on the coupling of cdisc design method with fpx rotor … · on the coupling of cdisc design method...

NASA / CR-2000-210314

On the Coupling of CDISC Design MethodWith FPX Rotor Code

Hong Hu

Hampton University, Hampton, Virginia

December 2000

https://ntrs.nasa.gov/search.jsp?R=20010014169 2018-06-02T01:25:50+00:00Z

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NASA / CR-2000-210314

On the Coupling of CDISC Design MethodWith FPX Rotor Code

Hong Hu

Hampton University, Hampton, Virginia

National Aeronautics and

Space Administration

Langley Research Center

Hampton, Virginia 23681-2199

Prepared for Langley Research Centerunder Contract NAS1-19935

December 2000

Available from: ........

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Hanover, MD 21076-1320

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal R0ad-_ _i_i

Springfield, VA 22!6!-2!,7! : =(703) 605:6000 _ -: =-

__=

=

I[

PREFACE

The work presented in this report is performed under contract NAS 1-19935, Task

No. 15 from National Aeronautics and Space Administration, Langley Research Center.

Dr. Henry E. Jones is the Technical Monitor. The author would like to express his

appreciation to Dr. Henry E. Jones for providing many helpful suggestions during the

entire investigation, and to Dr. Richard L. Campbell for providing the newest version of

the CDISC code and useful discussion about the code.

PREFACE

Summary

1. Introduction

2. The CDISC Method

3. The FPX Rotor Code

4. Implementation

5. Results

5.1 Basic DISC Results

5.2 CDISC Results

6. Conclusions

References

CONTENTS

ii

i

1

2

2

4

5

6

6

7

8

33

On the Coupling of CDISC Design Method with FPX Rotor Code

by

Hong Hu

Hampton University

Hampton, Virginia 23668

Summary

A rotor'section aerodynamic design package is developed by coupling Constrained

Direct Iterative Surface Curvature (CDISC) design method with FPX rotor code. The

coupling between the CDISC design and the FPX flow analysis is fully automated. The

CDISC design method employs a predictor-corrector procedure iteratively to determine

a surface geometry which produces a target pressure distribution, where target pressure

distribution is either pre-defined or automatically generated through flow and geometry

constraints. The FPX code is an eXtended Full-Potential rotor Computational Fluid

Dynamics (CFD) code, which solves three-dimensional unsteady full-potentiM equation

in a strong conservative form using an implicit approximate-factorization finite-difference

scheme with entropy and viscosity corrections. Application of the CDISC design method

coupled with the FPX rotor code is made for rotor blades in hovering motions. Several

design examples are presented to demonstrate the capability and efficiency of the new

package in rotor section design.

1. Introduction

The recent advances in Computational Fluid Dynamics (CFD) have provided accurate

and detailed flow solutions in an efficient way. These advances have generated interest in

integrating CFD code into design methods. Automated aerodynamic design methods are

beginning to become part of this process. These methods can be divided into two general

categories: inverse methods that use an inverse solver, and predictor-corrector methods

that use a direct flow analysis in an iterative manner. The predictor-corrector methods can

be coupled with any flow solver and hence take advantage of the advances in Computational

Fluid Dynamics.

The Constrained Direct Iterative Surface Curvature (CDISC) design method of Camp-

bell and Smith 1 and Campbell 2 is a pressure based predictor-corrector design method. The

CDISC method determines a surface geometry which produces a target pressure distribu-

tion, where target pressure distribution is either pre-defined or automatically generated

through flow and geometry constraints. The method has been coupled with several ad-

vanced CFD flow solvers 1-5 for fixed-wing section design, including design in the presence

of nacelles. Results from these codes indicate that the CDISC method is robust and

accurate.

This report presents the coupling of the CDISC method with a rotor Computational

Fluid Dynamics code - the. FPX code. As the best of author's knowledge, this is the

first time on using the CDISC method in helicopter rotor section design. In the next few

sections, a brief description of the CDISC method and the FPX rotor CFD code is given,

which is followed by the implementation of their coupling. Finally, several design examples

are presented to demonstrate the capability azld efficiency of the new design package in

rotor section design.

2. The CDISC Method

The Constrained DISC method (CDISC method) is an extension of the basic DISC

method. The DISC method employs a pressure based predictor-corrector design procedure,

where the calculated surface pressure distribution is compared with a target distribution

and the correction to surface geometry is then made to achieve the target pressure dis-

tribution. In more detail, the DISC method starts with an initial surface geometry and

flow condition at design point, a flow analysis code is used to generate surface pressure

distribution. The calculated pressure distributions are then compared with the target dis-

tribution and the difference gives the correction to the surface geometry through a design

module. A new geometry is obtained and the flow analysis code is used again to generate

a new surface pressure distribution until the target pressure distribution is achieved.

The DISC design module relates the difference between the calculated and the target

surface pressure coefficients (ACp) to the change in surface curvature (AC) at a given

chordwise location. Different modules are used in different regions during the design pro-

cess. For subsonic and low supercritical flows where a small change in surface geometry

can only result in a small change in surface pressure, the relationship is derived 1 from the

momentum equation as

/',C = A(1 + C2)BZXC, (1)

where A is 1 for the upper surface and -1 for the lower surface; B is input constant

ranging from 0.0 to 0.5, with the higher values giving faster convergence but decreasing

the numerical stability; and C is streamline curvature at aerodynamic surface. For the

moderate to high supercritical flows where a small change in surface geometry can cause a

large change in surface pressure coefficients, the relationship is obtained 1 from supersonic

thin airfoil equation as

AC - d(ACp) Av/ML - 1dx 2 [1 + (dy/dx)2] 1"5

(2)

where y defines airfoil surface.

The advantage of the DISC method over the inverse method is that the method can

be treated as a "black box". The "black box" can be incorporated into any CFD code,

and thus take the advantage of the advances of CFD.

The Constrained DISC method specifies desirable characteristics of the target pressure

distribution. The target pressure is automatically generated and updated at each step

based on the specified characteristics - the constraints. The typical flow constraints are lift,

drag, pitching moment and pressure gradient. The typical geometry constraints are airfoil

maximum/minimum thickness and leading edge radius, and so on. Including geometry

constraints in the design process will yield an airfoil/wing/rotor blade that not only satisfies

target pressure distributions but also be practical to build. In the CDISC design method,

constraints are easily included in the design process to satisfy various design requirements.

For example, upper and lower surfaces can be designed individually and therefore designing

only one surface is possible, which is very useful in design of very thin airfoil sections.

Partial surface design is an option. Surface smoothing eliminates sharp changes in surface

curvature. The limitation of surface curvature is useful in highly cambered airfoil section

design.

The three-dimensional (3D) wing/rotor blade design is considered as a set of airfoil

section design problems at specified span-locations. For 3D span-load distribution design,

the DISC method can also be used by modifying twist distributions. For simultaneous

airfoil section and span-load distribution design, the surface curvature and twist modifi-

cation methods can be used together. The CDISC design method has been shown to be

comprehensive and easy to use, it is therefore highly desirable to use the method in various

configuration designproblems. In the presentwork, the CDISC is usedfor helicopter rotorsection designwhen coupled with a rotor CFD code.

3. The FPX Rotor Code

While in the fixed-wing aerodynamic computational community more and more ex-

pensive and complex Euler and Navier-Stokes methods are used recently, potential methods

still serve=aS a major anaiysis tool :in the r0tary-wing aerodynamic computational commu-

nity. The eXtended Full-Potential (FPX) rotor code s i_s one such accurate and efficient

potential method, which represents an industry standard for rotary-wing computations.

The FPX code is a modified and enhanced version of Full-Potential Rotor (FPR) code 7.

The code (either FPR or FPX) has been used in various helicopter hover and forward flight

cases, including Blade-Vortex Interaction (BVI) calculations 8, nonlinear acoustic analysis 9

and coupling with the comprehensive helicopter code CAMRAD 1°. The application of the

code produces excellent results. The code is also highly Optimized and a typical steady

run takes 1-7 minutes on a Cray-C90 supercomputer with a single processor.

The FPX/FPR codes solve the unsteady three-dimensional full-potential equation in

a strong conservation form using an implicit finite-difference scheme for flow around rotor

blade. It is less expensive than either Euler or Navier-Stokes methods, and yet produces

accurate solutions for various helicopter flows without significant separations.

The unsteady, three-dimensional full-potential equation in strong conservation form

in blade-fixed body-conforming coordinates (_, 77,_, r) is writteff as ....

0 p 0 ___ 0 pV_ 0 p____0--;(7)+ ) + N(-7- , + N( ) = 0 (3)

with

p= {1 + _--_[-2_-(U + (t)_5¢- (V + rh)O , -

i

(W + (t)q_¢]} _-' (4)

where _ is the velocity potential, U, V and W are contravariant velocity components, p

is the density, and J is the grid Jacobian.

The FPX/FPR codes solve Eq. (3) using an implicit finite-difference scheme, where

the time-derivative is replaced by a first-order backward differencing and the spatial-

derivatives are replaced by second-order central differencing. The resulting difference

equation is approximately factored into three operators L_, L_, and L_ in _, 7? and (

directions, respectively

: L_L,tL_(_ n+i - _') = RHS (5)

The detail of the scheme is presented in References 6 and 7.

4

i

z

i#

The FPX is the substantially modified version of the FPR code. Both entropy and

viscosity corrections are included in the FPX code. The entropy correction potential formu-

lation accounts for the shock produced entropy to enhance physical modeling capabilities

for strong shock cases. Either a two-dimensional or a three-dimensional boundary layer

model is coupled with the FPX code to account for viscosity effects. In addition, an axial

flow capability is added into the FPX code to treat tilt-rotors in forward flight. In addi-

tion to the O-H grid topology, an H-H grid topology is added as well. More recently, the

Vorticity Embedding (VE) is incorporated into the FPX code to enhance the prediction

capability of parallel blade-vortex interactions 11.

A grid generation package GRGN3 is used to generate O-H mesh around rotor blade.

The blade surface is defined by an input file. The far-field boundary of the mesh is set at a

fixed number of chords from blade surface. The mesh points are generated between blade

surface and far-filed boundary. This grid generator is combined into the flow solver FPX

recently 12.

4. Implementation

The coupling of the CDISC design method with the rotor FPX code is the main scope

of the present work. Two methods chin be used for coupling the CDISC module with

the FPX flow analysis code: direct coupling where the CDISC module is treated as a

subroutine called by the flow solver; and indirect coupling where a job control language is

used. The indirect coupling offers advantages in code maintenance and portability, and the

design module does not add to the central memory requirement. In the present work, an

indirect coupling is used where a UNIX script file is used to control entire design procedure

automatically. User interference during the design processes is not needed.

Information is passed between the CDISC module and the FPX flow solver using blade

section geometry file and surface pressure coefficient file. The FPX flow solver with a built-

in grid generator 12 is used in this coupling, so that the grid can be re-generated within the

flow solver each time when a new blade section geometry file is obtained from the CDISC

module. Some modifications on input and output statements to the CDISC code and the

FPX code are made as required by the coupling, and thus any type of auxiliary pre- or

post-processor codes is not needed. The UNIX script file starts the FPX flow solver to

produce an output file containing blade section surface pressure coefficients. This file along

with the initial blade section geometry file is then fed into the CDISC design module. The

CDISC design module then produces a new geometry file. This new geometry file is used

as input for the FPX flow solver. The built-in grid generator generates a new grid and then

the flow solver produces a new surface pressure coefficient file. This procedure continues

for desired number of cycles as specified in the UNIX script file. Typical cases take 15-30

cycles to get a convergent design.

5. Results

As a test of capability of the new pac'l_ge using the CDISC and the FPX codes in

rotor section design, several sample design cases are made for a rotor blade. The planform

of the blade is shown in Figure 1 along with seven design stations as indicated. The

blade has a zero-twist. The first three cases are basic DISC design where target pressure

distributions are pre-deflned without any constraints. The next two cases are CDISC

design where target pressure distributions are automatically generated. The following

sub-sections present these results.

5.1 Basic DISC Results

In all three basic DISC design cases, initial blade sections are NACA0012 airfoil sec-

tions and target pressure distributions are obtained from a known "target" geometry. The

new design package is then used to "reproduce" the original "target" configuration. The

tip Mach number is set at 0.6288 for the first and second cases, 0.95 for the third case.

In the first case, the "target" geometry is NACA0008 airfoil section. Thirty design

cycles are executed to get a convergent (almost convergent at tip-station) design. This case

requires around 26 minutes on the Cray-C90 computer with a single processor. The results

of this case are presented in Figures 2a-2e. Figures 2a and 2b are design history in terms

of blade section geometry and surface pressure distributions, respectively. Figure 2c gives

design history of spanwise lifting coefficients, moment coefficients and drag coefficients.

A good approximation to the target pressure distributions is achieved after only a few

(ten) design cycles (target pressure is given next). Figures 2d gives a comparison of design

geometry and target geometry along with the initial geometry, while Figure 2e gives a

comparison for surface pressure distributions for four design stations as indicated (although

a total of seven stations are designed). The correlation between the final design and target

pressure distributions at each station is very good. The new airfoil sections generated

compare well with the original "target" geometry.

The second case is very similar to the first case. In this case however, the "target"

geometry is an "after-design" NACA0008 airfoil, where a CDISC procedure is first applied

to NACA0008 to produce a modified airfoil for reducing drag. The target pressure dis-

tribution is the final design pressure during this design process. The results of this =ease

are presented in Figures 3a-3e. Figures 3a-3c are design history. Figures 3d and 3e are

comparison of design and target. A good agreement between design and target is obtained

again.

In the third case, the "target" geometry and target pressure are provided from a

6

|

i

CDISC design case applied to MDHC HH02 and NACA64A006 airfoil sections. It is ex-

pected that a large number of design cycles is needed for this case to get a convergent

design due to a substantial difference between the initial geometry and the "target" ge-

ometry, particularly at tip station. As a consequence, 300 design cycles are executed for

this case to examine the nature of convergence. The results of this case are presented in

Figures 4a-4g. Figures 4a and 4b are design history in terms of airfoil section geometry

and surface pressure distributions, respectively. Figure 4c gives design history of spanwise

lifting coefficients, moment coefficients and drag coefficients. It is seen that the solution

is convergent between design cycles 150 and 200 for Stations 1, 3 and 5, and almost con-

vergent at design cycle 300 at Station 7 (the tip station). Figures 4d gives a comparison

of final design geometry and target geometry along with the initial geometry, while Figure

4e gives a comparison for surface pressure distributions for the four design stations. The

correlation between the final design and target pressure distributions at Stations 5 and 7

is very good. However, some discrepancies exist for Stations 1 and 3. Same is true for the

comparison of geometry. Figures 4f and 4g then made another comparison of target with

design where design geometry and pressure are obtained at design cycle 50 for Stations 1,

3 and 5. It is now noted that the agreement between design and target is better than that

of Figures 4d and 4e for Stations 1 and 3, particularly for Station 1.

5.2 CDISC Results

With the Constrained DISC approach, the emphasis is shifted to meeting the con-

straints where target pressure is generated automatically within the design module. In the

next sample cases, two constraints are imposed: one to fix the original spanload distri-

bution, and other one to reduce drag using the Modified Uniform Distribution (MUD) of

chordwise loading constraint option. A MUD value of 0.2 is used according to Campbell 5

to obtain a best result in reducing drag. The tip Math number is set at 0.95. In both

cases, 15 design cycles are executed.

Figures 5a-5c are the results of the first CDISC sample design case, where initial blade

sections are NACA0012 sections. Figures 5a and 5b give the history of design for blade

section geometry and surface pressure distributions, respectively. Figure 5c presents a

spanwise lifting coefficient, moment coefficient, drag coefficient and maximum local Mach

number distributions. It is seen that the design reduces the negative lifting force, pitching

moment a_nd drag force. By examining the drag coefficients, it is found that the drag is

reduced by 12.5_ at Station 3 and 7.5% at Station 5 through the CDISC design. The

maximum local Mach numbers are unchanged during the design process.

Figures 6a-6c are the results of the second CDISC sample design case, where initial

blade sections are MDHC HH02 airfoil for Stations 1 through 5, and NACA64A006 airfoil

for Stations 6 and 7. Figures 6a and 6b give the history of design for blade section geom-

etry and surface pressure distributions, respectively. Figure 6c presents a spanwise lifting

coefficient, moment coefficient, drag coefficient and shock Mach number distributions. By

examining the drag coefficients, it is found that the drag is reduced by 12.7% at Station 1,

9.6% at Station 3, 25.6% at Station 5 and 12.5% at Station 7 through the redistribution

of the loading and smoothing. Shock is also eliminated through the design as indicated,

in the figure, by zero-shock Math number along the span.

6. Conclusions

A rotor section aerodynamic design package is developed by coupling the CDISC

design method with the FPX rotor CFD code. The coupling between the CDISC design

and the FPX flow analysis is fully automated using a UNIX script file to control job flow.

Five sample design cases are presented for both basic DISC and Constrained DISC design

for a zero-twist blade in hovering motion. The results indicate that the CDISC method is

a robust and efficient design method when used in rotor section design coupled with theFPX code.

These sample cases demonstrate that the target pressure can be achieved even when

the initial geometry is not "close" to the "target" geometry. A constrained DISC design

case demonstrates a shock-free design using MUD method, where drag is significantly

reduced. Actual computational effort depends on the complexity of the target pressure

distributions and the difference between the initial and "target" geometry. A typical

design case with 30 design cycles for designing 7 stations requires around 26 minutes CPU

time on the Cray-C90 computer with a single processor. Presently, all sample design cases

are made to a zero-twist blade without in-flow angles for either symmetric or cambered

airfoil section design. The further work is needed in extending the current design package

into high-lifting flows with large twist and in-flow angles.

8

Station1

r/R=50%

Station 2 Station 3

Station 4

Station 5 Station 7

1 r_-mo0°_(tip)

II

Station 6

Figure 1. The rotor blade planform.

0.08

Y0.06

0.04

0,02

0.00

-0.02

-0.04

-0.06

Design station 1 at r/R = 50%

Initial ...Cycle 5

..........................Cycle 10Cycle 15Cycle 20Cycle 25Cycle 30

js"

•'J

rs "°

0.08

Y0.06

0.04


Initial

0.02 .......... (_yc!e 5.........................._ycle 10

Cycle 150.o0 Cycle 20

Cycle 25-0.02 Cycle 30

-0.04 ,,,'"

-0.06 ""............

-0.080.0 0.2 0.4 0.6 0.8 X 1.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.080.0

Design station 3 at dR = 79%

........... Initial

Cycle 5..........................Cycle 10

Cycle 15C yc!e 20_ycue 25Cycle 30

0.08 -Design station 7 at r/R = 100% (tip)

Y

0.06 ,-'" ............. ,

0.04

.......... Initial

0.02 Cycle 5

..........................Cycle 10

o.oo Cycle 15Cycle 20

-o.o2 Cycle 25Cycle

-0.04 .- "o• °

-0.06 ""...........

0.2 0.4 0.6-0.08

0.8 X 1.0 0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 2a. Design history of blade section geometry

for basic DISC design case 1, Mtir = 0.6288.

10

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0

Design station 1 at r/R=50%

"_-...--.'.-...

............. Initial, lowerCycle 10, upper },

.......... Cycle 1O, lower

................................Cycle 20, upper

..............."..............Cycle 20, lowerCycle 30, upper

o Cycle 30, lower.... I .... I .... I .... I . , . . I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


,;=._ ='::=:.

............. Initial_

............ Initial, lower }i

Cycle 10, upper

.............. Cycle 10, lower

................................Cycle 20, upper

...............o..............Cycle 20, lower

Cycle 30, upper

.... Cycle 30, lower,

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


............. Initial, lower t__

Cycle 10, upper

......... Cycle

................................Cycle

...............* ..............Cycle

Cycle

cycle0.2 0.4

10, lower

20, upper

20, lower

30, upper

?o,,Iower .... ,0.6 0.8 X 1.0

0.25

0.00

-0.25

-0.50

Design station 7 at r/R=100% (tip)

........ Initial, lowerCycle 10, upper !

............ Cycle 10, lower

-o.75 ................................Cycle 20, upper

I ...............* ..............Cycle 20, lower-1 .OOl- Cycle 30, upper

,,,, • .... C,yc!e 30, lower= . i = = , . = = I

0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 2b. Design history of surface pressure distributions

for basic DISC design case 1, Mtip = 0.6288.

11

0.02

CL

0.00

-0.0,_

-0.04

-0.06

Y;

............. Initial

Cycle 10

...............................Cycle 20Cycle 30

_,, , , I L, , , I , _ , , I .... I, ,_,_j,,l_ I

50 60 70 80 90 100

r/R (in %)

0.01

Co

0.00

-0.01

-0.02

-0.03 -

-0.04

............. Initial

............. Cycle' 10

................................Cycle 20

Cycle 30.... I .... I , i ..-i . , r t i .... I .... I

50 60 70 80 90 100

r/R (in %)

0.02

CM

0.01

0.00

-0.01

"%. _L

:" ........... Initial

............... Cycle 10

................................Cycle 20

Cycle 30, , , I ,-,-_;-.TT, , , I i I i i I T I _ , I ,_. i I

=50 60 70 8o 90r/R (in %)

Figure 2c. Design history of spanwise lifting (CL), moment (CM) and drag (CD)

coefficients for basic DISC design Case 1, Mtip = 0.6288.

12

0.08 - Design station 1 at dR = 50%

Y

0.06 ,,, .......... ,,

0.04 ,,_,,

........... Initial

0.00,, _ Design ,_o Target _j_. ,,"

-0.02 _ _,,'"

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06


r" -.

r7 ""'"""'_s

Design 2

0.?? F Design station 3 at fiR= 79%

Y_

0.06_- , ,........... ""-,,

0.04 I[ _'"',"

o........... Initial

0.00_- _ Designo Target ,.._.'• "

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08 _Design station 7 at r/R = 100% (tip)

Y0.06

0.04 _,,

0.02 oo_,,,

........... Initial %

0.00 _ Design _'o Target _ ._,,"

008 / .... J .... i .... i .... i .... i0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 2d. Comparison of blade section geometry


13

0.75_ V Design station 1 at r/R=50%

"_P i0.50 _--.'.'--.

1"/4k ....... A+ "" _ _'_0.25....,...,.,&...._....

i',_.. 2._..;+_

oo:i;;-0.2E

-0.50

Design, upper

-o.75 ................................Design, lower

° Target, upper

-1 .oo • Target, lower

, _ I .... I . , , , l , , , , I . j.+. _ ]

0.0 0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

_1.00

0.0


.... +l_'_+u -

Initial, upper

............. Initial, lower I

Design, upper

..............................Design, lower

° Target, upper

• Target, lower

, , , I , , _ , I , • _ I I z z , , I , , , , I

0.2 0.4 0.6 0.8 X 1.0

0:_75F Design station 3 at r/R=79%

-(';P i0.50 ,,_1- L'.::-,,_;/ "-._-..I_:l_ ........"-"-

0.25 _:...

-0 25 _]• - .......... Initial, upper

-0.50 ............. Initial, lower I

Design, upper

-0.75 ................................Design, lower

° Target, upper

-1 .oo • Target, lower

. . , , .I . , . .I ,_ , , I . , . , I !.! I i |

010 0.2 0.4 0.6 0.8 X 1.0

0.75

"Cp

0.5(

0.2.=

0.0(

-0.2E

-0.50

-0.75

-1.00

0.0

_ Design station 7 at r/R=100% (tip)

............. Initial, lower _-

Design, upper

................................Design, lower

° Target, upper

" Target, lower

.... I .... I , L , , I .... I _ , = , I

0.2+ 0.4 0.6+ o.s=X +.o

Figure 2e. Comparison of surface pressure distributions

for basic DISC design case 1, Mtil)= 0.6288.

14

0.08

Y0.06

0.04

0.02

0"00 f

iiill-0.06

-0.080.0

Design station 1 at r/R ---50%

Cycle 20_ C_/cle 25 _,_'"

i %., se

i I I I ] .... I .... I , , , , I , , , , ]

0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.080.0


InitialC_ycle 5

.........................._.,ycle ] uCycle 15Cycle 20Cycle 25Cycle 30

0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06


Initial

Cycle 5..........................Cycle 10

Cycle 15Cycle 20Cycle 25Cycle 30

0.08

Y0.06

0.04

0.02

0.00

-0.02

n station 7 at r/R = 100% (tip)

........... Initial

Cycle 5..........................Cycle 10

......... Cycle 15Cycle 20Cycle 25Cycle

o"

s

-0.080.0 0.8 X 1.0



15

0.75 I-Cp0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00,

0.0


............ In'dial, lower

L Cycle 10, upper!

...... Cycle 10, lower

................................Cycle 20, upper

...............* .............Cycle 20, lowerCycle 30, upper

Cycle 30: lower| , , , J • = = i | i i t I , | .... I

0.2 0.4 0.6 0.8 X 1.0

0.75 -

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

d

-1.00

0.0


o -o-;;'°-:::::..::.

............. Initial, lower 1

................ Cycle 10, upper

.................. Cycle 10, lower

................................Cycle 20, upper

...............° ..............Cycle 20, lower

Cycle 30, upper

--==o Cycle 30, loweri i i i ] ¢,4 , ' , , , . , , , , I , , , = I

0.2 0.4 0.6 0.8 X 1.0

0 75 Design station 3 at r/R=79%

I0.50 _,-'2.'.".... _.

0.25 . -.::::::. "-..

0.00

0 25 ............. Initial, upper "_

- ' ............. Initial, lower

-0.50 Cycle 10, upper i............... Cycle 10, lower

-o.75 ................................Cycle 20, upper

...............° ..............Cycle 20, lower

-1 .o0 Cycle 30, upperCycle 30, lower

= JL, , I , , = = I .... I , , , , I .... 1

0.0 0.2 0.4 0.6 0.8 X 1.0

0.25

0.00

-O.25

-0.50

-0.75

-1.00

0.0

Design station 7 at r/R=100% (tip)

............. Initial, lower _,

Cycle 10, upper !

............ Cyc!el O, lower

................................Cycle 20, upper

...............o..............Cycle 20, lower

Cycle 30, upperCycle 30, lower

,_, = , , _ , _/'= =L J I , , , , I , , , , i

0.2 0.4 0.6 0.8 X 1,0



16

0.02

CL

0.00

-0.02

-0.04

-0.06

-0.08

-0.10

mrs

i

,i

i I

...°-

............. Initial

Cycle 10

................................Cycle 20Cycle 30

, , , I = , , , | _ = _ i I .... I , , , , I , , , , I

50 60 70 80 90 1O0r/R (in %)

0.01

CD

0.00

-0.01

-0.02

-0.03

-0.04

11

,,

............. Initial

.............. Cycle 10

................................Cycle 20

Cycle 30,,,I,,.,I .... ImLlll .... I .... ]

50 60 70 80 90 100

r/R (in %)

0.01

0.00

-0.01

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

1

i

..... _ ..................... "-_

............. Initial

Cycle 10

................................Cycle 20Cycle 30

.,,,I,,,,I=L,,I,=,, I,,,,I,,,_1

so 6o 7o 8o 90 1oodR (in %)

Figure 3c. Design history of spanwise lifting (CL), moment (CM) and drag (CD)

coefficients for basic DISC design case 2, Mt,p = 0.6288.

17

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06

-0.080.0


, , , , I .... I .... I .... ! .... I

0.2 0.4 0.6 0.8 X i.0

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06


Design

0.08

Y0.06


I"

0.04 ' ""

0.020.00,

-0.02

-0.04 1 ""'" "'"'""'"

-0.06_- """............ ""

[008 r .... , .... , .... , .... , .... ,

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08 _Design station 7 at r/R = 100% (tip)

Y0.06

0.04

0.02

0.00

-0.06

........... Initial

Design

o Target

-0.080.0 012 0.4 0.6

Figur e 3d. Comparison of blade section geometry

for basic DISC design case 2, Mtip - 0.6288.

0.8 Xl.0

18

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0

- Design station 1 at r/R=50%

"L--2.-c->.../

........... Initial, Upp er _'_

....... Initial, lower L

Design, upper

...............................Design, lower

o Target, upper

• Target, lower

[ I _ , I .... I, i,, I _,, , I .... •

0.2 0.4 0.6 0.8 X 1.0

0.75[- Design station 5 at r/R=94%

0.00 i: " """: .... -=,_.

-0.25 Initial, upper '_

............. Initial, lower /-0.50

-0.75 I

-1.00 f

0.0

Design, upper

................................Design, lower

o Target, upper

• Target, lower

.... I,, , , I .... I A , = , I , , ,

0.2 0.4 0.6 0.8 X 1.0

0.75

-C 0

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00


" _.-:.-..-.::-..:...,"S" ---:--..

,=_ "-:-::-.

...... Initial, lower

Design, upper

................................Design, lower

o Target, upper

" Target, lower

, • i , | i i ,

0.o 0.2

, | , , , , i .... ! .... I

0.4 0.6 0.8 X 1.0

0 75- Design station 7 at r/R=100% (tip)

o.5o ,,,,"\

0.25 __.

0.00

-0.25 ........... Initial, upper I............. Initial, lower

-0.50Design, upper[

-o.75 _- ...............................Design, lower

i ° Target, upper-1 .oo " Target, lower

i , , , I , , , , I _ _ , , I , , , , I , , , • 1

0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 3e. Comparison of surface pressure distributions

for basic DISC design ease 2, Mtip = 0.6288.

19

0.08

Y0.06

0.04

0.02

0"00 I

-0.02 f

-0.04

-0.06

-0.080.0


......... Cycle 150 _,.

Cycle 20_

_ "J'e t

.... I .... I , , _ , I .... I .... I

0.2 0.4 0.6 0.8 X 1.0

0.08 Design station 5 at r/R = 94%

o.Y

0.04 ........... .

0.02 ............................Cycle 100 _...

......... Cycle 150 "_

0.00 _ Cycle 200

-0.02 _\, _'_ .."'"

004 F_'""'"'""

f """ ........... "'"

E_0.08 / .... I .... I , , , , I .... t .... ]

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08 -

Y0.06

0.04

0.02

0.00

-0.02


I_' _ Cycle 200 ,.

-0.041 ""'" "'"'"'"

-0.06_- """ ............ "'"

[008 r .... , .... i .... I .... _ .... J

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08 Design station 7 at r/R = 100% (tip)

Y

0.06 .... .......... -..

F ,," _f...._...--..;._.-:.--_-..>.. -,,,

0.04 IT ,' .._...-.S_...... "_"-......'>. "-., ....' ,. _ _ ...... _-..'.>. -.-..

o.o2_- __;.'..

ooor-:-" c vC',e oo_, ..... ,-- C_,cle 150 _?

-0.02 !_ ...... Cycle__.'"

-0.04 - ',, "_ii-..-_..-..=-..--..-.2.-222_ ,•'"

-0.06 Cycle 250

_----- Cycle 300-0.08 .... ' .... ' .... i,, .. i .... ,

0.0 0.2 0.4 0.6 0.8 X 1.0


for basic DISC design case 3, M, ip = 0.95.

2O

0.75

°Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


_-- I.ni.t!a!,upper "_----_-----Initial,/6wer _

u2ye; 1..... C' ,cle 50, lower........................ 01

......................C _

........ C____._---C I

C'_.__..o-...--C ,

i,,,1111

0.2

tcle 100, upperrcle 100, lower'cle 150, upper'cle 150, lower,cle 200, upper,cle 200, lower, I j = , , I .... ! .... I

0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


........................ O1

........... ,r .......... C'

C-------e------- C

Initial, lower'i/_' uppe_

.............. C _,cle 50, upperrcle 50, lower i,cle 100, upper,cle 100, lower,cle 150, upperfcle 150, lowerfcle 200, upper

----o--- Cycle 200, lower., , _ I , , 1 • I,. , , I = 1,. I, . , . I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.001

).0

Design station 3 at r/R=79%0.75

-Cp

0.50

_°pper

wer50, upper50, lower100, upper100, lower150, upper150, lower200, upper

0.250.00

.......... Initial,

......... Initial, -o.25Cycle

........... Cycle -0.50

........................Cycle

......................Cycle -o.75Cycle

....... CycleCycle -1.oo

___o--- Cycle 200, lower.... l = ., , l ,., , I,.,. I.,, i I

0.2 0.4 0.6 0.8 X 1.0

_Design station 7 at r/R=100% (tip)

_\. ,,,_y'%.\ ,,

----_----Initial, lower '_ICycle 100, upper

....... Cycle 100, lower i........................Cycle 200, upper......................Cycle 200, lower........ Cycle 250, .upper----,---- _ycle 250, lower

Cycle 300, upper._= Cycle 300, lower

,,,,=L .... I. ''' l' ''_l_'''l

0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 4b. Design history of s_face pressure distributions

for basic DISC design case 3, Mt,p = 0.95.

21

0.30

CL0.20

0.10

0.00

-0.10

-0.305O

............. Initial

Cycle 50

................................Cycle 100

........... Cycle 150C, 200

60 70 80 90 1O0

r/R (in %)

0.0;

0.01

O.OC

-0.01

-0.02

-0.03

-0.04

-0.05

-0.06

-0.07

-0.08

Co

............. Initial

Cycle 50

.............................Cycle 100

Cycle 150

Cycle 200

50 60 70 80 90 1O0

r/R (in %)

0.0;

0.00

-0.02

-0.04

-0,06

-0.08

-0.10

yemm_m-'--- - L •

+ -............ Initial

Cycle 50

. ...............................Cycle 100

Cycle 150

Cycle 200

L

-- -- Z

50. 60 70 80 90 ._100 . _- :

r/R %)Figure 4c. Design l_istory of spanwise lifting (CL), moment (CM) and drag (Co)

coei:Ficients for basic DISC design case 3, Mtis- 0.95.

22

0.08

Y0.06


0.04

0.02

........... Initial

0.00 Design

o Target-0.02

O jD

0 0 0 0 0 .1 •

04 ' ""0 '

-0.06 ""............

-0.080.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

0,04

0.02

i Design station 5 at r/R = 94%

0.00,

-0.02

-0.04

-0.06

-0.080.0

Design

_x o II

.... I .... = .... = .... L .... i

0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06


oo,0.02 "'",

°'0°:' L o Target Z -..,,-"

,- _ Design

-0.02 _°,,O;o_ o o .,1-'""0 0 0 0 0 s"

-0 04 [ ' .• o J

-0.06[,., _o, .... i .... , .... i .... i .... I

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

_Design station 7 at r/R = 100% (tip)

• " -.

S I ".

0.04 ,'

0.02 _.

oooky

-0.04 I'""'" "'" ""'"J'""

-0.06_- """ ............ ""

[_0.08 / .... i .... i .... i .... J .... I

0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 4d. Comparison of blade section geometry for basic DISC

design case 3, Mtip = 0.95, where final design is used.

23

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

4

-1.00 iI

0.0


o

"".,.,,

....;=............._..._ _,,

Initial, upper 1

............. Initial, lower

Design, upper

................................Design, lower

o Target, upper

• Target, lower

.... 1 .... I , , , , | L , _ , I .... I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

0.75

-1.00'


z ........... _"_ ",,

o %

%t

............. Initial, lower I!

Design, upper

................................Design, lower

o Target, upper

• Target, lower

0.0 0.2 0.4 0.6 0.8 x l.0

0.75 Design station 3 at r/R=79%-Cp

Os -I_ .

....."!

0.25 ' , •0.00

-0.25

-0.50

I _ Design, upper

-0.75[- ........ Design, lower

_ o Target, upper

-1.00[ • Target, i.ower .r .... 1 _ _ l , z • • I .... I .... I

0.0 0.2 0.4 0.6 0'8 X 1.0

0 75 Design station 7 at r/R=100% (tip)_c

o2o

0.00 . __:.. .....

0.25 .......... Initial, upper............. Initial, lower

0.50Design, upper

T-

o.75_- ................................Design, lower

i o Target, upper1.00 " Target, lower

.... I , . , = I _ , . . I .... t .... J

0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 4e. Comparison of surface pressure distributions for basic DISC

design case 3, Mtip = 0.95, where final design is used.

24


0.06 _9_

0.04 y

0.02 -_..

...........Initial %.0.00_- _ Design

o Target .._ ../

-°°°f "_0.081 . • , , I , _ . . i .... _ .... :,, ,, I

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06


0.04 _.

0.02 ........... Initial %

-0.02 _,, o o . ,..-".,

-0.04 1 "' "'"""

-0.06[008 ..... _ .... ,,,,, I , , ,,.I .... ,

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06


0.02

......... Initi I

o.oo :L _ Design

-o.o2 • o Target o_.o .__......-'"-_'-

_u s aj J_J

-0 04 v- ' -"

"0"06 f008" .... ' .... ' .... ' .... I .... I

0.0 0.2 0.4 0.6 0.8 X 1.0

0.08

Y0.06

0.04

0.02

0.00

0.02

Design station 7at r/R = 100% (tip)

0.041 '

0.0

•sp r'l

, . , I .... I .... I , , . a I a _ = = I

0.2 0.4 0.6 0.8 X 1.0

Figure 4f. Comparison of blade section geometry for basic DISC

design case 3, Mtip = 0.95, where the design at cycle 50 is used.

25

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


o

F o


Design, upper

................................Design, lower

o Target, upper

• Target, lower

L .... _J_ _ L_J , , I .... I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


,,. ":---- "_-..-....

............. Initial, lower /t

Design, upper

................................Design, lower

° Target, upper

• Target, lower

, , , I , , ] _ I.._.. _ , , I t I i I | J = _ = I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00


Initial, upper

............. Initial, lower 1',1

Design, upper

................................Design, lower

° Target, upper

• Target, lower

.... I , _,L , I .... 1 .... I .... I

0.0 0.2 0.4 0.6 0.8 X 1.0

-0.25

-0.50

-0.75

-1.00

0 75 Design station 7 at r/R=100% (tip)

o.5o , \0.25 \.

0.00 _ ............

_L

Initial, upper

............. Initial, lowerI

Design, upper

.............................Design, lower

o Target, upper

• Target, lower

.... I .... I .... I ,, ,, t , _ ,, I

0.0 0.2 0.4 0.6 0.8 X 1.0

Figure 4g. Comparison of surface pressure distributions for basic DISC

design case 3, M, ip = 0.95, where the design at cycle 50 is used.

26

0.08

Y0.0(

Design station 1 at dR = 50%0.08

Y0.06

Design station 5 at fir = 94%

0.02

0.00

-0.02

-0.04

-0.0(

-0.010.0

.......... Initial

......... Cycle 5

..........................Cycle 10

Cycle 15

0.04

o.0c

-0.02

-o.o4

-o.o6

-0,08o.o

........... Initial

Cycle 5

..........................Cycle 10

Cycle 15

o.o8

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06!

-0.080.0

Design station 3 at r/R = 79%0.08

Yo.o6

Design station 7 at r/R = 100% (tip)

0.04

.......... Initial 0.02 .......... InitialCycle 5

....... Cycle 5..........................Cycle 10 0.00

..........................Cycle 10Cycle 15

-0.o2 Cycle 15

0.4 0.6 0.8 X 1.0 -0.0[ 0.0 0.2 0.4


for CDISC design case 1, Mtip = 0.95.

0.6 0.8 X 1.0

27

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.75 -

-Cp

0.50Design station 1 at r/R=50%

0.25

o.00

............. Initial, lower _ -0.25

- Cycle 5, upper

........ Cycle 5, lower _ -o.5o

................................Cycle 10, upper

..............................Cycle 10, lower -o.75

Cycle 15, upper -1 .ooo Cycle 15, lower

.... I , , , j I .... I .... I , , , i I

0.0 0.2 0.4 0.6 0.8 X 1.0 0.0



----_i .... CYcle 5, upper /......... Cycle 5, lower },

................................Cycle 10, upper

...............° ..............Cycle 10, lower

Cycle 15, upper

o Cycle 15, lowerI ' ' ' I , , • , ! .... I , , , , | , , , . I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0

0.75

Design station 3 at r/R=79% -Cp

" :_:',.- ""'"'-_._ 0.50

0.25

0.00

............. Initial, lower _ -0.25

....... Cycle 5, upper /............ Cycle 5, lower ], -0.50

................................Cycle 10, upper-0.75

...............- ..............Cycle 10, lower

Cycle 15, upper -1.00o Cycle 15, lower

.... I , i i _ I i i i i I i , , , I .... I

0.2 0.4 0.6 0.8 X 1.0 0.0

(tip)

............. Initial, upper

...... Initial, lower "_

---_---- Cycle 5, upper /......... Cycle 5, lower _,

................................Cycle 10, upper

..............................Cycle 10, lower

Cycle 15, Upper

__-o---- Cycle !5, lower.... I .... I .... ] .... I: .... I

0.2 0.4 0.6 0.8 X 1.0

Figure 55: Design history of surface pressure distributions


28

:

0.02

CL

0.00

-0.02

-0.04

-0.06

-0,08

-0.10

........................................................................................ "'"""-"

__J" ;

r

t

............. Initial

......... Cycle 5

...............................Cycle 10Cycle 15

,,, I, , j ,I., ,, I. ,,, I , . . .I., , . I

50 60 70 80 90 100r/R (in %)

C D

0.00

-0.01

-0.02

-0.03

-0.04

-0.05

-0.06

............. Initial

Cycle 5

................................Cycle 10

Cycle 15

.... I , , z , I _ . . . I , , , , I , , , . 1

60 70 80 90 1O0r/R (in %)

0.02

CM

0.01

0.00

-0.01

-0.02

i

............. Initial

Cycle 5

................................Cycle 10

Cycle 15,.. I .... I .... I_ _,, I .... ,I .... I

50 60 70 eo 90 lOOr/R (in %)

1.50

1.00

0.50

0.00

-0.50

_A A A & &&

• Initial

z_ Cycle 5

o Cycle 10

o Cycle 15

50 60 70 80 90 1oor/R (in %)

Figure 5c. Design history of spanwise lifting (CL), moment (CM) , drag (CD)

coefficients and local maximum Mach No. for CDISC design case 1, Mtip = 0.95.

29

0.08 -

Y0.06


0.04 _"

0.02

..........................Cycle 10 "",_,,_X_

o.00 _ Cycle15 __

-o.o4 I

-o.06[

008- .... ' .... i .... r .... ,.,, LI0.o 0.2 0.4 0.6 0.8 X 1.o

0.08

Y0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06

-0.080.0

Design station 5 at r/R -- 94%

.......... Initial

........... Cycle 5

..........................Cycle 10

Cycle 15

0.2 0.4 0.6 0.8 X 1.0


Y .-:c'_':c_._.

u.uQ __

oo,F.......0 02 ............. Cycle 5

-0.04 F --

-0.06_

0 08 _ '.

0.0L_ J = , , = t • • • _ I t I I ' ] I J J _ |

0.2 0.4 0.6 0.8 X 1.0

::o :IOe'0n0,04P

0.02

0.00

-0.0;

-0.0_

-0.06

-0,080.0

station 7 at r/R = 100% (tip)

_ 1 I I ] .... I I 1 I I ( _ [ , , I , i i _

0.2 0.4 0.6 0.8 X 1.0

Figure 6a. Design history _0f })lade section geometry


30

0.75

-Cp f

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0


; ".........._...:.:_... ..............

Cycle 5, upper

.......... Cycle 5, lower

................................Cycle 10, upper

..............................Cycle 10, lowerCycle 15, upper

___o___cycle1,s:lower= " [ _ | * " " I I I = * = ' I I I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.0

- Design station 5 at r/R=94%

. ...... o°'-.

........... Initial, lower ',-'

................ Cycle 5, upper

......... Cycle 5, lower

................................Cycle 10, upper

...............•...............Cycle 10, lower

Cycle 15, upper

o .Cycle 15, !ower, , , , I , , , , , , , , I I I = , , I

0.2 0.4 0.6 0.8 X 1.0

0.75

-Cp

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

0.(


!

.......... Init'_, lower ,,,_; 1

Cycle 5, upper

........... Cycle 5, lower

................................Cycle 10, upper

...............° ..............Cycle 10, lower

Cycle 15, upper

o Cyc, le ! 5, Iowe r, = i x * | I I = = J i = I I I

0.2 0.4 0.6 0.8 X 1.0

0.75 Design station 7 at r/R=100% (tip)oC ol

-0.75

-1.00

0.25_0.00

............. Initial, upper-0.25


-0.50 ............. Cycle 5, upper............. Cycle 5, lower

................................Cycle 10, upper

...............•..............Cycle 10, lower

Cycle 15, upper

° Cycle 15, lower.... t .... I , , , , I , , , , I , , , , I

0.0 0.2 0.4 0.6 0.8 X 1.0



31

0.30 -

CL

0.20

0.10

0.00

-0.1 0

-0.20

-0.30

............. Initial

Cycle 5

................................Cycle 10Cycle 15

,r,___.A, ' I .... | .... | .... I .... ] .... I

50 60 70 80 90 100

r/R (in %)

0.02

CD

0.01

0.00

-0,01

-0.02

-0.03

-0.04

/.----

istai

............. Initial

Cycle 5

................................Cycle 10Cycle 15

.... I,,, , I=== = I, ,,,[_,,, I ,,,, I

50 60 70 80 90 100

r/R (in %)

=

0.06

CM0.04

0.02

0.00

-0.02

-0.04

-0.06

-0.08

-0.10

J!

,t

.y

.222- ....

............. Initial

Cycle 5

................................Cycle 10Cycle 15

,,,I,_,,1_,,,I .... I .... I .... I

5o so ....s0 90 loodR (in %)

1.50

1.00

0.50

0.00

0.50

:E

OoJ_U)

• . A A A

A A _ o o

• Initial,

,_ Cycle 5

•o Cycle 10

o Cycle !5..... I .... I .... I , , ,G=_ _ _ I .... I

50 60 ;70 80 90 _ 100

r/R (in %)

Figure 6c. Design history of spanwise rifting (CL), moment (CM), drag (CD)

coefficients and shock Math No. for CDISC design case 2, Mtip = 0.95.

32

References

1. Campbell, R. L. and Smith, L. A., "A Hybrid Algorithm For Transonic Airfoil andWing Design", AIAA Paper 87-2552, 1987.

2. Campbell, R. L., "An Approach to Constrained Aerodynamic Design With Applica-tion to Airfoils", NASA TP 3260, 1992.

3. Smith, L. A. and Campbell, R. L., "Applications of a Direct/Iterative Design Methodto Complex Transonic Configurations", NASA TP 3234, 1992.

4. Mineck, R. E. and Campbell, R. L., "Demonstration of Multipoint Design Procedures

for Transonic Airfoils, AIAA Paper 93-3114, 1993.

5. Campbell, R. L., "Efficient Constrained Design Using Navier-Stokes Codes", AIAA

Paper 95-1808, 1995.

6. Bridgeman, J. O., Prichard, D. and Caradonna, F. X., "The Development of A CFDPotential Method for The Analysis of Tilt-Rotors", the Proceedings of the AHS Tech-

nical Specialists Meeting on Rotorcraft Acoustics and Fluid Dynamics, Philadelphia,PA, October 15-17, 1991.

7. Strawn, R. and Caradonna, F. X., "Conservative Full-Potential Model for UnsteadyTransonic Rotor Flows", AIAA Journal, Vol. 25, No. 2, 1987, pp. 193-198.

8. Caradonna, F. X., Strawn, R. C. and Bridgeman, J. O., "An Experimental and Com-

putational Study of Rotor-Vortex Interactions", the Proceedings of the FourteenthEuropean Rotorcraft Forum, Milano, Italy, September 20-23, 1988.

9. Purcell, T., "A Prediction of High-Speed Rotor Noise", AIAA Paper -89-1130, pre-sented at the AIAA 12th Aeroacoustics Conference, San Antonio, Texas, April 10-12,

1989.

10. Strawn, R. C. and Bridgeman, J. O., "An Improved Three-Dimensional Aerodynam-ics Model for Helicopter Airloads Prediction", the AIAA 29th Aerospace Sciences

Meeting, Reno, Nevada, January 7-10, 1991.

11. Bridgeman, J. O., Ramachandran, K., Caradonna, F. X. and Prichard, D., "A Compu-tational Analysis of Parallel Blade-Vortex Interactions Using Vorticity Embedding",the Proceedings of the 50th AHS Annum Forum, Washington, DC, May 11-13, 1994,pp. 1197-1210.

12. Hu, H., "Development of an Automatic Differentiation Version of the FPX RotorCode", Technical Report, NAS-l-19935-Tll, Hampton University, Hampton, Virginia,1996.

33

REPORT DOCUMENTATION PAGE Fo.__op_vedOMB No. 0704-0188

--Public reporting burden for this Collection of information Is estimated to average 1 hour per response, including the time tOl reviewing instructions, searching existing data'sources, gathe_ng and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any o_eraspect of this collection of information, including suggestions |or reducing this burden, to Washington Headquarters Services, Directorate for Information Operations andReports, 12i5 Jefferson Davis Highway, Suite 1204, Arlington, VA 222_-4302, and to the Office o_ Management and Budget, PapenNork Reduction Project (0704-0188),Washin_tonLDC20503.1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE .... 3. REPORT TYPE AND DATES COVERED

December 2000 Contractor Report4. TITLE AND SUBTITI'E

On the Coupling of CDISC Design Method With FPX Rotor Code

6. AUTHOR(S)

Hong Hu

-7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES i

Hampton UniversityHampton, Virginia

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Langley Research CenterHampton, VA 23681-2199

i1_ SUPPLEMt=_£rARYNOTES

Langley Technical Monitor: Henry E. Jones

5. FUNDING NUMBERS

NAS1-19935

WU 505-598-705

8. PERFORMING ORGANIZATIONREPORT NUMBER

10. SPONSORINGJMONITORINGAGENCY REPORT NUMBER

NASA/CR-2000-210314

[

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified-Unlimited

Subject Category 70 Distribution: NonstandardAvailability: NASA CASI (301) 621-0390

!l

13. ABSTRACT (Maximum 200 words)

The rotor section aerodynamics design package is developed by coupling Constrained Direct Iterative Surface

Curvature (CDISC) design method with the FPX rotor code. The coupling between the CDISC design and the

FPX flow analysis is fully automated. The CDISC design method employs a predictor-corrector procedure

iteratively to determine a surface geometry which produces a target pressure distribution, where the targetpressure distributions is either pre-defined or automatically generated through flow and geometry constraints.

The FPX code is an eXtended Full-Potential rotor Computational Fluid Dynamics (CFD) code, which solves the

three-dimensional unsteady full-potential equation in a strong conservative form using an implicit approximate-

factorization finite-difference scheme with entropy and viscosity corrections. Application of the CDISC design

method coupled with the FPX rotor code is made for rotor blades in hovering motions. Several design examples

are presented to demonstrate the capability of the new package in rotor section design.

14. SUBJECT TERMS

Rotorcraft; CFD; Sensitivity Analysis; Design

17. SECURITY CLASSIRCATIONOF REPORT

Unclassified

NSN 7540-01-280-5500' '

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Unclassified

15. NUMBER OF PAGES

4016. PRICE CODE

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