DAVID W. TAYLOR NAVAL SHIP
RESEARCH AND DEVELOPMENT CENTER

Bethesda, Maryland 20084-5000

DTNSRDC-84/072

PRESSURE DISTRIBUTION ON PROPELLER BLADE SURFACE
USING NUMERICAL LIFTING SURFACE THEORY

by

Ki-Han Kim

Sukeyuki Kobayashi

APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

Presented at Propellers 1984 Symposium
Virginia Beach, Va.
15-16 May 1984

SHIP PERFORMANCE DEPARTMENT
RESEARCH AND DEVELOPMENT REPORT

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January 1985 DTNSRDC-84/072

MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS

OFFICER-IN-CHARGE
CARDEROCK

SYSTEMS
DEVELOPMENT
DEPARTMENT

SHIP PERFORMANCE
DEPARTMENT

15

STRUCTURES
DEPARTMENT

SHIP ACOUSTICS

DEPARTMENT

SHIP MATERIALS
ENGINEERING
DEPARTMENT

COMMANDER
TECHNICAL DI REST a

OFFICER-IN-CHARGE
ANNAPOLIS

AVIATION AND
SURFACE EFFECTS
DEPARTMENT

COMPUTATION,
MATHEMATICS AND
LOGISTICS ap neCd ite

PROPULSION AND
AUXILIARY SYSTEMS
DEPARTMENT

CENTRAL
INSTRUMENTATION
DEPARTMENT

SPO 867-440

NDW-DTNSRDC 3960/43b (Rev. 2-80)

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REPORT DOCUMENTATION PAGE
1. REPORT NUMBER 2. GOVT ACCESSION NO.) 3. RECIPIENT'S CATALOG NUMBER
DINSRDC-84/072

4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

PRESSURE DISTRIBUTION ON PROPELLER BLADE Final
SURFACE USING NUMERICAL LIFTING SEEREORNINGIORGEREEORINTVEER
SURFACE THEORY

- AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(a)

Ki-Han Kim
Sukeyuki Kobayashi

- PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK
; - AREA & WOR i
David W. Taylor Naval Ship Research oa ae eno.

and Development Center
Bethesda, Maryland 20084-5000

- CONTROLLING OFFICE NAME AND ADDRESS P 12. REPORT DATE |
David W. Taylor Naval Ship Research January 1985
and Development Center TOEENUNEERIORIDACES

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APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

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- SUPPLEMENTARY NOTES

Presented at Propellers 1984 Symposium,
Virginia Beach, Virginia, 15-16 May 1984

- KEY WORDS (Continue on reverse aide if neceeaary and identify by block number)
Propeller
Blade Pressure
Lifting Surface Theory
Discrete Vortex/Source Method

. ABSTRACT (Continue on reverse side if necessary and Identity by block number)

A procedure and numerical results are presented for the prediction of
the steady pressure distribution on a rotating propeller blade surface
based on lifting surface theory. A computer code, named the Propeller
Steady Pressure (PSP) program, has been developed by extending the existing
propeller analysis program, PSF, based on vortex/source lattice techniques,
developed at the Massachusetts Institute of Technology. Predictions by

(Continued on reverse side)

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DD , an 73 1473 EDITION OF 1 NOV 65 Is OBSOLETE UNCLASSIFIED
fs - - .
Sue hema Caleta, SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

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(Block 20 continued)

PSP are compared with selected experimental values that are believed to
be accurately and reliably measured. Comparisons are also made between
PSP predictions and other theoretical predictions. The predictions by
PSP are generally in good agreement with experimental values and with
other prediction methods except for the tip region where current pro-
cedures may not be accurate enough to represent the actual flow.

S/N 0102- LF- 014-6601

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SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)

TABLE OF CONTENTS

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FANE, SIGUA CoE tage howe: ich WA RRO Yes we See cates era EO ck- 4. oh ep coe pa dct EEN se A rei gan ad 1
INTRODUCTION: 4 s.c0 SHS” SMA Chesed lL sites «ae CSSReEOTeee. soablacec 1
OVERVEEW OFUPSP. 0.5 SAE RR Se naags Sato SRS Se nakenetsae Se. oxeaoee 2
MODERTCATION LO BSE GE (teas omen cmeiors Stoo etla eine haces Corotien fo mee 4
RESULTS. AND¥DESCUSSTONS tee. ealsB ons HSE cd ce ood cee. oP bo eBatehes Leas 8

TOADINTENSION/NL, AIRBOI SHEMIONS 59566 65-0 6 66 6 6 6 ao boo 6 8

ISOC SCOOT, TONOPIGILALO WOPY Deyae oe ee bale 6 a 6 6 loo 6 oe 8

DINSRD CaP ROP EIEERS A/liGe ey. SViee icons, won cuenta cues Lactose cat eal ES UnNe d Laer iece Cees 10

NSMBEMOD Pag ER ORE IER A tren 00 Se teeimy Saneics ametay ae sttt eu area, ren ata rt PO 11

COMPARISON WEE OUSIIR PROGRDURES , , 5 56 66660 ooo ooo oo 11
SUMMARYaVAN DIC ON CLUSION Se. ce eee atten lumen rein ee ote Pas et a me a 12
RECOMMENDATIONS an cece et ete node cat eran Le eT rte ance cla” aie ete Bases Denes 13
AGKNOWIEEDEMENs 12 pee cima nyract uat ea eaiccie he ee Rue ree Deo ea esn reels te cninete vies Wniee pane Uaeteee 3)
REAR ARUEIN GES nits ron weg a Rete Oe eR ar. he eA a ee 15
APPENDIX — PRESSURE IN A MOVING FRAME OF REFERENCE . .,........ 17

LIST OF FIGURES

1 - Fixed and Rotating Coordinate Systems for a Right—Hand-

RotatdonweLope ler Weta. ye Rien ae AMES 6 re ett VO nae os a neem Te 21
2 = piscine sicitem ou Wilecks Sainemilenitetes 5 6 5 5 6 46 6 oo oo oO DP
3) = ishoresyerinvoys Wropeterleas; onl Wile eiol stm WEIRD 5 5 5 6 6 0 0 5 0 6 0 0 23
4 - Trailing Wake Geometry after Wake Alignment .... sis. / Sia set ee 24

5 - Discrete Singularity Distribution for Two-Dimensional
Airroid: Section ~ Fw4 casas ahane Simediahs + aoe ell ww ae ene tee 25

iii

10

1l

12

13

14

1L5)

16

20

Schematic Representation of the Effect of Chordwise Vortices
omni (ene) El DR@eSuKEa Woilmie o co a a 6 0 oo 6

Pressure Distribution on Flat Plate at a = 4 Degrees

Pressure Distribution on NACA 0012 Section at a 0)

Degrees

Pressure Distribution on NACA 4412 Section at a = 6.4
Degrees

Open-Water Performance of IHI Model Propeller MP 282

Pressure Distribution on IHI Model Pee ae MP 282
aie JS O54 90 0 0 ¢ . 0 0 0

Pressure Distribution on IHI Model oe ae MP 282
ae oS We los 0 0 6 F 6 <r

Surface Flow Patterns by Oil-Film Test on IHI Model
Propeller MP 282 : Bd Gerno: 26" .on Ibe tc

Pressure Distribution on DINSRDC Propeller 4718 at
J = O75 0606006000 0

Pressure Distribution on Suction Side of DTNSRDC Propeller
4718 at r/R = 0.5: Comparison of Prediction and Two

Sets of Experiments PAPA aes colitis aos komon lornto 1 ton hating
Open-Water Performance of NSMB Model Propeller

Pressure Distribution on NSMB Propeller at J = 0.4
Pressure Distribution on NSMB Propeller at J = 0.6
Pressure Distribution on DTNSRDC Propeller 4118 at

J = 0.833: Comparison with ITTC Propeller

Committee Survey

Pressure Distribution on DINSRDC Propeller 4498 at
J = 0.888 LS Mae iets Seg! Dal eu Peo ne tele cette

Table 1 - Propeller Geometric Characteristics

iv

26

Zi)

28

BS)

30

31

32

33

34

35

36

37

39

41

42

43

J = V/nD

Oona)

A
It

T/(pn-D")

a

C= (p-p,,)/ (eVe/2)

NOTATION

Blade-section chord length

Pressure coefficient

Propeller Diameter
Meanline shape function
Gravitational acceleration

Unit base vectors in a cylindrical polar reference system

Unit base vectors in a Cartesian reference frame

Total rake: axial displacement of blade-section midchord
point from y-z plane

Advance coefficient

Torque coefficient

Thrust coefficient

Propeller rotational speed, revolutions per unit time
Pitch of blade section
Pressure

Ambient pressure

Torque absorbed by blades, or strength of discrete line
source per unit length

Distributed source strength
Propeller radius

Radial coordinate

Position vector of field point
Thrust produced by blades

Thickness shape function

V Total velocity vector

Vp Reference speed

GEai75 4) Cartesian coordinates fixed on propeller

(0 9¥ 5225) Cartesian coordinates in inertial reference frame

x, Fraction of chord, measured from leading edge

Xp Fraction of radius, measured from axis of rotation

Zz, Number of blades

a Angle of attack

r Strength of discrete bound vortex for two-dimensional
airfoil

ite Chordwise discrete vortex on the blade surface

Iie Spanwise discrete vortex on the blade surface

BG Fane pac. Total distributed vortex on the blade surface

Mi Chordwise distributed vortex on the blade surface

Jas Spanwise distributed vortex on the blade surface
=

8 = tan (z/y) Angular coordinate in propeller-fixed coordinates

O. = tan (2,/y,) Angular coordinate in inertial reference frame

85 Skew angle; circumferential displacement of blade-section
midchord point from z=0 plane

fe) Fluid density

(0) Pitch angle of blade section nose-tail line; measured
on cylinder of radius r

Q = 27n Propeller rotational speed; radians per unit time

w Vorticity vector in flow field

vi

ABSTRACT

A procedure and numerical results are presented for the
prediction of the steady pressure distribution on a rotating
propeller blade surface based on lifting surface theory. A
computer code, named the Propeller Steady Pressure (PSP)
program, has been developed by extending the existing pro-
peller analysis program, PSF, based on vortex/source lattice
techniques, developed at the Massachusetts Institute of
Technology. Predictions by PSP are compared with selected
experimental values that are believed to be accurately and
reliably measured. Comparisons are also made between PSP
predictions and other theoretical predictions. The pre-
dictions by PSP are generally in good agreement with experi-
mental values and with other prediction methods except for
the tip region where current procedures may not be accurate
enough to represent the actual flow.

INTRODUCTION
Knowledge of the pressure distribution on the propeller blade surface is
essential to understanding cavitation phenomena, boundary layer characteristics
and stress on blades. Measuring the pressure distribution on a rotating blade is
extremely difficult and time-consuming, and even then the reliability and repeat—
ability of the experimental data are often questionable. Nevertheless, a number
of experimental results of reasonable reliability are available, such as the ones

*
obtained by Mavludoff, | Kato,” Yamasaki, ° Takei et alia Tosswp.” and Versmissen

and Van Gent,”
The ability to predict the blade pressure distribution reliably and accurately
is also highly desirable. Many institutions throughout the world have their own
prediction methods; most of them are based on lifting-surface methods such as those
of Okamura, / Kuiper, ® Brockett,” and Tsakonas et silage and a two-dimensional pro-
cedure with some empirical corrections for three-dimensional effects by Bahgat./!
In this report, a procedure is presented to predict the pressure distribution
on the propeller blade surface operating in steady flow based on the discrete
vortex/source lattice method developed by Greeley and avis The discrete

vortex lattice method has been used in the field of aerodynamics as early as 1943

*A complete listing of references is given on page 15.

by Gaudimes:* for the calculation of aerodynamic forces on an arbitrary wing shape.
The accuracy of this simple method has been found very gaiieBackorr and in two-
dimensional flow "yemarkable't. +> The primary advantage in using the discrete
vortex/source lattice method is the ease and the flexibility to model the complex
geometries of the propeller blades and their trailing vortex wake. With the advent
of large computers, panel methods are widely used for the design and analysis of
three-dimensional aerodynamic configurations both as the simple vortex/source
lattice approximation and as more complex local elements.

In the area of marine hydrodynamics, Kerwin and ioe? developed a discrete
vortex/source method and corresponding computer code, PUF2, for the prediction of
steady and unsteady performance of subcavitating propellers. Rotsaserstn | and
eo developed a procedure to compute the pressure distribution based on the
method developed by Kerwin and 6,2? More recently, Greeley and Rea”
developed design and analysis procedures and corresponding computer codes, PBD-10
for design and PSF for analysis, for propellers operating in steady flow. Greeley
and Reman made improvements to the steady part of the procedure developed by
Kerwin and igen 2 in two major areas; one is the improved semi-empirical description
of the trailing vortex sheet and the other is the capability to model the flow
over the outer portion of the blade more accurately. In the present work, only
the "global" part of the procedure developed by Greeley and Renin has been
investigated for the pressure distribution. The more accurate local flow model
near the tip is yet to be examined.

A computer code, named the Propeller Steady Pressure (PSP) program, has been
developed by extending the propeller analysis program, PSF, presented by Geealey”
and Greeley and Kerwin. This report describes the computer code and presents
some comparisons of the predictions made by PSP with experimental measurements and

predictions by other theories.

OVERVIEW OF PSP
The Propeller Steady Pressure (PSP) code is basically the same as the Propeller
Steady Flow (PSF) analysis program developed by Greeley and Keruiln, except for
the additional capability in PSP of calculating the pressure distribution on the
blade surface. The PSF code assumes that the propeller operates in an axisymmetric
onset flow consisting of axial, radial, and tangential components. The presence

of the propeller hub and any other boundaries to the flow is ignored. The blade

boundary layers are assumed to be thin, so that the flow can be treated as inviscid,
except for the calculation of frictional drag.

The nonrotating coordinate system, (X59 5925)» and rotating coordinate system,
(x,y,z), fixed to the blades are shown in Figure 1. The x-axis of the fixed and
rotating system are coincident, as are the (y,z) and (¥ 5925) planes. The defini-
tion of the angular coordinates in the fixed system, 0» and in the rotating sys-
tem, 8, are also defined in Figure 1. The propeller rotates at a constant angular
velocity, 2 = -Mi. A field point, P, in the fluid with angular coordinate, 8, in

the rotating frame has an angular coordinate

6 = 6 - Nt Gib)

ie)

in the fixed frame for a right-handed propeller shown in Figure 1.

The blade geometry is defined relative to a midchord line, which is para-
metrically defined by the radial distribution of skew, 8), and total rake,

i, (r). The pitch angle, o(r), and chord length, c(r), define the angle and extent
of the sectional nose-tail line along the pitch helix on the surface of a cylinder
of radius r. The meanline offset, f(r,x.), and thickness distribution, t(r,x)5
describe the section characteristics of the blade as a function of radius, r, and
nondimensional arc length, Xoo along the nose-tail line. The meanline, f, is
measured along the cylindrical surface at right angles to the nose-tail line. The
thickness, t, is measured perpendicular to the meanline,*

The blades and vortex wake are represented by straight-line vortex and source
lattice elements of constant strength, distributed over the meanline surface of the
blade (see Figure 2) and the assumed surface of the trailing vortex sheet. The
vortices are arranged in the traditional horseshoe configuration (see Figure 3) so
as to satisfy Kelvin's conditions automatically, and the strength of each horseshoe
vortex is determined by solving a set of simultaneous equations, each satisfying
the flow tangency condition at a blade control point. Source strength is deter-

mined from the slope of the thickness distribution and resultant onset speed.

* at DINSRDC, the thickness is conventionally measured perpendicular to the
nose-tail line. In linear theory the differences of these two specifications is
of higher order.

The position of the shed vortex sheet is determined iteratively by first
solving the boundary value problem with an assumed position, and then aligning the
wake with the computed total velocity field for a specified radial contraction.
The boundary value problem is then re-solved and the procedure is repeated until
convergence (see Figure 4). This process of wake alignment is different from the
simple wake model in pur2, 1° where the trailing vortex wake geometry is defined at
the outset by several semi-empirically determined geometric parameters.

Once a converged solution is obtained, blade forces are computed by applying
the Kutta-Joukowski and Lagally theorems. The Lagally theorem is used to compute
the forces on the source elements as a modification for the effect of the thickness
onseae”” This modification is equivalent to subtracting the thickness-induced
velocity from the total velocity used to compute the Kutta-Joukowski force on the
vortex elements. If the thickness-induced velocity were included in the total
velocity, the resulting Kutta-Joukowski force would be larger than experimental
values. In PSF, as in PUF2, an empirical suction factor is used to estimate the
leading-edge suction force at off-design conditions. The reader is referred to

, eZ : :
Greeley and Kerwin for details of the computation.

MODIFICATIONS TO PSF

In PSF, the overall blade load is computed by summing up the elementary loads
(the jump in pressure across the surface) acting on each line vortex and source
element. The elementary load is computed at the midpoint of each spanwise and
chordwise singularity on the key blade by assuming the average velocity over the
length of a singularity can be approximated by the velocity at its midpoint. This
point is called "load point." Since the total velocity is calculated at each load
point to compute the load, it is logical to choose the same point as the "pressure
point" for pressure calculation. In the present study, pressure is computed at
only the pressure points on the spanwise singularities and is interpolated at
specified radii.

The velocity calculated at the load point in PSF is a mean velocity that does
not include the self-induced velocity due to the singularity segment where the
elementary load is calculated. However, when computing the pressure, not the jump

in pressure, the velocity jump across the singularity must be included.

Since the vortex/source sheet on the blade surface is represented by "discrete"
singularity elements, each discrete element represents a certain area. Therefore,
when computing the velocity jump across the vortex sheet, we have to redistribute
this concentrated vortex/source over the area.

Consider a two-dimensional airfoil illustrated in Figure 5. The discrete
bound vortices/sources are located on the meanline at the quarter chord of each
meanline segment to approximate the continuous distribution of the vortex/source
along the meanline. Suppose qr is the strength of the bound vortex at the Tee

segment whose length is Ac,. Then the distributed vortex strength, Y,> over this

segment can be approximated by:

(2)

assuming the vorticity is uniformly distributed over the segment. The velocity
jump across the vortex sheet is related to the local vortex strength, Yy> as

follows:

Ne Y.
ar aL = 1
Wi), = ye and We == os (3)

where the plus sign represents the upper surface and the minus sign the lower sur-
face. In this two-dimensional case, the velocity jump is tangent to the surface
in the chordwise direction.

Similarly, the distributed source strength, q,> over the same segment will be:

Gq, = (4)

where Q; is the strength of the discrete source element. The source sheet induces
a jump in normal velocity, that is related to the local source strength, q,> as
follows:

q. q.
pre tl 8 =e )

where the plus and minus signs represent the upper and lower surfaces, respec-—
tively. ’

For three-dimensional flow such as that on propeller blades, the direction of
velocity jump depends on both the spanwise and chordwise vortices. In this case,
both spanwise and chordwise singularities have to be properly accounted for when
computing the velocity jump. The following is the algorithm adopted in the pre-
sent study.

Suppose we want to compute the velocity jump at the qe pressure point on qian
spanwise vortex element. The total distributed vortex at this point, Yy> is the

sum of the spanwise and chordwise distributed vortices:
1 > Gide 9 OLs (6)

The spanwise distributed vortex, Gar is approximated by:
i = The, a
a

where Ac, is the length of the chordwise segment represented by the discrete span-
wise vortex, Ci: This is analogous to the two-dimensional distributed bound
vortex (see Equation (2)). The chordwise distributed vortex, (Y)> is approximated
by the vector average of the four adjacent chordwise vortices, (QO p (T)o9> 3

and De. (see Figure 6):
4
: AEA =e i
a ae Ar ie

where Ar, is the length of the radial segment represented by each discrete chord-
wise vortex, Wad a The total distributed vortex, Yi? is then converted to the
velocity jump in the tangential direction by using Equation (3).

The velocity jump due to the source sheet is identical to the two-dimensional
case (see Equation (5)) since the boundary condition for thickness effects results
in the same relation between source strength and slope of the chordwise thickness
distribution with radius as a parameter. These velocity jumps due to vortices and
sources are added to the velocity induced by all other singularities to obtain the

total velocity induced by the propeller.

The pressure on a propeller blade surface rotating at a constant angular
velocity, 2 = -Ni (see Figure 1), in an axisymmetric onset flow can be expressed

as (see Appendix):

1 2 ae
DS = Olh= WD), =e Wi wy (9)

where W = coral weiloeiliays W = Wap safle, oP Wap W
= Sand =W) =ois =p So
a - ; ; Fe mee an
Ve axisymmetric onset flow; wet Vii Vines Vo &o
V_ = perturbation velocity due to the propeller blades and
“P their wakes
Vg = perturbation velocity due to the other sources such

as appendages or lifting surfaces

(i4,e ,e,) = unit vectors in the axial, radial and tangential
directions in the cylindrical coordinate system
(x,r,8) rotating with the propeller

The subscript, A, in Equation (9) indicates a point on the same streamline where
the pressure is computed.

If a propeller is operating in a uniform onset flow with only an axial compo-
nent and with no other sources of disturbance, i.e., the flow condition for all
the experimental measurements correlated in this report, the pressure will be:

1 2 DP
a FAO Ts Tr +e Po (10)
where V = Wat Mer + woo and p, is the pressure at any point far upstream of a

propeller.

We define the pressure coefficient a as

PFA
QS eee ean Se (1)
Pp L y2 y2 = x
aR R

where Vp is a reference speed. In PSP, three options are given for VR; one is the

local inflow speed to the blade section, Vve + (2mnr)2 , the other two options are
the local inflow speed at r = 0.7R and the ship speed.

RESULTS AND DISCUSSIONS

The procedure to calculate the pressure distribution presented in the.pre-
ceding section has been applied to the following configurations:

1. Two-dimensional airfoil sections; flat plate, NACA 0012 and NACA 4412
sections

2. IHI Propeller MP 282

3. DINSRDC Propeller 4718

4. NSMB Model Propeller

5. DINSRDC Propeller 4118

6. DINSRDC Propeller 4498
The geometric characteristics of these propellers are summarized in Table 1. The
predictions by PSP are compared with either experimental measurements or other

theoretical predictions.

TWO-DIMENSIONAL AIRFOIL SECTIONS

In order to test the validity of the discrete vortex/source lattice method for
pressure computation, a computer program, FOIL2D, was developed for computing the
pressure distribution on two-dimensional airfoil sections. FOIL2D has all the
ingredients of the discrete vortex/source lattice method except for three-dimen-—
sional effects.

Figure 7 shows the comparison of the predicted pressure distribution on a flat
plate with an angle of attack a = 4 degrees by FOIL2D with the analytical solution in
Reference 20. In Figure 8, the pressure distribution is compared for the analytical
soilueioan” and the FOIL2D predictions on the NACA 0012 section at zero angle of
attack. In Figure 9, measured pressure distribution on NACA 4412 section at
a = 6.4 degrees is compared with predictions by different methods including FOIL2D.
Agreements between the predictions by FOIL2D and experiments as well as those
between the former and other prediction methods are excellent for two-dimensional

shapes.

IHI MODEL PROPELLER MP 282

The open-water performance and the pressure distribution were computed on the
Ishikawajima-Harima Heavy Industries (IHL) large model propeller MP 282 operating
in uniform flow. The diameter of the propeller is 0.95 m. This propeller has

radially varying meanline and thickness distribution. The predictions are

8

compared with the experimental measurements performed using individual tubes to

a hub sensor made at IHI Ship Model Besinne an
The open-water performance was calculated and compared with experimental

results in Figure 10. The predicted Ky values are in excellent agreement with

experimental measurements. The predicted K, values are about 5 percent greater

than the experimental values over the ifn be advance coefficients.

The pressure distribution on the blade of Propeller MP 282 was calculated for
two different J values; J = 1.054 and J = 1.163. The pressure coefficients were
calculated on both the suction and the pressure sides at selected radii (r/R = 0.6,
Os75 Os8> Os) -

In Figures 11 and 12, the experimental measurements and the predicted Us are
compared at J = 1.054 and J = 1.163, respectively. The experimental measurements
were made at a Reynolds number, RA = 1.9 x 10. The calculated pressure coeffi-
cients are in good agreement with measurements on the pressure side except near
the leading edge, but generally overpredict the suction side pressure. The agree-
ment at the reduced J value is better than that at the increased J value. In
general, the predicted values are in satisfactory agreement with the experimental
measurements throughout the radius at the two different J values.

In Figure 13, the oil-film test results reconstructed from the photographs in
Reference 21 are shown at two Reynolds numbers; 1.1 x 10° and 2.6 x 1°. The oil
film illustrates the surface streamlines on both sides of the blade. At the
reduced RK, condition, the flow patterns on the suction side have significantly
reduced shear stress over the forward part of the blade and a clear separation
occurs slightly past midchord. On the pressure side, reduced shear regions occur
toward the leading edge and some indication of a leading-edge laminar separation
bubble occurs at both Reynolds numbers.

No surface flow patterns are presented in Reference 21 for the test Ro of
le) x 10°. However, judging from the measured pressure coefficients shown in
Figures 11 and 12, it is possible that separation occurred near 0.7 fraction of
chord on the suction side and at the leading edge on the pressure side in the form
of a icra ile Such separation would explain the suction peak on the pressure side
near the leading edge and the pressure peak measured at 0.7 radius at 0.7 fraction
of chord (measurements were not made at a similar chordwise position at other

radii). It is further hypothesized that the suction side separation is a thin

layer with only minor influence on the pressure away from the separation line.
: 3 Fee nic ; ;
Previous data for this propeller indicated that the pressure at the point in

question exhibited the same property as a function of Reynolds number.

DINSRDC PROPELLER 4718

The steady pressure distribution was calculated on the surface of DINSRDC
controllable-pitch Propeller 4718 at the design advance coefficient, J = 0.75.
The propeller has three blades with diameter of 2 feet (0.61 meters), EAR of 0.44,
and tip skew of 20 degrees. In Figure 14, the predicted pressure coefficients are
compared with experimental HEASUTETEMES” on the blade surface with the propeller
operating in uniform flow at three different radii; r/R = 0.5, 0.7, and 0.9. The
pressure was measured by transducers mounted on both sides of the blade surface.

The experimental values were measured at six different RY values ranging from
Des) uo 10° EG. 4503) x 10° at the design J. For this range of Ro the flow on the
surface should be fully turbulent so that the pressure distribution would be nearly
independent of Rv However, the experimental measurements showed substantial
variations for different RO values. The variation is more pronounced on the
suction side than on the pressure side. In general, the pressure coefficients
increase with increasing RA values. The measured pressure coefficients shown in
Figure 14 represent the average values over the range of Rk: Unpublished flow
visualization* of the surface streamlines showed no anomolous flow over the blades.

At r/R = 0.7, the computed values are in reasonable agreement with experi-
mental values. However, the agreement at the other two radii is not as good as
that at r/R = 0.7. At r/R = 0.5, the experimental results show some irregular
peaks at ig 0.12 and 0.5 on both sides. jieeeue” explained that some of these
irregularities in the measured values might be partially attributed to the effect
of the relatively large fairwater and hub.

More recently, Jessup* measured blade pressure on the same Propeller 4718
using another technique. In this experiment, Jessup measured the pressure distri-
bution only on the suction side at two radii, r/R = 0.5 and 0.8 at the design

J = 0.751. In Figure 15, the two sets of experimental values are compared with PSP

*Private communication from S. Jessup, DTNSRDC, Code 1544.

10

predictions. Although both experimental measurements showed Reynolds number
effects, the correlation between PSP predictions and the new experimental values
improved substantially.

The larger discrepancy at r/R = 0.9 on the suction side may be due to real
flow effects. However, experimental inaccuracy demonstrated at r/R = 0.5, or the
coarse modeling for the global solution in the analytic treatment of the flow in

that region can also be a possible source of the discrepancy.

NSMB MODEL PROPELLER

The steady pressure distribution was computed on the NSMB model propeller at
J = 0.4 and 0.6 to correlate with experimental daca.” This propeller has simple
geometric characteristics; no rake, no skew, and a single section shape over the
radius. It was originally designed for bubble cavitation investigation.

The open-water performance was calculated and compared with experimental re-

sults in Figure 16. The predicted Kp and K, are in excellent agreement with the

experimental values for the range of J nth except for very reduced ones.

In Figures 17 and 18, the predicted pressure coefficients are compared with
experimental measurements obtained at NSMB° at J = 0.4 and 0.6, respectively, at
ive Ghittenene racine e/R = O64, 0.5, 0665 Oo7> emal O28, Ae e/R = O09, Omilly joie
dicted values are plotted since the pressure was not measured at that radius. The
pressure was measured by transducers mounted within both sides of the blade surface.

The experimental measurements were made twice within a six-month period in
order to assess the repeatability. The two series of experimental results are
shown in Figures 17 and 18. The repeatability is generally good. The predicted
values on both sides are in good agreement with experimental measurements at both

J values.

COMPARISON WITH OTHER PROCEDURES

In 1978, the ITTC Propeller Committee surveyed existing prediction methods for
pressure distribution on the propeller blade guvtaceu They compared the pre-
dictions made by various methods from sixteen participating institutions throughout
the world. The propeller selected for the comparative calculations was DTNSRDC
Propeller 4118, a three-bladed research propeller tested thoroughly at DTNSRDC for

open-water performance, cavitation, and unsteady forces.

Wil

In Figure 19, the predictions by PSP are compared with other predictions
represented by the envelope covering all the predicted results at the design
advance coefficient, J = 0.833. The predicted values by PSP are within the
envelope of the predictions by other methods.

In Figure 20, comparisons are made between predictions by PSP and by a lifting
surface method presented by Bapalwee. for a propeller similar to DINSRDC Propeller
4498 at J = 0.888. The propeller is warped with 72 degrees warp angle at the tip.
The section meanline is similar to the NACA a = 0.8 meanline.

The predictions made by the two different methods are in good agreement at
r/R = 0.254, but the discrepancies increase toward the tip region, as it did for

the experimental data of Jessup.

SUMMARY AND CONCLUSIONS

The discrete vortex/source lattice lifting surface method has been used for
the prediction of steady pressure distribution on a rotating propeller blade sur-
face. A computer code, PSP, has been developed by extending the existing propeller
global analysis program, PSF, developed at M.I.T.

For pressure computations on the propeller blades, the velocity jump across
the vortex/source sheet must be carefully treated and include the effects of both
the spanwise and chordwise vortices. In PSP, the effect of the chordwise vortices
at the pressure point, the midpoint of each spanwise vortex, was accounted for by
interpolating from the four adjacent chordwise vortices.

Comparisons of the predictions by PSP with experimental measurements and pre-
dictions by other methods on selected model propellers generally showed good
correlations. The correlations near the tip region, especially for skewed pro-
pellers, i.e., Propellers 4718 (20 degrees tip skew) and 4498 (72 degrees tip skew),
are not as good as those for the inner region. Possible explanations may be that
near the tip region of skewed propellers, viscous effects may be large or that the
current numerical modeling in lifting surface representations may not be accurate

enough.

*The predictions by Brockett shown in Figure 20 are taken from Figure A
(linear 3D method) in "Discussions and Authors' Closures" section of Reference 9.

2

RECOMMENDATIONS

Based on the investigations made in the present work, the following studies
are recommended in order to further improve the current prediction method:

1. The improved-accuracy, tip-flow part of the PSF should be used for the
prediction of the pressure distribution near the tip region. The tip flow is very
complicated and of practical importance, and yet the prediction near the tip region
is not as good as that for the inner region. Since the tip flow model contains
a finer lattice arrangement than does the global flow model, the tip flow solution
is expected to give more accurate results. The modification to the tip flow part
for pressure calculations is straightforward.

2. In order to be able to predict viscous phenomena such as suction-side
separation or leading-edge laminar bubble separation that is frequently observed
in experiments with model propellers, suitable analytical and numerical analysis
should be undertaken. Some initial efforts in this area have been ondezesken.

3. In order to further assess the validity and limitation of the current
procedure, comparative calculations are recommended with other theories for a
wide range of propellers and operating conditions.

4, Parametric calculations of propeller characteristics of practical
importance such as cavitation inception, boundary layer development, and blade

stress should be undertaken.

ACKNOWLEDGMENT
The authors are very grateful to Dr. Terry Brockett of DINSRDC for many

helpful comments and criticisms during the preparation of this report.

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.

REFERENCES
1. Mavludoff, M.A., "Measurement of Pressure on the Blade Surface of a Non-

Cavitating Propeller Model,'' Proceedings, 12th I.T.T.C., Tokyo, Japan (1965).

2. Kato, H., "An Experimental Study on the Pressure Fluctuations on a
Propeller Blade in a Wake," Proceedings, Symposium on Hydrodynamics of Ship and

Offshore Propulsion Systems, Oslo, Norway (Mar 1977).

3. Yamasaki, T., "On Some Tank Test Results with a Large Model Propeller -

0.95 m in Diameter, Part I,'"' Journal of the Society of Naval Architects of Japan,
Vol. 144 (Dec 1978).

4. Takei, Y. et al., "Measurements of Pressures on a Blade of a Propeller

Model,'' Ship Research Institute, Paper No. 55, Tokyo, Japan (1979).

5. Jessup, S.D., "Measurement of the Pressure Distribution on Two Model

Propellers," DINSRDC Report 82/035 (Jul 1982).

6. Versmissen, G.G.P. and W. Van Gent, 'Hydrodynamic Pressure Measurements
on a Ship Model Propeller," Proceedings, 14th Symposium on Naval Hydrodynamics,
National Academy Press, Washington, D.C. (1983).

7. Okamura, N., "Practical Calculating Method of Propeller Characteristics
W

under Viscous Effects,

(Apr 1977).

THI Engineering Review, Vol. 10, No. 2, Tokyo, Japan

8. Kuiper, G., "Scale Effects on Propeller Cavitation Inception," Proceed-

ings, 12th Symposium on Naval Hydrodynamics (Jun 1978).

9. Brockett, T.E., "Lifting Surface Hydrodynamics for Design of Rotating
g

Blades,'' Proceedings, SNAME Propellers '81 Symposium (May 1981).

10. Tsakonas, S. et al., "Blade Pressure Distribution for a Moderately Loaded

Propeller," Journal of Ship Research, Vol. 27, No. 1 (Mar 1983).

11. Bahgat, F., "Propeller Blade Pressure Distribution at Part Load, Pro-
ceedings, ISSHES-83 International Symposium on Ship Hydrodynamics and Energy

Saving, El Pardo, Spain (Sep 1983).

12. Greeley, D.S. and J.E. Kerwin, 'Numerical Methods for Propeller Design

and Analysis in Steady Flow," Transactions SNAME, Vol. 90 (1982).

15

13. Faulkner, V.M., "The Calculation of Aerodynamic Loading on Surfaces of

Any Shape," British Aeronautical Research Council, R & M 1910 (1943).

14. Faulkner, V.M., "The Scope and.Accuracy of Vortex Lattice Theory,"
British Aeronautical Research Council, R & M 2740 (1949).

15. James, R.M., "On the Remarkable Accuracy of the Vortex Lattice Method,"

Computer Methods in Applied Mechanics and Engineering, Vol. 1, No. 1 (Jun 1972).

16. Kerwin, J.E. and C.S. Lee, "Prediction of Steady and Unsteady Marine
Propeller Performance by Numerical Lifting Surface Theory," Transactions SNAME,

WOls 8 CUY7S))

17. Kobayashi, S., "Prediction of Pressure Distribution on Propeller Blade
Surface Using Numerical Lifting Surface Theory," ORI, Inc. Technical Report No.

2M. (Oeie IEY))

18. Kim, K.H., "Correlation of Pressure Distribution on the Blade of ITTC

Propeller Committee Model Propeller MP 282,'' DTNSRDC/SPD-1093/01 (Feb 1984).

19. Greeley, D.S., "Marine Propeller Blade Tip Flows,'' Massachusetts Institute

of Technology, Department of Ocean Engineering Report No. 82-3 (1982).
20. Abbot, I.H. and A.E. Von Doenhoff, "Theory of Wing Sections," Dover

Publications, New York (1949).

21. Namimatsu, M., "Experiments for MP 282 Large-Scale Model Propeller,'
IHI Ship Model Basin Report No. 450-0, Yokohama, Japan (1978).

22. Report of Propeller Committee, Proceedings, 15th International Towing

Tank Conference (1978).

23. Batchelor, G.K., "An Introduction to Fluid Dynamics,'' Cambridge Univer-

sity Press (1967).

16

APPENDIX
PRESSURE IN A MOVING FRAME OF REFERENCE

In a moving frame of reference, Euler's equation of motion of an inviscid

and incompressible fluid can be expressed as follows (see Bakeielloz-—)s
DV 1 ar dQ
— =- — Vp + F - /—~— + — xrt+22xVtiQx xr) (12)
Dt Fe) = 2 dt = et NT Oe Site es
dt
where BDE = material derivative defined by sel oe MM a Wo W
Dt Dt dt —
V = total velocity with respect to the moving reference frame
0 = fluid density
p = pressure
F = body force per unit mass
as position vector of the origin of the moving frame
Q = angular velocity of the moving frame about the origin
r = position vector of a field point in the moving frame

The last two terms, 22 x V and 2 x (2 x r), are called the Coriolis force and the
centrifugal force, respectively.

If we take neat i 0 and 2 = constant, Equation (12) becomes:
ar + WV) =-— V+ E- M@xV-Qx xr) (13)

Assuming that the gravity force is the only body force acting on the fluid, one

can express F by:

F= WiGeve (14)
where g is the gravitational acceleration and vie is the vertical coordinate in the
nonrotating coordinate system (X59 522) as shown in Figure 1. It is to be noted

that this term is time-dependent in the rotating frame of reference.

Utilizing Equation (14) and the vector identities,

17

SV(vev) = (WV) + Vx (Vx V) @

and
1 2
“2x Qx xr) = 5V(2x x|", (16)
one can express Equation (13) as follows:
fy jo. 1 2 om
ye eriey) cares WAL Vere we wile ahaa ae) (17)

Here, w is the vorticity in the fluid measured in the moving frame of reference.
Now, consider a propeller rotating at a constant angular velocity, 2 = —Qi

(a right-hand rotation propeller, see Figure 1), in an axisymmetric wake of a ship,

where the flow is steady in the rotating frame of reference. The ship wake velo-

Calieyy q Nie, can be expressed in polar components as:

We = Wek + Vien + Vg&q (18)

where VEG Wa and Vo are radially varying axial, radial, and tangential components,
respectively. It is assumed that the variation of the ship wake velocity in the
radial direction is small.

In addition to the ship wake velocity we assume that there exists another
axisymmetric disturbance velocity component, Ne that is introduced locally by

nearby appendages or other lifting surfaces:

WS Nal ae We
ox— fo)

9) rr % Voe2e (19)

Then the total velocity, V, in a cylindrical coordinate system rotating with

the propeller can be expressed as follows:

3 4 20
Veale alsa ew (20)

where a is the perturbation velocity due to the presence of the propeller.

18

In the rotating coordinate system, the vorticity vector, w, can be expressed

as the sum of two terms:
(21)
where W is the vorticity due to the rotation of the coordinate system and wis

the vorticity in the inertial reference frame. From the definition of vorticity,

it can be shown that:
WS Wx (rQe, ) = -22 (22)
Tf we let r = xi + re (6), |Q x r| term on the left-hand side of Equation (17)
will be:
|Q = 2) 2 (23)

Substituting Equations (21) to (23) into Equation (17) with the assumption

of the steady flow, we have:

ee cw eipall 2 a
V > WW ar 5 7) (rQ)7~ + BY, V x @ (24)

By integrating Equation (24) along a path in the flow between two arbitrary

points, A and B, we obtain the Bernoulli equation:

B
| (Vxw) + dr (25)
A

where H(r,t) is sometimes called the Bernoulli head and is defined by:

H(t) = > Vv + 2 - + (9)? + gy (26)

If we take the integral path dr along a streamline or a vortex line, i.e.,
parallel to V or Oo respectively, the integral in Equation (25) vanishes since the
dot product in Equation (25) is equal to zero. It then follows that the Bernoulli
head is constant along a streamline or a vortex line.

By taking a reference point, A, as a point along the streamline far upstream

of the propeller where the propeller perturbation velocity, ey and the other

19

disturbance velocity, Us are negligibly small, the Bernoulli constant, Ha» will

be:

Oe ieee 12
His E WE ar a + By]. (27)

Then the pressure at an arbitrary point in the fluid can be expressed as:

1 2 Pie?
p=- zequu - (7), - emt - on) y,,) + By (28)

where V = Ma) + rie, oF ue + NG and the subscript A indicates a point on the same
streamline (or vortex line) where the pressure is computed. The effect of gravity,
“pay, = Yon) in Equation (28) gives rise to a once-per-revolution periodic varia-
tion in the pressure in the rotating coordinate system. Since this term does not
contribute to the mean pressure and the loading, it is not considered in the pre-
sent study. However, this term may be important when cavitation inception is of
interest.

For a uniform onset flow (potential flow) with only an axial component and
with no other disturbance than the propeller itself, i.e., the flow condition
applicable to all the experimental measurements correlated in this report, the

pressure equation becomes even simpler:

it 1 Re Ae 2 | MID
i ogy Ol ve ral ep (29)

co

where V = Via + re

P + re and p,, is the known pressure far upstream. In this

case, the Bernoulli head is constant everywhere in the fluid since there is no

vorticity in the flow (see Equation (24)).

20

Qt

Figure 1 - Fixed and Rotating Coordinate Systems for a
Right-Hand-Rotation Propeller

21

~

Figure 2 - Discretization of Blade Singularities

22

TRANSITION ULTIMATE
WAKE WAKE

: = Moen WY

OO
MW

Figure 4 - Trailing Wake Geometry after Wake Alignment

24

. : DISCRETE BOUND VORTEX STRENGTH
Q: DISCRETE SOURCE STRENGTH
y : DISTRIBUTED BOUND VORTEX STRENGTH

IT.
1
RS eae
Ac;
q : DISTRIBUTED SOURCE STRENGTH
Q;
Gj =
Ac.

Figure 5 - Discrete Singularity Distribution for Two-
Dimensional Airfoil Section

25

it” PRESSURE POINT

: SPANWISE DISCRETE VORTEX
: CHORDWISE DISCRETE VORTEX

y, : SPANWISE DISTRIBUTED VORTEX, (yy); =

4
1
Y, | CHORDWISE DISTRIBUTED VORTEX, (y;=— > =
‘{ i 4
n=1 n
y, : TOTAL DISTRIBUTED VORTEX AT it” PRESSURE POINT

= Wie;

Figure 6 - Schematic Representation of the Effect of Chordwise
Vortices on the it) pressure Point

26

FLAT PLATE

a = 4°

0.2

O ANALYTIC SOLUTION

yx.) = 2a V,, ViI-x dix,

@ FOIL2D PREDICTION

0.4 0.6 0.8

FRACTION OF CHORD, x,

1.0

= 4 Degrees

Figure 7 - Pressure Distribution on Flat Plate at a

27

“0.0

Figure 8 —- Pressure Distribution on NACA 0012 Section

0.2

NACA 0012 SECTION

a=0Q°

oO ANALYTIC SOLUTION
(REF. 20)

@ FOIL 2D PREDICTION

0.4 0.6 08

FRACTION OF CHORD, x,

at a = O Degrees

28

1.0

O EXPERIMENT NACA 4412 SECTION
a = 6.4°

@ FOIL2D PREDICTION

EXACT POTENTIAL THEORY
(REF. 20)

0.6 0.8 1.0

0.0 0.2 0.4
FRACTION OF CHORD, x,

Figure 9 - Pressure Distribution on NACA 4412 Section
at a = 6.4 Degrees

29

THRUST AND TORQUE COEFFICIENTS

IH! PROPELLER
IH] EXPERIMENT
° PSP/PSF PREDICTION

ADVANCE COEFFICIENT, J

Figure 10 - Open-Water Performance of IHI Model
Propeller MP 282

30

IH! PROPELLER, J = 71.054
———— EXPERIMENT
PSP PREDICTION

SUCTION SIDE

_

——_——

PRESSURE SIDE

SUCTION SIDE

=—_-=——

_—

= vi, + (2nnr)? |

2
R

[Vv

PRESSURE SIDE

SUCTION SIDE

—— .

=—

0.0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD, x,

Figure 11 - Pressure Distribution on IHI Model Propeller
MP 282 at J = 1.054

Syl

IH!i PROPELLER, J = 1.163

— —— — EXPERIMENT
PSP PREDICTION

SUCTION SIDE

—_—=SX“ _——

PRESSURE SIDE

SUCTION SIDE

SUCTION SIDE

—_ —_

—_ —_

PRESSURE SIDE

0.0 0.2 0.4 0.6 0.8 1.0
FRACTION OF CHORD, x,

Figure 12 - Pressure Distribution on IHI Model Propeller
MP 282 at J = 1.163

32

= =~ \

: SS SSS == =
——— SS 5:

SUCTION SIDE PRESSURE SIDE
Rn=1.1x 108, J=1.14

SUCTION SIDE PRESSURE SIDE

R,=2.6 x 108, J=1.15

Figure 13 - Surface Flow Patterns by Oil-Film Test on IHI
Model Propeller MP 282

33

P— Po
% Q Ve

[v2 = v2 + (0.7R2)? |

DTNSRDC PROPELLER 4718, J = 0.75

SUCTION SIDE

PRESSURE SIDE

——e—— EXPERIMENT
——0—— PSP PREDICTION

SUCTION SIDE

—0.1

PRESSURE SIDE

=
ro)

PRESSURE SIDE

:

0.0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD, x.

Figure 14 - Pressure Distribution on DTNSRDC Propeller

4718 at J = 0.75

34

SquUowtTiedxg JO Sjeg OM] pue UOTIOTpei1g JO uostTaedwmopg :¢°C9 = u/4
38 QTL) JoeTTedorg JGYSNIG JO ePptS WoTJONS uo UOTIANGTAISTG sanssetg —- GT sAnsTy

°x ‘GHOHD JO NOILOWHS

OL 80 90 v0 c0

gOL x €S'Z

gOl x 98% = "¥

NOILOIGAYd dSd O————O
Z LN3INI4adX3 &——8
(G ‘43au) L LNAWIYadxXa @-—— —@

aals NOILONS
S'0= uY/4 GL‘0 = ¢ ‘8LZp HATIAadOUd OGUSNLG

010

35

THRUST AND TORQUE COEFFICIENTS

NSMB PROPELLER
NSMB EXPERIMENT
Oo PSP/PSF PREDICTION

0.2 0.4 0.6 0.8

ADVANCE COEFFICIENT, J

Figure 16 - Open-Water Performance of NSMB Model Propeller

36

1.0

Figure 17 - Pressure Distribution on NSMB Propeller at J = 0.4

-—0.5

NSMB PROPELLER, J = 0.4

mee EXPERIMENT 1
—-—-— EXPERIMENT 2

—0.3 PSP PREDICTION
-02
SUCTION SIDE
-0.1
0.0
PRESSURE SIDE
i 0.1
NS
& 0.2
a -0.4
act
>
f -03
ne SUCTION SIDE
>
= ~0.2
aise -0.
| Q
i 0.0
Me PRESSURE SIDE
O 0.1

°
N

—0.4

SUCTION SIDE

—0.3

—0.2

—0.1

0.0

——

0.1 PRESSURE SIDE

0.2

FRACTION OF CHORD, x,

Si)

Figure 17 (Continued)

NSMB PROPELLER, J = 0.4

———— EXPERIMENT 1
EXPERIMENT 2
PSP PREDICTION

SUCTION SIDE

PRESSURE SIDE

int
= -0.5
Ee
SV
ii -0.4
at
> -03 SUCTION SIDE
i] i
=
oo —0.2
siete, et
a|>
| Qa PRESSURE SIDE
a 0.0
a] ax
I 0.1
a
oO —0.6

PRESSURE SIDE

FRACTION OF CHORD, x,

38

r/R = 0.6

P-P,
Yeo V2.

Figure 18 - Pressure Distribution on NSMB Propeller at J = 0.6

[v2 = V2 + (2nnr)? ]

=

Cc

—0.5
NSMB PROPELLER, J = 0.6
—0.4
— —— — EXPERIMENT 1
03 — -—-— EXPERIMENT 2
; PSP PREDICTION
—0.2
SUCTION SIDE
—0.1
0.0
PRESSURE SIDE
0.1
0.2
—0.4
-—0.3
SUCTION SIDE
—0.2
—0.1
0.0
PRESSURE SIDE
0.1
0.2
—0.4
—0.3 SUCTION SIDE
—0.2
-0.1
0.0 a
PRESSURE SIDE
0.1
0.2
0.0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD, x,

39

P- Px
% 9 V2

[v2 = v2 + (2nnri?]

Cc

—0.6

-0.5

—0.4

-0.3

|
°
iN)

|
So
=

©
—)

|
a)
oi —_

|
S
b

|
©
w&

|
°
iy

|
S
=

Figure 18 (Continued)

NSMB PROPELLER, J = 0.6

———— EXPERIMENT 1
—'—-— EXPERIMENT 2
——— PSP PREDICTION

PRESSURE SIDE

FRACTION OF CHORD, x,

40

Figure 19 -

DTNSRDC PROPELLER 4118, J = 0.833 riR = 0.9

ZZ \NTTC SURVEY
@ PSP PREDICTION

SUC

‘ERT,

aa

v
Vw

y

FRACTION OF CHORD, x,

41

Pressure Distribution on DINSRDC Prop
J = 0.833: Comparison with ITTC Propeller Commi

Nyy

eller 4118 at
ittee Survey

DTNSRDC PROPELLER 4498 r/R = 0.946

BROCKETT (REF. 9)
PSP PREDICTION

SUCTION SIDE

PRESSURE SIDE

SUCTION SIDE

PRESSURE SIDE

r/R = 0.254

SUCTION SIDE

PRESSURE SIDE

“0.0 0.2 0.4 0.6 0.8 1.0

FRACTION OF CHORD, x,

Figure 20 - Pressure Distribution on DINSRDC Propeller
4498 at J = 0.888

42

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