DTNSRDC-82/077
ONAL PRINCIPLE ASSOCIATED WITH A LOCALIZED NUMERICAL SOLUTION
ADY FREE-SURFACE FLOWS
DAVID W. TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER
Bethesda, Maryland 20084
A VARIATIONAL PRINCIPLE ASSOCIATED WITH A LOCALIZED NUMERICAL SOLUTION OF UN- STEADY FREE-SURFACE FLOWS
DOCUMENT COLLECTION
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
SHIP PERFORMANCE DEPARTMENT RESEARCH AND DEVELOPMENT REPORT
September 1982 DTNSRDG-82/077
MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS
DTNSRDC COMMANDER 00 TECHNICAL DI athe hy
OFFICER-IN-CHARGE CARDEROCK
OFFICER-IN-CHARGE
ANNAPOLIS
SYSTEMS DEVELOPMENT DEPARTMENT
AVIATION AND SURFACE EFFECTS DEPARTMENT
SHIP PERFORMANCE DEPARTMENT
15
COMPUTATION, MATHEMATICS AND LOGISTICS SERA es
STRUCTURES
DEPARTMENT
PROPULSION AND
| SE Oeics AUXILIARY SYSTEMS
eal DEPARTMENT 19 SHIP MATERIALS CENTRAL ENGINEERING INSTRUMENTATION DEPARTMENT on DEPARTMENT
MBL/WHOI
AAA
0 0301 0037131 4
NRC NDW-DTNSRDC 5602/21 (2-80)
Dept. 9 UNCLASSIFIED ie OCT 1 2 1982
eee
SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
READ INSTRUCTIONS REPORT DOCUMENTATION PAGE T. REPORT NUMBER 2. GOVT ACCESSION NO 3. RECIPIENT'S CATALOG NUMBER DTNSRDC-82/077
4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED
A VARIATIONAL PRINCIPLE ASSOCIATED WITH A ae LOCALIZED NUMERICAL SOLUTION OF UNSTEADY are,
» AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(S) Bev Nam
. PERFORMING ORGANIZATION NAME AND ADDRESS 10. Aaah ai a Monee: TASK * . UNIT NUM David W. Taylor Naval Ship Research Program Element 61153N and Development Center Task Area RRO140302
Bethesda, Maryland 20084 Work Unit 1542-018
- CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE
September 1982
Office of Naval Research (ONR-432) is NUMBERID EE ACES
» MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of this report) | UNCLASSIFIED
1Sa. DECLASSIFICATION/ DOWNGRADING SCHEDUL
- DISTRIBUTION STATEMENT (of this Report)
APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
- DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)
- SUPPLEMENTARY NOTES
. KEY WORDS (Continue on reverse side if necessary and identify by block number)
Variational Principle Numerical Ship Hydrodynamics Finite Element Technique Nonlinear Theory
Free Surface Convolution
Functional
. ABSTRACT (Continue on reverse side if necessary and identify by block number)
In this report, a variational principle for unsteady body wave problems is treated both with and without a convolution integral and with both linear and nonlinear free-surface conditions. Functionals are obtained for the numerical computation of unsteady flow fields near a body that moves on or beneath the free surface. This formulation can be applied to ship hydro- dynamic performance problems of water entry and body slamming, as well as to arbitrary body motion.
DD . oon, 1473 EDITION OF 1 Nov 651s OBSOLETE UNCLASSIFIED
S/N 0102-LF-014-6601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Bntorad)
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)
UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered)
TABLE OF CONTENTS
Page INOPASMIONiswiter icy) aay (euenct= rel feted “\ shee) or cl fst Poll e) Wiomioe, Neleiest lewetin dire toeoree eet Mee UAeRME ols iv JNOSHMRINGIN GS a aa Ray hg ceo colsch oo) clon Geno data, cod ay\On earn vo-fos ce ono) Cola) vofoh ole (a a ADMINISTRATIVE, TENE ORMATION sa tse) uses ce veuuiog! cievte Vs pteq vu bomreue) Youlow cl ie imey lion 1) snare ie 1 JONAUSOVDIOLOIMILONS Goh Geo G6 6 ib doo 6 6 Gb oo6 we soo 6 Cele G6 bose 6 or ile INCOM IGIUNI NNR TINOITHIONE 5 5 GG Go 6) 6 6 6 8 Od Goo 6 Go 6 odd of a 8 4 of Gee 2 IDJUMIMAR INOIIH BGS 6 6 fo o 6 6 865.0 6 5 6 Ob Geo ed 6 SB so 8 ot 5 io 6% D (WE, LORS THOIMNVOIHOMEIOIN GS. G Gg 6 AG 6 dee ol 6 ogo Oe G6 be Boe o 6 Goo oom oe 7 SUNLUSTOMED YW WOMEION iors we A Goo) wenneo co fob Cleon em o do o oO © G@ oO obo oo oc 10 ICI IN Gal SoG ol od ob GG oo Me 6 OG Go eo 6 ob ced 6 o 6 HGS Go 10 CONCLUDING: REMARKS! 52 ar a Gn “ei seis © ie bo ee ie ie eels Ge) se Se es Ge als 2
TOD OGIO TR oe ene heen 8s ce ooo 0 Oo §. ovo Ge oc coe 8) pee ooo ea iehion loo BA UrG OTS ic 113}
ae iat
NOTATION
D Fluid domain
f; Function defined in Equation (23) g Acceleration of gravity
By Function defined in Equation (24) h Body or free surface defined in Equation @)) J Functional
m Source distribution
Pp Pressure distribution
Sp Free surface
Sy Interface of near and far fields S. Body surface
t Time
Viet Rectangular Cartesian coordinates 0) Variation
0 Water density
T Time
a) Potential
w Function defined in Equation (21) w Frequency defined in Equation (21) Subscript
i The ith order
n Normal derivative toward fluid
fe) Projection on the z = 0 surface
t The time derivative
iv
The z derivative Near field, the first order
Far field, the second order
ABSTRACT
In this report, a variational principle for unsteady body wave problems is treated both with and without a convolution integral, and with both linear and nonlinear free surface con- ditions. Functionals are obtained for the numerical computation of unsteady flow fields near a body that moves on or beneath the free surface. This formulation can be applied to ship hydro- dynamic performance problems of water entry and body slamming, as well as to arbitrary body motion.
ADMINISTRATIVE INFORMATION The work reported herein has been supported by the Numerical Naval Hydrodynamics Program at the David W. Taylor Naval Ship Research and Development Center. This
program is jointly sponsored by the Office of Naval Research and DINSRDC under Task Area RRO140302, Work Unit 1542-018.
INTRODUCTION
In the early 1970's the David W. Taylor Naval Ship Research and Development Center (DTNSRDC) recognized the demand for advanced numerical methods to predict the hydrodynamic performance characteristics of naval ships, particularly when classical methods proved inadequate.
Thus, in 1974 the Numerical Naval Ship Hydrodynamics Program was begun at DTNSRDC. Under this program the author previously investigated the steady ship-—wave problem using a variational principle associated with a localized finite-element Pochndaeee This method is useful particularly to analyze the flow field near the ship in detail; in the far field, the Michell approximation can be used. This report extends the problem to the unsteady case.
For both the steady and unsteady problems, the simple calculation is for a linear free surface condition with exact body boundary conditions. An iterative method is needed for a nonlinear free surface condition. However, in the unsteady problem, the variational principle requires an integration with respect to time using the initial conditions; in this instance, a convolution integral is useful. The variational principle for the unsteady body wave problem with exact body boundary
conditions is treated both with and without convolution, and with both linear and
*A complete listing of references is given on page 13.
ai
nonlinear free surface conditions. For the linear free surface problem, a func- tional for the variational principle is obtained with a convolution rather than a general integral. The convolution cannot be applied to a nonlinear free surface problem; the condition is required for large values of time. A nonlinear solution derived using an iteration scheme having the linear convolution form is also dis- cussed. The time integration can be eliminated if the motion is sinusoidal.
This formulation can be applied to problems of water entry and body slamming,
as well as to arbitrary body motion.
NONLINEAR PROBLEM Since problems dealt with here can be generalized easily to three-dimensions, for simplicity we first consider a two-dimensional problem in the rectangular Car- tesian (x,z) coordinate* plane. When a body whose surface is represented by
S. [z=h(x,t)] | @)
enters the water surface Sa (Ze= 10), bes a = h(x,t), t > 0) at time t = O, or when a semisubmerged or fully submerged body starts to move at time t = O and either exits the water or stops moving at t = th» then the boundary conditions for a velocity
potential $¢ are as follows:
¢ = >, = 0 for t < 0 everywhere
+ (1b)? - 6, + gh=0 oS (2)
h - VoV (h-z) = 0 h_ - ® eo = 0 t n x
Here, S(t) is the submerged body surface varying with time t, and n is the normal
direction into the fluid. We consider potentials 1 in the domain Dy and >, in the
*Definition of notations are given on page iv.
domain Dos where dD, is the near field including 85> and Dy is outside of D,- Then at the interface Sy of D, and Das we need to have
(4) ¢,--¢
n 2n The outer potential 5 in Ds is assumed to satisfy the linear free surface condition
ate t SPon © o
For such 5 we know the time-dependent Green fundetor
Now we will construct a Lagrangian for the previously described problem, con-
sidering the Lagrangian that feateee used
ic
‘ 2 1 re x i -| \j (5 Ma % 1-41, ) azexet +f | g > dxdt a | (0,- 5 by) bo. dzdt (6)
a 0 Dd, 0 Sip 0 Sy
where P> %, and h vary with time, and t is a sufficiently large time after the body has either exited from or come to rest in the water so that we can safely assume that the variation bo), Sb, aue 5b, vanishes at t = tT. It will be shown later that the use of a convolution integral necessitates only the initial condition without the Condition at t = T.
Since
hiGcat ye ~niGc, t) ma bdz = ods + $(z=h) a (7)
we have
re h(x,t) h(x,t)
{ fx] >. dzdt I aE al odz — o(z=h) hy dxdt 0
heat) T AE “| ee | | dt (z=h) he dx 0 or Ag cr 5 {| ), dzdxdt = S| | h, ¢dxdt +f bdxdz (8) Dis Ce) Q ss. D, (t=t)
Now we take a variation of J in Equation (6), and use the Green theorem, and the
He eye aL condition at large t = T obtaining
T 1 6J -{ | € Vo, Vy ,t2h ) Oh dxdt
0 Sie
au 40 “| il vo, 89, dzdxdt I { (19/65 *,) 6h, dxdt 0 0 3, ,Us.
Di 1F
i ic =| | (>, +45,) 66, dade = | (¢,-$5) 665, dadt
0 Ss; 0 Sy
i 1 + “| J (50. P5409 56, ) dzdt = 0 (9) 0 Ss
However trom the identity,
ff (9° 865-50" (66,)} ards -| {$, 66,-$5(8b,,)} ds = 0 S
7) Sor
and from the linear free surface condition on Sop Equation (5), and the condition
at t = T, we have
€ i | J (9 55,,-$5565,) dadt = =| A (8$505,-¢5505,,) dxdt 0 Sj 0 Se (10) iG . Al SUT he STP ores a | (8$.565,7$95¢5,) = dx = 0 ope w Sop
so that the last integral of Equation (9) vanishes. Since 5by5 5b, Sbo0> and 6h
are arbitrary, we obtain from Equations (9) and (10) the corresponding time- dependent, free surface boundary value problem represented by Equations (2)-(4) together with the Laplace equation for ¢. Therefore, solving the variational problem with the functional J of Equation (6) is equivalent to solving the Laplace equation with the boundary conditions as set forth in Equations (2)-(4), provided we assume
that
6b, = 5b, = Ob, = 0 at t=T
LINEAR PROBLEM If we assume a linear free surface condition in both Sip and Sop and keep the
exact boundary condition [Equation (3)] on the body surface,
Paper ie! nH ad
then we may use
18 a {fa Vo,V$, dzdxdt - ak [ $191 ep dxdt OD
iL
{Jom f]
where S is the projection of S, on z= 0. When we take the variation of J, we have
Fo S13 AD. Sace Veoh edule dsdese Oe ee deat me Tele eee pa | UA aes, lee) oe anny SN
1 (i> 2&2) $,,dsdt (12)
ie ( o,, ve -,) dxdt
T c -| j ($4 -%5) bo) dzdt -| j (6) 5,257 dzdt (12a)
0 Sy 0 Sy
Here, in addition to Equation (10), the following equation holds
J js Care dxdt -f J Tee dxdt f i ee dxdt
als
Z 2) a +f 9750 OO ter OX 2 0 “Ss 0
Fo ene ae (13)
Thus, as in the previous section, we can easily derive the corresponding linear free surface boundary value problem using Equation (5) with the exact body boundary con-
dition in Equation (11).
USE OF CONVOLUTION Equations (6) and (12) are Lagrangians in a time-dependent, two-dimensional
space with nonlinear and linear free surface conditions, respectively. They could
be localized in space but not in time. Namely, we had to specify the conditions on Se at t = 0 and t = Tt with a sufficiently large T. On the other hand, we did not require the initial condition un = 0 at t = 0. In addition, such time T when 1 = 0 on Sp may be too fleeces for practical use. For linear free surface boundary condi- tions, we can treat our variational problem in the same way as those who have treated
variation principles for linear initial value problems using convolutions defined
by i * = oe oT 5 :{ >, (x,z,t) (85257 t) dt 0 (14) ab ad ao ao = 1 2 1 D 15 * VO5 ~ Ox z ox us Oz ; Oz We change Equation (12) to Ta ye. eo deol] Caren ecee 2 al 1 22 il det an SG 5 ak ; | he x %) dx | (0° 7 +, * Pon dz (GLE) ne Si
If we use the identity relation
and the initial condition %) =o = 0 at t = 0, instead of the conditions Ot = 0 on
lt
Sp at t = 0 and t = Tt with large T used in the previous section, we obtain, for any
time, T
T 1G
s| 1 * ee dx -| 5o, (x, t) Prep Hott) dxdt | | >, (x,t) 5b pp He T-t)dxdt 0s 0s
Fo Fo Fo
T = 2 ( 6, (x,t) dy pp So Tot dxdt 05 Fo
+f {($, (x,t) S$, , (x, t-1)-$,, (x, t) 84, (x, t-t)} 14 dx S Fo
il ho o>
T | dp, (x,t) by pp Ho Tt) dxdt S
Fo
(16)
HI N n> OQ a ke > rR ct Gr a. *
where T need not be large, and x represents a point on the free surface z = 0. Thus,
we obtain as in Equation (12a)
2 x : D i
Sao
f2. - | 6b, * (1, hy+1 - hy] dx
S Ss
|| (5-95) * 86, dz - i (b, 45.) * 60,42 (17) eT aT
To obtain Equation (17), we used a convolution expression of Equation (16), where we
can use the initial condition 4 = =1 0;
Ve
Since Soy > Soo, and Soo, are arbitrary, we obtain the corresponding equations for a time-dependent linear free surface boundary value problem that has a unique solution.
If we lift out Sy so that D, occupies the entire fluid domain, then the last
integral of Equation (15) ieee The resulting equation appears much simpler than that obtained by Mapeae! due to a simple difference in the treatment of the free surface condition. Equation (15) does not give the wave height as a natural boundary condition, whereas Murray's corresponding equation does. However, from h = $,/8 the wave height can be obtained.
If we consider eigen solutions that satisfy only the Laplace equation; the linear free surface condition, Equation (5); and the radiation condition in dD, U Dy»
then >, which satisfies the body boundary condition in Equation (11), can be derived
from Equations (15) and (17) by using
1 Vid. = —_— — * J | (3 Oe hyt1 ny] odx (18) s s When we know a functional whose minimum value is attained by the solution, we can find the solution numerically by such methods as the finite-element eechatiques F P 9 or singularity method.
For example b= D7 a9) (19)
where o, is the Green function, which is available for this problem for a source distribution on the body surface. The source distribution m; will be obtained from
soltuion of the simultaneous equations,
SO . fa1'2,°.2N (20)
SINUSOIDAL MOTION
If we consider a sinusoidal ship oscillation such as h =f Bawe for S, of Equation (1), we substitute i iwt into Equation (12), integrate with respect to t, and obtain -iwt Al, Ne 2. e J= Jy = > Vb, dzdx - oe vy dx Si Sp +) fb, dx-] (vw -tu,)u, 4 (22) i ices ( P22 5) Dass © ji
This is exactly the same Lagrangian that Bai and Yeung. used. Working from Equation
(18), we can apply eigen solutions to the whole field by using
i =| (5 ¥,-F) ds
where h,/ vno+1 ape
A similar functional was used by Sao et Fale? to solve the problem of a heaving
oscillation of a dock.
ITERATIVE SCHEME For problems with the linear free surface condition, we can completely localize the numerical scheme in DS with 0 < t < Tt for any T with the help of the convolution form. However, for nonlinear problems, the finite-element technique has to rely on
: P “ : saa oe an iteration. We may thus use an iterative free surface condition on z = 0
10
OVS gel f=: 0 (23) gh, - bat +g, = 0 (24)
where, for the first order perturbation solution, fy = 0, 8) = QO and, for the nth
order, ae and g, are known functions of 5 of the (n-1)th or the lower order
solutions.
Then the Lagrangian for each f. is
1 i = —- * —_—— oe {J Paes eae | oie uae & Dy (z=0)ND, ae * * | $,, *f, det fo, 4, ax (z=0)9D,
oa oJ, = 0 (25) where the solutions for 1= 1, 2,...n - 1 should be used to determine the solution
when i = n. Equation (24) gives the wave height h for each i. If we specify a time-dependent, free surface pressure distribution p on the
projection oan of S, to z = O instead of hy in S. we may use
£, = 8) — p/P OD ee
in Equations (23) and (24) for the first order, where p is the water density.
lel!
Although we have discussed the two-dimensional time-dependent problem, Equations
(19) through (24) can be extended to the three-dimensional time-dependent problem.
| al il = = *k Sek D
That is
l (2=0)ND, - \| , * fs dxdy (fr, * 4 dxdy (z=0)ND, alt -{{ (¢)- 2 b,)* 6, de =F
and soon.
CONCLUDING REMARKS
We have formed functionals with both linear and nonlinear free surface boundary conditions. For the former but not the latter case, we could apply a convolution integral. However, the body boundary condition is satisfied exactly in both cases. In many cases, the flow field near an arbitrary body is of interest, and eigen solu- tions with linear free surface conditions are known. Even in any large unsteady motion such as ship slamming, the free surface condition for a short period in the beginning may be linear, then the convolution may be applied in the early time period. Especially in the slamming problem, the peak pressure is known to be reached early in the beginning and estimation of the early pressure distribution on the slamming body is required. With this functional, we can find the solution for an arbitrary body numerically by such methods as the finite element technique or singu-
larity method. Thus, a wide application of such functionals can be expected.
12
REFERENCES 1. Yim, B., "A Variational Principle Associated with a Localized Finite- Element Technique for Steady Ship-Wave and Cavity Problems," Proceedings of the First International Conference on Numerical Ship Hydrodynamics, David Taylor Naval Ship
R&D Center (1976).
2. Wehausen, J.V. and E.V. Laitone, "Surface Waves," Encyclopedia of Physics,
Springer-Verlag, Berlin, Vol. IX, pp. 446-778 (1960).
3. Stoker, J.J., "Water Waves," Interscience Publishers, Inc., New York (1957), pp. 187-196.
4, Yim, B., "Investigation of Gravity and Ventilation Effects in Water Entry of Thin Foils," Proceedings of the International Union of Theoretical and Applied Mechanics Symposium held in Leningrad (1971), NAUK Publishing House, Moscow, pp. 471-475 (1973).
5. Luke, J.C., "A Variational Principle for a Fluid with a Free Surface,"
Journal of Fluid Mechanics, Vol. 27, Part 2, pp. 395-397 (1967).
6. Gurtin, M.E., "Variational Principles for Linear Initial-Value Problems,"
Quarterly Journal of Applied Mathematics, Vol. 22, pp. 252-256 (1964).
7. Murray, J.C., "A Note on Some Variational Principles for a Class of Linear Initial-Boundary Value Problems," Journal of the Institute of Mathematics and
Applications, Vol. 12, pp. 119-123 (1973).
8. Bai, K.J. and R. Yeung, "Numerical Solutions of Free-Surface Flow Problems,"
10th Symposium on Naval Hydrodynamics, Office of Naval Research (1974).
9. Sao, K. et al., "On the Heaving Oscillation of a Circular Dock," Journal of
the Society of Naval Architects of Japan, Vol. 130, pp. 121—=13F~ GVA”:
dts}
ae qe n\n, dip ed Shovel gore sue” ; a, “AOBRT). pais:
- ne ¢ ae , 4 % wie ake al a "i a
aT
' woh “xg aes, oy vies 6 pis ate “P dene kal Lewion niesnt aia ae, paniiossoxs ” Pik <9 984 .woovelt 43a iaebilnd Reg | i SMENRL) bos gdb at bt gd mieog® us
eee OT SN 6) ie ENC
j oe 7 nace 1 of =i
rae ae . =< . : ; - the us De poatwe® gas? a ilate Grade & ro otqtoabsa\ te PatOd Dat Va! a ie ake hic
st hea : ree sessde, qe <8 3 “4 aie fo oat set bait Wemedcer? SLB LRLS Set aya “i snes Ay bin eek tavern” ee ne Pera - el ra is
* re eas 2) deer SES. SM — ; soy iad SEs naaljet Waking de, Ant Hof,
pe
i j KY ra " Pe) Per tie Os
el a
on: Kong’ * TPP GBEL Oe By sieht qantas ee 2 nel Ce ance
re
bys bre, 2d Otte a. etl MEAD ces Peentk Aires 7 Tigo Fo LBM o 2 =p td aptee USER coset ee
ria Shel thee, yt: Sah. SE Th. Sets aut Pi Ai eoimyit" ret Woe VA whl
- c~ 3 om ® cel ; i Peay 2A PA © re Bie Sf Seely “ra Laeeargen A230 ul a sy, , : i ae - ' b a a et - —rt TaPMLr 3 Os AL - 49f A} at bE ar» vv ltl ss 65 ant j 4 el , iy i R - " - Ma: . . e A ot : ,eit y 1)f fry Lona? L, Cl aw at . } : + : ea) 4. , i ' a" ‘ 4 ' v, -) . - — ia LP 4% . mn 7 --, 7 = Ts 4, 7 a . iy
Copies 1
2
ils}
12
INITIAL DISTRIBUTION
CHONR/438 Lee
NRL 1 Code 2027 1 Code 2627
USNA 1 Tech Lib 1 Nav Sys Eng Dept 1 Bhattacheryya 1 Calisal
NAVPGSCOL 1 Library 1 Garrison NELC/Lib NOSC 1 Library 1 Higdon NADC
NCEL/Code 131
NAVSEA 1 SEA 031, R. Johnson 1 SEA 031, G. Kerr 1 SEA 031, C. Kennel 1 SEA O5R, L. Benen 1 SEA O5R, Dilts 1 SEA O5R, N. Kobitz 1 SEA O5R, J. Schuler 1 (SEA 312, P.A.. Gale 1 SEA 312, J.W. Kehoe 1 SEA 55W, E.N. Comstock 1 SEA 55W, R.G. Keane, Jr. 1, SEA 61433, F. Prout 1 PMS 383, Chatterton
DIG NSF/Engineering Lib DOT/Lib, TAD-491.1
NBS/Klebanoff
Copies
1
1
4
MARAD/Lib
U. of Cal/Dept Naval Arch, Berkeley 1 Eng Library 1 Webster 1 Paulling 1 Wehausen
U. of Cal, San Diego 1 ALT. Els 1 Scripps Inst Lib
GEE Ll, -Aéro:,, Lib db PENG NAG
Catholic U. of Amer/ Civil & Mech Eng
Colorado State U./Eng Res Cen
Florida Atlantic U. 1 Tech Lib
U. of Hawaii/St. Denis U. of Illinois/J. Robertson
U. of LIowa l Library 1 Landweber
U. of Kansas/Civil Eng Lib
Lehigh U./Fritz Eng Lab Lib
Yeung Mandel Abkowitz Newman Sclavounos Ogilvie
PRR RRR
U. of Mich/NAME 1 Library
Copies
U. of Notre Dame 1 Eng Lib
New York U./Courant Inst 1 A. Peters I des otoker
SEE i Breslin 1 Savitsky 1 Dalzell 1 Kim
U. of Texas/Arl Lib Southwest Res Inst
1 Applied Mech Rev 1 Abramson
' Stanford Res Inst/Lib
U. of Washington
1 Eng Lib
1 Mech Eng/Adee Webb Inst
1 Library
1 Lewis
1 Ward Woods Hole/Ocean Eng SNAME/Tech Lib Bethlehem Steel/Sparrows Point Bethlehem Steel/New York/Lib Exxon, NY/Design Div, Tank Dept General Dynamics, EB/Boatwright Gibbs & Cox/Tech Info
Hydronautics/Lib
Lockheed, Sunnyvale 1 Potash
Copies iL Newport News Shipbuilding/Lib at Oceanics il Sperry Rand/Tech Lib
1 Sun Shipbuilding/Chief Naval Arch
2 American Bureau of Shipping i Lib 1 Cheng
it Maritime Research Informaticn Service
CENTER DISTRIBUTION
Copies Code Name
ili 012 D. Jewell
Al 1170 R.M. Stevens ali 1170 G.R. Lamb
i 1170 S. Hawkins
al 1500 W.B. Morgan
Al 1504 V.J. Monacella 1 1520 WG. ian:
1 1521 W.G. Day
1 isk A.M. Reed
ik: 522. G.F. Dobay
al 11522 M.B. Wilson
ih 1540 J.H. McCarthy ANS) 1540 B. Yim
i 1542 T.T. Huang
Al 1542 J. Bai
i 1560 D. Cieslowski iL 1560 Division Head 1 1561 GAG Cox
1 1561 S.L. Bales
1 1562 D.D. Moran
il 1562 Es. Zarniek il 1562 Y.S. Hong
16
Copies aL AL 1
10
Code 1563 1564 1564 Byala Db 522.1 D226 2
Name
W.E. Smith
J.P. Feldman
R.M. Curphey
Reports Distribution Library (C)
Library (A)
Ny
DTNSRDC ISSUES THREE TYPES OF REPORTS
1. DTNSRDC REPORTS, A FORMAL SERIES, CONTAIN INFORMATION OF PERMANENT TECH- NICAL VALUE. THEY CARRY A CONSECUTIVE NUMERICAL IDENTIFICATION REGARDLESS OF THEIR CLASSIFICATION OR THE ORIGINATING DEPARTMENT.
2. DEPARTMENTAL REPORTS, A SEMIFORMAL SERIES, CONTAIN INFORMATION OF A PRELIM- INARY, TEMPORARY, OR PROPRIETARY NATURE OR OF LIMITED INTEREST OR SIGNIFICANCE. THEY CARRY A DEPARTMENTAL ALPHANUMERICAL !DENTIFICATION.
3. TECHNICAL MEMURANDA, AN INFORMAL SERIES, CONTAIN TECHNICAL DOCUMENTATION OF LIMITED USE AND INTEREST. THEY ARE PRIMARILY WORKING PAPERS INTENDED FOR IN- TERNAL USE. THEY CARRY AN IDENTIFYING NUMBER WHICH INDICATES THEIR TYPE AND THE NUMERICAL CODE OF THE ORIGINATING DEPARTMENT. ANY DISTRIBUTION OUTSIDE DTNSRDC MUST BE APPROVED BY THE HEAD OF THE ORIGINATING DEPARTMENT ON A CASE-BY-CASE BASIS.