LOW-DRA G SECTION DESIGN METHOD UTILIZING INTERACTIVE GRAPHICS

DR. DAVID W. CODER & RICHARD M. NORTON

LO W-DRA G SECTION DESIGN METHOD UTILIZING INTERACTIVE GRAPHICS

THE AUTHORS Dr. Dadd W. Coder received his B.S. degree in Mechanical Engineering in 1962 and his Ph.D. degree in Mechanical Engineering in 1973, both from the University of Maryland. He is presently a Naval Architect in the Ship Performance Depart- ment at the David W. Taylor Naval Ship Research and De- velopment Center where he started his career in 1957 as a Stu- dent Trainee. He is a registered Professional Engineer in the state of Maryland. and in addition to ASNE, which he joined in 1978. is a member of Tau Beta Pi, Pi Tau Sigma, Sigma Xi, ASME, and SNAME.

Mr. Rlchud M. Norton received his B.S. degree in Mechanical Engineeringfrom the University of Maryland in 1972 and is presently taking graduate level classes at The George Washington University. He began his career at the David W. Taylor Naval Ship Research and Development Center as a Stu- dent Trainee in 1970 and is currently a Naval Architect in the Ship Performance Department at DTNSRDC. Mr. Norton is also a private aircraft pilot with an instrument rating working on his commercial certificate and a member of the Aircraft Owners and Pilots Association (AOPA).

ABSTRACT

An interactive graphiw computer program WM developed to implement the deaign of low-drag fdrinp to house componenb

useful to nduce either hydrodynamic I d on rtcucturea or the hydrodynamic rerirtrnce of vehicle appendaged.

section sbape~; one of airfoil section fluid-dynamic char- actehtiw; one of V ~ O M component s- and one of V ~ O M accangemnts of there components. Tbe program operator may d up any of the llbraq information for Curplay on a Cathode Ray Tube (CRT), make modifications, or cmate and catalog new llbrary information.

The n o d fitting mode proceeds M follows: After the operator L sotir&d with tbe internal component arrangement displayed on the CRT, Section S b a p ace called up from the libruy, modifled, or created and placed interactively around the arrangement by spec@ing tbe location of the kpdine edge and lralUng edge. The Section Sbape, arrangement, or in- dividual components, m y be modified until the user ie ~t&f&d with the o v e d geome@v.

The design then may be evaluated for hydrodynamic char- actehtica by cPlling up information from the appropriate llbrary or exerching an analysis program. The inpub to the anslysir program ace Section Sbape, ReynolaS Number, and surface roughness. Tbe outpub are lift, drag, moment coeffi- cknb, and prrrrme distribution. Thus, design and off-dedgn conditions may be evaluated easily and the user can drive tbe deaign In the dealred direftion.

INTRODUCTION

IT IS KNOWN THAT STREAMLINING A STRUCTURE that is exposed to the flow of a fluid can reduce its fluid-

of V ~ O M ge~metricpl ~baper. T b h - d r a g fdrinp

The pr~grrm fahm fow lib-: OIW Of h - d r a g airfoil

dynamic drag significantly [l]. For example, typical ex- perimental data for a circular cylinder [2] and unpublished data by the Authors for a symmetrical foil show that for comparable Reynolds Numbers, a circular cylinder with diameter equal to the maximum thickness of a foil (as shown in Figure 1) would have more than an order of magnitude higher drag than the foil. Or alter- nately, a circular cylinder of diameter about one-tenth of the foil maximum thickness (also shown in the Figure) would have about the same drag as the foil. Thus, fairings have been widely used to enclose various bluntly- shaped structures to reduce fluid-dynamic loads on these structures or to reduce the resistance of vehicle append- ages. Examples in marine engineering are submarine bridge fairwaters (Sails), cable fairings, and hydrofoil struts. Bridge fairwaters have been patterned after Taylor Model Basin - Ellipse Parabola Hyperbola (TMB-EPH) Sections [3] developed during the 1940s. During the 1950s, FEHLNER and PODE [4] developed cable fairings, some of which (particularly TMB Fairing No. 7) are still in use today. Hydrofoil craft designs during the 1960s made use of NACA 16-Series Sections, developed around 1940 [5][6], for the surface-piercing strut of T-foils [ 71. These designs usually depended upon the selection of a fairing shape from a “catalog” of shapes and corresponding fluid-dynamic characteristics. ABBO-IT and VON DOENHOFF [8] and HOERNER [l] are very useful “catalogs” for this purpose. More recently, foil designs have been developed where certain fluid- dynamic characteristics are prescribed and the corresponding foil offsets are determined by a computer program. For example, in the EPPLER METHOD [9][10], certain characteristics of the desired pressure distribution over the foil are specified and the corresponding foil offsets are obtained. SHEN has used these methods recently to design cavitation resistant hydrofoils [ 11][ 121. Thus, as designs of foil shapes and fairing have become more and more sophisticated, the designer must be ac- quainted better with these techniques, and he must take more care to obtain the optimum shape for the particular application. Low-drag optimization is especially impor- tant to marine engineering in these days of energy con- servation. Not only could less energy be expended for payload delivery, but power plant size could be reduced and range of the vehicle increased.

In order to aid in the design of an optimum fairing for naval applications. a design method was developed which utilizes interactive graphics to “fit” Sections around various components. Also included is interactive access to a foil hydrodynamic design and analysis program and a data bank of Section geometric and hydrodynamic characteristics. In this paper, a general description of this method is presented with attention to

133 Naval Englneels Journal, April 1980

INTERACTIVE GRAPHICS DESIGN METHOD CODERINORTON

4 C +

WXXEO I NACA W X X

TABLE lA SECTION %WE

SECTION ID NAME I DESCRIPTION SOURCE

1. OFFSETS FROMEOUATION ABMTT AND 2 MAX. THICK. - XX VON WENHOF 1 MAX. THICK. AT305CHORO

[ E l SECTIONID NAME

14XXEO NAVV STANDARD STRUT I N S 1 -

llXXEO CIRCULAR CYL WITH T.E. WEDGE

DESCRIPTION SOURCE

1. OFFSETSSCALED FROM TABLE. 2 M A X THICK. - XX SHEET 3. MIX.THICK.ATI?IYCHORD

DESIGN DATA

1. OFFSETS FROM EOUATION 2. MAX. THICK. - XX FEHLNER 3. MAX.THICK.AT I?I%CHORD [17]

WHICKER AND

07XXEO TMB FAIRING NO. 7

lOXXEO I JOUKOWSKI

l l X X E 0 I TM&EPH

I NOTE: [ 3 - See Reference Number Indicated.

1. OFFSETS FROM EWATION FEHLNER 2 MAX. THICK. - XX AND 3. MAX. THICK. I?lXCHORD FUDE C31

[FLAT SIDED1

1. OFFSETS FROM EOUATION BUSSMANN 2 MAX. THICK. - XX AND ULRICH 1 MAX. THICK. NEAR 25% CHORD

C131

1. OFFSETSFROMEOUATION FREEMAN 2. MAX. THICK. - XX 3, [email protected]%CHORD C4i 4. MAX. THICK AT418XCHORD

various hardware and software possibilfities. Some specific information on program “library” information is also presented. Finally a specific design of a fairing is carried out to demonstrate the present interactive design method.

1 P X E O I MODIFIED EPH

<-> 1. OFFSETS FROM EOUATION NAVSHIPS 2 MAX. THICK - XX DRAWING 1 MAX. THICK. Z8.8TO41.5%

CHORD IFLATIlDEDl 4 DEVELORD FROM SSN 608

SAIL SECTION

C141

I

l8XXEO NACA 18-OXX 1. OFFSETS SCALED FROM TABLE. ABBOTT AND VONWENHOFF

rR, 2. MAX. THICK. - XX 3. M A X THICK. AT M%CHORD

13XXEO I W I V E

1. OFFSETS INTERPOLATED FROM ABBOTT AND TABLE VON DOENHOFF

3. MAX. THICK. AT 40% CHORD

1. OFFSETS FROM EOUATION ROUSE 2 M A X THICK. - XX 1 MAX. THICK. AT 60% WORD ” 51

AsCOEF ! ALPHA-STAR

-/d 134 Naval EnQlneers Journal, Aprll 1980

1. OFFSETSOBTAINED FROM UNPUBLISHED

2. M A X THICK. FOR FORWARD THE AUTHORS EPPLER DESIGN PROGRAM DATA FROM

(BETWEEN 10 AND 30% CHORD1

CODERINORTON INTERACTIVE GRAPHICS DESIGN METHOD

0 b INFO.

r------ 1 I SECTION I I I STRUCT I ' CHAR. I I LIBRARY I

I

COMPONENT COMPONENT ARRANGEMENT

LIBRARY

M 0 LT----A

r----- 1 I I

I 1 PROGRAM ----------- L,,,-,A

SECTION SHAPE I STRUCT. I COMPUTER ------------4 ANALYSIS I

I PROGRAM I STRUCT. CHAR.

SECTION FLU1 D D Y N .

CHAR. LIBRARY

SECTION SHAPE

LIBRARY

FLU1 D-DYN. PRESS. DIST. PARAM. DESIGN 4

I & INST.

SECTION SHAPE

FLU1 D-DYN. C RT HARD * AND COPY KEYBOARD

4 INFO.

SECONDARY DESIGN OBJ. b ? I \ INFO.

DESIGNER

?

ANALYSIS PROGRAM

I PRIMARY

DESIGN OBJ.

DRAG1 - 7

I Figure 2. Organization of Interactive Graphics Design Method.

INTERACTIVE SYSTEM

System Organization 4

The interactive system used in the present low-drag section design method is shown schematically in Figure 2. The heart of the system is an interactive terminal with a Cathode Ray Tube (CRT) and keyboard so that the designer can give and receive instructions and information. This information received from the interactive system may be used immediately by the designer to drive the design in a desired direction or may be recorded for more leisurely analysis. A hard copy may be made of any information on the CRT that the designer wishes to save. A few samples of how this information may be used for particular design objectives will be demonstrated later.

The interactive terminal is the designer's link to a computer (or computers) that can store, retrieve, and create information. The present system has four libraries of information, a design program, and an analysis pro-

gram. Conceptually, additional libraries, design programs, and .analysis programs could be added easily. Specifically, the present system deals with geometric and fluid-dynamic attributes of fairing design and could be enhanced significantly by including programs concern- ing structural aspects.

The present libraries consist of a library of section shapes; a library of sectionfluid-dynamic characteristics; a library of various two-dimensional geometric shapes (hereafter referred to as components) that can be put together to represent almost any two-dimensional structure; and various arrangements of these components that represent certain structures.

Library Information

The SECTION SHAPE LIBRARY is composed of section offsets and/or equations to generate section offsets. At the present time the program can generate the various sections listed in TABLES 1A and 1B. It is planned to

Naval Engineers Journal, Aptill960 135

INTERACTIVE GRAPHICS DESIGN METHOD

SECTION ID

ooxx00

QOXX 00

lOXX00

l lXX00

16XXOO

CODER/NORTON

ANGLE OF PERCENT REYNOLDS ROUGHNESS NAME THICKNESS NUMBER PARAMETER ATTACK IN DEG.

(XX) (Rnl (Mu) (a)

0.2.4 ,..., 20 NACA OOXX 10, 11,. . ., 25 0.001. O.Ol,O.l, 3.5.7

NACA OOXX 16, 17.. . .. 24 5, 10, 20, 50, 3. 5.7 0. 1,. . ., 10

0.2.4 ,..., 20 JOUKOWSKI 10, 11,. . ., 25 0.001,0.01,0.1, 3, 5.7

TMB-EPH 10, 11,. . ., 25 0.001,0.01, 0.1, 3.5.7 0.2.4 ...., 20

NACA 16-0XX 10, 11, . . ., 25 0.001, 0.01.0.1. 3.5. 7 0.2.4 ..... 20

1, 10 MILLION

120MILLION

1,lO MILLION

1, 10 MILLION

1,lO MILLION

TABLE 2 SECTION HYDRDDYNMfIC CHARACTERISTICS

002050 NACA 0020

I 0.5,0.75,1.0, 1.5, I 3,5,7 1 0 . 1 ,..., 10 I NACA0020 2.0. 5, 10. 20. 50, 002000

20

20

20

120 MILLION

0.5, 0.75. 1.0, 1.5, 2.0, 5, 10, 20. 50,

0.5. 0.75. 1.0. 1.5, 3,5. 7 0.1,. . ., 10

BL TRIP AT 5% c

0.1,. . ., 10

120MILLION

2.0, 5, 10, 20. 50, 120MILLION

0.5. 0.75. 1.0, 1.5. 20. 5. 10. 20. 50.

BL TRIP AT 5% c

0.1,. . ., 10

122000 MODIFIED EPH

VARIOUS

VARIOUS

0.5, 0.75. 1.0, 1.5. 3. 5.7 0.1.. . .. 10 2.0, 5. 10, 20. 50. 120 MILLION

0.5, 0.75. 1.0, 1.5, 2.0, 5, 10, 20. 50, 120MILLION

BL TRIP AT 5% c

0. 1,. . ., 10

. . I 12OMlLLlON I I ABCDOF ALPHA-STAR

add several more sections in the near future. The Section Shapes labeled “Alpha-Star’’ were developed from the Eppler Design Program [lo] which will be discussed later.

The SECTION FLUID-DYNAMIC CHARACTERISTICS LI- BRARY at the present time consists of data for various sections, Reynolds Numbers, roughness variable (Mu) or location of boundary layer trip, and angles-of-attack as listed in TABLE 2. All these data have been obtained using the Eppler Analysis Program [lo]. The hydrodynamic data listed in the library are lift, drag, moment coefficients, and cavitation number.

The COMPONENT LIBRARY consists of general geometric shapes such as squares, triangles, circles, rectangles, et cetera, and also the outlines of specific ship- board equipment. The ARRANGEMENT LIBRARY consists of specific arrangements of components from the Com- ponent Library. The purpose of the Arrangement Library is to have “ready recall” of any particular arrangement of components without having to construct it again from components.

System Hardware and Software The interactive system shown in Figure 2 may be ac-

136 Naval Englneen Journal, April 1980

complished with a variety of hardware and software. The hardware chosen for discussion here was readily available at David W. Taylor Naval Ship Research and Development Center (DTNSRDC) at the time of the system development, and it is the equipment most familiar to the Authors. Nothing written here should be considered an endorsement of any product. The equipment selected does represent several “sizes” of computers: a desk-top computer, a mini-computer, and a third-generation computer.

The interactive system with a desk-top Textronix 4051 Graphic Computing System [ 181 is shown schematically in Figure 3. The Tektronix 4051 shown in Figure 4 is comprised of a 32 K byte memory computer, CRT, keyboard, and cartridge tape slot packaged together in a unit weighing about 29.5 kg (65 lbs) and measuring about 45.7 cm x 81.3 cm x 35.6 cm (18 in. x 32 in. x 14 in.). It is shown together with a hard copy unit and a telecommunication link apparatus in Figure 4. The telecommunication link is with the DTNSRDC CDC 6700 which has enough memory to handle the Eppler Design and Analysis Programs (70 K).

The programs needed for user instructions, information retrieval, modification, creation, and cataloging,


I

I I

I I

I I I I I

PRIMARY SECONDARY DESIGN OBJ. HAND PLOT DESIGN OBJ. HAND PLOT

4 DESIGNER 4 INFO. INFO. ? I \ DRAG^^

? ~ ~~~~~~~~

Figure 3. Interactive System with a “Desk-Top” Computer.

graphing, and communicating with a host computer are stored in the Tektronix 4051 memory or on tape car- tridges. Unfortunately the machine has only one tape unit (expandable to two) which requires much physical switching of tapes by the user for some of the operations. An expanded and faster version of the Tektronix 4051, the Tektronix 4054, has a 64 K byte memory and could accommodate all these programs in the memory. This would free the tape unit to be used exclusively with the libraries. It is anticipated that this improvement in the system will be made in the near future. However, the system with the 4051 was workable and was used to generate the results presented in this paper.

In order to include the design and analysis program, which requires about 70 K bytes of memory, a machine of about 100 K byte memory is needed. Even though the memory of a desk-top machine might be expandable to meet this requirement, a mini-computer system as shown in Figures 5 and 6 probably would be more satisfactory in terms of efficiency and speed of operation. However, for this physically larger machine, more space is required than the desk-top machine and its operation may prove to be slightly more difficult. Both the desk-top and mini-

computer systems have the advantage that classified work may be performed easily on them due to their “stand alone” capability.

A system comprised of a third generation computer and interactive terminal as shown schematically in Figure 7 would have plenty of memory even for several analysis programs. Again, operation of this system would probably be slightly more difficult than the desk-top system and might prove to be slow due to time-sharing with other users. One disadvantage of a machine of this type is that it is difficult, if not impossible, to perform work of a classified nature. The Authors’ views as to the advantages and disadvantages of these three system options for this particular interactive program are given in TABLE 3.

DESIGN METHOD

The interactive design method for low-drag fairings may be considered to be comprised of three phases. First, there is an interactive graphics phase to “fit”

Naval Engineers Journal, April 1980 137

INTERACTIVE GRAPHICS DESIGN METHOD CODER/NORTON

'REAR VIEW OF 4061 SHOWING RS 232 INTERFACE TEKTRONIX 4631 HARD COPY UNIT

TEKTRONIX 4051

Figure 4. GmpMc Computing System with €Id Core Copy Unit and Telecommunication Link.

various fairings around the component to determine relative geometry. In the second phase, a hydrodynamic analysis is performed on the fairings to determine their hydrodynamic characteristics. Finally, the first two phases are put together and analyzed by the designer to select the best fairing according to the design objectives. These. phases are discussed further in the rest of this Sec- tion.

Interactive Fitting

The first step in the fitting process is to represent the cross-section of the structure to be faired with the components from the Component Library. Most common geometric shapes can be found in the library, and they may be called up one at a time, scaled, and graphed anywhere on the CRT. In this way, the desired cross-

TABLE 3

INTERACTIVE PROGRAM SYSTEM OPTIONS

COMPUTER ADVANTAGES DISADVANTAGES

DESK-TOP 1. Initial cost relatively low 2. Low physical space required 3. Easy programming (uses basic) 4. Using machine very easy 5. Small operational costs 6. Classified material can be handled

MINI- 1. Can handle large programs 2. Small operational costs 3. Faster processing 4. Classified material can be handled

THIRD GENERATION

1. Can handle large programs 2. Access to computer libraries 3. Several copying media available

I . Cannot handle large programs 2. Tape search is slow

1. Initial cost relatively high 2. Larger physical space required 3. Using machine more difficult

1. Cost of user connect time 2. Time sharing can be slow 3. Classified material difficult

138 Naval Engineen Journal, April 1980


. - . - . - . - . - . - . - . - . - . - . - . - . - . -

COMPONENT FLUID-DYN.

COMPUTER

----------- STRUCT. CHAR.

HARD

VERSATEC b COPY

KEY BOARD F LUI D-DYN.

. PROGRAM

I MEMORY

INFO. L. - . - . - . -. - . - . - . J

I - I PRIMARY SECONDARY I I

I I

I I I .

DESIGN OBJ. HAND PLOT HAND PLOT DESIGN OBJ. b DESIGNER 4 ? I \ I INFO. ' INFO.

DRAG[

L - - - - - - - - - - - - - - --- - - - - - - - - - - - J

Figure 5. Interactive System with a Mini-Computer.

section can be represented graphically. In this paper, a structure cross-section corresponding to a 6:l rectangle has been chosen for a test case. The basis for this choice is that this rectangle tits fairly well into a NACA 16-015 Section, a typical section for a hydrofoil strut, leaving about the least amount of "unused" space for a variety of useable rectangles. Once the structure has been char- acterized by components, this arrangement of components may be cataloged as an arrangement in the Ar- rangement Library. It can then be called back anytime later without having to reassemble the components to represent the structure. For the test case here, of course, the 6: 1 rectangle can be called up easily from the Compo- nent Library so there is no need to catalog it as an arrangement. Now that the structure cross-section is represented graphically, it is ready to accept a fairing.

Cross-sections may be called up from the Section Shape Library to fit around the arrangement. Sections may also be created by the Section Design Program which will be discussed later. The Section is then placed interactively around the arrangement by specifying the

Naval Engineers Journal. Aptill980 139

Figurn 6. Mini-Compater Keyboard, and Hard Copy Unit.

fi0 'rape mvm, CRT &

INTERACTIVE GRAPHICS DESIGN METHOD CODERINORTON

CRT AND I KEYBOARD ,

TEKTRONIX ' 4014

- 1 I r . - . - . - . - . - . - . - . - . - . - . - . - . - . - . - . -

HARD COPY CALCOMP

I I I I I I I I I I I L 7

I I I I I I I L

PRIMARY SECONDARY DESIGN OBJ. HAND PLOT HAND PLOT DESIGN OBJ.

b DESIGNER 4 INFO. INFO.

DRAG[-

? ?

I I I I I

Flgure 7. Interactive System with a Third Generation Computer.

Section Design and Analysis location of its leading edge on the CRT and its length (in scaled units). The Section may be redrawn as many times as necessary until the designer is satisfied that the minimum size fairing has been obtained to fit around the arrangement. It may take five or six attempts for an un- skilled designer to obtain the optimum foil size. Figure 8 shows the process of fitting a NACA 0015 around the 6:l rectangle. For demonstration purposes here, four com- monly used Section Families (NACA OOXX, JOUKOW- SKI, TMB-EPH, and NACA 16-OXX) have been selected to fit around the 6:l rectangle. The results of these fits are givkn in Figure 9 where "c" is the foil chord (c) non- dimensionalized by the rectangle length (1).

It is noted here that the fitting process can be performed in reverse order, i.e., fitting components inside of foils, and also that at any time during the process, the components, arrangement, or foil can be changed or modified.

The Eppler Program [lo] may be used to design foils (obtain offsets) that have prescribed pressure distribution characteristics. The characteristics that can be specified are the pressure closure function at the trailing edge, the location of the beginning of pressure recovery (Lambda), the form of the pressure recovery, and angles- of-attack for which the pressure distribution will be flat over certain segments of the foil (Alpha-Star distribution). About forty Sections, labeled here as "Alpha-Star'' Sections, were generated by varying Lambda and the Alpha-Star distribution while maintaining a pressure recovery form specified by WORTMAN [19] to insure the flow would not separate for zero degrees angle-of-attack (and therefore have low-drag). Several of these low-drag shapes were cataloged into the libraries and others can be created interactively by specifying. the appropriate in-

140 Naval Engineers Journal, Aprll 1980

CODERlNORTON INTERACTIVE GRAPHICS DESIGN METHOD

r

ARRANGEMENT STEP 1 PIW = 6

STEP 2

FIRST GUESS

SECOND GUESS

STEP n

FINAL VERSION (CIP = 1.71

rci Figme 8. Fitting of NACA 0015 around a 6:l Rectangle.

put parameters. Instructions on how to do this are included as interactive messages.

The second part of the Eppler Program [lo] is an analysis program that calculates fluid-dynamic characteristics for a given foil section. The inputs to the program are section offsets, Reynolds Numbers, surface roughness factor (Mu) or location of boundary layer trip, and angle-of-attack. The program calculates the poten- tial flow velocity and the boundary layer over the surface. Transition from laminar to turbulent flow is assumed to occur if -

Re = 18.4 X H32 - 21.74

and flow separation is assumed to occur wherever -

1.515 for laminar flow 1.460 for turbulent flow H32 = {

where: Re is the local Reynolds Number = (disp. thickness) X (free-stream Reynolds Number)/(chord)

(energy thickness)/( momentum thickness).

H32 is the shape parameter =

From the boundary layer calculations the drag coefficient is calculated from the Squire-Young Formula [20]

and the lift and moment coefficients are approximated from the amount of separation present. The detailed results can be displayed then on the CRT for evaluation by the designer. A subset of the results including the drag, lift, and moment coefficients and the cavitation index (the absolute value of the most negative pressure coefficient can be cataloged into the Section Fluid- Dynamics Characteristics Library. Some of the typical data stored in this library are shown in Figures 10 through 12. The drag coefficient versus thickens for zero degrees and a Reynolds Number of 10 million, the cavitation index versus thickness for zero degrees, and the cavitation index versus angle-of-attack for thicknesses of 10, 15, and 20 percent are shown for the four chosen families of foil section. The drag coefficient is seen to increase with thickness. The cavitation index also increases with thickness and with angle-of-attack. These data will be combined in what follows to pick an optimum Section from these four families.

Optimum Fairing Selection

The method used to determine the optimum fairing for a particular application obviously depends on the design objectives. Often, the ultimate selection is a compromise between several objectives, relying on a weighted “figure of merit” or the intuition of the designer. Here we have

141 Naval Engineers Journal, April 1980


2.0

- '0 8 8 0 -I

z v) z

a 0

fi 1.0 is z 0 z

0.0

I I 1 I I I I

0

A

0

0

a NACA OOXX - TMB - EPH

NACA 16-OXX

- I----.+

E = CIP

10 12 14 16 18 20 22 24

THICKNESS W e ) IN PERCENT

Figme 9. Nondiwnrionnl Chord Length VERSUS Thlckneu for Various Famlliea of FoU Sectione needed to enclose a 6 1 Rectangle.

made low-drag (at zero degrees angle-of-attack) the primary or certainly one of the primary objectives, and have already determined the data necessary to calculate the

drag. The Section drag may be represented as:

D = CD (1/2)pvc

TABLE 4

APPROXIMATE THICKNESS RANGE FOR MINIMUM DRAG

SECTION

NACA - OOXX

JOUKOWSKI

TMB - EPH

NACA 16-Oxx

Mu (CD X S) MIN (t/c) FOR MIN Rn

10 Million

10 Million

10 Million

10 Million

3 5 7

3 5 7

3 5 7

3 5 7

0.0113 19 to 24 0.0130 18 to 21 0.0138 18

0.0118 18 to 23 0.0136 18 to 24 0.0148 17 to 21

0.0100 15 to 19 0.0134 15 to 17 0.0144 14 to 17

0.0074 18 to 19 0.0128 16 0.0136 10

142 Naval Engineem Journal, April 1980

CODERINORTON INTERACTIVE GRAPHICS .DESIGN METHOD

X

L

g 0.01 1

8 1

I 0 5 - 0 7 .:"I

a a O!O i 2 114 16 18 m 2 i 24 '

THICKNESS Wc) IN PERCENT

I _N -

K

0 OIL 12 14 16 18 2b k 24 '

0 u t U

; t; 0.01 1 4 Y

Mu U 3 s? U

2 EE

'10 12 14 16 18 20 22 24 a

THICKNESS ( t /d IN PERCENT

;ii 0.02 X a 0 t U

E

2

a ' 12 14 16 18 20 P 24

2

a ' 12 14 16 18 20 P 24 THICKNESS (t/cl IN PERCENT THICKNESS (t/c) IN PERCENT

Figure 10. Drag Coefficient VERSUS Thickness for Various F a m i k of Foil !Sections at 0" and Reyndda Number of 10 Mllllon.

where: D is drag per unit span. CD is drag coefficient. p is fluid density. V is free stream velocity. C is chord.

For a given flow velocity and fluid density, the drag is proportional to the product of drag coefficient and chord -

D ~ C D X C

For the present demonstration case, we have determined for the four Section Families the chords necessary to house a 6: 1 rectangle (Figure 9) and the drag coefficient at zero degrees (Figure 10). Holding the rectangle length constant, the drag for each Section can be compared by examining the variable as follows:

A graph of this variable versus thickness for the four families of foil sections is shown in Figure 13. This Figure shows that in general the drag is relatively high at a small thickness of 10 percent and decreases with in- creasing thickness until thicknesses around 14 to 19 per-

cent depending on the family and roughness. Thereafter, as thickness is increased, the drag may remain almost a constant or start to increase again for higher thicknesses. The approximate thickness range for minimum drag for each family is given in TABLE 4. The reults indicate that for the particular Reynolds Number of 10 million, a NACA 16-016 would have the least drag over the roughness range. It is further seen that for the very rough case (Mu = 7). the minimum drag is predicted by both the NACA 0018 and the NACA 16-016. In such cases some other criterion may be imposed to decide between these two low drag foils. We will now use this opportunity to demonstrate how this may be done.

Suppose that we have established as our test case the design of a surface-piercing hydrofoil strut that must:

1) Enclose a 6:l rectangular structure 0.7 M long. 2) Operate at 20 knots. 3) Have a very rough surface finish. 4) Have low drag at zero angle-of-attack (primary ob-

jective). 5) Be cavitation free at a depth of 1 M for the largest

angle-of-attack possible (secondary objective).

Of thz above list, the firstfour requirements are satisfied by a NACA 0018 or a NACA 16-016 as described earlier.

143 Naval Englneers Journal, April 1980


NACA OOXX

TMB - EPH

NACA 16-OXX

I I I I 1 I I 10 12 14 16 18 20 22 24

THICKNESS (tlcl IN PERCENT

Figure 11. Cavitation Index VERSUS Thickness for Varioue F d e r of Foil Sections at 0”.

The chord would be about 1 M which would produce a Reynolds Number (based on chord) of about 10 million. The roughness would be represented as Mu = 7 in the analysis program. The necessary foil cavitation index may be easily found from the Cavitation Nomograph shown in Figure 14. For the chosen depth and velocity, the required cavitation index is about 2.0. Thus, the foil will cavitate or not depending on whether its index is above or below this value. Cavitation indices versus angle-of-attack have been given for the four Families of Foil Sections in Figure 12. The range of angles for which cavitation will or will not occur for the two NACA Families in question are shown in Figure 15. This Figure shows that for the particular constraints imposed here, the NACA 0018 would be slightly more cavitation resistant than the NACA 16-016. It must be emphasized again that the selection of the optimum shape, here the NACA 0018, is extremely sensitive to design objectives and constraints. The exact design method used by the designer is dependent upon how he formulates these objectives and constraints. Whatever the exact method used, however, the interactive fitting, interactive access to the Fluid-Dynamics Analysis Program, and interac- tion access to the Section Fluid-Dynamics Data Bank

144 Naval Englneera Journal, April 1980

should prove to be of considerable aid to the fairing designer.

111

121

131

I41

151

161

171

REFERENCES Hoerner, Sighard F., Fluid-Dynamics Drag. Midland Park, N.J.: Published by the Author, 1957. Coder, David W., “Hydrodynamic Forces on Oscillating and Non-oscillating Smooth Circular Cylinders in Crossflow.” Carderock, Md.: Naval Ship Research and Development Center, NSRDC Report 3639, October 1972. Fehlner, L.F. and L. Pode, “The Development of a Fair- ing for Tow Cables.” Carderock, Md.: David Taylor Model Basin, DTMB Report C-433, January 1952. Freeman, H.B,, “Calculated and Observed Speeds of Cavitation about Two- and Three-Dimensional Bodies in Water.” Carderock, Md.: David Taylor Model Basin, DTMB Report 495, November 1942. Jacobs, Eastman N., “Preliminary Report on Laminar Flow Airfoils and New Methods Adopted for Airfoil and Boundary-layer Investigations.” Washington, D.C.: NACA, Wartime Report No. L-345. June 1939. Stack, John, “Tests of Airfoils Designed to Delay the Compressibility Burble.” Washington, D.C.: NACA, NACA TN No. 976, 1944. Ellsworth, W.M., “U.S. Navy Hydrofoil Craft,” Journal of Hydronautics. Vol. 1, No. 2 (1967) pp. 66-73.

2.0 2.0

0

X w

- - 0 - - 5 n n

E 9

2 1.0 0 1.0

5 5 a

z z I- I-

2 9

2 0

2.0 I

0

X w

- n z 0 1.0 z I-

> 0

2 a

I I I 0.0 I -6 ' -4 -2 0 2 4 6 0*01 -6 4 -2 0 2 4 6 '

-

-

ANGLE OF ATTACK ( a ) IN DEG.

O.O I -6 -4 -2 0 2 4 6 '

2.0 0 - 5 n z 0 1.0 z I-

> s 9

0.0

ANGLE OF AlTACK ((11 IN DEG.

I I

- 6 - 4 - 2 0 2 4 6 ANGLE OF ATTACK ( a ) IN DEG. ANGLE OF AlTACK ((11 IN DEG.

Figwe 12. Cavitation Index VERSUS Angle-of-Attack for Vario~ Families of Foil Seetiom

0.014 - u a 0.012?

5 - = 0.010

g 0.008

2 0.006

0 U U

0 (1

n 01 1 I I

t I I

10 12 14 16 18 20 22 24 THICKNESS (t /cl IN PERCENT

0.014 1 I - 0 u 0.012

I 0 7

O:O 12 14 16 18 20 A 24 ' THICKNESS (t /cl IN PERCENT

0.014 I I JOUKOWSKI

I- w

U U

-- 0.010 0

g 0.008 0 (3 2 0.006 n

01 I I I I I

10 12 14 16 18 20 22 24 THICKNESS (tic) IN PERCENT

0.014 r I

0 u 0.012 + f 0.010 : g 0.008 U

0 Q I

':O 1'2 14 16 18 2f2 24 THICKNESS (t lc l IN PERCENT

Figure 13. Drag Figure of Merit VERSUS Thickness for Various Fao~iUes of Foil Scctions at 0" and Reynolds Number d 10 Mulion.

145 Naval Englneers Journal, April 1980

V h + ha - hV

THIS NOMOGRAPH REPRESENTS THE EQUATION V = ,& J 9

10

U

g IS THE ACCELERATION DUE TO GRAVITY, h IS THE DEPTH BENEATH THE SURFACE, ha IS THE HEAD DUE TO ATMOSPHERIC PRESSURE (= 10M OF SEA WATER), h, IS THE VAPOR PRESSURE OF WATER (= 0.15M OF SEA WATER A T 13"C), V' IS THE SPEED OF THE BODY, AND u IS THE CAVITATION INDEX OF THE BODY.

h

TO ESTIMATE THE SPEED OF INCIPIENT CAVITATION FOR A BODY, L A Y A STRAIGHTEDGE ON THE GIVEN h AND u, THE RESULTANT CAVITATION SPEED IS THE INTERCEPT ON THE V SCALE. JJ

2 EXAMPLE: FIND u FOR

n Y k30

h = 1M V = 20 KTS ANSWER: u = 2

/ /

/ /

/ /

/ /

X

z w n

' S i= a c

(5

4.0

k 2.0

1 .o

0.5

0.4 f 0.3 /

1

70 4 90 7

100

146 Naval Englneers Journal, Aprll 1980 F l p n 14. Cavitation Nomograph.

CODEWNORTON

0

4.0 z - - r ” I- 4

3.0

Y

0

4

2 0

1.0

INTERACTIVE GRAPHICS DESIGN METHOD

-

-

-

-

[8] Abbott, Ira H. and Albert E. Von Doenhoff, Theory of Wing Sections. New York, N.Y.: Dover Publications, Inc., 1959.

[9] Eppler, R., “Direkte Berechnung von Tragflugel- profilenen aus der Druckverteilung,” Zngeneiur-Archiv.

[lo] Eppler, R. and D.M. Somers, “A Computer Program for the Design and Analysis of Low-Speed Airfoils.” NASA Tech. Memo (to be published).

[ l l ] Shen, Y.T. and R. Eppler, “Section Design for Hydrofoil Wings with Flaps,” Journal of Hydronautics. Vol. 13, No.

[12] Eppler, R. and Y.T. Shen, “Wing Sections for Hydrofoils,” Journal of Ship Research (to be published).

[ 131 Bussmann, K. and A. Ulrich, “Systematic Investigations of the Influence of the Shape of the Profile Upon the Posi- tion of the Transition Point.” Washington, D.C.: NACA, NACA TM 1185, October 1947.

[ 141 NAVSHIPS Drawing No. 0100-436, 845-4403236, “SSN 688 Class Sub.”

[15] Rouse, Hunter, Editor, Advanced Mechanics of Fluids. New York, N.Y.: John Wiley & Sons, Inc., 1959, pp.

(161 Bureau of Ships, Section DDS 1108-1 Design Data Sheet, “Shaft Struts, Twin Arm Type.” Washington, D.C.: Department of the Navy, May 1947.

[17] Whicker, L. Folger and Leo F. Fehlner, “Free-Stream Characteristics of a Family of Low-Aspect-Ratio, All- Movable Control Surfaces for Application to Ship Design.” Carderock, Md.: David Taylor Model Basin, DTMB Report 933, December 1958.

[ 181 Tektronix, Inc. Brochure, 4050 Series Applications Library. Beaverton, Oregon: Textronix, Inc., 1 June 1979.

[19] Wortman, F.X., “Progress in the Design of Low-Drag Aerofoils,” Boundary Layer and Flow Control, Vol. 2, Edited by G.V. Lachmann. London, Eng.: Pergamon Press, 1971, pp. 548-770.

Vol. 25 (1957) pp. 32-59.

2 (April 1979) pp. 39-45.

183-184.

[20] Squire, H.B. and A.D. Young, “The Calculation of the Profile Drag of Aerofoils,” ARC R b M 1838, 1938.

1.0 I 1 I I

ABOVE LINE CAVITATION

BELOW LINE: NOCAVITATION

A FINAL DESIGN POINTS

0.0

10 12 14 16 18 m

THICKNESS I t / d I N PERCENT

Figure 15. Cavitation Inception Angle for Cadtation Index of 2.0 for tbc NACA OOXX and NACA 16-OXX Foil Scctiwr.

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LOW-DRA G SECTION DESIGN METHOD UTILIZING INTERACTIVE GRAPHICS