In the past decade, there has been much activity in the development of computational methods for the analysis of unsteady transonic aerodynamics about airfoils and wings. Significant features are illustrated which must be addressed in the treatment of computational transonic unsteady aerodynamics. The flow regimes for an aircraft on a plot of lift coefficient vs. Mach number are indicated. The sequence of events occurring in air combat maneuvers are illustrated. And further features of transonic flutter are illustrated. Also illustrated are several types of aeroelastic response which were encountered and which offer challenges for computational methods. The four cases illustrate problem areas encountered near the boundaries of aircraft envelopes, as operating condition change from high speed, low angle conditions to lower speed, higher angle conditions

Edwards, John W.

English

NASA Technical Reports Server

1 q (i c .:"I: 
N89-19264 -. 
COMPUTATIONAL AEROELASTICITY 
CHALLENGES AND RESOURCES 
John W. Edwards 
NASA Langley Research Center 
631 
https://ntrs.nasa.gov/search.jsp?R=19890009893 2020-03-20T04:13:23+00:00Z
TRANSONIC AERODYNAMICS AND FLUTTER 
In the past decade there has been much activity in the development of computational methods for 
the analysis of unsteady transonic aerodynamics about airfoils and wings. The upper left figure 
illustrates significant features which must be addressed in the treatment of computational 
transonic unsteady aerodynamics. On the plot of equivalent airspeed versus Mach number, lines 
of constant altitude are straight lines through the origin with decreasing altitudes represented 
by steeper slopes. The flight mvelope, typically set by the maximum limit speed and a typical 
flutter boundary curve, characterized by the flutter speed gradually dropping to a minimum in 
the transonic speed range followed by a rapid upward rise, is shown. The ability to predict this 
minimum, termed the transonic flutter dip, is of great importance in design, since the flutter 
boundary must be shown by a combination of analysis and flight test to be outside the flight 
envelope by a margin of at least 15 percent in equivalent airspeed for military aircraft. 
The upper right figure indicates the flow regions for an aircraft on a plot of lift coefficient 
versus Mach number. Flows which are predominantly attached or separated are designated as 
type I and Ill respectively, while mixed attached and separated flows are designated type II. For 
aeroelastic problems the boundary of the type II flows will be enlarged over that for steady 
flows since a vibrating airfoil or wing may exhibit alternating attached and separated flow for 
sensitive conditions. The "picket fence" in the mixed flow region has been added to emphasize 
the possibility of "nonclassical" aeroelastic effects in this region. 
The diagram in the lower left of the figure illustrates the sequence of events occuring in air 
combat maneuvers. Upon the decision to engage, a maneuver is initiated with the objective of 
achieving maximum turn rate. This leads, in turn, to 'pull-up and turn at the structural limit 
load, decelerating at limit load to the intersection with the maximum lift coefficient curve; 
holding this "corner" condition until the pointing objective is achieved and completion of 
engagement and pull-out occurs. These maneuvers, encompassing the complete fight envelope, 
involve rapid transitions between type I, 11, and Ill flow conditions. 
Further features of transonic flutter are illustrated in the lower right diagram. Dynamic 
pressure at flutter tends to decrease with increasing Mach number to a minimum "critical 
flutter point" value in the transonic speed range. At subsonic speeds the flow can be reasonably 
assumed to be attached (type I) at flutter and linear theory is well calibrated for flutter 
analysis. At transonic speeds the situation is complicated by the onset of flow separation (type 
II flow) and linear theory must be used with caution. The low damping region indicated in the 
figure indicates the potential for nonclassical aeroelastic response and instabilities which may 
be encountered. 
Edwards, J. W.; and Thomas, J. L.: Computational Methods for Unsteady Transonic Flows, AlAA 
Paper No. 87-01 07. 
632 
TRANSONIC AERODYNAMICS AND FLUTTER 
GRAPHICAL REPRESENTATION OF MINIMUM 
REQUIRED FLUTTER MARGIN 
I Flutter boundary 15% In V, at 
”, 
Equlvalent 
alrspeed 
0 0.5 1 .o 1.5 2.0 
Mach number 
AIR COMBAT DYNAMICS 
Turn 
rate 
CHARACTERISTICS OF ATTACHED AND 
SEPARATED FLOW FOR COMPLETE AIRCRAFT 
Separated flow 
Attached flow 
0 1 .o 2.0 
Mach number 
FEATURES OF TRANSONIC FLUTTER 
‘crittcal 
Flutter 
dynamlc 
pressure 
llutter 
damplng polnt 
Mach number Machnumber ’ 0 
633 I 
COMPUTATIONAL AEROELASTICITY CHALLENGES 
This figure illustrates several types of aeroelastic response which have been encountered and 
which offer challenges for computational methods. The four cases illustrate problem areas 
encountered near the boundaries of aircraft flight envelopes, as operating conditions change 
from high speed, low angle conditions to lower speed, higher angle conditions. The nonclassical 
aeroelastic response observed on the DAST ARW-2 wing model (upper left) is a region of high 
dynamic response at nearly constant Mach number which was encountered at dynamic pressures 
well below those for which flutter was predicted. The motion is of the limit-amplitude type and 
the response is believed to be associated with flow separation and reattachment over the 
supercritical wing (type I1 flow). 
The upper right figure illustrates winghtore limited amplitude oscillations experienced by 
modern, high performance aircraft under various loading and maneuvering conditions at 
transonic Mach numbers. Such oscillations can result in limitations on vehicle performance. 
The conditions for which this response occurs appear to be near the onset of type II mixed flow. 
The response typically increases for maneuvering flight conditions. 
Dynamic vortex-structure interactions causing wing oscillations have been observed on a 
bomber type aircraft for high wing sweep conditions during wind-up turn maneuvers (lower 
left). The flow involves the interaction of the wing vortex system with the first wing bending 
mode and occurs over a wide Mach number range (0.6 - 0.95) at angles of attack of 7 - 9 
degrees. 
At higher angles, interaction of forebody and wing vortex systems with aft vehicle components 
results in vortex-induced buffet loads, illustrated in the lower right figure. The figure shows 
the operating conditions for which tail buffet may occur on a high performance fighter. Buffet 
of horizontal tails can occur at intermediate angles of attack and is a result of the vortex system 
encountering the horizontal tail lifting surface. As angle of attack increases, the location of 
vortex bursting moves upstream in the wake. Loss of lift is associated with the burst location 
reaching the vicinity of the aircraft, and vertical tail surfaces located in such regions can 
experience severe dynamic loads. 
634 
COMPUTATIONAL AEROELASTICITY CHALLENGES 
NOVEL SHOCK-INDUCED INSTABILITIES WINGSTORE LIMITED AMPLITUDE FLUTTER 
8oo r 
Llnur theory flunor baundrn \' 
0 Freon 
pressure, Dynamlc PSf 400 j , h--F;\lly prodlctod lnrtablllly 
0 
.6 .8 1 .o 
Mach numbor 
DYNAMIC VORTEX-STRUCTURE 
INTERACTION 
10 r - 
a REDUCE'D TOWARD om 
0 1 Mach number 
30K 
H 
0 1 
Mach numbor 
VORTEX-INDUCED BUFFET LOADS 
b 
0 60 a 
635 
COMPUTER RESOURCE REQUIREMENTS FOR FLUTTER ANALYSIS 
This table indicates the computer resources required to perform a flutter analysis of a complete 
aircraft configuration at one Mach number. Time-marching transient aeroelastic response 
calculations are used to determine the flutter condition. This involves, on average, four 
response calculations: two to calculate steady flow field conditions and two transient responses 
bracketing the flutter speed. Modal frequency and damping estimates from the responses are 
determined and the flutter speed interpolated from the damping estimates. Calculations have 
been performed for a complete aircraft configuration with a transonic small disturbance (TSD) 
potential code using 750,000 grid points. The calculation of one flutter point for this case on 
the CDC VPS-32 computer would require 2.3 CPU hours. Estimates of similar calculations 
using the full Navier-Stokes equations would require 77.8 CPU hours. Conditions for this 
estimate are a Reynolds number of 10 million, 7 million grid points and an assumed 
computational speed of 100 million floating point operations per second (MFLOPS). 
References: 
Whitlow, Woodrow, Jr.: Computational Unsteady Aerodynamics for Aeroelastic Analysis, NASA 
TM 100523, December 1987. 
COMPUTER RESOURCE REQUIREMENTS TO DETERMINE FLUTTER POINT 
AT A SPECIFIED MACH NUMBER 
(4000 TIME STEPS PER FLUTTER POINT) 
CPU HOURS 
CON FIG U R AT1 ON FLOW MODE4 GRID POINTS [VPS-321 
COMPLETE AIRCRAFT TSD 0.75M 2.3*  
COMPLETE AIRCRAFT FULL NAVIER-STOKES 7.00M 7 7 . 8 * *  
(RE = 10 MILLION) 
i 'BASED ON ACTUAL CASES 
**ASSUMES COMPUTATIONAL SPEED OF 100 MFLOPS 
636 
c 
COMPUTER RESOURCE REQUIREMENTS FOR 
COMPLETE FLUTTER BOUNDARY 
POTENTIAL WITH 2-D 
STRIP BOUNDARY LAYER 
This table summarizes computational requirements for flutter calculations of a 
wing/body/canard configuration on the CDC VPS-32 computer operating at 100 MFLOPS and on 
the NAS CRAY II computer operating at 250 MFLOPS. Again, four response calculations per 
flutter point are assumed. It is assumed that ten flutter points will be calculated to define the 
flutter boundary versus Mach number. The left hand column indicates the difficulty of the 
flowfield calculation as defined in figure 1; type I for attached flows, type II for mixed 
(alternately separated and attached) flows and type Ill for fully separated flows. The second 
column indicates the fluid dynamic equation level needed to accurately model the flow physics of 
the problem. Note that two-dimensional strip boundary layer models are assumed for 
interactive viscous-inviscid calculatiork for the potential and Euler equation methods. It is 
anticipated that potential equation models will be adequate for flutter calculations of type I 
attached flow conditions and may also be quite useful for some type II mixed flow cases. Full 
potential equation codes will require about 50 percent more computer resources than TSD 
methods due to the necessity of conforming, moving grids, among other considerations. Euler 
equation methods should also be adequate for these conditions and, in addition, be able to treat 
more difficult type Ill fully separated flows. Euler equation methods are estimated to require 
approximately twice the resources of TSD methods. The full Navier-Stokes equations, which 
should only be required for type II and Ill flows require approximately 30 times the resources 
of the Euler equations (at a Reynolds number of 100 million). 
~~ ~~~~~ 
45 HOURS 
WINGIBODYICANARD CONFIGURATION 
10 MACH NUMBERS (40 CASES) PER ANALYSIS 
I, II, MAYBE Ill EULER WITH 2-0 
! I STRIP BOUNDARY LAYER 65 HOURS 26 HOURS 
I I I 
I I I 
1 II, Ill 
I ,  MAYBE II I 
NAVl ER-STOKES 161 1 HOURS I 644HOURS 
I (RE = 108) 
TSD WITH 2-D 
STRIP BOUNDARY LAYER 
30 HOURS 12 HOURS 
I 
I, MAYBE II t. 
I 
18 HOURS 
637 
t 


Computational aeroelasticity challenges and resources

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