a user's manual for the vertical axis wind turbine
TRANSCRIPT
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SAND80-ll55 Unlimited Release
A USER'S MANUAL FOR THE VERTICAL AXIS WIND TURBINE PERFORMANCt COMPUTER CODE DARTER
Paul C. Klimas and Ralph E. French
UC-60
SF 2900 ·008(3-74)
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.
Issued by Sandia Laboratories, operated for the United States Department of Energy by Sandia Corporation.
NOTICE
This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.
SAND80-1155
A USER'S MANUAL FOR THE VERTICAL AXIS WIND TURBINE PERFORMANCE COMPUTER
CODE DARTER
Paul C. Klimas
Ralph E. French
.------------DISCLAIMER -------------.
This book was prepared as an account of work sponsored by an agency of tho United States Government, Neither the United States Government nor any agency thereof. nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility lor the accuracy, completeness. or usefulness of any information, apparatus. product, or process disclosed, or represents that its use ..-.ould not infringe privately owned rights. Reference herein to any specific commercial product, process. or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government Of any agency thereof. The views and opinions of authors expressed herein do not flecwaruy state Ul' r~rtl!l.:t tiiU:.euf tloe u.-,itcd Gt6tCl co .. etntl'lllnl Of any agoncy thorVtJf.
DISTRIBUTION OF THIS OOCtiMENT IS UllliM;T~
Contents
~·. Nomenclature 3
Introduction 5 )
Program Theory 5
Program Usage 6
References 1 3
APPENDIX A - Mo<111lP. [Jiagram 14
APPENDIX B - Program Flow Diagram 1 5
APPENDIX c - Program Listing 1 6
APPENDIX D Sample Control Stream at SNL 28
APPENDIX E - Sample Output 30
·~
2
Nomenclature
As Turbine swept area
c Blade chord
C~,n Blade section lift, normal force coefficient,
~' n
Cd'a Blade section drag, axial force coefficient~
c
D
J
L
N
p
Q
R
p
d ,_ a
Blade section moment coe.fficient,
Zero wind drag coefficient
Turbine drag coefficient,
Power coefficient, Qw
Turbine torque coefficient,
Turbine drag v <Xl
Advance ratio, Rw
Power coefficient,
Blade length
Number of blades
Wind shear exponent
Qw
Turbine aerodynamic torque
Turbine maximum radius
D
m
112 v2 2 p<Xl c
Q
3
4
X
z-· max
\)
w
p Rwc 00
Chord Reyno~ds number, l-100
Average·,freestream velocity at turbine centerline
Average freestream velocity at reference height Rw Turbine tipspeed ratio, -voo
Turbine height
Blade section angle of attack
Freestream viscosity
Freestream kinematic viscosity
Freestream. density /
Turbine rotation~l speed . I
SolidJty, ~cl s
' .
SANDB0-1155 A USER'S MANUAL FOR THE COMPUTER CODE DARTER
Introduction
The computer code DARTER (DARrieus Turbine, Elemental
Reynolds number) is an aerodynamic performance/loads predic-
tion scheme based upon the conservation of momentum princi-
ple. It is the latest evolution in a sequence which began·
with a model developed by Templin 1 of NRC, Canada and pro-
gressed through the Sandia National Laboratories-developed
SIMOSS 2 (Simple MOmentum, Single Streamtube) and DART 3
(DARrieus Turbine) to DARTER. '
Program Theory
The basic theory u~on which DARTER is based was first
reported 1 in a model which takes the rotor to be enclosed
in a single streamtube. Wind velocity across the area swept
by the rotor is assumed constant. By choosing some value
of this velocity, a combination of the simple actuator-disc
momentum model and blade-element theory will give the far-
·field windspeed, turbine power, torque and drag for a tur
bine with given blade characteristics, rotational speed,
and geometry. In SIMOSS 2 an iteration is incorporated which
allows the (upstream) far-field windspeed to be treated as
an input while wind velncity across the rotor-swept area is
5
6
calculated. DART 3 dtffers from SIMOSS in that a multiple·
streamtube system is used; i.e., the swept area is modeled
by an arbitrary number of adjacent and aerodynamically
independent areas over which the conservation of momentum
principle is applied. Advantages gained by this more de
tailed modeling stem from allowing disc-area-windspeeds to
vary from section to section. DARTER is an extension "of
DART which h~s the capability of u!inq airfoil data ~~~~~
upon elemental Reynolds numbers. When combined with the
ability of treating the effects of wind shear, DARTER repre
sents the most.detailed. momentum based· Darrieus turbine
aerodynamic model reported to date. Comp~rison~ between
measured performance and that predicted by DARTER. and
certain other models are reported in Ref. 4.
Progrilm ll~ii!JP
DARTER is a reasonably versatile code and possesses
options which are intended to make it useful to users with
varied.requirements. It allows selection of one of three
constant chord blade planforms: 1) straight line/circular
arc troposkien approximation, 2) parabolic, or 3) straight
blade geometries. Any symmetrical blade profile may be
cho~en, providing sufficient section data· are available.
Any number of blades may be treated. Varying degrees of
atmospheric wind shear may be included through stipulation
of a powe~ law profile. Up to 24 different op~rating condi
tions may be examined at any· one time by setting one value
of any of turbine angular velocity~ ambient windspeed or
equatorial tipspeed ratio and varying either one of the
remaining two parameters· over a prescribed range. Logarith
mic or linear blade airfoil sectiori data interpolation with
Reynolds number·m~y be chosen. ·The blade section data may
be either in the form or normal and axial force coefficients ·-
vs. angle-of-attack or lift and drag coefficients· vs angle-
of~attack. These may be i~put via cards·or from disc~
The following quantities are required inputs to DA~TER:
Description
Number of blades
Number of azimuthal integration steps, upwind half of rotor
Number of vertical integration steps, l~wer half of rotor
Turbine maximum r~dius
Turbine ~eight
Blade Chord
Kinematic viscosttj
Atmosphetic density
Shear e~ponent
Symbol
NUMB
NTH
NZBAR
RMAX
ZMAX
CHORD .
NU
RHO
p .
Units
None
None
None
m
m·
. m 2 m /sec
kg/m 3
None ·
i 7
•'
8
Vertical distance from ground plane to rotor bottom
* Reference anemometer height above ground plane
Turbine angular velocity, w
Ambient windspeed at reference height, Voo
Equatorial tipspeed ratio, Rw/V .
00
Numh~r of conditions to be calculated in a single code running
Tabulated blade section angle . of aftack, a.
Tabulited blade s~ction n6rmal or lift coefficient
Tabulated blade section axial or drag coefficient
Tabulated blade section moment coefficient
ZGC
ZR
RPM
VINF
XCL
NXCL
TAA
TCN
TCA
TCM
m
m
rev/min
m/sec
None
None
Degrees
None
None
None
*The effects of wind shear are calculated according to
V/V = ([Z + ZGC]/[ZR + ZGC])p 00
where V is the ambient air speed corresponding to a given height, Z.
·The required inP.ut data take the following form:
Card
1,2,3
4
Description
Title cards, 80 columns/card
NUMB, NTH, NZBAR, IFLG(I), I= 21, 28
I5 format is used for the first three quantities. Il format is used for the IFLG(I) array. This array keys various options and
- is defined as follows.
- 1FLG(21) ~ 0 will cause each iteration on streamtube velocity to be printed.
- IFLG(22) is used to select blade planform geometry. For IFLG(22) = 1, the blades will be of the straight line circular arc troposkien ·approximation. If IFLG(22) = 2, the planform.will be parabolic. Straight blades are chosen if IFLG(?2) = 3.
- IFLG(23) selects the angular velocity-freestream velocity tipspeed ratio combination
Parameter IFLG(23) Single Fixed Incremented Calculated
0 RPM X v 00
1 RPM v X 00
2 v X RPM 00
3 v RPM X 00
9
5
6
1 0
- IFLG(~4) sets the H/0 ratio for straight linecircular arc straight line troposkien approxi~~tion blade planform. For IFLG(24) = 0, H/0 = 1.0 and for IFLG(24) = 1, H/0 = 1.5.
- IFLG(25) chooses the type.of i·nterpolation on Reynolds number used in the ~ection data lists. If IFLG(2.5) = 0, logarithmic interpolation follows. For IFLG(25) f ·0~ linear interpolation is used.
IFLG(26) selecfs the proper form of ·the blade airfoil section coefficients. If the section data lists are in the en~ Ca vs a form, set IFLG(26) = 0. J.f of the form c
1, Cd vs a,
set IFLG(26) ~ 0.
- IFLG(27) depends upon the manner 1n which the blade airfoil section data are read. If IFLG(27) = 0, the data lists are read on a card-by-card bas1s. When IFLG(27) r 0, .the data are attached from a permanent file.
- IFLG(28). If IFLG(28) = 0, the blade section data are printed. For IFLG(28) ~ 0, the data are not printed.
RMAX, ZMAX, CHORD, NU, RHO, P, ZGC, ZR. The format here is FlO.O.
NXCL and, depending upon the value of IFLG(2~),
either RPM or V. If IFLG(23) is 0 or 1, RPM 00
is input. For IFLG(23) = 2 or 3, Voo is input.
7,(8),(9)
8 (or 9) (or 10)
Format for NXCL is IlO, that for RPM or V J 00
is FlO.O. NXCL cannot exceed 24.
Input here are values of X, V00
, X or RPM, if IFLG(23)-= 0, 1, 2 o~ 3, respectively. The format is FlO.O, and there can be up to 8 values/card.
These are the blade airfoil section data inputs. Data for up to 15 different values
· of Reynolds number (Re) can be accommodated. The first card in any of the up to 15 sets has the appropriate value of Re in a FlO.O format. The last 70 columns are used for a· title. The femaining cards in any Re set · each have I, TAA, TCN, TCA, and TCM in a Il, FlO.O format. Data for up to 182 values of TAA can be used. I is either 0, 1, or 2 depending upon whether the data card is not the last card i~ a Re· set, the last card in an intermediate Re set, or the last card in the last Re set, respectively.
The following are DARTER output quantities.
Description Symbol. Units
Advance Ratio, V /Rw 1/XCL 00
None
. Power coefficient based on rotational KPE3 None speed, KP x 103
Tipspecd ratio, Rw/V XCL 00
None
Power coefficient based on ambient CP None windspeed, cp
1 1
1 2
Turbi.ne (average) dras coefficient, CD
Turbine (average) torque coefficient, CQ
Turbine angular velocity, w
Reference ambient wiridspeed,·Vref
Blade equatorial Reynolds number, Rec
Averuge turbine torque
Average turbine power
·Average tu~bine drag ·
CT
CQ
RPM
VREF
REC
TORQUE
POWER
DRAG
None
None
revolutions/ minute
meters/sec
None
Newton-n1eters
Kilowatts
Newtons
References
1. R. J. Templin, 11 Aerodynamic Performance Theory for the NRC Vertical-Axis Wind Turbine, 11 Report LTR-LA-160, National Aeronautical Establishment of Canada, June 1974-
2. User's Manual for SIMOSS, Sandia National Laboratories (to be published).
3. J. H. Strickland, The Darrieus Turbine: A Performance Prediction Model Using Multiple Streamtubes, SAND75-0431, Sandia National Laboratories, Albuquerque, NM, October 1975.
4. P. C. Klimas, R. E. Sheldahl, Four Aerodynamic Prediction Schemes for Vertical Axis Wind Turbines: A Compendium, SAND78-0014, Sandia National Laboratories, Albuquerque, NM, June 1978.
1 3
APPENDIX A
Module. Diagram
:PROGRAM WIND .; .... . SUB ROUTINE ..... ,.
GEOM
.... ... SUBROUTINE ..... ,.. GRHS ·
...... ~~ .
,, '
;
.., .. SUBROUTINE '
, SUBROUTINE LOOK2D LOOK
..
Module Description Program WIND
Wind functions as the main calling program performing all input and output operations. WIND also handles the aerodynamic performance calculations. · ' 1
Subroutine GEOM
GEOM evaluates all the blade geometry.
Subroutine GRHS
GRHS evaluates local angle of attack, relative wind speed, blade Reynolds number, and thrust forces. Also, GRHS serves as caller to subroutine-LOOK2D.
Subroutin~ LOOK2D
LOOK2D performs a two-dimensional linear interpolation on a twodim~nsional matrix and calls subroutine LOOK.
Subroutine LOOK
LOOK does 1-D interpolation computations.
14
Start
/
Input
........
Compute
Tabulate
List
........
APPENDIX B
Program Flow Diagram
General
List
Converge contribu forces
Performa
' problem parameters
All input information
d solution for induc~d velocity and tion to torque and thrust blade
nee data
1 5
(
PROGRAM WIND<INPUTtTAPE5=INPUT,OUTPUTtTAPE6=0UTPUTtTAPE7,TAPE1Ct 1 TAPE20tTAPE39tTAPEJ3)
COMMON/TABLES/ IL0<200ltiHI(200JtiR<2~·0lt DEN~ lEX~ 1 VR
COMMON/GEOM/BETA,BETA2tZBAR(101)tRBAR<101JtASORZtSINGAH(101) 1 tASOS2
DIMENSION ERR<3>tTVCL<~O)tTRPMl40ltTXCL(~0) COHMON/STRUT/VFSOVCL(10l)tVCLtNUtlREtTRE<15ltTAA<182t15>t
1 TCN<182tl5JtTCA(l82t15)tTCHll82t15ltOIMtXl4),DX(4)t 2 OEGTRtKtiFLGl20ltKOUT,VBLADEtiFTAtiTER
DIMENSION LHEA0(24ltTITC(7t9l DIMENSION VfS(2),CQF(2ltCTFl2ltA1(2,3J,VOVFS(2)tAl2) REAL NCORtNUtLHS DATA OEGTR/57.29577951/ DATA PI /3.1415926535898/ DATA KINtKOUT/5,6/
.NMOOll) = 1 + I - ll/3)•3
C INPUT GENERAL.PROBLEH PARAMETERS C•****~*****************************************************************
ICNT = 0 10 CONTINUE
ICNT = ICNT + 1 READlKINt1000)lLHEA0(1Jti=lt24)
1000 FORMAT(8A10) IF<EOF(KIN)) 9999t20
20 CONTINUE READ<KINt1020) NUHBtNTH,NZBARtiDUHt<IFLG(I)tl=1,20)
1020 FORHAT<4I5t20Il) KAD = KIN IFliFLG<7>.NEe0) KAD = 10 IHO = IFLGl4) REAO<KINt1010) RMAXtZHAXtCHOROtNUtRHOt?tZGCtZR, IF<ZGC.LTeleOE-06) ZGC = 1eOE-Oo ZCL = ZGC + ZHAX IF<ZR.LT.l.OE-08) ZR = l• VCLOVR = <ZCL/ZRJ••P
10~0 FORMAT(8f10.0) !SHEAR = Q IF<P.GT.1eOE-08) !SHEAR = 1 NCOR = FLOAT<NUHB>•CHORD/RMAX IGEOH = IFLG(2) liN = IFLG(3) -+ 1 GO TO (30t40t50t60) liN
C*******~*************************************************************** C FIXED RPH WITH RANGE OF TIP SPEED RATIOS C•**********************************************************************
30 CONTINUE REAO<KINt3000) NXCLtRPH
3000 FORHAT(I10t7F10.0) REAO<KINt3010) <TXCL(IJti=ltNXCL)
3010 FORMATl8F10.0) DO 35 I=ltNXCL TXCL<I> = TXCL(I)/VCLOVR TRPH(I) = RPM TVCL(I) = RMAX•RPH•2.•PI/l60.•TKCL(I))
35 CONTINUE 1 7
GO TO 70 C*********************************************************************** C FIXED RPM WITH RANGE OF FREE STREAM VELOCITIES C***********************************************************************
t\0 CONTINUE REAOCKINt3000J NXCLtRPM READCKINt3010J (TVCLCIJti=1tNXCLJ DO 45 1=1tNXCL TVCL(l) : TVCL(IJ•VCLOVR TRPM( I) : RPH TXCL<IJ = RMAX•RPH~2.•PI/(60.•TVCLCIJJ
45 CONTINUE GO TO 70
C*********************************************************************** C FIXED VFS FOR A RANGE OF TIP SPEED RATIOS C***********************************************************************
50 CONTINUE READCKINt3000J NXCLtVCL READ( K1Nt301 0 J (TXCL( I J t I·=ltN XCL J VCL = VCL•VCLOVR DO 55I=1tNXCL TXCLCIJ = TXCL(IJ/VCLOVR TVCL<IJ = VCL TRPMCIJ = VCL•TXCLCIJ•60./C2.•PI•RHAXJ
55 CONTINUE GO TO 70
C•********************************************************************** C FIXED FREE STREAM VELOCITY FOR·~ RANG~ OF ROTATIONAL SPEEDS C***********************************************************************
60 CONTINUE READCKINt30QOJ NXCLtVCL READCKINt3010J CTRPHCIJti=ltNXCL) VCL = VCL•VCLOVR DO 65 I=ltNXCL TVCLCIJ = VCL TXCL<IJ = RMAX•TRPMCIJ*2e•PI/(6G.•VCLJ
65 CONTINUE 70. CONTINUE
C*********************************************************************** C READ IN NORMAL AND TANGENTIAL FaRCE COEFFICIENTS AS A FUNCTION OF C ANGLE OF ATTACK FOR A SERIES OF CHORD REYNOLDS NUMBERS. C THE TABULAR LIMITS FOR THE FORCE.COEFFICIENT"OATA ARE STORED IN C THE FOLLOWING OROER-- REYNOLDS NUMBER IFTA + 10 C ANGLE OF ATTACK IFTA + 1 THiW IFTA + 9 C*******************************************~***************************
IFCICNT.NE.1J GO TO 125 IFTA = 0 J = 0
100 CONTINUE J = J + 1 ·JJ = IFTA + J ILOCJJJ = IRCJJJ = 1 REAOCKADt1100J lRE(JJ,triTCCitJJti=lt1J
1100 FORMATCF10.0t7A10J I = 0
110 CONTINUE. l = I + 1 RtADCKADt1110J IFLAGtTAACitJJtTCA(I~JJ,TCNCI,JJtTCH(ltJJ
1110 FORHATClltF9.0t7F10.0J C***********************************************************************.
18
C THE PARAMETER IFLAG OETER~INES WHAT ADDITIONAL FORCE AND MOMENT C DATA SHOULD BE READ IN C IFLAG = Ot READ ANOTHER ANGLE ·OF ATTACK, CARD FOR GIVEN RE C !FLAG = lt LAST ANGLE OF ATTACK CARD FOR GIVEN RE BUT AT LEAST 'C ONE .ADDITIONAL RE TABLE WILL FOLLOW C !FLAG= 2t LAST CARD OF FORCE AND MOH~NT DATA· C************************************************•**********************
OEGTR = 57.29577951 IF<IFLG(6).£Q.OJ GO TO 115 TCL=TCA(It..JJ TCD=TCNUt..JJ AA·= TAA<It..JJ/OEGTR SALP = SIN(AAJ CALP = COS<AAJ TCN(lt..JJ = TCL•CALP + TCO•SALP TCA<It..JJ = TCL•SALP - TCD•CALP
115 CONTINUE IHH..JJ) = I IFPl = IFLAG + 1 GO TO <110t100t12Gt117J IFPl
117 IFLAG=1 GO TO 100
120 CONTINUE IRE=IFTA+15 NRE : IHI<IREJ = ..J ILO<IREJ = IR<IREJ = 1
125 CONTINUE C•• ** * * * *** ** *** ** ** *** **** *** ** *** ***** **** * * ** * *** * ***** ** ...... ******** *** C PRINT OUT ALL OF THE INPUT INFORMATION (***********************************************************************
WRITE<KOUTt2000J 2000 FORMAT(lHlJ
WR1TE(KOUTt2002J(LHEAD<IJtl=lt2') 2002 FORMAT<10Xt8A10J
WRITE<KOUTt2005J 2005 FORHAT<lOXt8A10)
WRITE<KOUTt2010J NCORtRMAXtZHAXtC~ORDtNUtRHO 2010 FORHAT<12X•NC/R•4X•RHAX•5X•ZHAX•4K•CH0~0•1X•NU*lOX•RHO•/
1 10XF6.3t2(2XF7e2Jt2XF7.3t2(2XE10.3)J WRITE<KOUTt2015J PtZGCtZR
2015 FORHAT<11X•EXP•6X•ZGC•7X•ZR•/10KF.5.3t2XF7.2t2XF7e2/J WRITE<KOUTt103~J NUMBtiGEOH;NTHtNZBAR
1030 FORHAT(//10X•NUMB IGEOM NDTH. NDZ•/11XI2t5XIlt~XI3t3Xl2J WRITE<KOUTt1035J <Iti=21t40J
1035 FORMAT<10Xt20<1Xtl2JJ WRITE(KOUTt1035J <IFLG(IJti=1t2lJ
. IF<IFLG(8J.EQ.OJ GO TO 127 WRITE<KOUTt1000J <TITC<ItlJti=lt7J GO TO 136
127 CONtiNUE 00 135 J=ltNRE WRITE<KOUTtl040J TRE<JJ,(llTC<I,JJ,I=lt7J
1040 FORMAJ(//10X•RE = •E10.3t5X7AlOI/12X*'LPHA*SX•CN•7X•CA*7X•CH•/) II = IHI<JJ 00 130 I=ltii WRITE<KOUTtlOSOJ TAA<ItJJtTCN(I,JJtTCA(ItJJtTCH(ItJl
1050 FORMAT<lOXF7.2t3<2XF7.4JJ 130 CONTI NU£ 135 CONTINUE 136 CONTINUE
1 9
IFCIFLGCSI.NE.O.OReiCNT.NE.ll GO TO 138 00 137 '-'=ltNRE TREC'-'1 = ALOG<TREC'-'))
137 CONTINUE 138 CONTINUE
BETA : RMAX/ZHAX BETA2 = BETA~•2 EPS = 0.0 KMAX = NZBAR + 1 + ISHEAR•CNZBA~ - 1) DZBAR = le/FLOATINZBARI ZBARCL = ZCL/ZMAX DO 140 K=1 tKMAX ZBAR(K) = FLOATCK-11•DZBAR-l.O VFSOVCL(K) = Cl. + ZBARCK)/ZBARCLI••P
140 CONTINUE CALL GEOH(IGEOMtKHAXtiHO) AS : ASORZ•RMAX•ZMAX S = SQRTCAS/ASOS2) SIG = FLOATCNUMBJ•CHORD•S/AS WRITEC6t2040) SIG
2040 FORMATClOX*SOLIOITY = •F8.4) WRITECKOUTt2020)
2020 FORHAT(3X*M*t2~•1/XCL•t2X•KP E3•t3X•XCL•t6X•CP•t5X•CT•,6X•CQ•, 1 4X•RPM•t4X•VREF•e6X•REC•t6X•TORQUE*t5K*POWER•,SX•DRAG*) KPl.: KP1 - ISHEAR
C************************************•********************************** C BEGIN TIP SPEED ·RATIO LOOP C************************************•**********************************
00 600 M=ltNXCL RPM = TRPMUU VCL = TVCL(M) XCL = TXCL(M) VBLADE = RMAX•RPM•2.•PII60. KCL = VBLADE/VCL REC = VBLADE•CHORD/NU CQ = CT = 0.0 SINEPS = SINCEPSI COSEP3 = C03(EP3J NTHPl = NTH + 1 OTH = PI/FLOATCNTH) TH = -DTH I ERR = 0 0
C*********************************************************************** C BEGIN THETA INTEGRATION LOOP C*************************************************•*********************
DO 500 L=1tNTHP1 · CTSUM = CQSUM = CLLSUM = CFSUM = 0.0
A(l) = A(2) = o.o 1\FST -::- 0.0 TH :: TH + DTH THO = TH•DEGTR SINTH = SINCTH) COSTH = COSCTH)
C**********************************************•************************ C BEGIN ZBAR INTEGRATION LOOP C********************************************•**************************
DO 400 K=2tKMAX IF<IFLG(l).NE.O) WRITECKOUTt600Q) THDtRBAR(K)9ZBAR(KitSINGAHCKI
6000 FORMAT(lXt•THETA = •F6.1• RBAR = •F6.3• ZBAR = •F6.3• SINGAM = * 1 F6.3/2K•ITER•t1X•ALPHA•t6X•RE•t5X•W/Vf•t6X•CN•t6X•CA*t7X•CM•t
20
2 6X•ANEW•tSX•AOLD•t7X•ERR•t7X•R~S•tSX•LHS•t7X•VFSL•t~X•V/VFSL• 3 2X•W/VFSLSQ•)
CQF(2) = CTFC2> = 0.0 VFSCll = VFSOVCL(K)•VCL VFSR2 = VFSOVCLCK>••2 XFS = XCL/VFSOVCLCK> JJ = 1
(*********************************************************************** C BEGIN ITERATION LOOP ON INTERFERENCE FACTOR AICJtN>--J=lt UPWIND (***********************************************************************
00 300 J = 1tJJ ERRMIN : 10000. ITER = 0 IFCK.EQ.2) AI<Jtl> = AFST AI(Jt1> : A(J) AICJt2> = AICJtl> + 0.05
200 CONTINUE N = NMODCITER> IMl = ITER - 1 NM1 = NMODCIMl> ITER:::: ITER +-1 NP1 = NMODCITER) IF<ABS<SINTH>.LE·l•OE-10) AICJ,N) = O.l VOVFS(J) = l• - AI<J•N> LHS = 4.•AICJtN>•VOVFS<J>
(*********************************************************************** C IF<AICJtN>.GT.O.S> LHS = leO (***********************************************************************
CALL GRHSCOtSINTH.SINGAMCKltRBA~(K)tCOSTHtSINEPStCOSEPStCHORDt 1 ALPHADtCNtCA,CMtWOVFS2tRHStVFS(J)tVOVFS(J))
IFCABS<SINTH).LT.l.OE-10) GO TO 220 RHS = RHS•NCOR/PI ERRCN> = RHS - LHS
(*********************************************************************** C APPLY MODIFIED ~EGULA-FALSI METHOD TO FORCE ERROR TERM TO ZERO C•• ** * * **** * * ***** ** ******* *** * * *** *** * *** **-* * ******* **** ** ***** *****·** *
IFCITER.LT.2) GO TO 200 FP = CERRCN> - ERRCNMl>>I<AICJ,N) - AICJ;NMl>> DERR = ERRCN>/FP AICJtNPl> = AICJtN> - OERR IFCAICJtNPl>.GT.l.O> AI<JtNPll = AICJ,~> - OeOS•OERR/ABSCDERR> ERRF = ABSCOERR> . IFCABS<ERRMIN).LT.ABSCERRCN>>> GO TO 220 ERRMIN = ERR(N) ASAVE = AICJtN)
220 CONTINUE .IFCIFLGC1).NE.O> WRITECKOUTt500D> AICJtNPl>tAICJtN>tERRCN>tRHSt 1 LHStVFS(J)tVOVFS<J>tWOVFS2
5000 FORMATC1H+t57Xt2C2XF7.4)t2XE10.3t2C1X=7.4)t2XF7.2t2XF7.~p2XF8.3) IF<ABSCSINTH).LT•l•DE-10> GO TO 230 . IF<<ERRF.GT.1.0E-03).ANO.CITER.LE.10>> GO TO 200 IFCAICJtN>.LE.O.S) GO TO 225 AICJtNPl) = 0.5- l.OE-10 ITER = ITER + 30 GO TO 200
225 CONTINUE IFCITER.NE.ll> GO TO 230. FFF = - 1.0 IFCASAVE.LT.C.S> FFF = 1.0 AICJtNPll : ASAVE + FFF•l.OE-06
21
IERR = IERR + 1 GO TO 200
230 CONTINUE If(K.EQ.2) AFST = AI<ltN) A(J) = Al(J,N)
C*************~*******************************~**********************~** C WE NOW HAVE A CONVERGED SOLUTION·FOR THE INDUCED VELOCITY C COMPUTE T:HE CONTRIBUTION. TO TORQUE ANO THRUST C*********************************************~****~****************~***
CQF(J) = R8AR<K>•WOVFS2•<CA•COSEPS - CN•SINEPSJ/SINGAMlK) CTF(J) = WOVFS2•<COSEPS•<CN•SINTH•SINGA~(K) - CA•COSTHJ
1 + SINEPS•<CA•SINTH•SINGAH<K> + CN•COSTH))/SINGAH(K) CQF(J) CQF(J)•VFSR2 CTF(J) = CTF<J>•VFSR2 VFS(2) = VFS(l)*(l. - 2.•A(1)) VFS(2) = AMAX1<VFS<2>,0.0) IF<IFLG(l).N£.0) WRITE(KOUTt501~) CTf(J),CQF(J)
5010 FORMATl82Xt~<lXElle4)) C**************************************~******************************** C COMPUTE THE BLADE FORCES WIICN Af)PLICA3LE C*****************~*****************************************************
DYNP = O.S•RHO•VFS(J)•*2 CLLLOC - WOVFS2w(CA•COSEPS - CN•SINEPSI CFLOC = WOVFS2•<CN•COSEPS + CA•SINEPS>
300 CONTINUE VFSRAT = (1. - 2.•A(1))**2 CQLOC = CQf(l) + CQF<2>•VFSRAT CTLOC = CTF<l> + CTF<2>•VFSRAT KMl = K - 1 KPl = K + 1 lf(K.EQ.l) KMl = KMl + 1 lf(K.EQ.KMAX) KPl = KPl - 1 FACTOR = 0.5•<ZBAR(KP1) - lRARl~Ml )) CTSUM = CTSUM ~ CTLOC•FACTOR CQSUH = CQSUM + CQLOC•FACTOR CFSUM = CFSUM + CF~OC•FACTOR CLLSUH = CLLSUM + CLLLOC•FACTOR
C*************************************'********************************* C THIS COMPLETES THE INTEGRATION OVlR T~E UPPER HALF OF THE ROTOR C SWEPT AREA (******************************•****************************************
400 CONTINU£ IF<IFLG<l>.NE•O) WRITE<KOUTt501Q) CLLSUH,CFSUHtCTSUHtCGSUM IF<L.EQ.l.OR.L.EQ.NTHPl) CQSUM = Q.S•CQSUM IF<L.EQ.l.OR.L.EQ.NTHPl) CTSUH = J.S•CTSUM CQ ·= CQ + CQSUM CT = CT + CTSUM
500 CONTINUE FF = NCOR•OTH/(2.~PI•ASORZ) CQ ·= CQ•FF CT = CT•FF
C*********************************************************************** C MULTIPLY BY A FACTOR TO ADO IN THE UPPER HALF AND DOWNWIND C PORTION OF THE ROTOR (***********************************************************************
22
FF= 2.•FLOAT<2-ISHEAR> CQ = FF•CQ CT = FF•CT CP = CQ•XFS TORQUE = 0.5•RHO•RHAX•AS•CQ•VCL••2
POWER : TORQUE•RPH•2.•PI/(60.•UOO.J THRUST = O.S•RHO•AS•CT•VCL••2 VREF : VCL/VCLOVR AOVR = 1./XCL RKP = CP•1000~/(XCLJ••3 WRITE<KOUTt5020J MtAOVR~RKPtXCLtC?tCT,CQ,RPM,VREFtRECtTORQUEt
1 POWERtTHRUSTtiERR . 5020 FORMAT<2XI2t1XF6e3t2<1XF6.2JtlXF7.4tl(F5.3tlXF7.4tlXF6.lt1XF7.2t
1 4C1XE10.3), 15J 600 CONTINUE
GO TO 10 9999 CONTINUE
END
SUBROUTINE GEOM(IGEOM,KP.l,IHDJ C***********************************~********************~************* C THIS SUBRdUTINE EVALUATES ALL o= THE BLADE GEOMETRY C IGEOM = 1 , STRAIGHT LiNE-CIRCULAR ARC C I GEOM = 2 t PARABOLA C IGEOM : 3t STRAIGHT BLADE C***********************************************************************
COMMON/GEOM/BETAtBETA2tZBAR(l01J,~BARI101JtASORZ,SINGAM(101J 1 tASOS2
IGP1 = IGEOM + 1 GO T0(10t2Ct30t40) IGPl
10 CONTINUE 20 CONTINUE
C**************************~******************************************** C STRAIGHT LINE-~IRCULAR ARC
IF<IHO.EQ.lJ GO TO 22 RJOZM = 0.6721~3 RJORM.= RJOZM/BETA ZJOZM : 0.565406 GO TO 23 ,,,
22 RJOZM : 0.413 RJORM : RJOZH/BETA ZJOZM = 0.604
23 CONTINUE RORM: RJORM·- ZJOZM•<l~ - ZJOZ~J/(RJO~M•BETA2J ASORZ : <1. - ZJOZMJ•RJORM.+ 2.•RORM•ZJOZM + ZJOZM•SQRT
1 ((1. - RORM>••2 - (ZJDZM/BETAJ••~J + BETA•<l. - RORMJ••2 2 •ASIN<ZJOZM/(BETA•<l• - RORMJJJ
ASORZ = 2.•ASORZ . Tl:i = ASINCZJOZM/(BETA•U. - ROR~JJJ
SOZM = BETA•(1. - RORMJ•TK + ((1. - ZJOZMJ••2 + <BETA•RORM 1 + SQRT<SETA2•<1• - RORMJ••2 - ZJJZM••2JJ••2J••Oe5
SOZM : 2.•SOZM ASOS2 = BETA•ASORZ/SOZM••2 DO 28 K=1tKPl ZBARA : ABS<ZBAR(KJJ IF<ZBARA.LT.ZJOZMJ GO TO 24 RBAR<KJ = RJORM•<l. - Z8ARA J/(1. - ZJOZHJ GAM= ATAN((l. - ZJOZMJ/(RJORH•BETAJJ SINGAM(KJ = SIN<GAHJ GO TO 28
24 CONTINUE RBAR<KJ = RORM + SQRT<<l. - RORMJ••2 - <ZBAR(KJ/BETAJ••2J
.23
COTGAH = ZBAR(KJ/((RBAR(K) - RORMl•BEfAJ SINGAM<K> = 1./SQRT(t. + COTGAH••2J
28 CONTINUE GO TO 50
30 CONTINUE ~ C******************************************~**************************** C PARAaOLA ~·***********************************~**********************************
ASORZ = 8./3. ASOS2 = 32.•BETA2/(3.•(2.•BETA•SQRT<t. + ~.•3ETA2J + ALOG<2•*
1 BETA + SQRT<l• + ~.•BETA2JJJ••2J
DO 35 K=ltKPl SINGAM<KJ = le/SQRT<l. + ~.•BETA2•ZBA~(KJ••2J RBAR(KJ = 1. - ZBAR<K>••2
35 CONTINUE GO TO 50
C************************************************~********************** C STRAIGHT VERTICAL BLADE
~0 CONTINUE ASOR.Z = ~.
no '+5 K=ltKPl SINGAM(K) = RBAR(KJ = 1.0
45 CONTINUE. 50 CONTINUE
RETURN END
SUBROUTINE GRHS<ISTRUT,SINTH;SINGAMtRBARtCOSTH,SINEPStCOSEPSt . 1 CHORDtALPHAO,CN;CAtCM,WOVFS2tRHStVFSLtVOVFSJ
COMMON/STRUT/VFSOVCL(101JtVCL,NUtiREtfRE<l5J,·TAA(l82t15Jt 1 TCN(l82t15JtTCA(l82tl5JtTCM<l82tl5),DIMt~(4)tDX<'+>t
.2 DEGTRtKtiFLG(20JtKOUTtVBLADEtlFTAtlTER RF.:At · NU
(~********************************************************************** C THIS SUBROUTINE ,EVALUATES LOCAL A~GLE Of:' ATTACK; RELATIVE. WINO C SPEEDt BLADE REYNOLDS NUMBER, AND THRUST FORCES FOR A GIVEN. C VALUE OF THE INDUCED VELOCITY FIELD. C***********************************************************************
24
Xl = VOVFS•SINTH•SINGAM X2 = VOVFS•COSTH + RBAR•VBLADE/VFSL
.WOVFS2 = Xl**2 + X2••2 WOVFS = SQRT(WOVFS2) EPS = ASIN(SINEPSJ ALPHA = EPS + ATAN2<XltX2) ALPHAD = ALPHA•DtGfR ALPHA = ABS<ALPHA)
·wov = WOVFS/VOVFS W = WOVFS•VFSL WOVT = W/VBLADE R-E = W•CHORD/NU IF<IFLG<SJ.EQ.OJ RE = ALOG(REJ CALL LOOK2D(lREtREtTREtiFTAtALPHADtTAAtTCN,TCAtTCHtDIMtXtDXt3tl82) CN = X<lJ CA = X(2) CM = X(3) CN = CN•SIGN<l.,ALPHADJ ASINTH = ABS<SINTH)
IF<ASINTH.LT.1.0E-10) GO TO 10 F = SINTH/ASINTH Fl = COSTH/(SINGAM•ASINTHJ F2=COSEPS•<ABS<CNJ-CA•FlJ F3 = 0.0 IF<ABS<SINEPS).GT.1.0E-10J F3 = SINEPS•(CA•F + CN•FlJ RHS ~ WOVFS2•<F2 + F3)/RBAR
10 CONTINUE IF<IFLG(lJ.NE.Q) WRITElKOUTtlOOQ) ITERtAL?HADtREtWOVTtCNtCAtCM
1000 FORMAT<3XI2tF7.2tlXE10.3tlXF6.3t3l2XF7.\)) RETURN END
SUBROUTINE LOOK <IItXLtXtAtBtCt~tYtDtiDNJ COMMON/TABLES/ IL0<200)tiHI(~00),IR<2JO>t DENt IEXt
1 VR DIMENSION X(1)t Al1Jt BllJt C(l)t E(1Jt Y<1Jt 0(1) IH=IHI<II) IL=ILO<IU DO 5 J=ltiUN I)(J) = o.o Y(J) = 0.0
5 CONTINUE VR = 0.0 I EX=O IF <X<IHJ-X<IL)) 10t1Ct30
10 I EX=l IF <XL-X<IH)) 120t130t20
20 IF (XL-X<ILJJ 50t150t140 30 IF <XL-XliH)) 40t130t120 40 IF (XL-Xl!L)) 140t150t50 50 I=IR<II)
I=MINO <ItiH) I=MAXO<ItiL) I S=l I T=l GO TO 70
6() I=I+1 I S=O
10 IF <IEX) ao,ao,9o 80 IF lXL-X(I)) 100t160t110 90 IF <XL-X(!)) 110t160t100 100 i=I-1
I T=O . IF (!S) 160tl60t70
110 IF <ITl 160tl60t60 ·120 I EX=3 130 I=IH-1
GO TO 160 140 I EX=2 150 I=IL 160 DEN=X~I+l)-X(JJ
IRlli>=I VR=XL-X ( IJ IF <ION> 230t230tl70
170 GO TO (210t200t190t180Jt ION 180 Y(4):E(l)
Dl4)=E<I+l>-EU)
25
190 YCJ):C(I) DC3l=CCI+l)-CCI)
200 Y(2):8(I) D(2)=BCI+1)-8(!)
210 YC1J=A<I> DClJ=A<I+lJ-ACI) IFCOEN.EQ.O.OJ RETURN DO 220 J=ltiDN D<J>=D<JJ/DEN
220 Y(J):Y(J)+DCJJ•VR 230 VR=VR/DEN
RETURN END
SUBROUTINE LOOK2D<IItXLtXtiFtYLtYtAtBtCtEtZtDZtNLOOKtNDl C*********************************************************************** C THIS SUBROUTINE PERFORMS A TWO JIMENSIONAL LINEAR INTERPOLATION C THE TAALFS MUST BE ARRANGED SUC-i TIIAT FOR A GIVe:N \tAllJf:.. Ul- fHE C INO~P~NDENT VA~lABLE k(J), THEN ALL OF THE DEPENDENT VARIABLES C A(I,J), BCitJlt C<ItJlt E(ItJ) ARE TABULATED AS A FUNCTION OF C THE SECOND INDEPENDENT VARIABL£ Y(l)--THIS MAY RF THOUGHT OF C CONCEPTUALLY AS ~A IS A FUNCTON 0~ Y WITH X AS A PARAMETER• c C II = INDEX OF THE TABULAR LIMITS OF THE TABULATED VARIABLE XCJJ C XL : VALUE OF THE INDEPENDENT VARIABLE X FOR INTERPOLATION C IF t IF + 1 = INDEX OF THE TABULAR LI~ITS OF THE TABLE ACitlJ ETC C YL = VALUE OF 2ND INDEPENDENT VARIABLE Y FOR INTERPOLATION C X = ARRAY IN WHICH XL IS SOUGHT C Y = ARRAY IN WHICH YL IS SOUGHT C AtBtCtEt TABULATED ARRAY OF DEP~NDENT VARIABLES C Z = ARRAY CONTAINING VALUES INT~RPOLAf~D FROM THE AtBtCtEt TABLES C NLOOK = NUMBER OF DEPENDENT VARIABLE TABLES SUPPLIED--NLOOK .LE. 4 C IF NLOOK LT. 4t THEN DUMMY ARGU~E~TS MUST BE SUPPLIED FOR Dt Ct C ETC C NO = DIMENSION SilE OF Yt A, Bt ETC c····~······································-····················•••aaa& COMMON/TABLES/ ILOC200JtiHI(200JtiR<2lOlt DENt !EXt
1 VR DIMENSION -X(l)t
1 E<NDtl>t ZC4lt 2 DZRC4l
YCNOtl)t ozn >,
B<NDtlJt DZL<'+lt
·c<NDt U t ZR<4) t
(*********************************************************************** C IF THERE IS ONLY A SINGLE X TABLE <IHI<II) = 1) THEN WE WANT TO C DO ONLY A ONE DIMENSIONA~ INTER?OLATTON C***********************************************************************
·IJRS = 1.0 J = 0 DO 10 I=l, NLOOK Z(l) = OZ(I) = 0.0
10 CONTINUE IF<IHICII).EQ.l) GO TO 20 '•!
c * * * * * * * * * * • * • * * * * * * * * * * * * * * * * * * * * * * * * * •• * * * * * •• * * * lr * *'*'* * * * ~ * * 'lr * * * fr * * * * * C DETERMINE THE INDEX J SUCH THAT XCJ) eLE• XL eLE~ X(J+l) C*******************************************•***************************
26
CALL LOOK<IItXLtXtOtOtOtOtZtDZtOl VRS = VR J = IR<IIJ JJ = IF + J
C***********~*********************************************************** C INTERPOLATE IN TABLE J WITH tL AS INO~?ENOENT VARIABLE (***********************************************************************
CALL LOOKCJJtYLtY<ltJ),A(l,J)tB<ltJ),C(ltJ>,E<l,J),Z,DZtNLOOK> DO 15 I=lt NLOOK. ZLCI> = ZCU DZL(l) = OZ(IJ
15 CONTINUE 20 CONTINUE
J = J + 1 JJ = IF + J
C•********************************************************************** C INTERPOLATE IN TABLE J+l WITH YL AS INDEPENDENT VARIABLE (***********************************************************************
CALL LOOKCJJ,YLtYCltJ>tACl,J),BCltJ),CCltJ>tECl,J>tZtDZtNLOOK) 00 30 I=l, NLOOK lRCI> = Z(IJ DZRCI> = DZCD
30 CONTINUE VRSP = 1. - VRS DO 40 I=l t NLOOK ZCI) = ZLCI)•VRSP + ZRCI>•VRS DlCI> = DZLCI>•WRSP + DZRCI>•VRS
IJQ CONTINUE RETURN E:ND
27
28
APPENDIX D
Sample Control Stream
The following is an example of a LGO control stre~m in using DARTER at Sandia National Laboratories.
OARTERtT15. R E FRENCHc •• BOX 1134 ** ACCOUNT~S432961153t05636t612tA0518400tRTtKUN~. ATTACHtTAPElO•KD-EPPLERCLCD-NACA•OEC789CY=15e · ATTACHtDARTERtKLIMAS~OARTER-PROG•Cf=02• OARTER;PL=25000. ••END-OF-RECORD••
SAMPLE RUN OF THE DARTER COO£ TWO BLAD£0(SYSTEM
.01000111 2 8.3628
18 10 a.s
2~50.6
o.60975 o.oooot731t.oat
1.0 1.5 2.0 5.0 5.5 6.0. 9.0. 9.5 10.0 * •E ND-0 F ~ I-NFORMATION**
2.5 6.5 10 .s'
3.0 ·. 7.0· 11.0
·3·5 ·7·5: 11.5.
4•8.2 ..
4.0 ... · ,, ·.,, a• .. o .. ·
12.0 ··'·.
13.32
29
30
APPENDIX E
Samp·l e Output
The following output was generated by DARTER in response to the input shown in Appendix D.
w ......
SAMPLE RUN OF THE ·DARTER CODE TWO BLADED SYSTEM
NC/R .H&
EXP .100
RHAX 8.36
ZGC 4.82
NUMB . IGEOH NOTH 2 1 18
ZHAX 8.50 ZR
13.32
NDZ 10
CHORD .610
NU ·179E-Jt
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 0 1 0 0 0 1 1 1 0 0 0 0 0 0 lJ
36 0
NACA 0015 SECTION DATAt EPPLER HODELt CLt co, DEC 7B. SOLIDITY = .1625
H 1/XCL KP E3 XCL CP CT CQ RPH 1 1 .coc 10.34 1.00 .0103 .oaa .:1108 50.S 2 .es7 7.31 1.50 .'J247 .120. .lJ 172 so.!) 3 • soc 7.:53 2.00 .0587 .168 .a 307 so.&
·4 .400 7.42 2eSO .1160 .233 . ;.o4a5 50.6 5 • 333 9.06 3.00 .2446 .340 .o 853 . so.s 6 .286 7.H 3.50 .3179 .455 .0950. so.s
.7 e2SC 5.59 4.00 .3575 .538 .0935 so.s 8 .222 4.16 4.50 .3794 .6:13 .o 882 50.5 9 .zoo 3.10 5.00 .3874 .657 .o 811 so.:.
10 .182 2.32 s.so .3853 • 7J 1 .o 733 50.!) 11 .16 7 1.74 6.00 .3760 .no .0655 so.r. 12 .154 1.:51 6.50 .3587 .774 .:)577 so.& 13 e143• .97 7.00 .3336 .an~ • J 499 so.:. H .133 .72 7.50 .3C51 .835 .!) 425 50·? 15 .125 .53 a.oo .2736 •867 .o 358 50. s 16 .118 .3'3 8~50 .2381 .901 .o 293 so.& 17 .111 .27 9.00 .1996 .935 .o 232 so.s 18 .105 .18 9.50 .1583 .• ., 72 .o 174 so.:. 19 .100 .11 10 .oo .1130' 1.009 .o 118 so. 0 20 .095 .as 10.SO .0615 1.01+7 ·.o 061 so.:. 21 .091 .oo u.oo .co 43 1.085 .0004. 50. Ei .
22 .087 .-.o,. 11.50 -.0605 1.12'+ -.a 055 so.:. 23 .083 -.~a 12.00 -.1326 1.153 -.J lH. so.& 24 .oac -.11 12.50 -.210'3 1.203 -. D 177 so. s
RHO ·1DOE+Ql
37 38 39 40. 0 0 0 0
VREF REC 44.31 .151E+07 29.54 .151E:+07 22.16 e1S1E+07 17.73 elS1E+07 1.tt.77 .151E+07 12.56 .151£+07 u.oa .151£+07
9. 85 e151E+07 8.86 .151£+07 a.c6 e151E+OJ 7-39 el51E+07 6.82 el51E+07 . 6.33 .151£+07 5.91 .151£+07 5.54 .151E+07 5.21 .151E+07 4e92 ·151E+07 4.56 .151E+07 4.,.3· .151E+07 4.22 .151E+:l7 4.03 ~1S1E+07
3.65 .151[+07 3.59 .151E+07 3.55 e151E+07
TORQUE .167E+D5 .118E+OS e119E+05 .120 E+O 5 e147E+05. e12:1E+05 .:J04E+04 .674E+04 .502E+04 .375E+04 ~282E+04 e211E+04 .l57E+l4 .117E+04 · e965E+03 .:, 28E+O 3 .tt,.3E+03 • 2 99E+O 3 e183E+O 3 .860E+D2 .520E+0'1.
-.544E+02 -.l24E+03 -.175E+03
PO\o!ER DRAG .887E+!J2 .163E+OS 0 .627E+!J2 .989(+04 0 • 629E+O 2 .77~E+04' 0 e637E+,02 .691E+04 0 .777E+02 .699E+04 0 .&36E+:l2 .68 7E+O 4 0 .473£+02 .622£+04 0 • 357E+O 2 .551E+04 0 .266£+02 .486£+04 0 .199E+~2 .42'3£+04 0 .149E+02 e38CE+04 0 .112E+02 .33SE+04 0 .834E+01 .30 4E+04 0 .620E+01· .275E+Oo\ 0 • 458E+O 1 .2S1E+04 0 • 333E+ 01 e231E+Q4 0 ·235E+01 e214E+O~ 0 .158E+J1 .19SE+O~ 1 .969E+OO .187E+O~ 1 .4SSE+JO .176E+04 2 .276E-O 1 - .16EE+04 3
-.3UE+OO e157E+04 4 -.b59E+OO el4.'3E+C .. .3 -.326E+:l0 •142E+04 •3
32
DISTRIBUTION:
TID-4500-R66 UC-60 (283)
Aero Engineering Department (2) Wichita State University Wichita, KS 67208 Attn: M. Snyder
w. Wentz.
R.·E. Akins, Assistant Professor Department of Engineering Science
and Mechanics Virginia Polytechnic Institute and
State University Blacksburg, VA 24060
Alcoa Laboratories (5) Alcoa Technical Center Aluminum Company of America Alcoa.Center, PA 150fiq Attn: D. K. Ai
A. G. Craig ·J. T. Huang J. R. Jombock P. N. Vosburgh
Mr. Robert B. Allen General Manager Dynergy Corporation P.O. Box 428 1269 Union Avenue Laconia, NH 03246
American Wind Energy Association 54468 CR31 Bristol, IN 46507
E. E. Anderson South Dakota School of Mines
and Technology Department of Mechanical Engineering
-Rapid City, SD 57701
Scott Anderson 318-Millis Hall University of Vermont Burlington, VT 05405
G. T. Ankrum DOE/Office of Commercialization 20 Masiachusetts Avenue NW Mail Station 2221C washington, DC 20585
Holt Ashley Stanford University Department of Aerona~tics and
Astronautics Mechanical. Engineering Stanford, CA 94305
Kevin Austin Consolidated Edison Company of
New York, Inc. 4 Irving Place New York, NY 10003
F. K. Bechtel Washington State University Department of Electrical Engineering College of Engineering Pullman, WA 99163
M. E. Beecher Arizona State University Solar Energy Collection University Library Tempe, AZ 85281
K. Bergey University of Oklahoma Aero Engineering Department Norman, OK 73069
Steve Blake Wind Energy Systems Route 1, Box 93-A Oskaloosa, KS 66066
Robert Brulle McDonnell-Douglas Aircraft Corporation P.O. Box 516 Department 341, Building 32/2 St. Louis, MO 63166
R. Camerero Facul~y of Applied Science ~niversit~ of Sherbrooke Sherbrooke, Quebec CANADA JlK 2Rl
CERCEM 49 Rue du Comman~ant Rolland 93350 Le Bourget FRANCE Attn: G. Darrieu~
J. Delassus
33
34
Professor v. A.·L. Chasteau School of Engineering University of Auckland Private Bag Auckland, NEW ZEALAND
Howard T. Clark McDonnell Aircraft Corporation P.O. Box 516 Department 337, Building 32 St. Louis, MO 63166
:&r.--R-;-N-. C 1 a r k USDA, Agricultural Research Service Southwest Great Plains Research Center. eushland, TX 79012
Joan D. Cohen Consumer Outreach Coordinator State of New York .Exec.utive Department State Consumer Protection Board 99 Washington Avenue Albany, NY 12210
Dr. D. E. Cromack Associate Professor Mechanical and Aerospace Engineering
Department University of Massachusetts Amherst, MA 01003
Gale B. Curtis Tumac Industries 650 Ford Street Colorado Springs, CO
DOE/AT.O {1) Albuquerque, Attn: G. P.
D. C. D. W.
NM 87185 Tennyson Graves King
80915
DOE Headquarters {20) · washington, DC 20545 Attn: L. v. Divone, Chief
Wind Systems Branch D. F. Ancona, Program Manager
Wind Systems Branch
C. w. Dodd School of Engineering Southern Illinois University Carbondale, IL 62901
Dominion Aluminum Fabricating Ltd. (2) 3570 Hawkestone Road Mississauga, Ontario· CANADA L5C 2U8 Attn: L. Schienbein
c. wood
D. P. Dougan Hamilton Standard 1730 NASA Boulevard· Room 207 Houston, TX 77058
J. B. Dragt Nederlands Energy Research Foundation (E.C.N.) Physics Department Westerduinweg· 3 Pa~ten (nh) THE NETHERLANDS
C. E. Elderkin Battelle-Pacific Northwest Laboratory P.O. Box 999 Richland, WA 99352
Frank R. Eldridge, Jr. The Mitre Corporation 1820 Dolley Madison Blvd. McLean, VA 22102
Electric Power Research Institute 3412 Hillview Avenue Palo Alto, CA 94304 Attn: E. Demeo
James D. Fock, Jr. Department of Aerospace Engineering Sciences University of Colorado Boulder, CO 80309
Dr. Lawrence c. Frederick Public Service Company of New Hampshire
_1000 Elm Street Manchester, NH 03105
E. Gilmore Amarillo ~ollege Amarillo; TX 79100
Paul Cipe Wind Power Digest P.O. Box 539 Harrisburg, PA 17108
35
36.
Roger T. Griffiths University College ~~ Swansea Department of Mechanical Engineering Singleton Park Swansea SA2 8PP UNITED KINGDOM
Professor N. D. Ham Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139
Sam Hansen DOE/DST 20 Massachusetts Avenu~ Wa~hington, u~ · 20545
c. F. Harris Wind Engineering Corporation. Airport Industrial Area Box 5936 · Lubbock, TX 79415·
w. L. Har'ris Aero/Astro Department Massachusetts Institute of Technology Cambridge, MA 02139 ·
Terry Healy (2) Rockwell International Rocky Flats Plant P.O. Box 464 ·Golden, CO 80401
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