An optimization procedure is developed for the design of high speed prop-rotors to be used in civil tiltrotor applications. The goal is to couple aerodynamic performance, aeroelastic stability, and structural design requirements inside a closed-loop optimization procedure. The objective is to minimize the gross weight and maximize the propulsive efficiency in high speed cruise. Constraints are imposed on the rotor aeroelastic stability in both hover and cruise and rotor figure of merit in hover. Both structural and aerodynamic design variables are used

Chattopadhyay, Aditi

Madden, John F., III

Mccarthy, Thomas R.

English

NASA Technical Reports Server

Optimum Design of High Speed Prop Rotors Including the Coupling of
Performance, Aeroelastic Stability and Structures
v
v
Aditi Chattopadhyay, Thomas R. McCarthy
Department of Mechanical and Aerospace Engineering
Arizona State University
Tempe, Arizona 85287-6106
and
John F. Madden, III
Rotorcraft Technology Branch
NASA Ames Research Center
Moffett Field, California 94035
Proposed Abstract for Presentation at the
AHS Forum, June 1993
St. Louis, Mo
https://ntrs.nasa.gov/search.jsp?R=19930008877 2020-03-17T09:15:29+00:00Z
OPTIMUM DESIGN OF HIGH SPEED PROP ROTORS INCLUDING THE
COUPLING OF PERFORMANCE, AEROELASTIC STABILTY
AND STRUCTURES
Aditi Chattopadhyay 1 and Thomas R. McCarthy 2
Department of Mechanical and Aerospace Engineering
Arizona State University
Tempe, Arizona
and
John F. Madden, III 3
Rotorcraft Technology Branch
NASA Ames Research Center
Moffett Field, California
Introduction
The primary design objectives of the 450 knot high speed civil prop-rotor are improved cruise
propulsive efficiency and acceptable hover performance [1-5]. The rotor system should also be
reasonably low weight and easy to operate. The vehicle design process is multidisciplinary in
nature and involves a merging of several technical disciplines, such as aerodynamics, aeroelastic
stability analysis, dynamics, structures and acoustics. For example, as speed increases, with the
increase in rotor aerodynamic forces, the coupled motion of the prop-rotor and the wing elastic
modes become unstable causing whirl flutter instability. IndividuaI rotor blade stability is also
important. Rotor aerodynamic performance requires ideal combination of planform, twist, airfoils
and sweep to achieve maximum cruise propulsive efficiency while maintaining sufficient lifting
capability and control properties in hover and in low-speeds. The complex rotor flow field
associated with high tip velocities further complicates the aerodynamic analysis. In the helicopter
mode, vibration can be a major source of problem and its alleviation will play an important role in
the rotor blade design process. In the area of structures, the objective is to achieve maximum
structural performance with minimum weight and cost requirements. Composite structures,
combining the stiffness flexibility and bending-torsion coupling, are ideal for providing superior
light-weight structure and Advanced Technology composite Blades (ATB) are currently being used
in the XV-15 tiltrotor aircraft. Acoustics also plays an important role, as both external and internal
noise generated by the vehicle are important design issues.
There also exists several conflicting design requirements. For example, cruise condition
demands thin blade airfoils for high drag divergence Mach number (Mdd), but thin airfoils have
1 Asst. Professor. Member, AHS, AIAA, ASME
2 Graduate Research Assistant. Student member
3 Aerospace Engineer. Member AHS
2
AHS, AIAA
lower values of Clmax ((21 is the lift coefficient). This reduces the rotor figure of merit (FOM) by
reducing CT/C (Or is the thrust coefficient and o is the thrust-weighted solidity). Therefore, to
satisfy hover requirements, the rotor solidity has to increase. This can be eliminated by selecting
airfoils with high Clmax and high L/D ratios at relatively low Mach numbers and low drag but high
Mdd at high Mach numbers and low lift. Similarly, although airframe drag can be alleiviated by
sweeping the outboard sections, that operate at high Math numbers, a swept rotor blade must be
aeroelastically tailored to minimize the blade torsional and bending loads. The tradeoff between
airfoil thickness and blade sweep angle therefore requires an indepth-study since they both
influence aerodynamic and aeroelastic performance in hover and cruise.
The application of formal optimization procedures to tiltrotor design, therefore, seems
appropriate as it can provide design trends while reducing the "man-in-the-loop" type of iterations.
However, it is essential to integrate the necessary disciplinary couplings within the optimization
process. Some initial investigations are due to Chattopadhayay and Narayan [7]. The purpose of
the proposed paper is to enhance the state of the art by developing a multidisciplinary optimization
procedure for high speed civil prop-rotors, including the couplings of aerodynamic performance,
aeroelastic stability and structures in both high speed cruise and hover flight conditions.
Problem Statement
.J_. i
An optimization procedure is developed for the design of high speed prop-rotors to be used in
civil tiltrotor applications. The goal is to couple aerodynamic performance, aeroelastic stability and
structural design requirements inside a closed-loop optimization procedure. The objective is to
minimize the gross weight and maximize the propulsive efficiency in high speed cruise.
Constraints are imposed on the rotor aeroelastic stability in both hover and cruise and rotor figure
of merit in hover. Both structural and aerodynamic design variables are used. =:
Multiobjective Optimization Formulation
Due to the fact that the optimization problem involves more than one design objective, the
objective function formulation is complicated. In most of the existing work, the individual
objective functions are combined using weight factors in a linear fashion [8]. Such methods are
judgmental as the answer depends upon the weight factors which are often hard to justify. Also, in
a rotary wing design environment, where complex nonlinear functions are involved, such methods
are not well posed. Therefore an investigation is cuurently under way to evaluate the best
formulation procedure appropriate for such applications. A Kreisselmeier-Steinhauser (K-S)
function approach is used in this paper and a brief description of the approach follows.
3
Kreisselmeier-Steinhauser (K-S) function approach: The optimization problem can be
stated as follows.
Minimize Fk(g_n)
subject to
k = 1, 2 ..... NOBJ
n = 1, 2 ..... NDV
gj(q_n) -< 0 j = 1, 2 ..... NeON
tPnL -<q_n < ¢4nu
(objective functions)
(inequality constraints)
(side constraints)
where NOBJ denotes the number of objective functions, NDV is the number of design variables
and NeON is the total number of constraints. The subscripts L and U represent lower and upper
bounds, respectively, on the design variable % Using the K-S function approach, the first step in
formulating the objective function in this approach involves transformation of the original objective
functions into reduced objective functions [9]. These reduced objective functions are of the form
• Fk(q )
Fk(q°) - Fko "l'gmax -< 0 k= 1,2 .... ,NOBJ (1)
where Fko are the values of Fk calculated at the beginning of each iteration. The quantity gmax is
the value of the largest constraint corresponding to the design variable vector q_ and assumed to be
constant for this iteration. Because these reduced objective functions are analogous to the previous
constraints, a new constraint vector gj(q0), j = 1, 2, .... M, is introduced, where M = NeON +
NOBJ. The new objective function to be minimized is then defined, using the K-S function as
follows.
F(q0) = gmax + I_ loge _e p(gm(q°) - gmax)
P m=l
(2)
where the multiplier 9 is analogous to a draw-down factor controlling the distance from the surface
of the K-S objective function to the surface of the maximum function value. The design variable
vector q0 is identical to that used in the Global Criteria approach. The method was found to provide
faster convergence by Chattopadhyay and McCarthy [10] in a rotor blade optimization problem.
Optimization Implementation
The basic algorithm used is the method of feasible directions as implemented in the
optimization program CONMIN [11]. The optimization is to be coupled with a comprehensive
analysis code. The blade is to be trimmed at each step of design optimization such that each
feasible design (i.e., a design that satisfies all constraints) produced by the optimizer represents a
trimmed configuration. Since the optimization process requires many evaluations of the objective
function and constraints before an optimum design is obtained, the process can be very expensive
if full analyses are made for each function evaluation. The objective function and constraints are
therefore approximated by an approximation technique which is described below.
Approximation Technique
A two-point exponential approximation [ 12] is proposed for approximation of the objective
functions and the constraints. This technique takes its name from the fact that the exponent used in
the expansion is based upon gradient information from the previous design point. This technique
is formulated as follows.
NDV ,-
x'/¢001 7°°
_(¢>) = F(*o)+ "L'dLt'41°n ) -1.O.j P. 341n
n=l
where
f¢0F(*,,)]
Jt_-J i,
It, a_n )J
+ 1.0 (4)
""-- 1
tabooj
The quantity q:'l refers to the design variable vector from the previous iteration and the quantity _0
denotes the current design vector. A similar expression is obtained for the constraint vector. The
exponent Pn can be considered as a "goodness of fit" parameter, which explicitly determines the
trade-offs between traditional and reciprocal Taylor series based expansions (also known as a
hybridapproximationtechnique).It canbeseenfrom Eqn.4 thatin thelimiting caseof Pn= I, the
expansionis identicalto thetraditionalfirst orderTaylor series,andwhenPn= -1, the two-point
exponentialapproximationequatesto thereciprocalexpansionform. Theexponentis thendefined
to lie within this interval,suchthatif Pn> 1,it is setidenticallyequalto one,andif Pn< -1,it is set
equal to-1.
Analysis
The aerodynamic, dynamic and aeroelastic analysis is performed using the comprehensive analysis
code CAMRAD/JA [13]. The structural analysis is performed using a code developed in-house.
Blade Modeling
The formulation and modeling assumptions used in the integrated optimization problem are
described in this section.
Aerodynamic Model
The aerodynamic lifting line offset, from reference axis, is based on a cubic model (Figure 1)
with in-plane curvature as follows.
XacG') = e-.O+el9 + t;2_ 2 + e3_' 3 (5)
where e0, el, e2 and e3 are constants that determine the curvature and _, is the nondimensional
radial location. These curvature parameters, ei (i = 0 - 3), are defined such that
l eil < _i (6)
where _i are prescribed bounds for the curvature parameters. These bounds allow for either
forward or backward in-plane curvature. When these parameters are equal to zero, the lifting line
will be a straight line. Based upon this quadratic lifting line, the sweep variation, in degrees, is
calculated as follows.
A(5,) = 180 (el + 2e2v + 3e35' 2)/r_ (7)
XY
.......
Figure 1 Blade model
The twist angle of attack, 0(50, is defined to have the following spanwise variation.
8@) = eideal+ Operturbation (8)
where
eideal = tan- 1(--_y 1
0perturbation@) = 01 (y -- 0.75) + 02 @ - 0.75) 2 + 03 (:y - 0.75) 3
(9)
(]o)
and Voo represent the free stream velocity. It is important to note that twist plays an important role
in both cruise and hover flight conditions and at high Mach numbers the twist has a significant
effect on the cruise efficiency. Therefore, the above cubic distribution is chosen to provide the
optimizer with more flexibility by using the coefficients 01 - 03 as design variables.
Structural Model
The load carrying structural member is a single cell composite box beam (Figure 2).
-x.
h = lO%c(y)
'_____ b = 40%c(y)
t _
I I
Figure 2 Single cell composite box beam
The beam is modeled with unequal vertical and horizontal wall thicknesses and the beam cross
section is described by stretching, bending, twisting, shearing and torsion related warping. The
box beam walls are made of layers of laminated orthotropic composite plies. A symmetric ply
arrangement of (900/45°/0°/-45°) s is used for the horizontal walls and a symmetric arrangement of
(0°/+45°/0°)siS used for the vertical walls. The spanwise thickness distribution, t(y), for each ply is
based on the following spanwise distribution.
1 1
t(y) = t o +tlY+t2--+t3 (II)y 7
where to - t3 are coefficients that determine the thickness distribution. The total thickness of an
individual ply with orientation _ is calculated as follows
t_@) = nvt@) (12)
where t_/ is the total thickness and nw is the total number of plies with orientation gt. The
stiffnesses, as required by CAMRAD/JA, are calculated based on the formulation developed by
Smith and Chopra [14].
Non structural tuning weights,w (),), are placed at the leading edge and the following cubic
spanwise distribution is assumed.
w @) = w 0 + wly + w2y 2 + w3 _ 3 (13)
wherew0 - w3 arethe coefficientsdescribingthe weightdistribution. The total bladeweight
comprisestheweight of the box beam,the tuning weights,theskin and thehoneycombweight
(usedin thetrailingedgesection).
Objective function, design variables and constraints: The objective function to be
minimized is the total weight which comprises the drive system weight and the total weight of the
three blades as shown below.
W -- Wdriv e + Wblad e (14)
where
Wdriv e = Wengine + Wtrans + Wfuel
and the individual weights are based upon the following empirical formulae.
Wengin e = rlef2(SHP)(O.12) + 175
(15)
(16)
Wtrans = 300(1.1--_M) °8
Wfuei = 1.5(SFC)(SHP)
(17)
(18)
In the above equations, SFC is the specific fuel consumption, rle_ is an empirical efficiency
parameter, RPM is the rotational velocity of the rotor and SHP is the shaft horse power. The blade
weight, Wblad e, includes the box beam, the skin, the honeycomb and the non structural or tuning
weights, placed at the leading edge. Both structural and aerodynamic design variables are used
during the optimization. Following is a summary of the design variables.
(i) thickness distribution coefficients, tl - t3.
(ii) number of plies with orientation ¢, nq_i (i = I-5)
(iii) non structural weight distribution coefficients, w0 - w3
(iv) coefficients of sweep distribution, e0- e 3
(iv) coefficients of twist distribution, 01 - 0 3
9
To ensureaeroelasiticstabilityin bothhoverandhighspeedcruise,constraintsareimposedon the
realpartof thestabilityrootasfollows.
O_ki< 0 k -- 1, 2 ..... NMOD (19)
i = 1, 2 (1 - hover, 2 - axial)
where NMOD represents the total number of modes constrained. Also a lower bound constraint is
imposed on the hover figure of merit FM as follows.
FM > FMaUow (20)
where FMallow is the required figure of merit in hover.
Results
Some preliminary results obtained are presented in this section. The objective function
used is minimizing the blade weight increment from reference to the composite model. Constraints
are imposed on the rotor aeroelasfic stability in hover and cruise. The rotor used, as a reference, is
the XV-15 Advanced Technology Blade which is three bladed rotor with a rigid hub and zero
sweep. The blade radius is 12.5 feet. The rotor was designed for a cruise velocity of 300 knots.
The optimization is performed with both multi and single objective function formulation
techniques. The program CAMRAD/JA is used for the aerodynamic, dynamic and aeroelastic
analysis. The blade is discretized into 51 segments structural stations and 21 aerodynamic stations.
Using a wind tunnel trim option, in each case, the optimum rotor is trimmed to the same CT as the
baseline or the reference rotor such that the same lifting capability is maintained after optimization.
The optimization is performed at a cruise velocity of 400 knots at an altitude of 25,000 feet above
sea level. In hover, a rotational velocity of f'2 = 570 RPM (tip speed of 746 ft,/s) is used at sea-
level conditions. An uniform inflow model is used for both hover and axial analysis. In hover the
rotor is trimmed to a design CT/CY = 0.13 and an L/D value of 5.3 is used in cruise. The material
used for the composite box beam is T300/5208 Graphite Epoxy with a volume fraction of 70
percent. The aeroelastic stability of the reference blade is significantly improved as indicated in
Figs. 4 and 5 for hover and and cruise, respectively.
The final paper will contain results of the comprehensive optimization problem using total
vehicle weight and high speed cruise propulsive efficiency as objective functions. The results of
10
the optimization, performed at a cruise velocity of 400 knots, will be compared against the baseline
XV-15 ATB blade which has never been tested at such speeds.
CD
t,-
u
t_
E
3O
2O
10
0
-10
-20
-30
-5
!
-4
0
0
0
0
!
-3
0
Oo.j
0 Optimum
• Reference
ooO 
I
-2
Figure 3
O
! i q'
-1 0 1 2
real
Stability roots in hover
I I
3 4 5
I1
3O
Iu
I.
D,.
e.-
E
2O
10
-10.
-2O
O
O
O
O
O Optimum
• Reference
-30 i i i , i r......... l i
-5 -4 -3 -2 -1 0 1 2 3 4 5
real
Figure 4 Stability roots in cruise
Acknowledgement
The work was supported by NASA Ames Research Center, Grant NAG2-771, Technical
Monitor, Mr. Joseph Torah.
References
o
.
°
.
Talbot, P., Phillips, J. and Torah, J. " Selected Design Issues of Some High Speed
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Conway, S., "Conclusions from High speed Rotorcraft Studies," presented at the
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13


Optimum design of high speed prop rotors including the coupling of performance, aeroelastic stability and structures

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