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