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
1S) = ” =) Q iy ne cc =) ” wu aQ < 4! ies) oc Lu -! —! uu a O oc [om 2 e) 2 2 fj 2 = = oe a) uu oc
> cc Oo Ww Se = Oo <x WL o > 77) 1) = re = a J x 2
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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READ INSTRUCTIONS 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
- DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)
- 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)
FORM DD , an 73 1473 EDITION OF 1 NOV 65 Is OBSOLETE UNCLASSIFIED fs - - . Sue hema Caleta, SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
UNCLASSIFIED ee SECURITY CLASSIFICATION OF THIS PAGE (When Deta Entered)
(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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TABLE OF CONTENTS
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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
8677 OdYSNLG
SIIy tet Tedorg SILY OCUSNLA aWSNn OCUSNLG
SOLLSTYXLOVYVHD OLYLHWOUD YATIAdOdd -
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43
sy peer. rere.” ee ETD wt ama Tas ies be sae 3 hae hae? hte
4
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INITIAL DISTRIBUTION
Copies Copies 1 ARMY CHIEF OF RES & DEV NAVSEA (Continued) 1 PMS-391 3 CHONR 1 PMS-392 1 Code 438 1 PMS-393 Lib 1 PMS-397 kee 1 PMS-399 1 PMS-400 NR BOSTON : . 1 SEA Tech Rep Bath, England 4 ONR CHICAGO 2 DET NORFOLK (Sec 6660) 4 ONR LONDON, ENGLAND 2 MMA IL iGatla) N d By 1 Maritime Res Cen 2 USNA i tap 1 NAVFAC 032C 1 Johnson 1 MILITARY SEALIFT COMMAND (M-4EX) 1 NAVPGSCOL Lib 1 NAVSHIPYD/PTSMH 1 NROTC & NAVADMINU, MIT 1 NAVSHIPYD/PHILA 1 NADC 1 NAVSHIPYD/NORVA 5) NOSC 1 NAVSHIPYD/CHASN i US iWib ia 1 6005 1 NAVSHIPYD/LBEACH Ho SSL Whats) 1 NAVSHIPYD/MARE 2201 /Movie 1 NAVSHIPYD/PUGET 1 Nelson 1 NSWC 1 NAVSHIPYD/PEARL 43 NAVSEA ue DIC 5 ah OBR 2 HQS COGARD a SHANODIR 1 US COAST GUARD (G-ENE-4A) i SA 55) 3. SEA 55D 1 LC/SCI & TECH DIV 3. SEA 55N 8 MARAD 1 SEA 55W iL IDC SSBUILD ID)IDIS) 3 SEA 56D 1 COORD RES 1 SEA 56X 1 Shubert 3 SEA 56X1 iL igILilgs 1 SEA 56X2 1 Dashnaw 3 SEA 56X4 1 Hammer 1 SEA 56X5 1 Lasky 1 SEA 56XP 1 Siebold ; sneiee 2 NASA STIF F 1 DIR RES 1 PMS-381 Dre 1 PMS-383
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U LOWA IL battle) 1 TIHR/Kennedy 1 IHR/Landweber 1 IHR/Stern 1 IHR/Patel
JOHNS HOPKINS U/Phillips
U KANSAS CIV ENGR/Lib KANSAS ST U ENGR EXP/Lib LEHIGH U/FRITZ ENGR LAB Lib
U MICHIGAN/DEPT NAME 1 NAME Lib 1 Brockett
Copies
46
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U MICHIGAN/DEPT NAME (Continued)
1 Parsons 1 Vorus
MIT 1 BARKER ENGR Lib 2 OCEAN ENGR/Kerwin
U MINNESOTA SAFHL 1 Killen 1 Song 1 Wetzel
STATE U MARITIME COLL 1 ARL Lib 1 ENGR DEPT 1 INST MATH SCI
NOTRE DAME ENGR Lib
PENN STATE U ARL I Whatlo) 1 Henderson 1 Gearhart Pans ksi! 1 Thompson
PRINCETON U/Mellor RENSSELAER/DEPT MATH ST JOHNS U
VIRGINIA TECH
SWRI 1 APPLIED MECH REVIEW 1 Abramson
BOEING ADV AMR SYS DIV BB&N/Jackson
BREWER ENGR LAB CAMBRIDGE ACOUS/Junger CALSPAN, INC/Ritter STANFORD U/Ashley STANFORD RES INST Lib
SIT DAVIDSON LAB IL © Tato) 1 Breslin 1 Tsakonas 1 McKee
Copies
No KF RF ee
SS Sy SS Sree rea ee
TEXAS U ARL Lib UTAH STATE U/Jeppson
VPI/DEPT AERO & OCEAN ENGR 1 Schetz 1 Kaplan
INST 1 Ward 1 Hadler
WHOI OCEAN ENGR DEPT
WPI ALDEN HYDR LAB Lib ASME/RES COMM INFO
ASNE
SNAME/Tech Lib
AERO JET-GENERAL/Beckwith ALLIS CHALMERS, YORK, PA AVCO LYCOMING
BAKER MANUFACTURING
BATH IRON WORKS CORP 1 Hansen 1 FFG7 PROJECT OFFICE
BETHLEHEM STEEL/Sparrows Point BIRD-JOHNSON CO/Norton DOUGLAS AIRCRAFT/Lib
EXXON RES DIV 1 ab 1 Fitzgerald
FRIEDE & GOLDMAN/Michel GENERAL DYNAMICS, EB/Boatwright GIBBS & COX/Lib
ROSENBLATT & SON/Lib
GRUMMAN AEROSPACE/Carl
TRACOR HYDRONAUTICS/Lib
INGALLS SHIPBUILDING
INST FOR DEFENSE ANAL
ITEK VIDYA
LIPS DURAN/Kress
Copies
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Ka ea pe ei es re
47
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LITTLETON R & ENGR CORP/Reed LITTON INDUSTRIES LOCKHEED, SUNNYVALE/Waid
MCDONNEL DOUGLAS, LONG BEACH 1 Cebeci 1 Hess
MARITECH, INC/Vassilopoulis
HRA, INC 1 Cox 1 Scherer
NATIONAL STEEL & SHIPBUILDING NEWPORT NEWS SHIPBUILDING/Lib NIELSEN ENGR/Spangler
NKF ASSOCIATES/Noonan
NAR SPACE/Ujihara
ORI, INC 10 Kobayashi ean
ATLANTIC APPLIED RESEARCH 1 Brown 1 Greeley
PROPULSION DYNAMICS, INC PROPULSION SYSTEMS, INC
SCIENCE APPLICATIONS, INC 1 Von Kerezek
GEORGE G. SHARP
SPERRY SYS MGMT Lib/Shapiro SUN SHIPBLDG/Lib
ROBERT TAGGART
TETRA TECH PASADENA/Furuya UA HAMILTON STANDARD/Cornell
Copies
| end a on] — nd Ye — a — Yo Ya a> Yu Nt a yt a | ee ee a
CENTER DISTRIBUTION
Code
0120 12 012.1 15 1506 1509 152
1521 1521 1521
1522 S22; 1522
154 154.1
1542 1542 1542
1543 1543
1544 1544 1544 1544 1544 1544 1544 1544
156 1561 1562 1563 1564 172 1720. 19 1901
Name Copies
Nakonechny W.B. Morgan Hawkins Powell Lin 10
Day 1 Karafiath Hurwitz
Dobay Remmers Wilson
McCarthy Yim Huang
Shen Chang
Platzer Santore
Peterson Boswell Caster Reed Fuhs Jessup Kim
Lin Cieslowski Cox Davis Milne Feldman Krenzke Rockwell Sevik
Strasberg
48
Code
1905
1942 1942
1962 1962 1962
2814
5211.1 S746 Il 5752
Name
Blake
Archibald Mathews
Zaloumis Noonan Kilcullen
Czyryca Reports Distribution TIC (C) & 1(m)
TIC (A)