of back bubble cavitation is the controlling factor and leading-edge cavitation is inevitable, the N = I . I slightly blunter hydrofoil is better, and,
when the criteria is to maximize the range of cavitation-freespeed, the sharper foil is better.
For the third example assume that the cavitation characteristics of a propeller or other
control surface are to be evaluated experimentally in a water tunnel. Suppose cavitation is observed at the designed operating condition at two radial positions which are defined by NACA 66 (TMB modified) hydrofoils with a r = 0.23 and = 0; r = 0.23 and = 0.18.
respectively. Assume that inception occurs at or near the designed cavitation index. Figures 16 through 1 8 show it is possible to modify the hydrofoil without changing the hydrodynamic performance significantly so as to improve cavitation characteristics. Figure 16 shows. for the
37
TABLE 5 - HYDROFOIL DESIGN PROBLEM, COMPARING DIFFERENT FOIL CHOICES
Hydrofoil T 0 'Tui'T)5% Chord For c = 36"
t5% Chord BUSHIPS Type II 0.07' 0.20 0.20908 0.527" E Modified 0.07 0.63 0.22633 0.570' (1/cr = 0.05277) BUSHIPS N = 1.1 0.07 0.31 0.23189 0.584" BUSHIPS N = 1.1 0.08 0.30 0.23189 0.668"
For maximum cavitation-free range of cavitation-inception indices.
= 0.02 Cavitation Criteria
= +10
Foil of Choice
N=1.0 N=1.1
For Maximum Cavitation Free Speed
r=0.06 a = 0.38 a-max = -0.6° =0.08 o = 0.4 a-max = -0.55°
For a = 0.3, Avoidance of Back Bubble and Inevitable Leading-Edge Cavitation
T0.04
a=0.63 a-max = -0.6° I a-max = -0.35° or005
o=0.5 a-max. = -0.6° I a-max = -0.35° o38
uncambered hydrofoil. that decreasing the leading-edge thickness slightly yields an increase in cavitation-free, angle-of-attack range in the vicinity of the designed cavitation index, along
with a slight decrease in the shock-free-entry. cavitation-inception speed. Between N equal to 0.8 and 0.9 a minimum sharpening parameter exists higher values of N yield new hydrofoils
with progressively worse cavitation-inception characteristics. Also note that the relative
divergence L' of the inception characteristics (Figure 7) decreases with increasing sharpness of
the leading edge. Therefore, the benefits realized are only in the vicinity of the design u.
Figure 1 7 shows, for the uncambered hydrofoil. that increasing the leading-edge thickness
decreases the cavitation-free, angle-of-attack range about the design cavitation index, along with a slight increase in the cavitation-free, shock-free-entry range of speed. Similar effects
result t'or the cambered hydrofoil as shown in Figure 1 8. The usefulness of these results can
be illustrated as follows. Suppose intermittent leading-edge cavitation (flashing) is observed at the design cavitation index, which is assumed to he also the operating cavitation index.
Sharpening the foil slightly would reduce or eliminate the amount of flashing cavitation as the hydrofoil passes through the t'low nonuniformities. e.g., a propeller blade rotating in a wake.
CONCLUSIONS
The effect of varying the leading-edge radius of the NACA 66 (TMB modified) and BUSHIPS sections on the cavitation-inception characteristics was determined. The
modifica-tion methods and the modified basic thickness forms were presented. For the hydrofoils con-sidered the following can he said:
The NACA 66 (TMB modified) and BUSHIPS hydrofoil sections are good hydrofoil shapes t'or design purposes when cavitation suppression is desired on a hydrofoil section oper-ating in a range of attack angles.
The range of N. the leading-edge radius parameter, for the NACA 66 (TMB modified) and BUSHIPS sections, which leads to slight deviations from the typical cavitation-inception
characteristics was found to be within the range 0.8 < N < 1 .3. A limit to the increase in
bluntness exists between N = I.I and 1 .3. A limit to the increase in sharpness of the leading edge exists between N = 0.8 and 0.9.
Increasing the leading-edge radius, while keeping the maximum thickness and chord
length constant, results in the development of a suction peak in the vicinity of the leading
edge. The suction peak at midchord decreases with increase in the leading-edge radius. Changing the leading-edge radius by changing the hydrofoil thickness indicates the possibilities of improving the cavitation-inception characteristics of propellers or other lifting
surfaces, depending on the design criteria and the geometric constraints. One example showed
and that tile consideration and method of modification of the hydrofoil depends on the
design problem.
5. The
modified basic thickness form has cavitation characteristics which are notwithin tile range of good shapes found in this investigation. A second design example has
shown that a better method exists for increasing the leading-edge thickness without sacrificing a large loss in cavitation-inception speed.
RECOMMENDATIONS FOR FURTHER INVESTIGATION
I. Since possibilities exist with the modifications investigated for improving inception
characteristics of fully wetted foils, the next logical step in this investigation is to plot similar
inception curves for enough foils to obtain more easily usable design curves for the N-modified series. Thus, tradeoffs can be evaluated by the propeller designer to make a better choice of hydrofoil sections. However, before this undertaking, several modification methods should
be investigated to determine tile best modifying procedure. Subsequently, it would be
desirable to develop an optimization computer program, having an optimum foil shape as its solution.
2. The results of this investigation indicate that only a limited range of fully wetted hydrofoil shapes exist that possess cavitation characteristics appropriate for propeller designs. Since the possibility exists for designing a base-vented hydrofoil, having better cavitation-inception characteristics than fully wetted hydrofoil designs at high speeds,15 the wetted-surface inception characteristics of several base-vented section shapes should he determined.
15Lang, T. G., "Base-Vented Hydrofoils," Naval Ordnance Test Station, NAVORD Report 6606, China Lake, Calif. (19 Oct 1959).
REFERENCES
L Brockett, T., "Steady Two-Dimensional Pressure Distributions on Arbitrary
Profiles," David Taylor Model Basin Report 1821 (1965).
Brockett, T., "Minimum Pressure Envelopes for Modified NACA-66 Sections with NACA a = 0.8 Camber and BUSHIPS Type I and II Sections," David Taylor Model Basin
Report 1780 (1966).
Ecklìardt. M. K. and W. B. Morgan, "A Propeller Design Method," Society of Naval Architects and Marine Engineers Transactions, Vol. 63, pp. 325-374 (1955).
Milam, A. and W. B. Morgan, "Section Moduli and Incipient Cavitation Diagrams for a Number of NACA Sections," David Taylor Model Basin Report 1177 (1957).
Caster. E.. "Incipient Cavitation Diagrams for BUSHIPS Type I and Il Sections," David Taylor Model Basin Report 1643 (1962).
Morgan. W. B. and J. P. Lichtman. "Cavitation Effects on Marine Devices," Cavitation State of Knowledge published by American Society of Mechanical Engineers (Jun 1969).
Mandel. P., "Some Hydrodynamic Aspects of Appendage Design," Society of Naval Architects and Marine Engineers Transactions. Vol. 61. pp. 464-5 15 (1953).
Alef. W. E., "Propeller Sections to be Used in a Non-Homogeneous Wake," Hamburg Model Basin Report 1187 (Jun 1959).
Breslin. J. P. and L. Landweber. "A Manual for Calculation of Inception of Cavitation on Two and Three Dimensional Forms," Society of Naval Architects and Marine Engineers T & R Bulletin 1-21 (Oct 1961).
Berggren. R. E. and D. J. Graham, "Effects of Leading Edge Radius and Maximum Thickness-Chord Ratio on the Variation with Mach Number of the Aerodynamic Character-istics of Several NACA Airfoil Sections," National Advisory Committee for Aeronautics
TN 3172 (1954).
il.
Collins. I. F. and A. M. Evans, "Theoretical Study of the Cavitation Resistance ofAerofoil Sections at Incidence." Admiralty Research Laboratory Report ARL/R4/G/AE/2/5 (Nov 1965).
12. Moeckel, G. P., "The Effect of Distortion of Subcavitating Foil Contours on Cavitation-Inception Velocity," Journal of Ship Research, pp. 253-262 (Dec 1966).
1 3. Pinkerton, R. M., "Effects of Nose Shape on the Characteristics of Symmetrical
Airfoils," National Advisory Committee for Aeronautics TN 386 (Aug 1931).
Publications. Inc., New York (1959).
Lang. T. G.. "Base-Vented Hydrofoils." Naval Ordnance Test Station. NAVORD
Report 6606. China Lake, Calif. (19 Oct 1959).
INITIAL DISTRIBUTION
42
Copies Copies
2 CHONR 1 NOL
1 Fluid Dynamics (Code 438)
1 Sys & Res Gp (Code 492) 1 NWL
i NRL 1 NUSC
ONR Boston 1 NAVSHIPYD Boston
1 ONR Chicago 1 NAVSHIPYD Bremerton
ONR Pasadena 1 NAVSHIPYD Charleston
1 ONR San Francisco 1 NAVSHIPYD Long Beach
USNA i NAVSHIPYD Philadelphia
1 USNPGSCOL, Monterey 1 NAVSHIPYD Portsmouth
USN ROTC 8 NAVSEC
i SEC 6100 NAVWARCOL 2 SEC 6110 1 SEC 6140 19 NAVSEA i SEA 031 2 SEC 6144 2 SEC 6148 2 SEA 035A i SEA 037 i SEA 08
1 NAVSEC Norfolk (Code 6660)
3 SEA 09G32 i PMS-358
12 DDC
1 PMS-78 i PMS-79
i Chief of R&D, OCS, Army
1 PMS-80 1 Army Eng R&D, Ft. Belvoir
1 PMS-81 1 PMS-82 i PMS-83
1 Army Trans R&D, Ft. Eustis
1 PMS-84 i US MA
1 PMS-89
1 PMS-9i 1 CMDT, USCOGARD
1 PMS-92
NASA College Park
NAVORD 05411 (SEA 05) Attn: Sci & Tech Info, Acquisitions Br
1 NELC 9 MARAD i Ship Div 1 NWC 1 Coord of Research i Mr. F. Ebel i NURDC i Mr. R. Schubert i Mr. R. Falls i NCEL i Mr. E. S. Dillon
MARAD (Continued) 1 Long Island Univ
1 Mr. F. Dashnaw Graduate Dept of Marine Sci
1 Mr. Hammar 40 Merrick Ave
1 Mr. C. Foltis East Meadow, N. Y. 11554
Attn: Prof David Price
i BUSTAND
Institute for Defense Analysis
Library of Congress Merchant Marine Academy
1 National Science Foundation
4 Cal Inst of Tech
i Dr. A. J. Acosta
1 Dr. T. Y. Wu
i Dr. M. S. Plesset i Library
1 New York Univ
Colorado State Univ University Heights
Dept of Civil Engr Bronx, New York 10453
Fort Collins, Colorado 80521 Attn: Prof W. Pierson, Jr. Attn: Prof M. Albertson
3 New York Univ, Courant Institute
Cornell Univ i Prof A. S. Peters
Ithaca, New York 14850 1 Prof J. J. Stoker
Attn: Prof W. R. Sears i Prof K. O. Frederick
Harvard Univ i Penn State U, ORL
2 Divinity Ave
Cambridge, Mass. 02138 1 Rensselaer Polytechnic Inst., Dept Math
Attn: Prof G. Birkhoff Troy, N. Y.
Dept of Mathematics
St. John's Univ, Dept of Mathematics
2 JHU, Baltimore Jamaica, New York 11432
i Dept of Mechanics Attn: Prof Jerome Lurye
1 Inst of Cooperative Research
Kansas State Univ
Engineering Experiment Station Seaton Hall
Manhattan, Kansas 66502 Attn: Prof D. A. Nesmith Lehigh Univ
Bethlehem, Pa. 18015
Attn: Fritz Lab Lib
43
10 MIT
Aeronautics & Astronautics Dept Dept of Ocean Engineering
1 Prof A. T. Ippen 1 Dr. R. H. Lyon i Prof P. Mandel i Prof J. E. Kerwin i Prof P. Leehey 1 Prof M. Abkowitz i Dr. J. N. Newman i Prof D. Cummings i Prof M. Landahl i Prof S. Widnall
2 Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78206 i Dr. H. Abramson
i Applied Mechanics Review
2 Stanford Univ
Dept of Aeronautics & Astronautics Stanford, Calif.
i Prof M. Van Dyke i Prof H. Ashley
Copies Copies
Stanford Research Institute 2 Univ of Calif.
Menlo Park, Calif. 94025 Scripps Inst of Oceanography
Attn: Lib i J, Pollock
1 M. Silverman
2 State Univ of New York
Maritime College i Univ of Connecticut, Box U-37
Bronx, N. Y. Storrs, Conn. 06268
i Engineering Dept Attn: Prof V. Scottron
1 Inst of Math Sciences Hydraulic Research Lab
3 Stevens Institute of Technology
i
Univ of Illinois, College of EngrDavidson Lab Urbana, III. 61801
711 Hudson Street Attn: Dr. J. M. Robertson
Hoboken, N. J. 07030 Theoretical & Applied Mech Dept
1 Dr. J. P. Breslin
1 Dr. S. Tsakonas 1 Univ of Iowa
1 Library Attn: Dr. Hunter Rouse
Utah State Univ 2 Univ of Iowa
College of Engineering Iowa Institute of Hydraulic Research
Logan, Utah 84321 1 Dr. L. Landweber
Attn: Dr. Roland W. Jeppson i Dr. J. Kennedy
4 Webb Institute of Naval Architecture 2 Univ of Michigan
Crescent Beach Road Dept of Naval Architecture & Marine Engr
Glen Cove, L. I., N. Y. 11542 1 Dr. T. F. Ogilvie
1 Prof E. V. Lewis 1 Library
1 Prof L. W. Ward
1 Prof C. Ridgely-Nevilt 2 Univ of Minnesota
1 Library St. Anthony Falls Hydraulic Lab
i Director
Woods Hole Oceanographic Institute 1 Dr. C. S. Song
Woods Hole, Mass. 02543
Attn: Reference Room 1 Univ of Notre Dame
Dept of Mech Engr Worcester Polytechnic Institute
Alden Research Labs 1 Univ of Washington
Worcester, Mass. 01609 Applied Physics Lab
Attn: Director Attn: Director
44 3 Univ of Calif, Berkeley
College of Engr, Fluid Mech Dept i AVCO, Lycoming Div., Washington Naval Architecture Dept
1 Library i Baker Mfg, Evansville
1 Prof J. V. Wehausen i Prof J. R. Paulling
Univ of Bridgeport Aerojet-General Corp
Bridgeport, Conn. 06602 1100 W. Hollyvale Street
Attn: Prof Earl Uram Azusa, Calif. 91702
Mech. Engr. Dept. Attn: Mr. J. Levy
Bethelehem Steel Corp 3 Lockheed Missiles and Space, Sunnyvale
Central Technical Division i Dept 5701
Sparrows Point Yard, i R. L. Ward
Sparrows Point, Md. 21219 1 T. Thorsen
Attn: Mr. A. Haff, Tech Mgr
1 Martin Co., Baltimore
Boeing Aircraft, AMS Div, Seattle
2 McDonnell-Douglas Aircraft Corp
Bolt Beranek & Newman, Inc. i Mr. John Hess
50 Moulton Street 1 Mr. A. M. O. Smith
Cambridge, Mass. 02138
Attn: Dr. N. Brown
i
National Steel & Shipbldg. Co. Habor Drive & 28th Street Cambridge Acoustical Associates, Inc. San Diego, Calif. 92112 129 Mount Auburn StreetCambridge, Mass. 02138 1 Newport News Shipbldg. & DD Co.
Attn: Mr. M. C. Junger Attn: Technical Lib Dept
Esso International 1 Puget Sound Bridge & Drydock Co.
15 West 51st Street Seattle
New York, N. Y. 10019
Attn: Mr. R. J. Taylor 1 George G. Sharp, Inc.
Manager, R&D Tanker Dept
1 SNAME, 74 Trinity Place
General Dynamics, Electric Boat New York, N. Y. 10006
Groton, Conn. 06340
Attn: Mr. V. Boatwright, Jr. 1 Sperry-Gyro Co.
Great Neck, L. I., N. Y. 11020
2 Gibbs & Cox, Inc. Attn: Mr. D. Shapiro (Mail Sta G2)
40 Rector Street
New York, N. Y. 10006 1 Sun Shipbldg. & DD Co.
1 Tech Lib Chester, Pa. 18013
i Mr. Frank Butler Attn: Mr. F. Pavlik
Chief Naval Architect Grumman, Bethpage
Attn: Mr. W. Carl 1 Tectra Tech, Inc.
603 Rosewood Blvd
2 Hydronautics, Inc. Pasadena, Calif. 91107
Pindell School Road Attn: Dr. Chapkis
Laurel, Md. 20810
i Mr. P. Eisenberg i United Aircraft, Hamilton Standard Div.
i Mr. M. Tulin Windsor Locks, Conn.
ITEK Corp, Vidya Div, Palo Alto 6 Rutgers Univ
Mechanical and Aerospace Engineering
2 Litton Systems, Inc. New Brunswick, N. J. 08903
P. 0. Box 92911 1 Dr. R. H. Page
Los Angeles, Calif. 90007 1 Dr. C. E. G. Przirembel
1 Mr. S. Denn 1 Dr. C. F. Chen
i Mr. I. Rains i Dr. D. G. Briggs
1 Mr. G. F. Melick, Jr. i Dr. L. S. Fletcher 45
Copies Code 0000 1 1124 1 1500 1 1502 1 1504 1 1505 1 1506 1 1520 2 1521 2 1524 2 1528 1 1532 1 1540 1 1542 30 1544 3 1552 1 1560 1 1568 2 1735 1 1805 1 1843 30 5614 1 5641 1 5642 1 9422 CENTER DISTRIBUTION 46
!["Jana hr. Potockiego prace i zasługi naukowe", Aleksander Brückner, Warszawa 1911 : [recenzja]](data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==)