unsteady separated flow and low- reynolds number flow ... · pdf filereynolds number flow...
TRANSCRIPT
Unsteady Separated Flow and Low-Reynolds Number Flow using A Similitude
Approach for Aeroelastic Applications
Danny. D. LiuDanny. D. Liu
Professor EmeritusProfessor Emeritus
Prepared for Workshop on Recent Advances in Aeroelasticity: Computation, Experiment and Theory
Held in ITA, SaoJose dos Campos, Brazil, June 30th- July 3rd, 2010
Similitude Model for Unsteady Flows (I)
• Largely Based on Governing PDEs (2D vs 3D Eqs)
• Allow Linear or Nonlinear BCs (hence wake BC)
• Expressed in Cp-similitude format
• Follow Equivalence Strip/Lifting line concepts
• Valid for :
- All Aspect Ratio wings
- Unsteady transonic flow ( 3D/ k-domain)
- Unsteady separate flow (3D/t-domain/UAVs)
- Low Re-number flow (3D/k-domain/MAVs)
Transonic Flutter Boundaries
AGARD Standard 445.6 Wing
Transonic Unsteady Pressures Along Wing Mid-Span
Lessing Wing in First-Bending Oscillation
(M=0.9, k=0.13, h =0.5 x span)
Pressure Similitude for Unsteady Transonic Flow: TES
Transonic Equivalent Strip (TES): TSDE Similitude Analysis
( )3 3 2 2, , ; N Nl lnCp f Cp Cp Cp k=
3D NL Solution 3D/2D Linear
Solutions
2D NL Solution
LTRAN2/Euler2D
or Test Data
• ∼ Obtained by any linear method, ZAERO/DLM
• ∼ Subject to Effective AoA Evaluation by LLT
• ∼ Pressure matching by Equivalent airfoil Inverse
design with given 3D measured steady data or by
CFD computed 3D solution
2 2, NlCp Cp
2N
Cp
3 2, l lCp Cp
TES using Measured Steady Flow Input vs Computed Input
Northrop F-5 wing at 18% span, M=0.95,k=0.528
TES: In & Out of Phase Pressures with Oscillating Flap
Northop F-5 wing :Hingeline at 82% chord, Span at 51% span, M=0.9, k=0.528
•∆CpN3 ∼ 3D separate flow solution
•∆ CpN2 ∼ 2D separate flow solution, measured or computed, e.g., XFOIL, Other 2D
separate flow methods
• ∆ CpV3, ∆ CpV
2 ∼ non-separate flow vortical flow solution UVLM (roll up) or
Bollay/Gersten’s nonlinear –lift solution (3D) and UVLM (2D)
• Fn and Gn ∼ Similitude functions derived by Equivalence concept
• ∼ given by vortical flow solution
• ∼ given by linear method, e.g., ZAERO
• ∼ 2D zero-lift AOA
Similitude model for Unsteady Separated Flow
Flow Effects due to High AoA
9
• Vortex Roll ups
• Flow Separations/Stall
• Combined Effects of all above
Vortex Roll Up
Delta and Rectangular Wings
10
Aero Model: Nonlinear Time-Domain UVLM of Mook et al
X
Y
Z
wingwingside view
top view
X
Y
Z
wingwingside view
top view
Wake position solved as part of solution
Gi
Gk
AB
CD
A B
D
C
×
→L
1
→L2
→L
4
→L
3Γ
3
Γ4Γ
1
Γ2
Flow Separations and Stall
• NACA0012 at High AoA
12
• Oil Flow Patterns for
Rectangular Wings at AoA =
18.4° Re = 3.85x105 (14%
Clark Y Sections)
A BC
• Pod A and B weight 50 lbs each
• Central pod C also acts as a bay for payload and
weighs between 60 lb (‘empty’) and 560 lb (‘full’)
HALE/Helios Model Wing Geometry
14
NL-Structural/Aero: Modeled HALE Wing
Gust Input
� At 1-g trim angle of attack, VG=20 ft/s, LG = 30 Chord Length:
Wing Motion Animation with the Wake
15
Extension of UVLM to Include Stall
• 3-D/ time-domain UVLM as the basis aerodynamic model.
• Effective angle of attack serves as the bridge:
_ 0 + where 1,2,V
lieff i
l
ci n
c α
α α= = �
( ) ( )3 2 3 2, expN N V V
p p n p p i i iC C C C yλ α∆ = ∆ ∆ ∆ − F
• Concept of similarity and the use of the 2D nonlinear and
linear flow solutions generated by numerical methods (e.g.,
XFOIL and UVLM 2D) or by measured data:
• The intermediate values of pressures are obtained by using
a spline interpolation technique.
16
Extension of UVLM to Include Stall Flow (II)
• Validation of Stall Modeling through
an aspect-ratio-6 rectangular wing
with NACA-0012 airfoil section
AoA (deg)
CL
0 5 10 15 20 25 300
0.5
1
1.5
2
2D Exp. [14]
3D Exp. [15]
3D Num. by UVLM
3D Num. by UVLM + Stall
• Span wise Lift distribution
• Total CL vs. AoA
AoA = 6°, 20°, 30°
17
Time (s)
Out-of-pla
ne
Tip
Deflection
(ft)
0 10 20 30 40 50-20
0
20
40
60
80
AoA=6.5 deg; UVLM + Stall
AoA=16 deg; UVLM + Stall
AoA=6.5 deg; UVLM
AoA=16 deg; UVLM
Time (s)
In-p
lane
Tip
Deflection
(ft)
0 10 20 30 40 50-80
-60
-40
-20
0
20
AoA=6.5 deg; UVLM + Stall
AoA=16 deg; UVLM + Stall
AoA=6.5 deg; UVLM
AoA=16 deg; UVLM
Time (s)
Out-of-pla
ne
Tip
Deflection
(ft)
0 20 40 60-20
0
20
40
60
80
UVLM
UVLM + Stall
Time (s)
In-p
lane
Tip
Deflection
(ft)
0 20 40 60-80
-60
-40
-20
0
20
40
UVLM
UVLM + Stall
NL-Structural/Aero: Modeled HALE Wing w/ & w/o Stall Effects
• The HALE wing responses by UVLM with and without stall -No Gust
• The HALE wing responses by UVLM with and without stall + Gust
(VG=20 ft/s, LG=30 Chord-length)
18
NL-Structural/Aero: Modeled HALE Wing Un-Stall vs Stall (II)
Wake flows at unstall/stall conditions, AoA=16 deg – Gust absent
UnStall Stall
19
Concluding Remarks - overall
• Method and Performance time-domain simulation of a tightly-coupled
nonlinear general unsteady vortex-lattice method (UVLM) with an
intrinsic nonlinear FEM beam model.
• Validated with linear methods in terms of unsteady aerodynamics/flutter
solutions.
• Aeroelastic instabilities resulted in largely deformed HALE wing at high
enough AoA with or without Gust and/or Stall flow. One instability
correlated well with a previous HALE-mishap case.
• When the HALE wing is in stall flow , the wing critical failure takes place
sooner than those cases without flow separation
• The stall model developed here should be applicable to almost all ranges
of Reynolds-number flows, including that for Micro Air-Vehicles (MAV)
20
Concluding Remarks
• Finite element implementation of a beam model which accounts for the nonlinear
dynamics of initially curved and twisted anisotropic beams. The intrinsic form of the
geometrically exact, nonlinear equations governing the motion of beams possesses
some advantages over other conventional methods
• Tight coupling of the nonlinear general unsteady vortex-lattice method with the
nonlinear beam model
• Development of an efficient algorithm to numerically integrate all governing
equations interactively and simultaneously in the time domain
• Development of a time-domain nonlinear gust analysis capability
• Validation of the computer program by conducting feasibility studies on a rather rigid
wing model, Goland wing, and a HALE-type wing. Under certain discrete gust profile,
the HALE wing was found to be instable in the in-plane deflections
In this work we have successfully developed a time-domain nonlinear flow-structure
interaction software system providing a novel methodology for the aeroelastic analysis
of HALE aircraft with gust excitation. We summarize the work as follows:
21
Concluding Remarks (II)
• When the HALE wing is subject to wing gust and stall flow combined, the critical
failure time (while with significant in-plane deflection) occurs earlier than that due
to gust alone.
• For all cases considered, the critical wing-tip deflection would invariantly reach
nearly two third of the semi wing span. This might indicate that the wing failure is
related to its large dihedral. At small or moderate deformations, the HALE wing
tends to be aeroelastically stable but becomes unstable at large deformed shapes.
The physical reason of these findings is not entirely clear at present. Further
numerical studies and wind tunnel tests are warranted.
• Further investigation and improvements of the present NANSI method are
necessary. As opposed to the time-domain CFD methods, the present enhanced
NANSI method should be an effective solver applicable to wings for large size
aircraft. The stall model developed should be applicable in almost all ranges of
Reynolds-number flows, including that for the micro air-vehicles, MAV.
Levels of Nonlinearity
• Cpl -- Linear / ZAERO,DLM
• CpV -- Nonlinear Lift/UVLM
TE Wake + Vortex Rollup
• CpN -- Stall /Flow separation
Low-Re Correction of ZAERO Unsteady Aerodynamics
Based on a Viscous Similitude Analysis
Wing:
Airfoil:
( )3 3 2 2, , ; Re, v l l vnCp f Cp Cp Cp k∆ = ∆� � � �
( )2 2 2, ; Re, v vnCp f Cp Cp k∆ = ∆� � �
Low-Re
CorrectionZAERO
Unsteady
XFOIL or
Test DataCp�
Note: (·) = unsteady (·) = steady~
Low-Re-Corrected ZAERO vs. CFL3D: AR6.0 Rectangular Wing
0 0.5 1 1.5 2 2.5 3 3.5 40
0.05
0.1
CL
α
α
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
CL
ZAERO
CFL3D, Re=6000
ZAERO Corrected, Re=6000
0 0.5 1 1.5 2 2.5 3 3.5 40
0.01
0.02
0.03
CM
α
α
0 0.5 1 1.5 2 2.5 3 3.5 40
0.05
0.1
CM
ZAERO
CFL3D, Re=6000
ZAERO Corrected, Re=6000
• CL and CLα with AoA
• ZAERO inviscid versus Low-Re
correction.
• NACA0008 airfoil, M = 0.02,
Re = 6000, Xo = 0.5c
• CM and CMα with AoA
• ZAERO inviscid versus Low-Re
correction.
• NACA0008 airfoil, M = 0.02,
Re = 6000, Xo = 0.5c
CL , CM , , andLdC
dαMdC
dα
Low-Re-Corrected ZAERO (Re=6000) vs. ZAERO (I)
In-Phase Lift/Moment Derivatives w/ Reduced Frequency
Low-Re-Corrected ZAERO (Re=6000) vs. ZAERO (II)
Out-Of-Phase Lift/Moment Derivatives w/ Reduced Frequency
Conclusions (I)
• A systematic procedure has been developed for the FEM
development of a Gull wing but this process is generic and
could be broadly adopted by the MAV industry.
• The procedure includes:
– Shape characterization (e.g., digitization)
– Coupon testing for structural property identification using:
• mechanical testing (standard materials/composites)
• vibration testing (e.g., woven material)
– Finite element development and validation on entire/part
of MAV (e.g. wing)
Conclusions (II)
• Aeroelastic investigation for Gull wing using Nastran and
ZAERO are conducted with the findings:
– Divergence precedes flutter for all 3 dihedral configurations
– Divergence/Flutter q decreases with increasing Γ.
• Low-Reynolds-number correction to ZAERO aerodynamics
yields comparable stability derivatives with that of CFL3D for
an AR=6.0 rectangular wing(NACA0008) indicating the Low-
Re/ZAERO applicability to control and ASE of MAV wings.
Simpler Vortical-Flow Models vs UVLM
Vortical-Flow Models of (a) Bollay and (b) Gersten:
- Expedient Nonlinear-Lift Methods as opposed to UVLM
- Roll-up detail and free wake are not accounted for
- Unsteady flow model remains to be developed
Vortical-flow Solutions of Gersten (I)
Vortical-flow Solutions of Gersten (II)
Sweptback wings
(a)AR =1.0, λ=1.0
(b)AR = 0.78, λ=0.2
32
Extension of UVLM to Include Stall Flow (II)
• Validation of Stall Modeling through
an aspect-ratio-6 rectangular wing
with NACA-0012 airfoil section
AoA (deg)
CL
0 5 10 15 20 25 300
0.5
1
1.5
2
2D Exp. [14]
3D Exp. [15]
3D Num. by UVLM
3D Num. by UVLM + Stall
• Span wise Lift distribution
• Total CL vs. AoA
AoA = 6°, 20°, 30°
XY
Z
Wake Pattern for AR = 1/4Left Side Obtained by Mirror ImageHalf-span Model: 32×6 Mesh
200 Steps; AOA= 6 deg.
AoA (D eg)
CN
0 2 4 6 8 10 120
0.05
0.1
0.15
0.2
AR 1-4th U VLMAR 1-4th H KCAR 1-4th Experiment
AoA (D eg)
CN
0 2 4 6 8 10 120
0.05
0.1
0.15
AR 1-30th U VLMAR 1-30th H KC
AR 1-30th Experiment
H.K. Cheng, “Remarks on Nonlinear Lift and Vortex Separation”, Journal of the Aeronautical Science, Vol. 21, No. 3, 1954.
Aerodynamic Check: UVLM vs. HK Cheng’s Solution
Some thoughts on Unsteady Separated Flow Models
• Engineering Model
- Classical Integral methods (Panel methods) + Similitude
approach: Computational efficient for AE applications
- Fixed wake model of Bollay,Gersten,Garner etc
- Vortex roll up model of HK Cheng, Bryson,etc
- Perturbed amplitude+ k-domain model for unsteady flow
• Reduced Order Model
- Time-domain Vortex Lattice method (UVLM)
- CFD methods
- ROM of the above solutions drastically saves computing time