Ice-Induced Aircraft Stability Upsets An experimental investigation to identify linear and non-linear fluid-structure lock-in

Woutijn J. Baars, BSc. July 31, 2009 Ice-Induced Aircraft Stability Upsets An experimental investigation to identify linear and non-linear fluid-structure lock-in

Master of Science Thesis

For obtaining the degree of Master of Science in Aerospace Engineering at Delft University of Technology

Woutijn J. Baars, BSc.

July 31, 2009

Faculty of Aerospace Engineering Delft University of Technology · Copyright c Woutijn J. Baars, BSc.

All rights reserved.

Front page photo: Cessna 208B Grand Caravan, 2009 c Cessna Aircraft Company, all rights reserved. Examination Committee

The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace Engineering for acceptance the thesis entitled ”Ice-Induced Aircraft Stability Upsets , An experimental investigation to identify linear and non-linear fluid- structure lock-in” by Woutijn J. Baars, BSc. in fulfillment of the requirements for the degree of Master of Science.

prof. dr. F. Scarano (Delft University of Technology)

dr. ir. L.L.M. Veldhuis (Delft University of Technology)

dr. C.E. Tinney (The University of Texas at Austin)

M.Sc. Thesis Woutijn J. Baars, BSc. Preface

This report presents my thesis work to obtain the degree of Master of Sci- ence in Aerospace Engineering at the Faculty of Aerospace Engineering of Delft University of Technology (DUT), the Netherlands. A few months after my in- ternship at Lockheed Martin Aeronautics in Fort Worth, Texas, I decided to set up an exchange position at the Aerospace Engineering and Engineering Mechanics (AE) depart- ment of The University of Texas at Austin (UT Austin). The research for this work is entirely performed at UT Austin in the period of September 2008 till July 2009. I would gratefully acknowledge prof. dr. Ronald Stearman for making arrangements concerning my exchange. Many thanks as well to the advisors from the International Student and Scholar Services UT Austin center, who provided me with a lot of know-how about my exchange position. The research I have conducted is in the area of ice accumulation on aircraft. More specifically, identifying the stability and control upsets of small general aviation type aircraft, resulting from ice accumulation on particular parts of the aircraft. Wind tunnel experiments have been conducted to get more insight in the possible lock-in mechanisms that occur between the ice- induced unsteady flow field and the motion of the aircraft. During my work at UT Austin I have experienced all the people as very friendly, helpful and with a lot of willingness to supervise me. A special thanks to Geovani Lopez (undergraduate researcher) for helping me during the experiments. Also, many thanks to the technicians, Eddy Zihlman, Timothy Valdez and Pablo Cortez, for their support during the wind tunnel experiments. I would like to thank my supervisors for their assistance and guidance that made me focus on the right research topics. First of all, I would like to thank prof. dr. Ronald Stearman and dr. Charles Tinney (AE, UT Austin) for their daily supervision and encouragement to write two conference contributions about this work: the papers by Baars, Stearman, & Tinney (2009) and Baars, Tinney, & Stearman (2009), which are presented in June 2009. Secondly, I would gratefully acknowledge dr. ir. Leo Veldhuis, from the Faculty of Aerospace Engineering for supervising my project at DUT. Likewise, many thanks to prof. dr. Fulvio Scarano for being part of my examination committee and for reviewing my thesis work. I would like to thank prof. dr. Edward Powers, from the department of Electrical & Computer Engineering (ECE), UT Austin, and dr. Hyeonsu Park (former ECE PhD student), for their assistance and advice

M.Sc. Thesis Woutijn J. Baars, BSc. Preface v on the application of the Higher-Order Spectra analysis technique. Furthermore, many thanks to prof. dr. David Goldstein, from the AE department, UT Austin, and Claus Endruhn, MSc. (former AE graduate student), for their excellent earlier experimental work. Last but not least, I would like to thank my family for their encouragement, support, and confidence in me during my entire study and I would like to thank my friends in Texas. I had a fantastic time experiencing the life in Austin and throughout the United States. The BBQ’s, nights downtown, mountain bike rides and adventurous trips in the beautiful Austin area resulted in an unforgettable time in the capital city of Texas.

Thank ”y’all” for this great experience.

Lijnden, The Netherlands Woutijn J. Baars, BSc. July 31, 2009

Faculty of Aerospace Engineering Department of Aerospace Engineering and Engineering Mechanics

M.Sc. Thesis Woutijn J. Baars, BSc. Abstract

Research related to the impact that war head induced damage had on the aeroelastic integrity of lifting surfaces and in turn the resulting upset of the complete aircraft, prompted a current look at similar aeroelastic events that might be triggered by damage of the aircraft due to icing. This possible aeroelastic impact due to icing damage is not a very commonly explored area of research. Although seldom studied, icing can also significantly impact the aeroelastic stability and hence the overall stability and control of the aircraft. In this latter context, classical flutter events of the lifting surfaces and controls can occur due to ice-induced mass unbalance or control force reversal. Also, a loss of control effectiveness or limit cycle oscillations of the controls and lifting surfaces may appear, due to significant time dependent drag forces introduced by separated flow conditions imposed by the ice accumulation. Two commonly observed ice-induced upset scenarios were selected to investigate. The first scenario involves an elevator limit cycle oscillation and a resulting loss of elevator control effectiveness. The second upset is related to a violent wing rock or Dutch roll instability. In both proposed ice-induced upsets, lock-in mechanisms of two unsteady events occur, (1) the ice-induced unsteady flow field and (2) the unsteady structural acceleration of the aircraft. A wind tunnel study is employed to investigate the lock-in mechanisms of the structural acceleration and the unsteady flow field induced by ice accumulation that is only present on the elevator horn balance leading edges. The purpose is to determine the linear and non-linear coupling mechanisms between these events. An experimental data set has been obtained where the unsteady, ice-induced, flow field and the acceleration of a 1:10 scale, reduced-stiffness, aircraft model is synchronously acquired using pressure transducers and accelerometers, respectively. The experiments are performed at various angles of attack of the aircraft, αp, with and without simulated ice accumulation on the elevator horn balance leading edges and with various settings of the elevator deflection angle, δ. Statistical signal processing techniques, that are able to compute linear and quadratic coherence spectra, are presented in this thesis work and are applied in the pressure-acceleration coherence study. The first-order processing technique, based on the well-known linear coherence spectrum, revealed a low-frequency lock-in (f = 6Hz, αp > 7◦) for the case where ice accumulation was simulated on the leading edges of the horn balances, while no lock-in was observed without ice simulations. This indicates that violent aircraft motions can indeed be a result from the

M.Sc. Thesis Woutijn J. Baars, BSc. Abstract vii ice-induced flow field over the horn balances. Although a reduced-stiffness aircraft model was used in the experimental setup, and thus the quantitative results are not translatable to the full-scale case, the identification of this linear lock-in mechanism indicates that their is a significant chance that similar lock-in mechanisms occur in full-scale flight applications. An attempt to identify the quadratic relations between the two unsteady systems was performed by employing higher-order statistical signal processing based on a non-orthogonal, second- order, single-input/output (I/O) Volterra model. Due to current limitations, related to the implementation of this technique, no physical interpretations could be done based on the higher-order coherences. Recommendations are given to improve the identification capability of this higher-order technique, which might become a powerful identification and estimation tool in (experimental) fluid dynamics.

M.Sc. Thesis Woutijn J. Baars, BSc. Contents

Examination Committee iii

Preface iv

Abstract vi

Nomenclature xiii

Acronyms xvii

1 Introduction 1 1-1 Background ...... 1 1-2 Motivation...... 3 1-3 ApproachofThesisWork ...... 5 1-4 OutlineofThesis ...... 6

2 Ice-Induced Stability & Control Upsets 7 2-1 SmallGeneralAviationAircraft ...... 7 2-1-1 IceProtectionSystems ...... 8 2-1-2 ElevatorHornBalance ...... 8 2-1-3 WingRootLeadingEdgeShoulder ...... 10 2-2 IceAccumulationCharacteristics ...... 11 2-3 Proposed Ice-Induced Destabilizing Mechanisms ...... 16 2-3-1 Identification of Multiple Failure Mechanisms ...... 16 2-3-2 Upset Number I: Loss of Elevator Control Effectiveness ...... 18 2-3-3 UpsetNumberII:DutchRollInstability ...... 21

M.Sc. Thesis Woutijn J. Baars, BSc. Contents ix

3 Experimental Apparatus 24 3-1 FacilityandTestModel ...... 24 3-1-1 Low-SpeedWindTunnelFacility ...... 24 3-1-2 AircraftTestModel ...... 25 3-1-2-1 IceSimulation...... 25 3-1-2-2 Parameters of Similarity ...... 26 3-2 Instrumentation ...... 30 3-2-1 DataAcquisitionArrangement ...... 30 3-2-2 SamplingCriteria ...... 31 3-3 ConductionofExperiments ...... 36 3-3-1 TestConditions ...... 36 3-3-2 ExperimentalSystemCharacteristics ...... 37

4 Single-I/O System Identification 38 4-1 Lock-InMechanisms...... 38 4-2 First-Order Statistical Signal Processing ...... 39 4-2-1 AutoPowerSpectrum...... 39 4-2-2 LinearCoherenceSpectrum...... 41 4-3 Higher-Order Statistical Signal Processing ...... 44 4-3-1 VolterraModelTechnique...... 44 4-3-1-1 GaussianInputSignal...... 45 4-3-1-2 Non-Gaussian, Random, Input Signal ...... 46 4-3-1-3 Higher-Order Coherence Spectra ...... 47 4-3-2 Implementation of the Volterra Model Technique ...... 48 4-3-2-1 MonteCarloSimulation ...... 48 4-3-2-2 TurbulentMixingLayerinaJet ...... 50 4-3-3 BispectrumAnalysis...... 52

5 Results of Higher-Order System Identification 55 5-1 Improvement due to Higher-Order Terms ...... 55 5-2 Pressure-AccelerationCoherence ...... 56 5-2-1 Linear Pressure-Acceleration Coherence ...... 56 5-2-2 Higher-Order Pressure-Acceleration Coherence ...... 59 5-3 Effect of Lock-In on Aircraft Stability & Control ...... 59

6 Concluding Remarks 63 6-1 Conclusions ...... 63 6-2 Recommendations...... 65

Bibliography 68

A Volterra Technique - Linear Algebra 74

M.Sc. Thesis Woutijn J. Baars, BSc. List of Figures

1-1 Location of the elevator horn balances on the aircraft...... 2 1-2 Schematicofelevatorhornbalance...... 3 1-3 Schematicoverviewofresearch...... 4

2-1 Leadingedgede-icingboots...... 8 2-2 TKSiceprotectionsystemandheatedwing...... 9 2-3 Schematicofelevatorhornbalance...... 9 2-4 Shoulder on the RHS of the aircraft wing root/fuselage junction...... 10 2-5 Total pressure head contour plots downstream of small aircraftmodel...... 10 2-6 Relevant features on a small general aviation aircraft...... 11 2-7 Fuselagecrossflowschematic...... 11 2-8 Mixed ice accumulation on the tail of a full-scale NASA test aircraft...... 12 2-9 Horizontal tail, shielded, horn balance tested in the NASA Glenn icing tunnel. . . 12 2-10 Schematic of ice-induced flow features on an airfoil...... 13 2-11 PIV study on the ice-induced separation bubble...... 13 2-12 Flow visualization on a horizontal stabilizer with elevator and horn balance. . . . 14 2-13 Flow visualization on a horizontal stabilizer with elevator and horn balance. . . . 15 2-14 First ice-induced unsteady flow feature characterization...... 15 2-15 Second ice-induced unsteady flow feature characterization...... 16 2-16 Aeroelastic model for the slender, shielded, elevator hornbalance...... 18 2-17 Total pressure head contour plots downstream of the horizontal stabilizer model. 20 2-18 Schematicofvortexfieldinteractions...... 20 2-19 Directional destabilizing mechanism of the EA-6B Prowler...... 22 2-20 Dynamic-cable-mounted aircraft model in the wind tunnel...... 22 2-21 Highspeed camera screen shots indicating the violent pair of wing root vortices. . 23 2-22 Cross bicoherence function of a pressure transducer and an accelerometer. . . . . 23

M.Sc. Thesis Woutijn J. Baars, BSc. List of Figures xi

3-1 Low-speedwindtunnelfacilityatUTAustin...... 24 3-2 Experimentalsetupinthewindtunnel...... 25 3-3 Aircraft model with ice simulation and instrumentation...... 26 3-4 Effect of increasing Reynolds number on boundary layer flow...... 28 3-5 Drag characteristics as function of Reynolds number and tripperstrips...... 29 3-6 Sensor arrangement on the aircraft model...... 30 3-7 Pressuretransducersetup1and2...... 31 3-8 Schematicofthedataacquisitionsystem...... 31 3-9 Auto-correlation coefficients for accelerometers...... 34 3-10 Auto-correlation coefficients for pressure transducers...... 35 3-11 Relative standard errors of the mean for transducers...... 36 3-12 Identification of natural modes of the experimental system...... 37

4-1 Tacoma Narrows bridge torsional motion just prior to failure...... 39

4-2 Auto power spectra of accelerometer 4 as function of αp...... 40

4-3 Power of accelerometer 4 as function of αp...... 41 4-4 LTImodelinthetime-domain...... 41 4-5 Linear coherence spectra, accelerometer 4 - pressure transducerA...... 43 4-6 Single-I/O HOS system modeling approach in the frequency-domain...... 45 4-7 Schematic of the implementation of the Volterra model technique...... 49 4-8 Auto power spectra in the Monte Carlo Simulation...... 50 4-9 Monte Carlo Simulation, LSE, QSE and coherence spectra...... 51 4-10 Auto power spectra in the turbulent mixing layer...... 51 4-11 Turbulent mixing layer, LSE, QSE and coherence spectra...... 53

5-1 Linear coherence spectra according to first-order technique,AC4-PTA. . . . . 57 5-2 Linear coherence spectra according to first-order technique,AC5-PTA. . . . . 58 5-3 Linear coherence spectra according to Volterra model technique, AC 4 - PT A. . 58 5-4 Higher-order coherence spectra, linear and quadratic, AC 5-PTA...... 60 5-5 Higher-order coherence spectra, interference and total, AC5-PTA...... 61

6-1 Schematicoverviewofresearch...... 64

M.Sc. Thesis Woutijn J. Baars, BSc. List of Tables

2-1 Dimensions of the elevator horn balance model...... 9

3-1 Parametersofsimilarity...... 28 3-2 Standard errors of the mean for transducers...... 34 3-3 Test matrix for the experimental investigation...... 36

5-1 Strouhal numbers of unsteady flow features...... 57

M.Sc. Thesis Woutijn J. Baars, BSc. Nomenclature

Greek Symbols α Angle of attack, [degr]

αp Angle of attack of aircraft, [degr] β Non-dimensional form of φ, [-] ∆f Frequency resolution of spectra, [Hz] δ Elevator deflection angle, [degr] δ Kronecker Delta function, [-] δ Non-dimensional parameter (Tate & Stearman, 1986), [-]

x Relative error in the estimator, [-] ε Depth parameter of wake velocity field, [-] ε(f) Modeling error in higher-order model, frequency-domain, [m/s2 s] ε(t) Modeling error in Linear Time Invariant (LTI) model, time-domain, [m/s2] φ Phase angle, [degr] φ Torsional DOF of elevator horn balance, [rad]

φ1 Phase angle of spectral peak in the input signal, [degr]

φ2 Phase anlge of spectral peak in the input signal, [degr] γ Ratio of specific heats, [-] 2 γAPP (f1, f2) Cross bicoherence, accel. a(t) and pres. p(t), [-] 2 γAP (f) Linear coherence spectrum, accel. a(t) and pres. p(t), [-] 2 γLQ(f) Coherence spectrum based on higher-order model, interference term, [-] 2 γL(f) Coherence spectrum based on higher-order model, linear term, [-] 2 γQ(f) Coherence spectrum based on higher-order model, quadratic term, [-] 2 γtotal(f) Coherence spectrum of higher-order model, combined, [-] η¯ Non-dimensional form of η, [-] η Geometry parameter of wake velocity field, [-]

M.Sc. Thesis Woutijn J. Baars, BSc. Nomenclature xiv

µ Dynamic viscosity of air, [kg/m/s] µ Dynamic viscosity of the free stream air, [kg/m/s] ∞ ρ Density of air, [kg/m3] ρ Density of the free stream air, [kg/m3] ∞ ρxx(τ) Auto-correlation coefficient of x(t), [-]

σx Standard deviation of x, [-]

σx,rel¯ Relative standard error of the mean of x, [-] σx¯ Standard error of the mean of x, [-] τ Time delay, [s]

τn Time delay related to order n, [s]

Ωf Structural acceleration frequency peak, [Hz] ωi Pressure frequency peak, [Hz]

ωj Pressure frequency peak, [Hz] Roman Symbols Aˆ(f) Higher-order model, f-domain, acceleration signal (output), [m/s2 s] aˆ(t) Linear Time Invariant (LTI) model, t-domain, accel. signal (output), [m/s2] a Non-dimensonal parameter to describe wake velocity field, [-] a Speed of sound, [m/s] A(f) Physical discrete, frequency-domain, acceleration signal (output), [m/s2 s] a(t) Physical discrete, time-domain, acceleration signal (output), [m/s2] 2 AL(f) Higher-order model, L, f-domain, acceleration signal (output), [m/s s] 2 AQ(f) Higher-order model, Q, f-domain, acceleration signal (output), [m/s s] b Non-dimensonal parameter to describe wake velocity field, [-]

bhorn Horn balance span, [m] bs Horizontal stabilizer span, [m]

c¯s Mean aerodynamic chord of the horizontal stabilizer, [m]

c¯w,model Mean aerodynamic chord of the aircraft model main wing, [m]

c¯w,real Mean aerodynamic chord of the aircraft wing, [m] c¯wing Mean aerodynamic chord of aircraft main wing, [m] c Aerodynamic chord length of airfoil, [m]

chorn Horn balance chord length, [m] cs,root Horizontal stabilizer root chord length, [m]

cs,tip Horizontal stabilizer tip chord length, [m]

CD0,min Minimum profile drag coefficient, [-] D Drag force, [N] D Jet exit diameter, [m]

dtu Minimum time interval to obtain uncorrelated samples, [s] e Non-dimensional distance between c.p. and e.c., [-]

el Non-dimensional distance between e.c. and c.g., [-]

M.Sc. Thesis Woutijn J. Baars, BSc. Nomenclature xv f (Discrete) frequency, [Hz] f1 Frequency of spectral peak in the input signal, [Hz] f2 Frequency of spectral peak in the input signal, [Hz] fb Blade passage frequency, [Hz] fs Sampling frequency, [Hz] fmax Maximum frequency expected in the measured signal, [Hz] g Gravitational acceleration, [m/s2] h Transfer function column vector, [m/s2/P a] h Altitude, [m] th Hn Higher-order model n -order Volterra operator, [-] 2 hn Higher-order model, t-domain, transfer kernel related to order n, [m/s /Pan sn] 2 HL(f) Higher-order model, frequency-domain, linear transfer kernel, [m/s /P a] 2 hL(t) LTI model, time-domain, linear transfer kernel, [m/s /P a] 2 HQ(f1, f2) Higher-order model, frequency-domain, quadratic transfer kernel, [m/s /P a] i Counter, integer, [-] J Advance ratio, [-] j Square root of minus one, complex number, [-]

k¯0 Non-dimensional parameter (Tate & Stearman, 1986), [-] k Ice horn height, [m]

Kφ Torsional spring stiffness for DOF φ, [N/rad] Kw Linear spring stiffness for DOF w, [N/m] L Lift force, [N] L Temperature gradient, [K/m]

LP Projected airfoil height, [m] LR Mean reattachment length of separation bubble, [m] M Mach number, [-] M Number of measurement samples in the data acquisition process, [-] N Number of Discrete Fourier Transform (DFT) coefficients, [-] N Number of independent measurement samples, [-] n(t) Noise introduced in the physical acceleration signal, [m/s2] st p¯θ(t) 1 Fourier mode of azimuthal unsteady pressures in jet flow, [P a s] p Polyspectral pressure column vector (input), [P a s] P Number of partitions in the process of ensemble averaging, [-] p Pressure of air, [Pa] p Total pressure, [Pa] P (f) Physical discrete, frequency-domain, pressure signal (input), [P a s] p(t) Physical discrete, time-domain, pressure signal (input), [Pa]

p0 Pressure of air at sea level, SA, [Pa] p Total pressure at free stream, [Pa] ∞ R Specific gas constant, [J/kg/K]

M.Sc. Thesis Woutijn J. Baars, BSc. Nomenclature xvi

Rxx(τ) Auto-correlation function of x(t), [-] Rel Reynolds number based on a characteristic length l, [-] 2 SAPP (f1,f2) Bispectrum of A(f) and P (f), [Pa s m/s] 2 SAP (f) Cross spectrum of A(f) and P (f), [m/sp P a s] SXX (f) Auto power spectrum of measured quantity x(t), X(f)= DF T [x(t)], [variable] Stl Strouhal number based on a characteristic length l, [-] T Sampling time, [s] T Temperature of air, [K] t Discrete time, [s]

T0 Temperature of air at sea level, SA, [K] TI Integral time-scale, [s] u(z) Gaussian approximation of wake velocity field, [m/s] 2 ucl(t) Unsteady jet centerline velocity, [m/s ] urms RMS stream wise velocity, [m/s] Vc Fuselage cross flow velocity, [m/s] V Free stream velocity, [m/s] ∞ Vcruise Cruise speed of the aircraft, [m/s] Vparallel Fuselage parallel flow velocity, [m/s] w Linear DOF of elevator horn balance, [m] x¯ True average of measured quantity x, [-] X X coordinate, aircraft reference frame, [-] x Measured quantity for sampling criteria analysis, [-] x(t) Discrete, time-domain, input signal (for the MCS), [-]

XM Estimator of measured quantity x, [-] Y Y coordinate, aircraft reference frame, [-] y(t) Discrete, time-domain, output signal (for the MCS), [-]

yL(t) Linear estimate of, time-domain, output signal (for the MCS), [-] yQ(t) Quadratic estimate of, time-domain, output signal (for theMCS), [-] Z Z coordinate, aircraft reference frame, [-] z Coordinate along the centerline of the jet, [-]

M.Sc. Thesis Woutijn J. Baars, BSc. Acronyms

AC Accelerometer. AD Airworthiness Directive. AE Aerospace Engineering and Engineering Me- chanics. AOPA Aircraft Owners and Pilots Association. ASF Air Safety Foundation.

BMF Bandwidth Moving Filter.

c.g. Center of Gravity. c.p. Center of Pressure. CFR Code of Federal Regulations. CPU Central Processing Unit.

DFT Discrete Fourier Transform. DOF Degree of Freedom. DUT Delft University of Technology.

e.c. Elastic Center. ECE Electrical & Computer Engineering.

FAA Federal Aviation Administration. FAR Federal Aviation Regulation.

HOS Higher-Order Spectra.

I/O input/output.

M.Sc. Thesis Woutijn J. Baars, BSc. Acronyms xviii

LCO Limit Cycle Oscillation. LDA Laser Doppler Anemometer. LHS Left Hand Side. LSE Linear Stochastic Estimation. LTI Linear Time Invariant. LWC Liquid Water Content.

MCS Monte Carlo Simulation. MDD Mean Droplet Diameter. MSL Mean Sea Level. MW Multi-Weibull.

NACA National Advisory Committee for Aeronau- tics. NASA National Aeronautics and Space Administra- tion. NI National Instruments. NTSB National Transportation Safety Board.

PIV Particle Image Velocimetry. PT Pressure Transducer.

QSE Quadratic Stochastic Estimation.

RHS Right Hand Side. RMS Root Mean Square.

SA Standard Atmosphere. SR Safety Recommendation.

TACC Texas Advanced Computing Center. TKS Tecalemit Killfrost Sheep-bridge-Stokes.

UT Austin The University of Texas at Austin.

VG Vortex Generator.

WFA Weibull Failure Analysis.

M.Sc. Thesis Woutijn J. Baars, BSc. Chapter 1

Introduction

Ice accumulation on aircraft, and the resulting aerodynamic unsteadiness and possible sta- bility upsets of the entire aircraft, are undesired. Research on these upsets are of high im- portance, since ice protection systems are not able to totally eliminate the presence of ice accumulation on aircraft. Ice-induced stability upsets of small general aviation aircraft, and an experimental investigation related to this topic, are presented in this work.

1-1 Background

Aircraft flying at subsonic speeds are subject to ice formation on all frontal surfaces when exposed to icing conditions. Structural ice formation on the leading edges of wings and control surfaces can initiate significant regions of unsteady flow (Bragg, Whalen, & Lee, 2002). These regions over the aerodynamic surfaces alter their performance. This type of damage to the lifting surface can result in a major change in handling of the aircraft; the aircraft may stall at higher speeds, the stall angle of attack may decrease and irreversible upsets can occur (ASF-AOPA, 2008). Therefore, ice formation is a significant threat to aircraft safety. In the period of 1990 - 2000, a total of 3, 230 aircraft accidents were recorded by the Aircraft Owners and Pilots Associations (AOPAs) Air Safety Foundation (ASF). 388 (12%) were related to icing. Fatalities were involved in 105 (27%) of those ice-related accidents (ASF-AOPA, 2008). One of the small general aviation aircraft that has safety issues, when exposed to icing conditions, is the Cessna 208B Grand Caravan, which is under close review by the National Transportation Safety Board (NTSB) and Federal Aviation Administration (FAA). Since its introduction in 1984, 158 incidents oc- curred and were reported by the NTSB. 55 incidents, almost 35%, were related to ic- ing. Several Safety Recommendations (SRs) were sent by the NTSB to the FAA as dis- cussed by Endruhn, Stearman, & Goldstein (2006). In March 2005 the FAA stated in an Airworthiness Directive (AD) that ”an unsafe condition was likely to exist” when flying this aircraft in icing conditions (FAA-AD, 2005). The last SR was given on January 17th 2006 by the NTSB, suggesting that this aircraft should be restricted to allow flight into light, instead

M.Sc. Thesis Woutijn J. Baars, BSc. 1-1 Background 2 of moderate, icing conditions only (the aircraft was certified in 1986 by the FAA and was originally certified to fly in moderate icing conditions). Most of the accidents occur during the approach and landing phase (FAA-AD, 2005; NTSB-SR, 2004, 2006), where the aircraft is flying at a higher angle of attack, αp, when compared to cruise flight. Furthermore, studies on ice-related accidents of small general avi- ation aircraft revealed that in many cases even the most experienced pilots have less than 5 to 8 minutes to escape the harmful icing conditions before their aircraft experiences violent upsets. This indicates that in cruise the ice accumulation, and associating effects on stability, remain mostly unobserved. When changing the attitude of the aircraft to a higher angle of attack, the ice induces unsteady flow phenomena that are able to upset the aircraft. After reviewing two NTSB SRs (NTSB-SR, 2004, 2006), ADs from the FAA (FAA-AD, 2005), and two pilot reports presented by Endruhn et al. (2006), two ice-induced aircraft destabilizing mechanisms have been identified for study. The plausible failure mechanisms are presented in this thesis. In both destabilizing mechanisms a part of small general aviation aircraft that is involved is the elevator horn balance. The elevator horn balance is located at the tip of the horizontal stabilizers as indicated in Figure 1-1 and 1-2, and acts as an aerodynamic/mass balance that lowers the pilots control force needed to deflect the elevator. The horn balance is relatively long when compared to the control surface length; that results in a significant exposure of the leading edge of the horn balance to the freestream flow when the elevator is slightly deflected. This is the case during, for example, a climb maneuver or flare just before touchdown, which are the phases of flight where most of the accidents occur.

Z RHS elevator horn

X

Y

LHS elevator horn

Figure 1-1: Location of the elevator horn balances on the aircraft.1

The first destabilizing upset scenario, a loss of elevator control effectiveness, involves an elevator Limit Cycle Oscillation (LCO), caused by an ice-induced unsteady flow field that locks-in with the motion of the relative flexible horn balance. The second upset mechanism results in a violent wing rock2 or unstable Dutch roll3 event, caused by a coupling event between the ice-induced separated flow field behind the elevator horn balance and the fuselage

1picture: Cessna Aircraft Company (http://www.cessna.com/caravan/grand-caravan/grand-caravan- gallery.html, retrieved 14 March 2009). 2Alternately one side of the aircraft stalls and recovers. 3Instability caused by flow mechanisms that initiate a yaw or roll motion. The yaw motion then initiates a roll motion due to the difference in lift generated by the wings which initiate a reversed yaw moment. This cycle continues, resulting in an oscillating instability.

M.Sc. Thesis Woutijn J. Baars, BSc. 1-2 Motivation 3

fixed hor. stabilizer

elevator hinge line

X

Y elevator

Figure 1-2: Bottom view. Schematic of LHS horizontal stabilizer and location of elevator and horn balance. cross flow. Although the aircraft that are certified to fly in icing conditions are equipped with anti-icing and de-icing devices, that are respectively preventive and repressive ice protection systems, it is still possible that the ice-induced upsets occur. Namely, those systems partly prevent the effects of ice accumulation and not totally eliminate the ice accumulation and associated effects. The upsets can occur through remaining ice on the wing and stabilizers after a few boot de-icing cycles, so-called residual icing, or through icing that builds up in between the de-icing cycles, so-called intercylce icing. Furthermore, the elevator horn balance is rarely equipped with an anti-ice protection system.

1-2 Motivation

The discussion above indicates that flying small general aviation aircraft in icing conditions can be dangerous. There is an urgent need to identify the exact source of the ice-induced aircraft stability and control upsets. Research on the fluid mechanics phenomena that lead to the stability and control upsets of those aircraft can provide useful knowledge to solve this in-flight safety issue. The proposed ice-induced upset mechanisms are presented in this thesis based on a literature survey and previously conducted experiments. Lock-in mechanisms between two unsteady events occur in both mechanisms, (1) the ice-induced unsteady flow field and (2) the unsteady structureal acceleration of the aircraft. The lock-in mechanism of the structural acceleration and the unsteady flow field induced by ice accumulation that is only present on the elevator horn balance leading edges is investigated in more detail. Flow-induced vibration and lock-in identification have been studied theoretically, as presented in the work by Blevins (1977). However, those analyses are limited to simple geometries like a cylinder or sphere, and will fail when dealing with relative complex geometries of the ice accumulation, horn balance and aircraft structure. Therefore, the motivation of the current research is to experimentally investigate the nature of the possible fluid-structure lock-in mechanisms. The field of research is schematically indicated in Figure 1-3 by three blocks. The ice accumulates on the aircraft structure (block A) that initiates an unsteady flow field (block B). The flow field unsteadiness and aircraft structureal acceleration (block C) could have signatures of coherence, meaning that a lock-in mechanism is present between them. Previous experimental research (block A & B) has been conducted on the process of ice accu-

M.Sc. Thesis Woutijn J. Baars, BSc. 1-2 Motivation 4

A B C

ice accumulation ice-induced unsteady flow aircraft

elevator horn balance

Figure 1-3: Schematic overview of research.

mulation and the (unsteady) flow phenomena resulting from this accumulation. Most research was performed on airfoils only, as presented in Section 2-2. Research on the entire aircraft (block C) can be performed by full-scale flight testing. Flight testing in icing conditions or with simulated icing shapes is time consuming, costly and dangerous because of the unknown change in aircraft performance. Furthermore, it is impossible to capture the ice-induced un- steady flow field behind the aircraft which is needed for the study towards fluid-structure lock-in mechanisms. The motivation of the current research is to acquire knowledge about the relation between block B and C, while the previous research was mostly limited to either block A, B or C. Endruhn et al. (2006) investigated the lock-in mechanism experimentally, using a 1:10 scale, dynamic-cable-mounted, 6 Degree of Freedom (DOF) model. However, the results were questionable due to experimental difficulties associated with a dynamically supported model, and likewise, the lack of capturing the unsteady flow field behind the flying aircraft model.

Previous research suggests that the lock-in appears to be mostly of the non- linear type (Park, Stearman, Kim, & Powers, 2008; Kruger, Endruhn, & Stearman, 2005; Tate & Stearman, 1986). Therefore, the current work considers the linear and non-linear coupling mechanisms in this fluid-structure lock-in identification study. The linear coherence between a single-point pressure measurement in the wake of the structure and a single struc- tural acceleration measurement, can be computed using single-I/O system identification tech- niques in the time-domain. These techniques were used in turbulent flow research, where the first-order techniques, dubbed Linear Stochastic Estimation (LSE), were investigated early on by Adrian (1979) and Adrian & Moin (1988) to demonstrate the presence of coherent structures in a turbulent shear flow. Extensions to these techniques have been developed and presented by Ewing & Citriniti (1997), Naguib, Wark, & Juckenh¨ofel (2001), Tinney et al. (2006) and Durgesh & Naughton (2007). In particular, Ewing & Citriniti (1997) performed a comparative between the single-time LSE and the multi-time LSE (effectively a frequency- domain approach), concluding that the multi-time LSE resulted in remarkably better es- timations. Tinney et al. (2006) later dubbed this spectral LSE, a frequency-domain tech- nique. This technique is similar to the first-order technique in the field of statistical signal processing that is based on cross spectra and auto power spectra (Bendat & Piersol, 1980; Otnes & Enochson, 1987). The reason for such remarkable differences between the time- domain LSE and the spectral LSE are two fold. The first is that the time delay between the

M.Sc. Thesis Woutijn J. Baars, BSc. 1-3 Approach of Thesis Work 5 two unsteady events is not uniquely defined. The spectral technique avoids this by trans- forming the time-domain signals to the frequency-domain. Secondly, the shift in time-scale between the input and output event of a system are embedded in the computations. The LSE technique identifies the one-to-one resonance between the input and output of the system. However, the non-linear relations, where multiple spectral peaks in the in- put signal’s power spectrum excite the output signal through a non-linear sense, are al- leviated in this first-order analysis. A second-order technique, capable of identifying quadratic coupling signatures, was introduced in the area of turbulent flow research as time- domain Quadratic Stochastic Estimation (QSE). This technique was recently investigated by Naguib et al. (2001) where it was shown that QSE is more powerful when dealing with systems where the physical process is driven by a non-linear coupling. The motivation of this research is to introduce a higher-order system identification technique in the field of fluid mechanics, that is capable of finding higher-order coherences in a single-I/O system. This technique can eventually be used as spectral QSE technique in (turbulent) flow research.

1-3 Approach of Thesis Work

This thesis work, with the subject of flying small general avaition aircraft in icing conditions, has the objective

to propose ice-induced destabilizing mechanisms of small general aviation aircraft and to experimentally investigate the linear and non-linear, fluid-structure, lock-in phenomena resulting from ice accumulation on the elevator horn balance leading edges.

This objective comprises the following items during the study:

Conduct literature survey on the ice accumulation and resulting (unsteady) flow phe- → nomena, related to aircraft applications.

Propose ice-induced destabilizing mechanisms for small general aviation type aircraft → based on literature survey, NTSB-, FAA-, and pilot-observation-reports.

Conduct data acquisition experiments in the wind tunnel using a representative aircraft → model to obtain data sets by synchronously measuring the acceleration of the aircraft model and the pressure fluctuations in the (ice-induced) unsteady flow field downstream of the aircraft. Measurements will be performed at various angles of attack of the aircraft and elevator deflection angles, and with and without ice simulations on the elevator horn balance leading edges.

Present a general system identification technique that is capable of identify- → ing linear and non-linear coherences in a single-I/O system. This techniqure is based on Higher-Order Spectra (HOS) statistical processing to identify the higher-order coherences between the I/O signal. An outline of those tech- niques as well as demonstrations of the techniques can be found in the litera- ture (Boashash, Powers, & Zoubir, 1995; Im, Kim, & Powers, 1993; Im & Powers, 1996;

M.Sc. Thesis Woutijn J. Baars, BSc. 1-4 Outline of Thesis 6

K. I. Kim & Powers, 1988; S. B. Kim & Powers, 1993; Nam, Kim, & Powers, 1989; Nam & Powers, 1994; Nikias & Petropulu, 1993; Powers, Im, Kim, & Tseng, 1993; Fitzpatrick, 2003). This technique is the foundation for future spectral QSE techniques in (turbulent) flow research.

Apply the system identification techniques to the pressure-acceleration data set to iden- → tify and investigate the nature of the lock-in mechanisms. The frequency range and angle of attack range of the aircraft, for which a linear and non-linear fluid-structure lock-in mechanism occurs, are computed for the case with and without ice simulations on the horn balance leading edges.

Present the results and make concluding remarks concerning the analyses and the sta- → bility and control upsets of aircraft.

1-4 Outline of Thesis

A literature survey is presented in Chapter 2, on relevant features of the small general avi- ation type aircraft, followed by a review of ice accumulation characteristics and the induced unsteady flow phenomena. This chapter ends with a description of the proposed ice-induced destabilizing mechanisms, presented in Section 2-3. Chapter 3 outlines the experimental in- vestigation by describing the experimental hardware and the data acquisition approach. The first-order and higher-order system identification techniques, to identify the lock-in mecha- nisms, are presented in Chapter 4. The results of applying these techniques to the pressure- acceleration lock-in identification problem are presented in Chapter 5, as well as the effect of the lock-in mechanisms on the stability and control of aircraft. Chapter 6 concludes this thesis by presenting the concluding remarks and recommendations for future work.

M.Sc. Thesis Woutijn J. Baars, BSc. Chapter 2

Ice-Induced Stability & Control Upsets

This chapter presents relevant features of the small general aviation type aircraft, followed by a review of ice accumulation characteristics and the induced unsteady flow phenomena. The proposed ice-induced destabilizing mechanisms are presented in Section 2-3.

2-1 Small General Aviation Aircraft

The small general aviation aircraft are Part 23 FAA Federal Aviation Regulation (FAR) cer- tified aircraft, that are mostly propeller driven vehicles with features somewhat different than found on the larger Part 25 FAR aircraft that are more often turbine powered and much higher performance aircraft. With the increasing take-off and landing cycles each year, the small general aviation aircraft are statistically more exposed to potential icing conditions for a greater percentage of flight time than aircraft flying longer routes and at higher altitudes, such as the larger, Part 25 FAR, jet aircraft. Although Part 23 aircraft are certified to fly in icing through 14 Code of Federal Regulations (CFR) Part 23, this 14 CFR Part 23 refers to the 14 CFR Part 25 appendix for icing certification, so the icing requirements are equivalent. However, some differences are found between Part 23 and 25 aircraft. In a Part 23 aircraft, for example, the flight control systems are generally activated directly by pilot manual input and are reversible. The control systems are not of the hard hydraulic irreversible type that are typically found on fighter aircraft and larger Part 25 aircraft. The implication is that the general aviation control surfaces can be activated by hand through a manual oscillation or movement of the trim surfaces. This cannot be done on aircraft with irreversible controls. From the point of view of aircraft upset events, an aerodynamic input external to the pilot, such as an aerodynamic gust, can force the controls into an action that could overpower the pilot control input when the aircraft has reversible controls. This could upset the stability and control of the total aircraft.

M.Sc. Thesis Woutijn J. Baars, BSc. 2-1 Small General Aviation Aircraft 8

2-1-1 Ice Protection Systems

The formation of ice on aircraft is categorized in two groups: structural icing and induction system icing. Structural icing is icing that forms at critical, external, surfaces. Induction system icing is icing in the carburetor of the engines or ice formations that block the air intake. Almost 40% of the icing accidents in the period 1990 - 2000 were associated with structural icing. Although induction system icing is causing most of the icing accidents (52%), the ice protection systems presented in this section are designed to protect the aircraft from structural icing only, since structural icing can cause stability and control upsets. The remaining 8% of the accidents is due to ice accumulation when the aircraft is stationed on the ground (ASF-AOPA, 2008). The aircraft certified to fly in icing conditions are equipped with anti- or de-icing systems that are able to de-ice the leading edges of the wings and horizontal and vertical stabilizers. The (turbo)-prop aircraft are mostly equipped with pneumatic de-icing boots on the leading edges of the wings, wing struts, and horizontal and vertical stabilizers. The boots, schematically indicated in Figure 2-1, can expand and contract using pressure from the engine bleed-air system. These systems are designed to remove ice accumulation in flight rather than prevent the formation of ice.

(a) (b)

Figure 2-1: Leading edge de-icing boots. (a) boot is not in operation, (b) boot is inflated to break of the structural ice accumulation (ASF-AOPA, 2008).

Some aircraft are equipped with the more advanced ice protection system that is available on the market. The Tecalemit Killfrost Sheep-bridge-Stokes (TKS) ice protection system is an anti- and de-icing system. The system squeezes ethylene glycol-based fluid through laser drilled porous titanium panels attached over the airfoil leading edges (Figure 2-2a), hereby preventing the formation of ice. Using 6.5USgallons (25liter) a typical TKS system, on a small aircraft (Cessna 172- or Beechcraft Baron-type), can be continuously operated for 2.5 hours. Jet aircraft are usually equipped with heated wings. Bleed air from the jet engines heat the leading edges of the wings through air slots as indicated in Figure 2-2b.

2-1-2 Elevator Horn Balance

The elevator horn balance is a combined aerodynamic/mass balance, usually found in the class of small general aviation aircraft, with the purpose of lowering elevator control forces and alleviating low flutter speeds associated with control surfaces found in the reversible

M.Sc. Thesis Woutijn J. Baars, BSc. 2-1 Small General Aviation Aircraft 9

(a) (b)

Figure 2-2: (a) TKS porous laser drilled titanium leading edge panel (ASF-AOPA, 2008), (b) Leading edge of a heated wing (NASA Ames).

Table 2-1: Dimensions of the elevator horn balance model (part of total aircraft model, see Sec- tion 3-1-2).

Variable Dimension [m] Variable Dimension [m] k 0.007 bs 0.299 bhorn 0.015 cs,root 0.127 chorn 0.067 cs,tip 0.076

control systems. The balance is located at the tip of the horizontal stabilizer, as indicated in Figure 1-1. A schematic representation of the horizontal stabilizer and elevator horn balance geometry, indicating the angle of attack of the aircraft, αp, and elevator deflection angle, δ, is shown in Figure 2-3.

simulated ice accumulation Z X fixed horizontal stabilizer bhorn

X Y fixed hor. stabilizer cs,tip αp elevator

V∞ −δ cs,root c elevator hinge line horn LP

k elevator horn balance bs elevator (a) (b) Figure 2-3: (a) Side view from tip. Schematic of LHS elevator horn balance, (b) Bottom view. Schematic of LHS horizontal stabilizer and location of elevator, horn balance, and simulated ice accumulation. Dimensions are presented in Table 2-1.

In the de-icing philosophy of ice protection on horn balances, no inflatable de-icing boots are employed since their activation causes significant control hinge moment variations that upset the aircraft trim conditions in cruise flight. On the other hand, when using the TKS ice protection system, no such problems exist. Aerodynamic control horns are currently using the TKS ice protection system successfully.

M.Sc. Thesis Woutijn J. Baars, BSc. 2-1 Small General Aviation Aircraft 10

2-1-3 Wing Root Leading Edge Shoulder

Next to the elevator horn balance, the wing root vortex pair is a relevent feature in this study. The vortices are originated at the wing root/fuselage junctions. These vortices are the result of the trailing edge flow at the wing root of the main wing that has the tendency to flip over to the relative low pressure side of the fuselage, the top side. Therefore, the orientation of the two wing root vortices are equivalent to the well-known wing tip vortices. In addition, some small general aviation aircraft increase the strength of the wing root vortices due to the vortices trailing off from the so-called ’shoulders’ at the wing root leading edge/fuselage junctions, as indicated in Figure 2-4. These shoulders act as an ’inboard’, second, wing tip. It is believed that those shoulders are added to generate extra vortex lift, since elliptical shaped bodies at a slight angle of attack with respect to the incoming flow, generate significant lift.

Figure 2-4: Shoulder on the RHS of the aircraft main wing root/fuselage junction.

Water tunnel studies, conducted by Stearman, Goldstein, & Endruhn (2005) on a represen- tative 1:32 scale aircraft model, confirmed the existence of the wing root vortex pair. Similar studies were performed in the wind tunnel, where quantitative stream wise velocity contours were obtained using a total head pressure rake (Stearman et al., 2005). The vortical regions show up as low pressure zones. The vortex pair would trail below the horizontal stabilizers at αp = 0◦, as indicated in Figure 2-5a. When increasing the angle of attack to αp = 6◦, the vortex pair would trail at the same level as the horizontal stabilizers, as shown in Figure 2-5b. For αp = 10◦, the vortex pair is clearly located above the horizontal stabilizers and next to the vertical tail plane as shown in Figure 2-5c. Furthermore, it was observed that when the aircraft is in a conventional landing approach or climbing mode, the vortex pair would be above the horizontal stabilizers and next to the vertical stabilizer (Endruhn et al., 2006). (a) (b) (c) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Figure 2-5: Total pressure ratio, 1 p/p∞, contour plots downstream of the aircraft model, ◦ − ◦ ◦ Rec¯wing = 85, 000, (a) αp = 0 , (b) αp = 6 , (c) αp = 10 (Stearman et al., 2005).

A third important feature of small general aviation aircraft are the commonly present drip plates mounted above the rear doors of the fuselage, as indicated in Figure 2-6.

M.Sc. Thesis Woutijn J. Baars, BSc. 2-2 Ice Accumulation Characteristics 11

drip plate shoulder

elevator horn balance

Figure 2-6: ’shoulder’, drip plate and elevator horn balance on the LHS of a small general aviation aircraft.1

Those drip plates act as gurney flaps2 relative to the cross flow, to ensure that the separation points of the cross flow around the fuselage are fixed. The cross flow, Vc, is present when the aircraft is flying at an angle of attack, as schematically indicated in Figure 2-7. The trailing edge vortical unsteadiness originating from the wing root, as discussed above, is further aggravated when the fuselage chines or drip plates ice up. The blunted chines can no longer hold these two wing root trailing vortices to the fuselage.

Z simplified fuselage

X cross flow vortex shedding event

V parallel Y Vc αp

V∞

combined cross flow and parallel flow

Figure 2-7: Fuselage cross flow schematic.

2-2 Ice Accumulation Characteristics

Structural ice that accumulates on the surfaces of aircraft is generalized into three categories: glaze ice, rime ice and mixed ice (ASF-AOPA, 2008). Clear ice or glaze ice is the result of large water droplets. It is most likely to form in freezing rain or when super-cooled water droplets are present in the atmosphere. The super-cooled, liquid, water droplets will freeze when they get in contact with a surface of which the temperature is below 0◦C. During the freezing process, part of the water droplets flow downstream. The result is solid, clear, glazed ice. The characteristics of glaze ice are that no or little air is entrapped in the ice accretion, the surface is smooth, and it is hard to remove. Rime ice forms when little, super- cooled, water droplets freeze on the surface. Because of the smaller droplet size, the entire droplet will freeze almost instantaneously and no water will flow downstream. The result is

1picture: Cessna Aircraft Company (http://www.cessna.com/caravan/grand-caravan/grand-caravan- gallery.html, retrieved 14 March 2009). 2A gurney flap is a profile (L-shape) placed in chordwise direction at the bottom trailing edge of a relative thick airfoil/wing to ensure a fixed location of the separation point, namely, at the sharp edge of the L-bracket.

M.Sc. Thesis Woutijn J. Baars, BSc. 2-2 Ice Accumulation Characteristics 12 a mixture of tiny ice particles and entrapped air. The characteristics of rime ice are that the ice is brittle, the surface is rough, it has a white color, and it is relatively easy to remove by the de-icing systems. Mixed ice occurs due to the presence of large water droplets (glaze ice formation) and small water droplets (rime ice formation). Most ice that is encountered is of this form. When flying in mixed icing conditions, it is common for the ice to accumulate in the form of an ice horn normal to the surface, as shown in Figure 2-8 on a tail leading edge of a National Aeronautics and Space Administration (NASA) test aircraft.

Figure 2-8: Mixed ice accumulation on the tail of a full-scale NASA test air- craft (Tailplane Ice on Twin Otter Flight, 1992).

Unique wind tunnel experiments in icing conditions were conducted at the NASA Glenn Research Center icing tunnel by Wilson (1967) on a horizontal tail, shielded, horn bal- ance. One of the experiments was performed at a free stream velocity of 90m/s and in sub zero temperatures ( 10 C). The horizontal stabilizer was set at α = 0 while the − ◦ ◦ horn balance was deflected by δ = 4 . The Mean Droplet Diameter (MDD) and the − ◦ Liquid Water Content (LWC) were 15 and 1.2, respectively. The experiments showed sig- nificant accumulation of ice in the form of ice horns, on both the leading edge of the stabilizer and the lifting surface of the horn balance. An illustration of the ice formation after a 5 and 7 minute exposure to the icing conditions is shown in Figure 2-9a and 2-9b. After 8 minutes the horn balance started to show a significant sub-critical-flutter event denoted as a LCO. Wind tunnel studies performed by Tate & Stearman (1986), using simulated icing, have demonstrated this LCO behavior. Actually, this control horn LCO was first observed on a Fokker FR-1 brought to the front during World War I in September of 1917 (Kruger et al., 2005).

(a) 5 min. exposure (b) 7 min. exposure

Z

X

Figure 2-9: Horizontal tail, shielded, horn balance tested in the NASA Glenn icing tunnel by Wilson (1967).

Several studies have been performed on the (unsteady) effects of simulated ice accretions on the leading edges of airfoils (J. J. Jacobs & Bragg, 2007; Gurbacki & Bragg, 2002, 2004; Broeren, Addy, & Bragg, 2004; Khodadoust, 1988; Bragg & Khodadoust, 1992). The flow

M.Sc. Thesis Woutijn J. Baars, BSc. 2-2 Ice Accumulation Characteristics 13 features are schematically indicated in Figure 2-10. The air flow around the upper ice horn (on the lifting surface of the airfoil) separates due to an adverse pressure gradient. A re- circulation region is present downstream of the ice horn followed by a reattachment region and a vortex shedding event from the shear layer (J. J. Jacobs & Bragg, 2007). The char- acteristics are consistent with the well-studied backward-facing step flows such as in review by Eaton & Johnston (1981).

vortex shedding shear layer primary eddy corner eddy reattachment zone

lifting surface Z V∞ LR X ice accumulation

Figure 2-10: Schematic of ice-induced flow features on an airfoil with leading edge ice accumu- lation, duplicate from Gurbacki & Bragg (2004).

J. J. Jacobs & Bragg (2007) investigated the separation bubble on a National Advisory Committee for Aeronautics (NACA) 0012 airfoil with simulated, lead- ing edge, glaze ice accretions, at a chord Reynolds number of Re = 0.9 106, using c · Particle Image Velocimetry (PIV). The time-averaged flowfield behind the ice horn is shown in Figure 2-11a. The presence of the clockwise recirculation region behind the ice simulation and small counter-rotating eddy in the lower left corner are consistent with the backward-facing step flows. Figure 2-11b presents the Root Mean Square (RMS) stream wise velocity normalized by the free stream velocity to indicate the shear layer. The shear layer fluctuations decrease after reattachment.

(a) (b)

Figure 2-11: PIV study on the ice-induced separation bubble, (a) Mean streamlines, α = 0◦, –: separation (upper), stagnation (lower) streamline, (b) RMS stream wise velocity, urms/V∞, α = 0◦ (J. J. Jacobs & Bragg, 2007).

The studies conducted by Gurbacki & Bragg (2002) on a NACA 0012 airfoil (Re = 1.8 106) c · with leading edge ice simulations showed an increase in mean reattachment length (the length of the separation bubble), LR, with increasing angle of attack. At α = 0◦, the reattachment point was located at 0.13c, while at α = 8◦ the separation bubble extended over the full chord of the airfoil (J. J. Jacobs & Bragg, 2007; Gurbacki & Bragg, 2002). In the study

M.Sc. Thesis Woutijn J. Baars, BSc. 2-2 Ice Accumulation Characteristics 14

by Broeren et al. (2004) it was indicated that the ice simulation caused a large increase in LR at α = 6 . Furthermore, Bragg & Khodadoust (1992) concluded (NACA 0012, Re = 1.5 106) ◦ c · that at α = 6◦ the bubble is highly unstable and at α > 6◦ the flow is unable to overcome the adverse pressure gradient, resulting in an intermittent reattachment of the flow or no reattachment at all. This bubble bursting phenomenon can initiate a premature airfoil stall across the entire span (J. J. Jacobs & Bragg, 2007; Khodadoust, 1988) at α = 6◦ (the stall angle of attack for a clean NACA 0012 airfoil is αstall = 16◦ (Abbott & Doenhoff, 1959)). Khodadoust (1988) performed a study where ice horn simulations were placed on both the lifting- and non-lifting surface. The separation bubble on the lifting surface was having a significant larger size than the bubble at the non-lifting surface. Similar results were found by Busch, Broeren, & Bragg (2008) who concluded that the horn at the non-lifting surface is less critical, because small geometry variations of this horn resulted in small variations of the drag coefficient only at low angles of attack. A qualitative wind tunnel visualization study was conducted at UT Austin by Newman et al. (2004) to validate the occurrence of unsteady flow events behind the simulated ice accumu- lation on a shielded elevator horn balance. The experiment was conducted on a small-scale horizontal stabilizer as is seen on small general aviation aircraft. The study was performed at a chord Reynolds number of Re = 1.7 105. The dimensions of the elevator horn bal- c¯s · ance are presented in Table 2-1. The profile of the horizontal stabilizer tip, and likewise the elevator horn balance, is a NACA 0009 airfoil. The root of the stabilizer has a NACA 0012 airfoil profile. Figure 2-12 and 2-13 present the flow visualization, using a smoke-wire, on the tip of the horizontal stabilizer for α = 0 and δ = 8 . The coherent type of span wise ◦ − ◦ vorticity structures and the flow separation are visible. From the rear view, Figure 2-12b, it was observed that the two dimensional span wise vorticity signatures were still present albeit the highly 3d flow effects at the stabilizer tip.

(a) (b)

separation Z hor. stabilizer tip vortex Y

Z stream wise vortex shedding

vortex shedding X

Figure 2-12: Flow visualization on a horizontal stabilizer with elevator and horn balance, (a) ◦ ◦ 5 side view, (b) view aft, α = 0 , δ = 8 , Rec = 1.7 10 (Newman et al., 2004). − ¯s ·

Unsteady flow features resulting from the ice induced separation bubble were experimentally investigated by Gurbacki & Bragg (2004) on a NACA 0012 airfoil. The first unsteady flow feature is quantified by a Strouhal number based on the free stream velocity, V , and the reat- ∞ tachment length, L , as St = f LR/V∞ = 0.53 0.73 (Gurbacki & Bragg, 2004). Figure 2-14 R LR · − presents StLR and LR as function of α. This unsteady flow feature is associated with the shear layer vortex structures (vortex movement in and aft of the shear layer) and is referred to as the regular mode. This mode was found by spectral analysis of time-dependent surface pressure measurements at c = LR. Likewise, spectral analysis of lift and moment coefficients,

M.Sc. Thesis Woutijn J. Baars, BSc. 2-2 Ice Accumulation Characteristics 15

smoke wire Z X

Y Y X

hor. stabilizer

coherent type structures camera travelling downstream top view

Figure 2-13: Flow visualization on a horizontal stabilizer with elevator and horn balance, α = 0◦, ◦ 5 δ = 8 , Rec = 1.7 10 (Newman et al., 2004). − ¯s ·

captured by a three component balance system, revealed the second unsteady flow feature,

corresponding to a Strouhal number of St = f LP/V∞ = 0.0048 0.0101 (Gurbacki & Bragg, LP · − 2004), where L is the projected airfoil height according to L = c sin(α), see Figure 2-3. P P · This mode is referred to as the low-frequency mode and is often associated with shear layer

flapping. The experimental results of StLP (α) are presented in Figure 2-15. Essentially, the experimental investigation for the current study, described in Chapter 3, is performed using the same analogy: (1) unsteady pressure measurements capturing the flow field and (2) ac- celerometers capturing the structural acceleration. Gurbacki & Bragg (2004) did not present the linear and non-linear coupling between the two unsteady measurements. The unsteady quasi-harmonic motion of the structure can actually be a result of a non-linear lock-in of the structure with the unsteady quasi-harmonic, ice-induced, flow features.

α [degr]

Figure 2-14: First ice-induced unsteady flow feature, (a) Strouhal number of regular mode (Gurbacki & Bragg, 2004), (b) Flow characteristics on the NACA 0012 airfoil with 2d 6 glaze ice casting at Rec = 1.8 10 (Gurbacki & Bragg, 2002). · Low-frequency oscillations in the flow over a clean airfoil near stalling conditions were observed by Zaman, McKinzie, & Rumsey (1989). Although the studies were performed on a clean airfoil, this is relevant because at high angles of attack (α> 16◦) the ice horn has less to no influence because the airfoil has stalled or the flow is fully separated, absent of the adverse pressure gradient induced by the ice horn. The wind tunnel experiments were conducted at a chord Reynolds number range of Re = 0.15 105 3.0 105. Around α = 18 the ’bluff-body c · − · ◦ shedding’ occurs, quantified by a Strouhal number of StLP = 0.2, while at the onset of static stall, at around α = 15◦, a low-frequency periodic oscillation is observed with a corresponding

Strouhal number of StLP = 0.02 (Zaman et al., 1989).

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 16

α [degr]

Figure 2-15: Second ice-induced unsteady flow feature, Strouhal number of low-frequency mode (Gurbacki & Bragg, 2004).

The fundamental results from the experimental studies, that are discussed in this section, will be used in the interpretation of the experimental data. An attempt was made to relate some of the observed phenomena to those fundamental characteristics and physics.

2-3 Proposed Ice-Induced Destabilizing Mechanisms

This section starts by outlining the presence of multiple destabilizing/failure mechanisms of small general aviation aircraft accidents related to icing. Two failure mechanisms, introduced by pilot and witness reports, are selected for further discussion in the last two sections 2-3-2 and 2-3-3.

2-3-1 Identification of Multiple Failure Mechanisms

Published NTSB icing-related accident data of a representative small general aviation aircraft was used by Endruhn et al. (2006) to identify multiple failure mechanisms. Even though the NTSB accident data set has been prescreened to include only accidents occurring in the presence of atmospheric icing conditions, several failure modes are still known to be present. These different failure modes could involve icing induced tail stall, icing induced wing stall or malfunction of different elements of the de-icing systems, for example. The identification was accomplished by employing a Weibull Failure Analysis (WFA) according to the theory developed by Abernethy (2006). The objective of the analysis is to determine the number of failure modes that are embedded in the accident data set. For more reading about the WFA, the interested reader is referred to Baars, Stearman, & Tinney (2009). The so-called Multi-Weibull (MW) approach demonstrated that an estimated four failure modes are present in the data set consisting of 28 accidents. Two failure modes, identified in pilot reports to the FAA and NTSB, were chosen for further analysis. The first failure mode is initially triggered when the aircraft is flying at a normal cruise attitude. The upset occurred by a sudden onset of an elevator LCO, creating a ”flutter- ing” of the elevator control column. This LCO of the elevator stalled the aircraft and pitched

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 17 it over into a dive. A complete elevator control ineffectiveness occurred while being in the dive, with no way for the pilot to recover. In a last desperate move the pilot activated the de-icing system which initiates the tail boot de-icing system first. The removal of the tail ice re-established the elevator control and averted a fatal accident. A brief description of this ice-induced upset is presented in the following pilot report. Narrative, Upset Number I: (Pilot Report, 2003a) Acft. was in light rime ice at 9, 000ft Mean Sea Level (MSL). The wings and windshield were showing light rime ice accumulation, but not enough to warrant turning the boots on. The pitot static and prop heat were already on. The aircraft yoke started to flutter and almost immediately the aircraft stalled and pitched over into a dive. The elevator would not respond to any pilot elevator input, but only to pilot rudder and aileron input. I turned the pneumatic boots on while in the dive and regained elevator ctl. at approximately 4, 000ft MSL. I then proceeded to climb to 7, 000ft MSL where I remained for the rest of the flight at a temp. of +2 degs. C. The main reason I wanted to rept. this is that similar circumstances occured to me approx. 14 months ago. It would appear that the tail is accumulating more ice or is unable to carry as much ice as the main wing. Another pilot experienced a similar upset, making a total of three similar upset events reported by two pilots. The pilots had two major unknowns. First, in November 1991 the FAA and NASA realized that the stabilizers are generally a more efficient collector of ice than the wing, because of the smaller leading edge radii. Reports have been made of ice accumulation on the stabilizers that was 3 to 6 times thicker than ice on the wing (DoT, 1992). The pilots were only monitoring the wing and windshield, therefore, the icing was more extensive than they realized. Secondly, a difficulty occurred because little is known about the ice accumulation on Vortex Generators (VGs) and the exact mechanism as to how icing can disable their function. A VG is a type of passive control element for flow separation. The vortex generator is a small vane-type element mounted perpendicular to the surface of the wing at an angle of incidence with respect to the free stream flow. Just like a delta-wing at an angle of attack, the VGs create an array of stream wise trailing vortices that increase the momentum in the boundary layer close to the surface (Figure 2-18). A boundary layer with more momentum close to the surface is much more resistant to flow separation. As a result, the airflow remains attached to the surface resulting in better flight performances at lower airspeeds and high angles of attack and resulting in better control effectiveness (Artois, 2005; Lin, 1999). The VGs and their function is important in the discussion of this first upset, as is presented in Section 2-3-2. The second upset event has been experienced when the aircraft enters a climbing attitude to escape the icing conditions during cruise flight or during the take-off, for example. The accumulation of ice on the leading edges of the elevator horn balances is a strong possibility here due to the exposure of these leading edges to the free stream flow and the significant ice build up, as shown in Section 2-2 by Wilson (1967). The fact that no de-icing boots are employed on the control horns, complicate this issue. It is believed that the upset is (partly) caused by the iced-up elevator horns. The following narrative, indicating this upset during take-off, was extracted from ten on sight witness statements submitted to the NTSB. Narrative, Upset Number II: (Pilot Report, 2003b) Ten witnesses submitted written state- ments and their locations were plotted on a chart. Several of these witness observations were nearly identical. Witness 1 observed the airplane emerge from a 200 foot ceiling. ”It was rocking very badly from side to side. It rocked 2 to 3 times before diving 100 to 150 feet onto the highway and skidded into the lake.” Witness 2 saw the airplane ”bank to the left and then

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 18 bank to the right, then bank to the left, then took a hard bank to the right. The cockpit of the plane and the right wing hit the road ... (And the airplane) slid into the lake on its back and landed approximatley 30 feet into the water.” Witness 3 who was sitting in her office saw the airplane’s ”right wing go down sharply. It came back up and the left wing tipped down sharply. The left wing came up and the (airplane) flipped completely over.” A more quantitative identification of the violent Dutch roll instability can be found in NTSB-SR (2006) where a Russian aircraft was equipped with both a cockpit voice recorder as well as a flight data recorder that have quantitatively identified significant wing rock ex- cursions on the order of 40 degrees. It was concluded from conversations found on the voice ± recorder that significant icing was present on the aircraft, just prior to the wing rock or Dutch roll upset.

2-3-2 Upset Number I: Loss of Elevator Control Effectiveness

The category I upset described in the previous section caught the pilot off guard as he was not acquainted with the fact that tail plane icing accumulates 3 to 6 times thicker over time than ice on the main wing. By considering a free body diagram of the elevator control horn as a typical slender wing section, where drag caused by icing may be significant, one can rationalize a theoretical model of the form employed by Petre & Ashley (1976) for investigating drag effects on elevator (horn) flutter events. Tate & Stearman (1986) developed the analytical model, shown in Figure 2-16, to investigate the occurence of elevator (horn) flutter events without ice. L 2 ηz u(z) = V∞ 1 − εe D  

hor. stab. tip φ ec c.p. c elc shielded horn

e.c. wake c.g.

Kφ

φ w

Z 2 DOF system: w,φ

Kw X

Figure 2-16: Aeroelastic model for the slender, shielded, elevator horn balance in a Gaussian approximated wake velocity field u(z), duplicate from Endruhn et al. (2006).

The result of this analysis was the following equation of motion for the elevator horn

2 2 2 β” δ a bβ β0 + k¯ 2δ a bβ β = 0, (2-1) − − 0 − −
h
i M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 19

where β is a non-dimensional form of φ, a = (ε 1), b = εη¯/2!,η ¯ a non-dimensional − shear layer geometry, and δ & k¯0 are non-dimensional parameters. The reader is referred to Endruhn et al. (2006); Tate & Stearman (1986) for a complete discussion on the deriva- tion of this Van der Pol type equation of motion. From Figure 2-16 it is easy to rationalize why a LCO could be triggered for a sheltered control horn. That is, for the proposed model it is well-known that the equation of motion, Eq. (2-1), can exhibit relaxation oscillations (i.e. pulsing of the elevator horn, some times felt by the pilot in icing conditions) or a steady LCO possibly occuring at slightly higher velocities or for different icing parameters. This latter event is the case for the discussed category I upset event. For slender rectangular wings, the aerodynamic loads are impulsive in character and concentrated at the leading edge of the aerodynamic horn. By looking at Figure 2-16, simple statics tells us that for slender body airloads, the shear layer aerodynamics wants to suck the leading edge of the elevator horn out of the sheltering pocket of the stabilizer tip. Only sufficient elevator bending and torsional stiffness in the neighborhood of the horn geometry, friction in the control circuit, pilot input or a opposing force from the remaining elevator input can help prevent this from happening. Once the elevator horn pops out of the sheltering stabilizer pocket, the aerodynamic forces on the leading edge of the horn, based on slender body theory, will vanish once the leading edge is exposed to uniform flow. The elastic restoring forces move the horn back, producing a natural limiting amplitude and hence a LCO. This model does not incorporate the effects of icing on the drag term, but the superposition of an unsteady ice-induced drag term can only aggravate this upset event. To further understand the loss of elevator control effectiveness, reference is made to the book by (Thompson, 1992). The author comments on the Grand Caravan C208B development, hereby answering a question commonly asked by the layman and experts, concerning why a row of VGs is added to the horizontal stabilizer just ahead of the elevator hinge line. The answer of Thompson is: ”A unique problem of marginal nose-down elevator power was observed in transitional out-of-trim flight evaluations. This was alleviated by a single row of vortex-generators on the top surface of the horizontal tail just ahead of the gap between the stabilizer and elevator.” A lack of elevator nose down authority during a landing maneuver could give rise to an upset event during this critical transitional phase of flight. The answer of Thompson indicates that the VGs are a crucial element in non-cruise phases of flight. Since most of the upset number I aircraft icing accidents occur in the landing glideslope and flairing maneuver, and little is known about the influence of icing on VGs, a study was initiated at UT Austin. A limited number of comments found in flight test reports of small general aviation aircraft, indicated that the VGs, located upstream of the elevator hinge line, did not ice up to any degree of significance. Thus, the 3:1 to 6:1 tail-icing:wing-icing growth rate does not hold in the limit of smaller radii lifting surfaces, such as VGs, since the frontal area is too small for ice to deposit on. Then the question arises what mechanism is at work, if any, that nullifies the benefits of VGs? Results from an experimental wind tunnel study conducted at UT Austin, by Dearman & et al. (2007), can answer this question. Total pressure contours were acuiqred downstream of a 1:10 scale horizontal stabilizer, with VGs placed upstream of the elevator hinge line. Figure 2-17 (top) presents the total pressure contour downstream of the clean stabilizer. The generated vorticity of each vortex generater is clearly visible as the low pressure zones. When simulated residual plus intercycle icing is applied to the stabilizer, a complete annilition of the organized vorticity from the VGs is oberved as shown in Figure 2-17 (bottom). An examination of Figure 2-18 suggests that an overlay of spanwise vorticity, shed

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 20 off from the ice-induced shear layer, is interacting with the orthogonal vorticity created by the VGs. In essence, the orthogonal overlay of these two distinct vorticity fields annilate each other. This action then nullifies the benefit of the VGs, creating a loss of elevator pitch down control authority induced by icing conditions. Furthermore, if a LCO occurs, driven by the iced up elevator horns, a much stronger spanwise bound vorticity is being shed which will certainly annihilate the benefit of the VGs. A complete loss of elevator control authority is to be expected.

base case, no icing 0.5 0.55 0.6 0.65 0.7

leading edge residual plus inctercycle icing 0.75 0.8 0.85 0.9 0.95 1.0 Figure 2-17: Total pressure head contour plots downstream of a 1:10 scale horizontal stabilizer, ◦ ◦ 5 (cs,root+cs,tip) α = 0 , δ = 0 , Rec = 1.8 10 , where c¯s = (Dearman & et al., 2007). ¯s · 2

ice-induced vorticity field fixed horizontal stabilizer vorticity field from VGs

Z

X Y

elevator

see Figure 2-10

δ V∞

Figure 2-18: Schematic of the interaction between the ice-induced vortex field and the vortex field created by the VGs.

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 21

2-3-3 Upset Number II: Dutch Roll Instability

The Dutch roll instability or wing rock type of event has been observed in a number of acci- dents by several witnesses and has been experienced by at least one surviving pilot (FAA-AD, 2005; NTSB-SR, 2004, 2006; Endruhn et al., 2006). According to Hancock (1995), ”A key ingredient in wing rock is the loss of Dutch roll damping”. Wing rock can occur in at least three different forms which are itemized below:

1. Wing rock can occur in flow regimes where lag effects are not prominent, this form of wing rock is repeatable.

2. Wing rock can occur in flow regimes where lag effects due to onset of flow breakdown and reattachment, including vortex breakdown and reassembly, are prominent. This form of wing rock is sometimes random in occurrence with variations in amplitude. Forebody vortices can play an influential role in this type of wing rock.

3. Persistent small amplitude irregular oscillations in roll can be generated at high subsonic speeds by asymmetric fore and aft movements of shock waves on the upper surface of the wing.

The first type of wing rock is most likely the one that is influencing the small general aviation aircraft considered in this study, since the relevant vortices are not developed from a forebody, but are generated at the wing root/fuselage junction as discussed in Section 2-1-3. This implies that no prominent phase effects exist. This would allow a quasi-steady analysis, where the dynamic terms and airplane inertias in the equations of motion play a less important role. It has also been observed in aircraft with well damped stability and control modes that the precise value of their three major inertias are not so critical to the study of their wing rock phenomenon. The EA-6B Prowler, a twin-engine, electronic warfare aircraft, is exposed to stability and control upsets that were related to the pair of wing root vortices. Visualization studies were performed by Jordan, Hahne, Masiello and Gato (referenced by Bertin & Smith (1989)), in- dicating that a pair of vortices was generated at the wing root leading edge. At low angles of attack those vortices were located below the horizontal stabilizers, as presented in Fig- ure 2-19a. At angles of attack below the stall angle, the vortex pair trailed at the same location due to the wing downwash. However, at angles of attack close to the stall angle, where the downwash effect of the wing was significantly reduced by the flow separation over the wing, the vortex pair was located above the horizontal stabilizers next to the vertical stabilizer as indicated in Figure 2-19b. In case of a slight side slip, i.e. due to a gust, the vortex pair would flip over to one side of the vertical stabilizer, as indicated in figure 2-19c. The vertical stabilizer may now be exposed to unsteady net forces which directly impact the directional stability of the aircraft. A net force to the RHS will cause a yaw motion that can result in the stall of the left wing and will thus result in a roll motion; the wing rock or Dutch roll event is initiated. It is claimed that the Dutch roll instability of small general aviation aircraft, with significant wing root trailing vortex strength, involves an upset mechanism that is equivalent to that of the EA-6B Prowler. This is claimed to be due to the fact that both wing root vortices

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 22

(a) (b) (c)

Figure 2-19: Directional destabilizing mechanism of the EA-6B Prowler caused by the wing root vortex pair (Bertin & Smith, 1989). originate from the wing root leading edges and end up next to the vertical stabilizer, as was shown in Figure 2-5. The mechanism, which in combination with the EA-6B equivalent mechanism cause the Dutch roll instability, is made clear by a study that has been conducted at UT Austin on a 1:10 scale, powered, radio-controlled, dynamic-cable-mounted, 6 DOF model, shown in Figure 2-20. The purpose of this study was to demonstrate the possible stability and control upsets caused by ic- ing on the elevator horn balances only. Several experiments have been conducted by Endruhn (2006). When ice simulations were placed at the elevator horn balances, a violent wing rock instability or Dutch roll instability occurred when the aircraft was placed at approximate αp = 6◦ to αp = 10◦. When the model was flying at a lower angle of attack no wing rock instability occurred. Also, when no icing was simulated on the elevator horn balances no stability and control upsets were identified in any flight mode. Furthermore, it was shown that if the aerodynamic chines or drip plates above the rear doors were extended back along the fuselage, to about 0.5m (in full-scale size) forward of the leading edge of the horizontal stabilizers, the wing rock was suppressed. Highspeed camera screenshots, presented in Fig- ure 2-21, indicate that the wing root vortices become very violent when the lock-in mechanism occurs, as they flip over to the opposite side. In essence, the highspeed video taping of this event also indicated that the extended chines actually hold the vortices down and away from the vertical stabilizer, so no cross flow can induce yawing and rolling of the aircraft as shown in Figure 2-19c of the EA-6B aircraft.

Figure 2-20: Dynamic-cable-mounted aircraft model in the wind tunnel (Dearman & et al., 2007).

From the experimental study by Endruhn et al. (2006), it was also concluded that the Dutch roll instability is initiated by the cross flow vortex shedding event that breaks loose from the aerodynamic chines, resulting in a cross flow vortex shedding that locks-in with the unsteady ice-induced flow frequencies over the elevator horn balances. This phenomena can initiate the unsteady behavior of the wing root vortices and thus creates an upset event

M.Sc. Thesis Woutijn J. Baars, BSc. 2-3 Proposed Ice-Induced Destabilizing Mechanisms 23

(a) (b)

Figure 2-21: Highspeed camera screen shots indicating the violent pair of wing root vortices. The orange boxes highlight the tuft, attached to the farside of the fuselage just behind the trailing edge, flipping over to the nearside. that is similar to that of the EA-6B Prowler. To deal with the non-linear aspects of these interacting mechanisms, a bispectrum analysis (Section 4-3-3) was performed. Although the ice-induced unsteady flow phenomena had different frequencies (measured using a pressure transducer near the elevator horn balance as ωi = 10Hz and ωj = 20Hz, see Figure 2-20a) than the Dutch roll wing rock frequency (measured using accelerometers at Ωf = 1Hz), it was concluded that a lock in of these three separate frequencies occurred in a quadratic sense, only when icing was present on the horn balance leading edges (Endruhn et al., 2006). Figure 2-22 presents the bicoherence function, illustrating these events by the presence of spectral peaks at coordinates of (ω, Ωf ) = (10, 1)Hz and (ω, Ωf ) = (20, 1)Hz.

Ωf [Hz]

ω [Hz] Figure 2-22: Cross bicoherence function of the pressure transducer and z-component of the accelerometer when ice was simulated on the elevator horn balance leading edges, Ωf indicates acceleration and ω indicates pressure (Endruhn et al., 2006).

The previous tests conducted on the dynamic-cable-mounted model were limited in run time to the order of 10 - 20 seconds due to turbulence in the tunnel and difficulties to remotely control the aircraft. Furthermore, no data was available of the unsteady flow field behind the dynamic-cable-mounted aircraft model. The current experimental investigation, presented in the next chapter, is conducted to get a better quantitative insight about the lock-in mechanism of the structural acceleration and the ice-induced flow field over the elevator horn balance.

M.Sc. Thesis Woutijn J. Baars, BSc. Chapter 3

Experimental Apparatus

The wind tunnel facility, test model and data acquisition equipment are outlined in this chapter. Likewise, analyses concerning the justification of the scaled-model tests and data acquisition settings are presented.

3-1 Facility and Test Model

3-1-1 Low-Speed Wind Tunnel Facility

The experiments were conducted at the low-speed wind tunnel facility of UT Austin, located at the J.J. Pickle Research Center. The tunnel is an atmospheric-intake, open-circuit, contin- uous flow type tunnel. The test section is 1.5m 2.1m wide and 15m long. Power is provided × by four 200hp, fixed-rpm (1170rpm), 9-blade electric fans mounted in parallel at the outlet. The tunnel is designed for a maximum speed of 90m/s and a turbulence intensity factor of 0.3% RMS in the 0 100Hz range (Westkaemper, n.d.). This relative high turbulence inten- − sity factor might help to trigger the non-linear lock-in mechanisms as how they would appear in full-scale flight applications. The convergent and divergent section, outside the building where the test section is located, is shown in Figure 3-1.

(a) (b) Figure 3-1: Low-speed wind tunnel facility at UT Austin, (a) Convergent section, (b) Divergent section and fans.

M.Sc. Thesis Woutijn J. Baars, BSc. 3-1 Facility and Test Model 25

The fixed-rpm fans, driving the wind tunnel, can cause upstream flow fluctuations in the test section and should therefore be considered in the post processing phase. The blade passage frequency, fb, can be calculated from the fan rotational speed (1170rpm) and the number of blades (9 blades per fan). The blade passage frequency is

1170rpm f = 9 = 175.5Hz. (3-1) b 60s ·

3-1-2 Aircraft Test Model

The aircraft test model, presented in Figure 3-2a, is a rigid 1:10 scale model of a representative small general aviation aircraft. The wing span and length of the model are respectively 1.56m and 1.26m. The dimensions of the horizontal stabilizers are indicated in Table 2-1. The wooden model has an aluminium frame and is therefore very rigid. It is possible to change the elelvator deflection angle δ. The experiments are conducted at a Reynolds number based on the mean aerodynamic chord of the aircraft model main wing of Re = 4.2 105 c¯w,model · (Section 3-1-2-2). This corresponds with a Reynolds number based on the chord of the elevator horn balance of Re = 1.8 105. chorn · (a) (b) wind tunnel ceiling mounting point / point of rotation

V∞

head wind tunnel floor

foundation

link piston piston

Figure 3-2: (a) Aircraft model and instrumentation mounted in the wind tunnel, (b) Schematic of sting support system.

The model is supported by a two-arm sting system, illustrated in Figure 3-2b, consisting of a hydraulically operated link and head, that are used to change the angle of attack, αp, of the aircraft model. The model/sting connection allows 3, limited, rotational DOF of the aircraft. The actual model weight, weight distribution and moments of inertia are not scaled to match that of the full-scale aircraft, and therefore, only a qualitative indication of the presence of upsets can be obtained from the experiments using this so-called ’reduced-stiffness’ model. However, if lock-in regions are identified, the chance that those will also occur in full-scale flight applications is significant.

3-1-2-1 Ice Simulation

Ice accumulation is simulated by a 1/4 round spar, attached to the bottom side of the elevator horn balance leading edges, as indicated in Figure 2-3 and 3-3, as revealed by the study

M.Sc. Thesis Woutijn J. Baars, BSc. 3-1 Facility and Test Model 26 of Wilson (1967). The effects of horn geometry were investigated by Busch et al. (2008), where it was concluded that the lift coefficient increases 11% and the airfoil stall is delayed by 1◦ when changing the ice horn aspect ratio, k/c, from 0.027 to 0.020. In all the studies referenced in Section 2-2 (J. J. Jacobs & Bragg, 2007; Gurbacki & Bragg, 2002, 2004; Broeren et al., 2004; Khodadoust, 1988; Bragg & Khodadoust, 1992), the k/c values were in the 0.020 0.027 − range. The k/c value in the current study, k/chorn = 0.097, is a factor 3 to 4 larger. However, the current study focusses on the unsteady flow induced by the ice horn, and the related fluid- structure energy transfer mechanism, instead of the quantitative drag and lift characteristics. The unsteady flow signatures, as discussed in Section 2-2, are present in a representative way albeit the larger value of k/c according to the author. Furthermore, k/chorn = 0.097 is a realistic value, since k/c values up to 0.095 have been observed on the shielded horn balance by Wilson (1967).

Z sting support system pressure transducers X Y

ice simulation

Figure 3-3: Aircraft model with ice simulation and instrumentation installed in the wind tunnel, δ = 24◦. −

3-1-2-2 Parameters of Similarity

Since the experiment is conducted using a 1:10 scale model, parameters of similarity are im- portant to validate the real aircraft behavior of the model. The three parameters of similarity are the Reynolds number, the Mach number, and the Froude number. Because the model is held relatively stationary by the sting support system, the Reynolds number and Mach num- ber are the significant similarity parameters (Barlow, Rae, & Pope, 1999). If the experiment has the same Reynolds and Mach numbers as the full-scale application, the flow behavior around the model and full-scale aircraft will be dynamically similar. The Reynolds number, based on the mean aerodynamic chordc ¯, is given by

ρ V c¯ Re = ∞ ∞ , (3-2) c¯ µ ∞ where ρ is the density of the free stream air, V is the free stream velocity,c ¯ is the mean ∞ ∞ aerodynamic chord, and µ is the dynamic viscosity of the free stream air. The viscosity ∞ of air, µ is a function of temperature, T , (for T < 3000K) and can be calculated using Sutherland’s equation according to

1.5 6 T µ = 1.458 10− . (3-3) · T + 110.4

M.Sc. Thesis Woutijn J. Baars, BSc. 3-1 Facility and Test Model 27

The pressure, p, of air is varying with altitude h according to

g L h −R·L p = p0 1+ · , (3-4)  T0 

where p0 = 101.325Pa is the pressure at sea level at Standard Atmosphere (SA) conditions, L = 0.0065K/m is the temperature gradient in the lower layer of the atmosphere, h is − 2 the altitude, T0 = 288.15K is the temperature at sea level at SA conditions, g = 9.81m/s is the gravitational acceleration and R = 287.05J/kg/K is the specific gas constant. The corresponding density can be calculated using the equation of state for a perfect gas, which is given by

p ρ = . (3-5) R T ·

The temperature during the experiments was on average 24◦C or 297.15K (Baars, 2008). The experiments are performed at sea level conditions; the density of air at sea level is 1.225kg/m3. The free steam velocity during the data acquisition phase of the experiments was 40m/s and the mean aerodynamic chord of the model isc ¯w,model = 0.159m. Using these parameters, the Reynolds number during the wind tunnel tests is calculated as Re = 4.24 105. c¯w,model · The temperature is required to calculate the Reynolds number of the full-scale aircraft ap- plication. The temperature at a specific altitude in the lower layer of the atmosphere can be calculated according to

T = T + L h. (3-6) 0 ·

The viscosity, pressure and density of the air can be calculated at cruise altitude of a typical small general aviation aircraft, which is 4, 572m (Pilot Manual, n.d.). The cruise speed of the aircraft is Vcruise = 300km/h = 83.3m/s (Pilot Manual, n.d.). It is assumed that the airplane is flying in those conditions when the upset phenomena occur that are proposed in Section 2-3. Those conditions will result in the highest Reynolds number possible for which aircraft upsets can occur (i.e. Reynolds number will be higher than when the landing phase is considered). Because the Reynolds number during the experiments will be lower, the worst case scenario (Reynolds number difference is maximum) is analyzed. The mean aerodynamic chord of the aircraft isc ¯w,real = 1.59m. Using these parameters, the Reynolds number during the full-scale flight application is Re = 5.75 106. c¯w,real · The Mach number is given by the following equation

V M = , (3-7) a where a is the speed of sound. The speed of sound for a perfect gas is given by

M.Sc. Thesis Woutijn J. Baars, BSc. 3-1 Facility and Test Model 28

a = γRT, (3-8) p where γ is the ratio of specific heats. γ = 1.4 for the range of temperatures where air behaves as a perfect gas. Using the parameters presented above, the Mach number during the experiments is M = 0.12 and for the full-scale application M = 0.29. The parameters of similarity are summarized in Table 3-1.

Experiment Full-Scale Re 4.24 105 5.75 106 c¯w · · M 0.12 0.29

Table 3-1: Parameters of similarity.

The Reynolds number during the experiments is about an order of magnitude lower than the Reynolds number during the real flight application. Figure 3-4 indicate the effects of increasing the Reynolds number. Case (a) in Figure 3-4 occurs at a typical chord Reynolds number of Re = 2.0 105. Considerable separation occurs because the laminar boundary c · layer does not have enough vorticity close to the wall to keep the flow attached to the airfoil surface. The large wake area generates relative high drag. In case (b), Re = 6.5 105, the c · transition point has moved forward, resulting in a turbulent boundary layer that keeps the flow better attached to the surface. The drag is decreased due to a decrease in pressure drag. In case (c) the Reynolds number is increased to Re = 1.2 106 resulting in the transition c · point being more forward. The overall drag is not decreased because of the increase in friction drag, resulting from a larger portion of the boundary layer being turbulent (Barlow et al., 1999).

Figure 3-4: Effect of increasing Reynolds number on boundary layer flow, NACA 23012 pro- file (Barlow et al., 1999).

Cases (a) and (b) are plotted in Figure 3-5a together with the Reynols numbers corresponding to the experimental- and full-scale-case. It is important to know that the aircraft model main wing is a NACA 23012 airfoil as well. The full-scale reality case is beyond case (c) in terms of Reynolds number. Although the drag of the airfoil/wing is more or less equal for

M.Sc. Thesis Woutijn J. Baars, BSc. 3-1 Facility and Test Model 29 the experimental and reality case, the flow patterns are different. Therefore, the Reynolds number mismatch should not be neglected.

experiment full-scale

(a) (b)

Figure 3-5: (a) CD0,min as function of Rec (E. N. Jacobs & Sherman, 1937), (b) Tripper strip on the main wing of the aircraft model.

Because it is not feasible in any way to match the Reynolds numbers of the experimental and full-scale case, it is desirable to match the boundary layer behavior. The two features that are most critical are the location of the boundary layer transition and the location of flow separation (Barlow et al., 1999). A boundary layer trip device is used to artificially transition the boundary layer from laminar to turbulent. The tripper strips are shown on the aircraft model main wing in Figure 3-5b. In essence, the tripper strips are installed on the wings and stabilizers of the model. A thorough discussion on the use of tripper strips is presented in chapter 8 of Barlow et al. (1999). The Reynolds number dependency of the time-averaged flow pattern behind simulated ice ac- cumulation is discussed by Addy, Broeren, Zoeckler, & Lee (2003) and Broeren et al. (2004). The study conducted by Broeren et al. (2004) was performed at a Reynolds number of Re = 3.5 106 and Re = 6.0 106. It was concluded that the changes in Reynolds number c · c · did not significantly affect the separation bubble characteristics. Furthermore, in the study by Addy et al. (2003) it was concluded that there was no change in performance as a result of changing the Reynolds number over the range Re = 3.0 106 to Re = 10.5 106. It c · c · was stated that the results supported the notion that ice accretions dominate the bound- ary layer behavior on iced airfoils, and therefore, the Reynolds number has minor influence. Gurbacki & Bragg (2004) performed unsteady flow field measurements on an iced airfoil (as discussed in Section 2-2) with a Reynolds number of Re = 1.0 106 and Re = 1.8 106. c · c · There are no noticeable differences in the shear-layer reattachment oscillation and unsteady lift and moment variations of the airfoil. Based on the discussion above it is assumed that the wind tunnel experiments, conducted with a lower Reynolds number than used by these icing studies, show similar characteristics in a time-averaged sense and in the unsteady flow field. There is also a mismatch in Mach number between the experiments and full-scale application. In the incompressible flow regime (M < 0.3), the Reynolds number effects predominate. Therefore, in the incompressible flow regime the matching of Mach number is not as critical. Although compressibility effects will become more significant in the full-scale case (M = 0.29), when compared to the test case (M = 0.12), no additional measures are taken. According to the study by Broeren et al. (2004), variations in the icing effects were observed

M.Sc. Thesis Woutijn J. Baars, BSc. 3-2 Instrumentation 30 when the Mach number was changed from 0.12 to 0.28, but were rather small. Addy et al. (2003), who considered M = 0.12 and M = 0.21, concluded that the increase in Mach number resulted in a slightly larger separation bubble behind the glaze ice horn at α = 6◦. No information is found about the influence of the Mach number on the unsteady flow characteristics. It is assumed that the mismatch of Mach number does not result in major differences in flow behavior during the experimental phase. Because the experiments are conducted on a powered aircraft model it is favourable to match the advance ratio, J. Due to a broken speed controller the experiments were conducted with- out powered propeller. All the effects of the propeller (including the effects on stability and control) are discussed by Barlow et al. (1999) in chapter 13.4. Those effects are destabilizing due to their asymmetric behavior. Therefore, it is believed that the tests are conducted for a best case scenario, with other words, if the experiments were performed with a powered propeller, the strength of the possible upset would not have been less.

3-2 Instrumentation

3-2-1 Data Acquisition Arrangement

Three Pressure Transducers (PTs) and five Accelerometers (ACs) were used to acquire the unsteady flow field and acceleration of the aircraft model, respectively. The pressure trans- ducers are Kulite XCE-093 types, rear vented, having a 0 35kPa gauge pressure range, a 1 − nominal sensitivity of 2.9µVPa− and a dynamic response range up to 50kHz. The transduc- ers were connected to one power supply, an Endevco signal conditioner unit, model 136, with a 200kHz bandwidth and built-in, four-pole, Butterworth low-pass filters. The transducers were mounted on the sting support as indicated in Figure 3-6.

AC 5 Z

rear view PT B Z AC 3 AC 2 PT C PT B PT A Y vert. stabilizer AC 1 PT A X PT C hor. stabilizers AC 4 elevator horn balance

Y

Figure 3-6: Sensor arrangement on the aircraft model using pressure transducers A, B, C (setup 2) and accelerometers 1-5.

Actually, the data acquisition experiments were conducted using two different setups of the three available pressure transducers, which are shown in Figure 3-7. Setup 1 has two PTs (A & B) located at either side of the vertical stabilizer and above the horizontal stabilizers. These PTs should capture the asymmetrical vortex shedding event on both sides of the aircraft while the bursting or stall of the horizontal stabilizer is captured by PT C. PT A is mounted directly behind the elevator horn balance in setup 2. This setup can provide more information about the ice-induced unsteady flow and will be used to identify the fluid-structure lock-in mechanisms.

M.Sc. Thesis Woutijn J. Baars, BSc. 3-2 Instrumentation 31

(a) (b) Z Z

PT B PT A PT B

Y Y

vertical stabilizer PT A vertical stabilizer PT C PT C horizontal stabilizers horizontal stabilizers

elevator horn balance elevator horn balance

Figure 3-7: Pressure transducer setup, (a) setup 1, (b) setup 2 - plane perpendicular to airflow and behind the aircraft model.

One Kistler 8692A5 PiezoBEAM tri-axial accelerometer, comprising a 5g range, a nominal ± sensitivity of 1000mV/g and a resolution < 0.001g, is used for location 1 3, as indicated − in Figure 3-6. The accelerometer is connected to a net-powered, three-channel, PCB 480B21 sensor signal conditioner. For location 4 and 5 two PCB 353B17 accelerometers are used, comprising an acceleration range of 500g, a nominal sensitivity of 10mV/g and a resolution of ± 0.005g. The two PCB accelerometers are powered by two PCB 480D06 battery-powered sensor signal conditioners. The eight transducers are connected to a National Instruments (NI) BNC-2120 board followed by a 16-bit resolution NI PCI-6143 data acquisition device installed in a Dell Precision 340 PC with NI LabVIEW V7.1 software. The eight transducer signals are synchronously digitized at a 2kHz sampling frequency. For each run, data was recorded for 125s resulting in data sets of 250,000 samples (Section 3-2-2). Figure 3-8 presents a schematic of the data acquisition system.

Accelerometers - 5 channels Power Supply and Signal Conditioner Tri-axial Kistler 8692A5 (1x) PCB 480B21 (1x) Linear PCB 353B17 (2x) PCB 480D06 (2x)

Pressure Transducers Power Supply and Signal Conditioner Kulite XCE-093 (3x) Endevco model 136 (1x)

Connector Board A/D DAQ Board Dell Precision 340 PC NI BNC-2120 (1x) NI PCI-6143 (1x) LabVIEW V7.1

Figure 3-8: Schematic of the data acquisition system.

3-2-2 Sampling Criteria

The parameters that define a data acquisition experiment are the sampling frequency, fs, the number of samples, M, and the sampling time, T . The relation between these parameters is given by

M.Sc. Thesis Woutijn J. Baars, BSc. 3-2 Instrumentation 32

M T = . (3-9) fs

To design a certain experiment, two of those three parameters need to be determined. The first criterion to determine those parameters will be derived from the so-called amplitude-domain analysis. In the after-processing phase of an experiment where a quantity x is measured, the estimators will be computed from the discrete data set consisting of M discrete samples, x1, x2, ..., xM . The average of these samples, denoted by the estimator XM , is computed by

M 1 X = x . (3-10) M M i Xi=1

The estimator XM is the sum of random variables, therefore, it is a random variaby by itself and the variance of XM is defined as

var X = (X x¯)2, (3-11) { M } M − where the bar denotes the true ensemble average andx ¯ is the true average. The question in the amplitude-domain analysis is whether the variance of the estimator becomes negligible small as the number of samples, M, becomes large. In George, Beuther, & Lumley (1978) it is shown that the acceptable fluctuation in the estimate or relative error in the estimator, x, is given by

1 σx x = , (3-12) √N x¯ when the samples are identically distributed and are statistically independent/uncorrelated. The quantity σx is the standard deviation, which is defined as

N 1 σ = v (x x¯)2, (3-13) x uN 1 i − u Xi=1 t −

σx where x¯ is the relative fluctuation of the random variable itself and N is the number of independent measurment samples. In general it turns out that N

M.Sc. Thesis Woutijn J. Baars, BSc. 3-2 Instrumentation 33

1 T Rxx(τ)= lim [x(t) x¯][x(t + τ) x¯] dt. (3-14) T T Z − − →∞ 0

The auto-correlation coefficient as function of time delay, τ, is defined as ρxx(τ) = R (τ) xx /Rxx(0). The integral time-scale TI is now obtained from the integral

∞ TI = ρxx(τ) dx. (3-15) Z0

However, the integral of the auto-correlation function is in general not computable due to the finite length of the signal. A reasonable estimate of TI is the time it takes the auto-correlation coefficient to drop from the unity start value at τ = 0 to a zero value. In Figure 3-9 and 3-10 the auto-correlation coefficients are shown for 3 accelerometer data sets and 2 pressure trans- ducer data sets. The signals were acquired synchronously at f = 2000Hz and T = 450s. s ± The aircraft model was placed at αp = 9◦ because one of the highest fluctuations in the estimators are expected in that position. For more information on the acquisition of this data set, the reader is referred to ’test 20’ in the wind tunnel documentation presented by Baars (2008). The time it takes the auto-correlation coefficient, of accelerometer 1 and pressure

transducer A, to drop to a zero value is approximate TIAC1 = 0.004s and TIPTA = 0.005s, respectively. It is well-known that uncorrelated samples are obtained when the minimum sampling interval is twice the integral time-scale, thus 1/fs > 2 TI . If the samples are uncorrelated, it returns the highest rate of convergence for the estimator. Concerning this criterion, the optimal sampling rate is one sample for every two integral scales in time. From the integral time- scales TIAC1 and TIPTA , the minimum time interval for uncorrelated samples, dtu, is computed according to

1/f > 2 T dt > 2 T = 2 0.005 = 0.01s. (3-16) s I → u I,max ·

Thus, to obtain a data set with statistically uncorrelated samples, the sampling frequency should be fs < 100Hz. There is still a certain number of uncorrelated samples required in order to have an acceptable fluctuation according to Eq. (3-12). This expression cannot be evaluated when the mean is zero. Therefore, the standard error of the mean will be analyzed, denoted by σx¯, representing the uncertainty in the meanx ¯ as the best estimate for the mean of the data set. The standard error of the mean is given by (Taylor, 1982)

σx σx¯ = . (3-17) √N

The standard error of the mean is now computed as function of independent samples, N, and expressed relative to the value of the standard error of the mean when all the statistically

M.Sc. Thesis Woutijn J. Baars, BSc. 3-2 Instrumentation 34

1 AC 1 AC 4 0.5 AC 5 ) [−]

τ 0 ( xx ρ

−0.5

−1 0 0.005 0.01 0.015 0.02 0.025 τ [s]

◦ Figure 3-9: Auto-correlation coefficients for accelerometers 1, 4 and 5 (test 20, α = 9 , fs = 2000Hz, dt = 0.0005s).

independent samples are used (Nmax = 32, 960 for this data set). To summarize, the relative standard error of the mean as function of N is computed as

σx(N) σx(Nmax) N N √N √Nmax 1 2 1 σx,rel¯ (N)= − , where σx = v (xi x¯) , and x¯ = xi.(3-18) σx(Nmax) uN 1 − N u Xi=1 Xi=1 √Nmax t −

The standard error of the mean for the accelerometers and pressure transducers are pre- sented in Figure 3-11 as function of independent samples, N. The values of σx¯(Nmax) =

σx(Nmax)/√Nmax are presented in Table 3-2.

Transducer AC1 AC4 AC5 PTA PTB 2 2 2 σx¯(Nmax) 0.0004m/s 0.0053m/s 0.0016m/s 0.49Pa 0.11Pa

Table 3-2: Standard errors of the mean when Nmax = 32, 960 statistically independent samples are used (test 20, α = 9◦).

Assuming that the value of the standard error of the mean is converged when all the available statistically independent samples are used in the computation, the relative standard error of the mean is less than 1% if N = 10, 000 independent samples are acquired to construct the data sets.

M.Sc. Thesis Woutijn J. Baars, BSc. 3-2 Instrumentation 35

PT A PT B 0.8

0.6 ) [−]

τ 0.4 ( xx ρ 0.2

0

−0.2 0 0.01 0.02 0.03 0.04 τ [s]

Figure 3-10: Auto-correlation coefficients for pressure transducers A and B (test 20, α = 9◦, fs = 2000Hz, dt = 0.0005s).

The second criterion used to design an experiment is based on the frequency-domain analysis. The Nyquist frequency determines up to which frequency spectral information can be ex- tracted from the data set. The Nyquist criterion can be summarized as follows (George et al., 1978): The spectral information in a discretely sampled time signal can be retained only if the sampling rate is at least twice the highest frequency present in the original signal. Thus, f 2 f , where f is the maximum expected frequency in the measured signal. s ≥ max max Low-frequency characteristics are expected during the experiments, and therefore, spectral information up to fmax = 1000Hz is desired. According to the Nyquist criterion the sampling frequency should be fs > 2000Hz. From the ’amplitude-domain analysis’ and ’frequency-domain analysis’ it can be concluded that for digital processing of random signals there is a conflicting requirement (fs < 100Hz versus fs > 2000Hz). In order to extract information up to the desired frequency of 1000Hz, we should sample at the rate of 2000Hz. However, the additional data points (points in the interval of two consecutive statistically independent samples) do not contribute to the convergence of the estimators. The ’waste factor’, defined by 2 TI,max/dt = 20 is a measure for this phenomenon (George et al., 1978). To keep the ’waste’ in computing power minimal, one could work with the full data set if spectral information is required and one could work with an extracted, statistically independent data set, when estimator information is required. To conclude the data acquisition analysis, the experiments are conducted at a sampling frequency, fs, of 2000Hz. 10, 000 independent samples are acquired such that the rela- tive standard error of the mean is smaller than 1%. According to the waste factor of 20,

M.Sc. Thesis Woutijn J. Baars, BSc. 3-3 Conduction of Experiments 36 ¯ x,rel σ

N 10, 000 [-] × ¯ x,rel σ

N 10, 000 [-] × Figure 3-11: Relative standard errors of the mean for AC 1, 4 and 5 and PT A and B (test 20, α = 9◦).

Table 3-3: Test matrix for the experimental in- vestigation.

* Condition Icing† δ [degr] 1 no 0 2 no -24 3 yes 0 4 yes -24 * For each condition runs are performed at αp = 0◦, 5◦, 6◦, 7◦, 8◦, 9◦ and 10◦. † The ice simulation is placed at the elevator horn balance as indicated in Figure 2-3.

M = 10, 000 20 = 200, 000 samples should be acquired in the experiment. As a safety factor, · M = 250, 000 samples are acquired for each run, which results in a total recording time, T , of T = M/fs = 250,000/2000 = 125s.

3-3 Conduction of Experiments

3-3-1 Test Conditions

Different states in the aircraft climbing and landing phases are simulated by different values of the angle of attack, αp, and elevator deflection angle, δ. The measurements are performed with and without simulated ice accumulation attached to the elevator horn balance leading edges. The different test conditions are summarized in Table 3-3. An extensive documentation of the experimental wind tunnel study and acquired data sets is presented by Baars (2008).

M.Sc. Thesis Woutijn J. Baars, BSc. 3-3 Conduction of Experiments 37

3-3-2 Experimental System Characteristics

The sting system support will have influence on the dynamics of the model. This should be considered, and therefore, wind-off vibration studies are performed to identify the natural frequencies of the experimental system. The qualitative auto power spectra of the responses of the total system are shown in Figure 3-12 when the system was excited in various ways. The peaks indicate the natural frequencies of the system. The expected periodic upsets of the model might lock-in with one of those frequency peaks. If that is the case, the observed lock-in frequency is not relevant, but the fact that an energy transfer mechanism occurs is important.

5−AC4 − Roll 4−AC2 − Hit y−axis 3−AC1 − Hit z−axis 2−AC1 − Hydr osc 1−AC3 − Pitch Auto Power Spectra

100 101 102 103 freq [Hz]

Figure 3-12: Qualitative auto power spectra to identify the natural modes of the experimental system.

M.Sc. Thesis Woutijn J. Baars, BSc. Chapter 4

Single-I/O System Identification

Single-I/O system identification techqniques are presented in this chapter, which are capable to compute coherences in a black-box single-I/O system, where the relations are of the linear and (second-order) non-linear type. These techniques are of great interest in the field of (experimental) fluid dynamics and can be applied to a variety of other research fields.

4-1 Lock-In Mechanisms

In the application of this study, the system identification technique is used to detect lock-in mechanisms between the synchronously acquired pressure and acceleration data set. During a linear lock-in mechanism, the frequency of the periodic motion of the aircraft model coincides with a dominant periodic pressure fluctuation in the ice-induced unsteady flow. There is a one-to-one resonance. Physically, this lock-in mechanism is very complex. It has been demonstrated experimentally in a fluid-structure lock-in experiment, that once a motion of the structure starts, the flow frequency of oscillation ”locks into and is controlled by the structural motion and not its shape or the velocity of the flow” (Fung, 1993). Thus, if the flow velocity is increased, the lock-in mechanism will still be present. Once a significant mismatch occurs between the locked-in structural oscillation frequency and the Strouhal number frequency of the unforced shedding event, a so-called lock-out occurs; the ice-induced shedding frequency does not coincide with the fuselage motion frequency anymore. This fluid-structure lock-in effect can also be produced if the vibration frequency is equal to a multiple or sub-multiple of the shedding frequency. This is denoted as a non-linear lock-in mechanism. A further increase in amplitude of the lock-in mechanism, and finally failure of the structure, can occur if the frequency of the exciting fluid force locks-in to a structural eigenfrequency. Usually, the lock- in phenomena are not desired in engineering applications, for example, the lock-in of a car antenna vibration with its shedding frequency. The most famous example of undesired lock-in is the well-known Tacoma Narrows bridge fluid-structure interaction problem (Figure 4-1), where the torsional mode of the road surface was locking-in with the wind, and what resulted in a collapse of the structure.

M.Sc. Thesis Woutijn J. Baars, BSc. 4-2 First-Order Statistical Signal Processing 39

Figure 4-1: The Tacoma Narrows bridge, indicating the torsional motion of the road surface prior to failure on November 7, 1940. A classic example of undesired fluid-structure lock-in.

4-2 First-Order Statistical Signal Processing

The first-order statistical signal processing techniques, used to identifty the linear lock-in, will be applied to the experimental data consisting of discrete time series of the pressure input, p(t), and acceleration output, a(t), where t is the discrete time. P (f) and A(f) are the Discrete Fourier Transforms (DFTs) of the time series data, where f is the dis- crete frequency. For the pressure signal, consisting of a sequence of N measurement points p(0),...,p(N 1) in the time-domain, the DFT is given by −

N 1 − −2πj ft P = p(t)e N , where f = 0,...,N 1. (4-1) f − Xt=1

N is the number of DFT coefficients and j is the square root of minus one. The result is a sequency of N complex numbers P , f = 0,...,N 1, forming the discrete series of the f − pressure in the frequency-domain, P (f).

4-2-1 Auto Power Spectrum

The discrete of the acceleration, a(t), is defined as

S (f)= E A(f)A∗(f) , (4-2) AA { } where E . denotes an expected value and denotes the complex conjugate. The auto power { } ∗ spectra of accelerometer 4 (Figure 3-6), for test condition 1 & 2 (Table 3-3) and for various angles of attack of the aircraft model, αp, are shown in Figure 4-2. A so-called moving average filter is applied to the spectra before plotting so that the significant energy peaks, which are embedded in the noisy parts of the spectra, can be identified better. The filter should be applied with care because important peaks in the power spectra should not be filtered out.

M.Sc. Thesis Woutijn J. Baars, BSc. 4-2 First-Order Statistical Signal Processing 40

The moving average filter that is applied is the Bandwidth Moving Filter (BMF). The BMF replaces an individual point in a discrete set of data points with the mean of a specified number of surrounding data points. The mean sample set is determined by a specified percentage of the bandwidth frequency. When a 5% BMF is applied to the power spectra, the data point at a frequency of 100Hz is replaced by the mean of the data points within the range of 95Hz to 105Hz, while the data point at a frequency of 1000Hz is replaced by the mean of the data points ranging from 950Hz to 1050Hz. The filter causes thus more smoothing in the higher frequency range.

f = 14.5Hz 1 2 ] −1 −2

Hz 10 2 10−4 0 ) [g

p −6 α 10 5 (f, 100 6 AA S 7 101 8 2 10 9 α [degr] 3 10 p freq [Hz] 10

Figure 4-2: Auto power spectra, 3d plot (5% BMF applied), accelerometer 4, see table 3-3 for test conditions.

Power spectra provide information about the amount of energy embedded in a periodic mo- tion. The power of accelerometer 4 at f = 14.5Hz is relatively low for test conditions 1 & 3 (δ = 0◦), while the power is up to a factor 2 to 4 larger (α > 7◦) for test conditions 2 & 4 (δ = 24 ), as indicated in Figure 4-3 (a, b, ... indicate various runs). In the case of − ◦ δ = 24 , condition 2 has no icing present on the elevator horn balance and is associated − ◦ with the highest power observed, while condition 4, where icing is present, shows a lot of variation in the power for the five different runs. However, the average power is lower than observed in condition 2. The more violent motion of the aircraft structure is thus mainly caused by the deflection of the elevator horn balance instead of the ice simulation. In order to identify the peaks in the power spectra that are corresponding to a lock-in mechanism, the linear coherence spectrum is introduced in the next section, which involves the computation

M.Sc. Thesis Woutijn J. Baars, BSc. 4-2 First-Order Statistical Signal Processing 41

x 10−4 1 0.9 f = 14.5Hz 0.8 1 a 1 b 0.7 2 a

] 2 b −1 0.6 3 a Hz 2 3 b 0.5 ) [g

p 3 c α ( 0.4 4 a AA

S 4 b 0.3 4 c 4 d 0.2 4 e

0.1

0 0 5 6 7 8 9 10 α [degr] p

Figure 4-3: Auto power spectra, 2d slice extracted from Figure 4-2, accelerometer 4, see table 3-3 for test conditions. of power spectra.

4-2-2 Linear Coherence Spectrum

Finding the linear coherence between two events is based on analyzing a single-I/O Linear Time Invariant (LTI) system (Bendat & Piersol, 1980; Otnes & Enochson, 1987), in- dicated in Figure 4-4. The input and output of the physical model are the acceleration signal, a(t), and pressure signal, p(t), respectvely.a ˆ(t) is the response ”predicted” by the LTI model, n(t) is noise introduced in the physical system and ε(t) is the error between the output of the physical model and the linear model.

n(t), noise

a(t) a(t) + n(t) Physical Model +

p(t) − ε(t) = a(t) + n(t) − aˆ(t) aˆ(t) Linear Kernel, hL(t)

Figure 4-4: LTI model in the time-domain.

The output signal of the model is obtained by multiplying the input signal by a linear transfer st kernel function hL(t). By taking the DFT of this equation we obtain the 1 -order (linear) frequency-domain Volterra model representation given by Schetzen (1980)

aˆ(t)= h (t)p(t) Aˆ (f)= H (f)P (f), (4-3) L → L L where subscript L denotes the linear Volterra transfer function. An expression for the linear Volterra transfer function, HL(f), is obtained by multiplying Eq. (4-3) with P ∗(f) and by

M.Sc. Thesis Woutijn J. Baars, BSc. 4-2 First-Order Statistical Signal Processing 42

taking the expected value. The output quantity of the linear model, AˆL(f), is now replaced by the physical output, A(f), that is available from the experiments. HL(f) is a fixed char- acteristic system property, and therefore, can be taken outside the expected value operator. This results in the following moment equation for HL(f)

E A(f)P (f) S (f) H (f)= { ∗ } = AP , (4-4) L E P (f)P (f) S (f) { ∗ } PP where SAP (f) is the cross spectrum. For a random input signal, a system output in the frequency-domain can now be computed according to Eq. (4-3) where the linear transfer kernel, HL(f), is computed according to Eq. (4-4). The estimate of the response computed by the model in the time-domain is found by taking the inverse DFT of the frequency-domain estimate, according toa ˆ(t)= 1[Aˆ (f)]. This analysis method is known as the spectral LSE F − L technique that was discussed in Chapter 1. It is common to express the I/O-relation in the LTI system in terms of the linear coherence spectrum defined by (Otnes & Enochson, 1987)

2 2 SAP (f) γAP (f)= | | . (4-5) SPP (f)SAA(f)

The linear coherence as function of frequency is thus computed by dividing the cross spectrum with the individual power spectra. The linear coherences for the ’roll’ acceleration of the aircraft (accelerometer 4) and the pressure field behind the balance (pressure transducer A, setup 2) are presented in Figure 4-5 for all four test conditions as function of αp.

Three lock-in regions are identified in the f, αp-plane, as the coherence amplitudes are larger than a general coherence threshold value of 0.1, indicated by region A, B and C. It is ± believed that lock-in regions B & C are due to natural modes of the model/support system and associated model vibrations and pressure fluctuations, because those regions were present during all runs, with random and small amplitudes. The region where significant lock-in occurs between the structural acceleration and the unsteady flowfield, denoted as region A, is located around f = 6Hz and α> 7 . The linear lock-in mechanism is present (γ2 = 0.25) ◦ AP ± when the elevator is deflected by 24 for the case without ice (condition 2). The coherence − ◦ is significantly higher (γ2 = 0.35) if icing is located at the elevator horn balance leading AP ± edges (condition 4). No lock-in mechanism is present for the cases with and without ice formation when δ = 0◦. The linear coherence spectra indicate that there might be non-linear lock-in mechanisms present. Namely, if the physical system is indeed purely linear by nature, and the physical system is correctly modeled by only a single-I/O model that has fully converged, and no noise is introduced in the system, n(t) = 0, then the error is zero, ε(t) = 0 (Figure 4-4). In this case the linear coherence spectrum is equal to one for the complete frequency range, 2 γAP (f, αp) = 1 (Otnes & Enochson, 1987). From the analysis above it can be concluded 2 that the LTI system is not representing the real physical system, since γAP (f, αp) < 1. Higher-Order Spectra (HOS) analyses are able to increase the prediction performance of the model and quantify unobserved higher-order lock-in mechanisms as actually expected in this application according to the literature (Tate & Stearman, 1986; Kruger et al., 2005; Park et al., 2008).

M.Sc. Thesis Woutijn J. Baars, BSc. 4-2 First-Order Statistical Signal Processing 43

1 2 3 region C 4

0.4

) [−] 0 p 0.2 α (f, 0 5 2 AP γ 100 6 region A 7 101 region B 8 2 10 9 α [degr] p 3 10 freq [Hz] 10

Figure 4-5: Linear coherence spectra, 3d plot (5% BMF applied), accelerometer 4 and pressure transducer A (setup 2), see table 3-3 for test conditions.

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 44

4-3 Higher-Order Statistical Signal Processing

During a non-linear lock-in phenomenon, harmonics, sum, and difference combinations of original frequency peaks in the input signal can result in ”new” frequencies at which the input and output of the system are non-linearly coupled. Non-linear coupling exists only when the spectral peaks of the input and output signal satisfy the spectral selection rule, f = f1 + f2, and when they are phase coherent according to φ = φ1 + φ2. Subscript 1 and 2 denote the two spectral peaks in the input signal. A combination of those spectral peaks in the input signal cause an excitation, quantified by frequency f and phase φ, in the output signal. Phase information is not preserved in the first-order technique, and therefore, only the HOS techniques are able to identify those non-linear coherences.

4-3-1 Volterra Model Technique

In the time-domain, the output signal a(t) can be expressed in terms of Volterra operators, operating on the input signal p(t) according to the Volterra series given by Schetzen (1980)

∞ a(t)= H1[p(t)] + H2[p(t)] + ... + Hn[p(t)] + ... = Hn[p(t)], (4-6) nX=1

where the nth-order Volterra operator is expressed as

∞ ∞ Hn[p(t)] = ... hn(τ1,...,τn)p(t τ1)...p(t τn)dτ1...dτn. (4-7) Z Z − − −∞ −∞

Note that Eq. (4-6) is equal to Eq. (4-3) when truncated after the 1st (linear) term. In the re- maining of this section, a frequency-domain, non-orthogonal, Volterra model will be presented. The approach is outlined by Powers in chapter 1 of Boashash et al. (1995) and in the literature by Im et al. (1993); Im & Powers (1996); K. I. Kim & Powers (1988); S. B. Kim & Powers (1993); Nam et al. (1989); Nam & Powers (1994); Nikias & Petropulu (1993); Powers et al. (1993); Powers & Im (2004). The frequency-domain Volterra model is obtained by taking the DFT of the time-domain Volterra model. In this HOS investigation the order is limited to second-order to reduce the computational effort associated with the cubic and higher-order terms. Thus, only the linear and quadratic signatures in the pressure-acceleration coherence study will be considered. The Volterra model analysis is schematically presented by the block diagram in Figure 4-6. P (f) and A(f) are respectively the frequency-domain input of the system and output of the physical model (measured signal). The response ”predicted” by the 2nd-order, frequency- domain, non-orthogonal, Volterra model is given by Aˆ(f) = AL(f)+ AQ(f), which is ob- tained using the linear and quadratic transfer kernels HL(f) and HQ(f1, f2), respectively. The subscripts L and Q denote the linear and quadratic terms. The error between the output of the physical model and the linear model is given by ε(f) = A(f) Aˆ(f) (noise is omit- − ted). The Volterra model is represented using the equation (Im et al., 1993; Im & Powers,

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 45

A(f) Non-Linear Physical Model

− ε(f) P (f) AL(f) Linear Kernel, HL(f)

+ Aˆ(f) Quadratic Kernel, HQ(f1, f2) AQ(f)

2nd-order Volterra model

Figure 4-6: Single-I/O HOS system modeling approach in the frequency-domain.

1996; S. B. Kim & Powers, 1993; Nam et al., 1989; Nam & Powers, 1994; Powers et al., 1993; Powers & Im, 2004; Park et al., 2008)

Aˆ(f) = H (f)P (f)+ H (f , f )P (f )P (f )δ(f f f ) L Q 1 2 1 2 − 1 − 2 Xf1 Xf2

= AˆL(f)+ AˆQ(f), (4-8)

where f, f1 and f2 are discrete frequencies and δ is the Kronecker Delta function. To solve for the two unknowns that identify the system, the linear and quadratic transfer kernel coef- ficients, HL(f) and HQ(f1, f2), two moment equations are obtained by multiplying Eq. (4-8) with P ∗(f) and P ∗(f10 )P ∗(f20 ), respectively, and by taking the expected value. This results in the following set of moment equations

E Aˆ(f)P ∗(f) = H (f)E P (f)P ∗(f) { } L { } + H (f , f )E P (f )P (f )P ∗(f) , (4-9) Q 1 2 { 1 2 } Xf1 Xf2

E Aˆ(f)P ∗(f 0 )P ∗(f 0 ) = H (f)E P (f)P ∗(f 0 )P ∗(f 0 ) { 1 2 } L { 1 2 } + H (f , f )E P (f )P (f )P ∗(f 0 )P ∗(f 0 ) . (4-10) Q 1 2 { 1 2 1 2 } Xf1 Xf2

4-3-1-1 Gaussian Input Signal

The system of equations, given by Eq. (4-9) and Eq. (4-10), is coupled. However, for a system with a zero-mean, Gaussian input signal, all odd-order spectral moments are zero. Therefore, the bispectrum terms on the RHS are zero (Powers & Im, 2004). The moment equations become uncoupled and the linear and quadratic transfer kernel coefficients are solved independently, according to (Tick, 1961; Hong, Kim, & Powers, 1980) (where Aˆ(f) is replaced by the measured quantity A(f))

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 46

E A(f)P (f) S (f) H (f)= { ∗ } = AP , (4-11) L E P (f)P (f) S (f) { ∗ } PP

E A(f)P (f )P (f ) S (f , f ) H (f , f )= { ∗ 1 ∗ 2 } = APP 1 2 , (4-12) Q 1 2 2E P (f )P (f ) E P (f )P (f ) 2S (f )S (f ) { 1 ∗ 1 } { 2 ∗ 2 } PP 1 PP 2 where SAPP (f1,f2) is the bispectrum term. Note that Eq. (4-11) is equal to the expression for the linear transfer kernel coefficient, Eq. (4-4), as derived in Section 4-2.

4-3-1-2 Non-Gaussian, Random, Input Signal

For acquired data in real, physical, experiments, the excitations are rarely Gaussian. There- fore, the coupled set of moment equations need to be solved using linear algebra techniques, as discussed in detail by K. I. Kim & Powers (1988) and Nam & Powers (1994). The Volterra model, given by Eq. (4-8), is rewritten as a vector multiplication. The linear part, a single term, and the quadratic part, involving the double summation term, can be written as a multiplication of two column vectors, p and h, according to

Aˆ(f)= pT h, (4-13)

where T denotes the vector transpose. Vector p is called the polyspectral input vector and consists of all the pressure input terms, P (..), present in Eq. (4-8). Vector h consists of all the discrete transfer function coefficients, H(..). For an even discrete frequency, f, the transfer function vector h and polyspectral input vector p are given by the following expressions (from K. I. Kim & Powers (1988), p. 1761)

hT = H (f) ,H f , f , 2H f + 1, f 1 ,..., 2H (f, 0) ,..., 2H N , 0 (4-14) L Q 2 2 Q 2 2 − Q Q 2 h    
i

pT = P (f) , P f P f , P f + 1 P f 1 ,...,P (f) P (0) ,...,P N P (0) (4-15) 2 2 2 2 − 2 h        
i

In order to calculate the transfer coefficients, h, Eq. (4-13) is multiplied with p∗ and the expected value is taken. This results in a moment equation in matrix form

T E p∗p h = E p∗A(f) . (4-16) { } { }

Since the above equation is linear in terms of the transfer function vector, h, the approach that is outlined above reduces a non-linear identification problem to a linear problem. The block

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 47 matrix E p pT consists of 2nd, 3rd and 4th-order moment terms as schematically indicated { ∗ } in Eq. (4-17) and in full detail in Appendix A. Note that the size of system (4-16) is a function of discrete frequency, f. The final solution, h =[E p pT ] 1E p A(f) , is obtained using a { ∗ } − { ∗ } linear algebra solver. Since matrix E p pT is hermitian and positive definite, the problem { ∗ } can be solved using the Cholesky factorization method (Golub & van Loan, 1983).

2nd order 3rd order − ··· − ···  ......  T . . . . E p∗p = (4-17) { }  3rd order 4th order   − ··· − ···   . . . .   ......   

The response output of the model, Aˆ(f), can now be computed by inserting the solution for h in Eq. (4-13). The estimate in the time-domain is found by taking the inverse DFT of the frequency-domain estimate,a ˆ(t)= 1[Aˆ(f)]. This technique is a spectral QSE technique in F − the frequency-domain and is the second-order variant of the spectral LSE technique.

4-3-1-3 Higher-Order Coherence Spectra

The linear and quadratic relations in the single-I/O, second-order, non-orthogonal Volterra system (Figure 4-6) are obtained using the model output Aˆ(f). The concept of coherence is generalized by defining the coherence as the power of the output signal predicted by the model, divided by the power actually observed in the physical system, as discussed in the literature K. I. Kim & Powers (1988); Nam & Powers (1994); Powers & Im (2004). The gen- eralization of the concept of coherence has proven to be very useful when decoupling and identifying the linear and quadratic coherences in a system. The auto power spectrum of the model output is given by

S (f) = E Aˆ(f)Aˆ∗(f) AˆAˆ { } = E Aˆ (f)Aˆ (f)∗ + E Aˆ (f)Aˆ (f)∗ + E Aˆ (f)Aˆ (f)∗ + E Aˆ (f)Aˆ (f)∗ { L L } { Q Q } { L Q } { Q L } 2 2 = E Aˆ (f) + E Aˆ (f) + 2Re[E Aˆ (f)Aˆ (f)∗ ]. (4-18) {| L | } {| Q | } { L Q }

The total model coherence can now be defined as the fraction of output power according to

ˆ 2 ˆ 2 Re ˆ ˆ 2 SAˆAˆ(f) E AL(f) E AQ(f) 2 [E AL(f)AQ(f)∗ ] γtotal(f)= = {| | } + {| | } + { } SAA(f) SAA(f) SAA(f) SAA(f) 2 2 2 = γL(f)+ γQ(f)+ γLQ(f), (4-19)

2 2 2 where γL(f) and γQ(f) are respectively the linear and quadratic coherence spectra. γLQ(f) is an interference term and is the only term that can be negative due to the phase preser- vation by the cross terms in Eq. (4-18). The interference term, caused by these cross terms

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 48 in Eq. (4-18), can be removed by using an orthogonal Volterra model as discussed in the lit- erature (Im & Powers, 1996; Powers et al., 1993; S. B. Kim & Powers, 1993; Im et al., 1993). In the application presented in this study, the interference terms are small compared to the purely linear and quadratic term. Therefore, it is not necessary to make use of an orthogonal Volterra model as is shown in the next two sections, 4-3-2-1 and 4-3-2-2, where the Volterra model technique is applied as illustration.

4-3-2 Implementation of the Volterra Model Technique

The higher-order system identification technique, where a non-gaussian, random, input signal is considered, is implemented on a conventional desktop computer in Matlab ( c The Math- works). A schematic of this implementation is presented in Figure 4-7. Starting off with the raw data in the time-domain, the data is transformed to the frequency-domain to assemble the matrix system given by Eq. (4-16). The matrix p pT and vector p A(f) are com- { ∗ } { ∗ } puted for all partitions (a total of P partitions), and for each frequency f. In the next step, the transfer kernels in the vector h are computed by solving system (4-16) using the Cholesky factorization method. Once the transfer kernels are obtained, the output of the model can T be computed according to Aˆ(f)= p h = AˆL(f)+ AˆQ(f), Eq. (4-13), which is essentially the spectral QSE technique. In the last step of the system identification technique, the linear, quadratic, and interference coherence spectra are computed according to Eq. (4-19). The technique is computational expensive; the memory requirements are increased on the order of N 3 due to the 3d matrix p pT . Furthermore, the Central Processing Unit (CPU) { ∗ } hours are increased on the order of MN 2, since a double for-loop is involved in the matrix assembly process and the polyspectral input vector, p, is assemblied using a for-loop as well. The available memory of the conventional desktop computer limited the computations up to N = 512. This resulted in a relative low frequency resolution for the coherece spectra in the application of this technique to the experimental wind tunnel data of the ice-induced aircraft upset identification, as will be discussed in Section 5-2-2.

4-3-2-1 Monte Carlo Simulation

A Monte Carlo Simulation (MCS) is performed to illustrate the Volterra model technique. An artificial input and output signal are created in the time-domain, respectively x(t) and y(t), consisting of harmonics. The frequencies of the harmonics are chosen such that there will be a linear coherence at f = 200Hz and a quadratic coherence according to the frequency selection rule f = f1 + f2, where f = 700Hz, f1 = 200Hz, and f2 = 500Hz. The phase coherence is chosen such that it satisfies the phase selection rule φ = φ1 + φ2. Noise is added to the signals to simulate a physical experiment. The auto power spectra of the input and output signal are shown in Figure 4-8. The result of the spectral QSE is presented in Figure 4-9a; the original and computed output signals in the time-domain. The signals are linearly coupled by the lower frequency, and therefore, the linear estimate, yL(t), only captures the 200Hz frequency of the output signal. The 700Hz frequency in the output signal is captured by the quadratic estimate, yQ(t), due to the purely quadratic interaction. Figure 4-9b presents the higher-order coherence spectra according to Eq. (4-19) and presents the linear coherence spectrum according to Eq. (4-5). The

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 49

Data Set

Time-domain 1 2 3 4 P − 1 P

Frequency-domain 1 2 3 4 P − 2 P − 1 P

Assemble Linear Algebra System, Eq. (4-16)

Polyspectral input vector p for-loop P Matrix {p∗pT } for-loop f Vector {p∗A(f)}

Compute Transfer Kernels

Solve system (4-16) for h for-loop f Obtain HL(f) & HQ(f1, f2)

spectral Quadratic Stochastic Estimation

T Model output Aˆ(f) = p h = AˆL(f) + AˆQ(f), for-loop P for-loop f ( Eq. (4-8) and Eq. (4-13) for each partition P )

Coherence Computation

Determine S ˆ ˆ(f) and SAA(f) AA for-loop P 2 2 2 2 Compute γtotal(f) = γL(f) + γQ(f) + γLQ(f), Eq. (4-19)

Figure 4-7: Schematic of the implementation of the Volterra model technique (non-gaussian input signal).

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 50

(a) (b) × 104 × 104 10 6

Sxx(f)Sxx Syy(f)Syy 4 5 PSD PSD PSD PSD 2

0 0 0 200 400 600 800 1000 0 200 400 600 800 1000 freqfreq [Hz][Hz] freq [Hz][Hz]

Figure 4-8: Auto power spectra in the MCS, (a) input signal - 200Hz and 500Hz harmonics, (b) output signal - 200Hz and 700Hz harmonics.

2 amplitude of the interference coherence spectrum, γLQ(f), is relatively small, which satisfies the use of a non-orthogonal Volterra model for a correct interpretation of the linear and 2 2 quadratic coherence spectra. γL(f) peaks at 200Hz while γQ(f) peaks at 700Hz. The latter would have never been observed when spectral LSE would have been applied. The spectral QSE technique results thus in a major improvement of the predicted output signal by the model, Aˆ(f), due to the incorporation of the second-order term AˆQ(f). The amplitude of the coherence is equal to 1 at the peaks where total coherence is expected, namely at f = 200Hz and f = 700Hz. The fact that the amplitudes drop slowly is not fully understand yet. The auto power spectra of the input and output signal are highly harmonic and no coherence is expected in the frequency region in between those power spectral peaks. However, significant coherences, both linear and quadratic, are indicated by the coherence spectra. The author believes that this phenomenon is related to some property of the artifical generated signals 2 x(t) and y(t), because the well-studied linear coherence spectrum, γxy(f), shows the same behavior. If the two artifical signals would have satisfied the orthogonal Volterra model, the interference term would have been zero and the linear coherence spectrum would have been equal to the linear coherence spectrum based on the Volterra model technique, thus 2 2 γxy(f) = γL(f). It should be noted that if the auto power spectral peaks are not this clear, the source frequencies f1 and f2 resulting in the quadratic spectral coherence peak at frequency f should be determined based on the bispectrum analysis as discussed in Section 4-3-3.

4-3-2-2 Turbulent Mixing Layer in a Jet

The spectral QSE technique is applied to a turbulent mixing layer in a Mach 0.60 axisym- metric jet. The unsteady velocity at the centerline is measured with a single-component Laser Doppler Anemometer (LDA) and pressure measurements are performed in the mix- ing layer of the jet using an azimuthal array of 15 equidistantly placed pressure trans- ducers. For a complete overview of the experiment, the interested reader is referred to Hall, Glauser, & Tinney (2005). The linear and quadratic coupling signatures between st the unsteady centerline velocity, ucl(t), and the 1 Fourier mode of the 15 azimuthal un- steady pressures, expressed asp ¯θ(t), is computed at two jet exit diameters, D, downstream of the jet exit. The auto power spectra of the unsteady velocity and the 1st azimuthal pressure Fourier mode are shown in Figure 4-10. The QSE of the 1st azimuthal pressure Fourier mode is shown in Figure 4-11a, indicating that

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 51

(a) (b)

2 y (phys) 1.5 y + y L Q 1 y 1 L 0.8 y Q 0.5 0.6

0 [−]

2 0.4 γ ampl [−] −0.5 0.2 −1 0 −1.5 γ2 γ2 γ2 γ2 γ2 −0.2 L Q LQ total xy −2 0 2 4 6 8 10 0 200 400 600 800 1000 time [ms] freq [Hz]

Figure 4-9: MCS (a) QSE, where y(t) is the original output signal and yL(t) and yQ(t) are 2 the linear and quadratic estimates, (b) Coherence spectra, linear coherence spectrum γxy(f) and 2 2 2 higher-order coherence spectra γL(f), γQ(f) and γLQ(f).

(a) (b) × 104 4 30 ] s S ] 3 2 u u Sxx(f)cl cl Sp¯ p¯ s Syy(f)θ θ /s 2 20 2 m P a

[ 2 [ 10 PSD PSD PSD [Pa^2Hz−1] 0 PSD [Pa^2Hz−1] 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 StStD(f)D (f)[ [−]−] StStD(f)D (f)[ [−]−]

Figure 4-10: Auto power spectra in the turbulent mixing layer, (a) Suclucl at z/D = 2, (b)

Sp¯θ p¯θ at z/D = 2.

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 52

the quadratic contribution,p ¯θ,Q(t), remarkably improves the estimation of the original signal p¯θ(t). The coherence spectra are shown in Figure 4-11b. The amplitude of the interference 2 term, γLQ(f), is again relatively small, satisfying the use of a non-orthogonal Volterra model for a correct interpretation of the linear and quadratic coherence spectra. The linear coher- 2 ence, γL(f), peaks at StD = 0.5. This is consistent with the spectral LSE analysis presented by Tinney et al. (2006), however, the amplitude of the coherence, 0.6, is two times larger. This is because Tinney et al. (2006) computed the linear coherence using one unsteady pres- sure measurement. Higher coherences are expected when the (most energized) 1st azimuthal pressure Fourier mode is used, as is done in the current investigation. The quadratic coher- 2 ence spectrum, γQ(f), is a slowly decaying function showing a bucket shape where the linear 2 coherence spectrum, γL(f), peaks. A possible explanation for this can be that the unsteady events are mainly quadratically coupled in the frequency range outside the range where linear 2 coherence is dominant. The total coherence, γtotal(f), is not equal to 1. This indicates that the Volterra model, as presented in Figure 4-6, does not represent the real physics. This can either be due to noise in the experiments, the presence of cubic and higher-order coherences in the physical system, or multi-point inputs that are not taken into account in the single-I/O system analysis. The amplitude of the quadratic coherence spectrum decreases when more data points are used in the process of ensemble averaging. Figure 4-11a & 4-11b are produced using 400 partitions of N = 512 samples each. When more partitions are used, like 1000 partions in the case of Figure 4-11c & 4-11d, the amplitude of the quadratic coherence spectrum decreases significantly. This phenomena has not been observed in the MCS, where relative clean signals were used. It is believed that this is related to a convergence issue in the second-order coherence computation, since there is hardly any change in the linear coherence spectrum. An investigation in this convergence issue and the uniqueness of this spectral QSE technique will be outlined in future work (Section 6-2).

4-3-3 Bispectrum Analysis

The bispectrum analysis has the ability to detect the phase coherent frequencies, f1 and f2, satisfying the frequency selection rule f = f1 + f2. The cross bispectrum is given by

S (f , f )= E A(f + f )P ∗(f )P ∗(f ) . (4-20) APP 1 2 { 1 2 1 2 }

The cross bispectrum can be interpreted as a correlation function in the two dimensional frequency space f1,f2. Namely, if the input of the quadratic system, P ∗(f1)P ∗(f2), and the sum frequency present in the output of the system, A(f1 + f2), are phase coherent, in a quadratic way, the bispectrum SAPP (f1, f2) will not be zero. If the terms do not have a phase coherence, the bispectrum term is ideally zero. For a correct interpretation of the coherence amplitude, the cross bispectrum is normalized to obtain the cross bicoherence, according to

2 2 SAPP (f1, f2) γAPP (f1, f2)= | | . (4-21) SPP (f1)SPP (f2)SAA(f1 + f2)

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 53

(a) (b)

0.2 2 pθ (phys) γ2 γ2 γ2 γ2 γ p u p + p L Q LQ total θ cl θ,L θ,Q 0.8 0.1 p θ,L pθ 0.6 ] ,Q 0 P a s [

[−] 0.4 2 γ

ampl −0.1 0.2

0 −0.2

−0.2 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 St (f) [−] t [ms] D

(c) (d)

0.2 p (phys) γ2 γ2 γ2 γ2 γ2 θ p u L Q LQ total θ p + p cl θ,L θ,Q 0.8 0.1 p θ,L pθ 0.6

] ,Q 0 P a s [

[−] 0.4 2 γ

ampl −0.1 0.2

0 −0.2

−0.2 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 t [ms] St (f) [−] D

Figure 4-11: Turbulent mixing Layer. (a) & (c) QSE, where p¯θ(t) is the original output signal and p¯θ,L(t) and p¯θ,Q(t) are the linear and quadratic estimates, (b) & (d) Coherence spectra, linear 2 2 2 2 coherence spectrum γp¯θ ucl (f) and higher-order coherence spectra γL(f), γQ(f) and γLQ(f). Figures (c) & (d) (1000 partitions of N = 512 data points) are produced with 2.5 times as much data in the process of ensemble averaging, compared to figures (a) & (b) (400 partitions of N = 512 data points).

M.Sc. Thesis Woutijn J. Baars, BSc. 4-3 Higher-Order Statistical Signal Processing 54

For further reading on bispectrum analyses, and the symmetry properties of the bispectrum, the reader is referred to the literature by Nikias & Raghuveer (1987); Nikias & Mendel (1993); Mendel (1991); Nikias & Petropulu (1993); Boashash et al. (1995); Powers & Im (2004); Fitzpatrick (2003). The cross bicoherence is a powerful tool to identify the system. However, a lower dimensional presentation of the coherence is presented by the higher-order coherence spectra, as shown in Section 4-3-1-3. This lower-dimensional character is especially usefull when higher-order coherences, like cubic, need to be identified.

M.Sc. Thesis Woutijn J. Baars, BSc. Chapter 5

Results of Higher-Order System Identification

This chapter presents the results of the pressure-acceleration coherence study, based on the first-order technique to detect linear coherences, and the second-order Volterra technique to detect the quadratic coherences. The improvement in estimating the output signal of the model due to the inclusion of the quadratic, non-linear, terms, is discussed in the first section. The actual results of the pressure-acceleration coherence, in the application of ice- induced aircraft upsets, are presented in Section 5-2. The impact of the lock-in mechanisms on the stability and control of aircraft is discussed in Section 5-3.

5-1 Improvement due to Higher-Order Terms

The MCS, presented in Section 4-3-2-1, involved one linear coherence at 200Hz, and one quadratic coherence at f = f1 + f2 = 700Hz between the artifical created I/O signal. In this simulation, it is easy to rationalize that when the second-order terms are not included in the estimation process, only the 200Hz harmonic is present in the output signal. The 700Hz harmonic is captured by those second-order terms, and the estimated response resulting from that can be superimposed on the linear estimate. This total estimate, linear and quadratic, coincides very well with the original output signal. The improvement in the estimate due to the inclusion of the second-order terms is thus remarkable when significant quadratic coupling is present in the single-I/O system. In the application of this technique to the turbulent mixing layer, Section 4-3-2-2, a lin- ear coherence is highly expected when looking at the auto power spectra of the I/O signal, presented by Figure 4-10. Possible quadratic coherences are not easy to identify, based on the auto power spectra. Again, the inclusion of the second-order terms results in a remark- able improvement of the estimated output signal. The linear coherence spectrum, computed according to Eq. (4-19), is as expected. On the other hand, the shape of the quadractic coherence spectrum is questionable, since it was shown in Section 4-3-2-2 that the amplitudes

M.Sc. Thesis Woutijn J. Baars, BSc. 5-2 Pressure-Acceleration Coherence 56 of the quadratic estimate and the quadratic coherence spectrum decrease when more data is used in the process of ensemble averaging. This indicates that the results are non-unique when using the current implementation of the technique (Section 4-3-2). One can argue that the definition used to compute the coherence, Eq. (4-19), fails when the auto power spec- trum of the original output signal, SAA(f) (the denominator in the coherence computation), is close to zero. However, when the linear coherence is computed this way, it matches the linear coherence spectrum, computed by the well-known first-order formulation given by Eq. (4-5), when various numbers of partitions, P , are used in the process of ensemble averaging. Therefore, the non-uniqueness of the quadratic solution is related to a convergence issue. Fu- ture research is needed to investigate this. To summarize, the current implementation of the second-order Volterra technique results in a remarkable improvement in the estimate when a small number of ensemble averages is taken (just enough partitions such that the system, given by Eq. (4-16), is solvable, i.e. no ’badly scaled/singular matrix’ related issues arise), but the quadratic coherence spectrum can not be interpreted correctly, as is shown by the decrease in amplitude when more partitions, P , are used. It seems that the current imple- mentation of the higher-order Volterra technqiue is better suitable for estimation than for identification.

5-2 Pressure-Acceleration Coherence

5-2-1 Linear Pressure-Acceleration Coherence

The first result of the identification of linear lock-in mechanisms was presented in Section 4-2. The linear coherence spectra between the ’roll’ accelerometer (AC 4) and the pressure trans- ducer behind the elevator horn balance (PT A, setup 2), is again shown in Figure 5-1. It was concluded that region A was the only region where significant lock-in occured when the elevator was deflected by 24 (condition 2 & 4). The coherence is maximum (γ2 = 0.35) − ◦ AP ± if icing is located at the elevator horn balance leading edges (condition 4). A similar lock-in region is observed when computing the coherence between the ’yaw’ accelerometer (AC 5) and the same pressure transducer (PT A, setup 2), as presented in Figure 5-2. This indicates that a Dutch roll type of event is observed, since the reduced-stiffness aircraft model oscillates in the ’roll’ and ’yaw’ DOF at the same rate of f = 6Hz. This Dutch roll event is only initiated when the elevator horn balance is deflected. A stronger lock-in occurs when ice is present on the leading edges of the elevator horn balance, as indicated by the stronger coherence. The coherence amplitudes at f = 6Hz are presented in more detail in Figure 5-3. It should be noted that the 6Hz lock-in frequency coincides with two dominant natural modes of the sting support system (the two auto power spectra at the bottom of Figure 3-12), and thus the system could be forced to oscillate at that specific frequency. When looking at Figure 5-2, a second lock-in region is observed at a frequency of f = 14.5Hz for αp > 8◦, denoted by region D, which was not present when the ’roll’ accelerometer was analyzed. This mechanism is probably caused by an ice-induced drag term that has more influence on the ’yaw’ motion/acceleration than on the ’roll’ motion/acceleration of the aircraft. A Strouhal number comparison will provide more information about the source of the lock-in mechanism related to the unsteady flow effects as presented in Section 2-2. Although the lock- in frequency is not quantitatively interpretable (Section 3-1-2 and 3-3-2), the linear coherence

M.Sc. Thesis Woutijn J. Baars, BSc. 5-2 Pressure-Acceleration Coherence 57

1 2 3 region C 4

0.4

) [−] 0 p 0.2 α (f, 0 5 2 AP γ 100 6 region A 7 101 region B 8 2 10 9 α [degr] p 3 10 freq [Hz] 10

Figure 5-1: Linear coherence spectra, 3d plot (5% BMF applied), accelerometer 4 and pressure transducer A (setup 2), see table 3-3 for test conditions. Copy of Figure 4-5.

Table 5-1: Summary of Strouhal numbers of unsteady flow features as discussed in Section 2-2, the third row indicates at which value of α the phenomena were studied.

Gurbacki & Bragg (2004) Zaman et al. (1989) St = 0.53 0.73 St = 0.0048 0.0101 St = 0.02 St = 0.2 LR − LP − LP LP α = 0 8 α = 5 12 α = 15 α = 18 range ◦ − ◦ range ◦ − ◦ around ◦ around ◦

spectral peaks will identify where (part of) the peaks are present in the auto power spectra of the pressure signal. Namely, no obvious peaks were identified when looking directly at the auto power spectra of the pressure signals. The minimum angle of attack of the elevator horn balance (α + δ = 10 24 = 14 ) is actually outside the range of angles of attack p ◦ − ◦ − ◦ in the studied references presented in Section 2-2, and because the Strouhal number is not constant as function of angle of attack of the horn, a mismatch is expected. The maximum Strouhal number corresponding to the 6Hz coherence peak, based on the mean reattachment length of the bubble behind the ice formation (LRmax = chorn), is StLRmax = 0.010. The maximum Strouhal number based on the projected airfoil height of the elevator horn balance is St = 0.004, where L = c sin (α + δ) = c sin (0 24 ). Those LPmax Pmax horn p max horn ◦ − ◦ Strouhal numbers are lower than the unsteady flow phenomena
observed in the literature as summarized in Table 5-1, and therefore, the actual unsteady ice-induced flow phenomenon that cause the ice-induced linear lock-in mechanism can not be identified.

M.Sc. Thesis Woutijn J. Baars, BSc. 5-2 Pressure-Acceleration Coherence 58

1 2 3 region C 4

0.4

) [−] 0 p 0.2 α region B (f, 0 5 2 AP γ 100 6 region A 7 101 region D 8 2 10 9 α [degr] p 3 10 freq [Hz] 10

Figure 5-2: Linear coherence spectra, 3d plot (5% BMF applied), accelerometer 5 and pressure transducer A (setup 2), see Table 3-3 for test conditions.

(a) (b)

0.4 0.4 1 f = 5.9Hz 1 f = 5.9Hz 0.35 2 0.35 2 3 3 0.3 4 0.3 4

0.25 0.25

[−] 0.2 [−] 0.2 2 AP 2 AP γ γ 0.15 0.15

0.1 0.1

0.05 0.05

0 0 0 5 6 7 8 9 10 0 5 6 7 8 9 10 α [degr] α [degr] p p

Figure 5-3: Linear coherence spectra at f = 6Hz, (a) accelerometer 4 and pressure transducer A, (b) accelerometer 5 and pressure transducer A (setup 2), see Table 3-3 for test conditions.

M.Sc. Thesis Woutijn J. Baars, BSc. 5-3 Effect of Lock-In on Aircraft Stability & Control 59

5-2-2 Higher-Order Pressure-Acceleration Coherence

An attempt to identify the quadratic lock-in mechanisms, in the application of ice-induced air- craft upsets, is performed using the second-order, non-orthogonal, Volterra model approach, as was earlier applied in the MCS and the turbulent mixing layer of a jet. The frequency res- olution of the coherence spectra is determined by the sampling frequency, fs, and the number of DFT coefficients, N, according to ∆f = fs/N. In order to have a high frequency resolution, a large value of N is required, since fs is fixed by the conducted experiments. Due to the implementation of this technique in Matlab ( c The Mathworks), on a conventional desktop

computer, the computations were limited to N = 512, as discussed in Section 4-3-2. This results in a frequency resolution of ∆f = 3.9Hz for the higher-order coherence spectra. 2 The linear coherence spectra, γL(f, αp), for AC 4 and PT A (setup 2) are presented in Figure 5-4a. The interference spectra, presented in Figure 5-5a, are low in amplitude, 2 γLQ(f, αp) < 0.05, concluding that the non-orthogonal model should be sufficient in this 2 case. Therefore, the linear coherence spectra, γL(f, αp), should be similar to the linear co- herence spectra computed according to Eq. (4-5), as presented in Figure 5-1. However, the relative small bandwidth coherence peaks are not captured by the low frequency resolution (∆f = 3.9Hz) in the higher-order approach, as the coherence amplitudes are not larger than 0.1. The coherence peaks were identified well in the first-order approach (which is computa- tional inexpensive), where a frequency resolution of ∆f = 0.5Hz was used. 2 The quadratic coherence spectra, γQ(f, αp), are shown in Figure 5-4b. The spectra are more or less straight lines, without significant peaks, at a relative high amplitude of 0.6. One ± of the causes can be that small bandwidth peaks are not captured due to the low frequency resolution, as was the case with the linear coherence spectra. An investigation of this will be among the topics of future research. Furthermore, the relative high amplitudes are not unique, as was the case in the application to the turbulent mixing-layer, since variations in amplitudes have been observed when using more or less data in the process of ensemble averaging. The total coherence spectra are shown in Figure 5-5b; their amplitudes are domintated by the quadratic coherence spectra.

5-3 Effect of Lock-In on Aircraft Stability & Control

One linear lock-in region was identified in the f, αp-plane, with the reduced-stiffness model, at a frequency of f = 6Hz and for αp > 7◦. This Dutch roll instability was initiated by the deflec- tion of the elevator horn balance, and was significantly increased in strength when leading edge ice accumulation was simulated at the elevator horn balance. The frequency of this upset event was equal to one of the eigenfrequencies of the experimental system. Due to the high damping in the sting support system this upset did not result in failure. In real flight applications, the frequency of an ice-induced Dutch roll instability might lock-in with the natural Dutch roll mode of the aircraft. Aircraft are designed such that the instability modes have positive damp- ing. However, the ice-induced lock-in can result in negative damping in the Dutch roll mode, and therefore, this might result in failure of the aircraft. A further analysis should be per- formed based on flight dynamics theory (Mulder, van Staveren, van der Vaart, & de Weerdt, 2006), for a specific aircraft of interest, to investigate the exact strength and frequency-domain of the ice-induced Dutch roll upset that might trigger this undamped Dutch roll event.

M.Sc. Thesis Woutijn J. Baars, BSc. 5-3 Effect of Lock-In on Aircraft Stability & Control 60

(a)

1 2 region C 3 4

0.2

) [−] 0 p 0.1 α

(f, 0 5 2 L γ 4 region A 6 10 7 8 region B 9 100 α [degr] 10 p freq [Hz] 200

(b)

1 2 3 4

0.8 ) [−]

p 0.6 0 α

(f, 0.4 5 2 Q γ 4 6 10 7 8 9 100 α [degr] 10 p freq [Hz] 200

Figure 5-4: Higher-order coherence spectra (5% BMF applied): accelerometer 4 and pressure 2 2 transducer A, (a) γL(f, αp), (b) γQ(f, αp), ∆f = 3.9Hz, see table 3-3 for test conditions.

M.Sc. Thesis Woutijn J. Baars, BSc. 5-3 Effect of Lock-In on Aircraft Stability & Control 61

(a)

1 2 3 4

0.1 ) [−] p 0 α

(f, −0.1 0 2 LQ

γ 4 10 5

6 100 α [degr] p freq [Hz] 200

(b)

1 2 3 4

0.8 ) [−] p 0 α 0.6 (f, 0.4 5 2 total

γ 4 6 10 7 8 9 100 α [degr] 10 p freq [Hz] 200

Figure 5-5: Higher-order coherence spectra (5% BMF applied): accelerometer 4 and pressure 2 2 transducer A, (a) γLQ(f, αp), (b) γtotal(f, αp), ∆f = 3.9Hz, see table 3-3 for test conditions.

M.Sc. Thesis Woutijn J. Baars, BSc. 5-3 Effect of Lock-In on Aircraft Stability & Control 62

The proposed ice-induced mechanism that results in the Dutch roll instability also includes the destabilizing pair of wing root vortices as an aggravating mechanism that can initiate this upset. During the experiments, pressure transducers were located where the cores of those stable wing root vortices were expected to trail in the stabilizer region (Section 3-2-1). The total pressure, measured by the transducers, is lower in the core of the vortex. In the after processing phase, this pressur data was supposed to give a better insight in the behavior of those vortices. If the mean pressure is increased it means that the vortices are not at the location of the transducers anymore, thus, if the mean pressure is fluctuating it could mean that the cores are oscillating in front of the transducer. Unfortunately, in the after processing phase, it was observed that the pressure transducers were not sensitive enough for this application. Therefore, no quantitative results are available about this wing root vortex induced aircraft stability and control upset mechanism.

M.Sc. Thesis Woutijn J. Baars, BSc. Chapter 6

Concluding Remarks

The objective of this thesis work, with the subject of flying small general aviation aircraft in icing conditions, was to propose ice-induced destabilizing mechanisms of small general aviation aircraft and to investigate experimentally the fluid-structure, linear and non-linear, lock-in phenomena resulting from ice accumulation on the elevator horn balance leading edges. A summarizing conclusion is presented in Section 6-1, followed by the final section of this thesis work where the topics for future work are presented.

6-1 Conclusions

Two ice-induced upset scenarios, associated with small general aviation aircraft, were investi- gated to obtain more insight about the actual mechanisms causing the upsets. The first upset involves an elevator horn, ice-induced, Limit Cycle Oscillation (LCO), followed by a complete loss of elevator control authority. In the second upset event, various aircraft- and ice-induced flow phenomena cause a destabilizing mechanism that is identical to a violent wing rock or Dutch roll instability. It was outlined that the loss of elevator control authority encountered in the first upset, was due to a spanwise vorticity shedding off the ice-induced, stabilizer leading-edge, seperation bubble, which will occur even in the absence of an elevator LCO. This vorticity is approxi- mately orthogonal to the Vortex Generator (VG) vorticity which is incorporated to overcome a loss of elevator nose down trim authority of relative long-fuselage aircraft. The orthogonal overlay of two vortex fields, of the appropriate relative strength and wave length, will de- stroy both vorticity fields. This was demonstrated by wind tunnel experiments (Figure 2-17). When the elevator is in a state of LCO, the continual shedding of the bound vorticity of the surface will utterly destroy any vorticity produced by the row of vortex generators on that surface. The obvious solution to this problem is to employ an anti-icing system on the elevator, as well as to any aerodynamic horn balance. Some commercial aircraft are now successfully employing the TKS ice protection system on aerodynamic control horn balances.

M.Sc. Thesis Woutijn J. Baars, BSc. 6-1 Conclusions 64

The second, Dutch roll type, upset event is caused by a destabilizing mechanism of a pair of vortices in the stabilizer region, which are originated at the main wing root/fuselage junction. The destabilizing mechanism of the two vortices trailing back along the top of the fuselage, is caused by either a cross flow shedding event around the fuselage or a structural oscillation of the aircraft caused by another ice-induced lock-in phenomenon. The latter can be the lock-in mechanism of the structural acceleration and the unsteady flow field behind the elevator horn balance with ice accumulation. In 2006, wind tunnel studies were employed at UT Austin to investigate this upset event. Two potential areas were identified for modification to alleviate this problem. First, anti-icing procedures are recommended for the elevator horn balances to avoid rapid ice accumulation on tail planes, that always seem to occur if no ice protection is employed here. Secondly, the aerodynamic chines on the sides of the fuselage (if present) should be equipped with an anti-icing system, since they hold the wing root vortices to the fuselage, hereby preventing the two wing root vortices from having violent motions next to the stabilizers.

In both proposed ice-induced destabilizing mechanisms a lock-in of two unsteady events, (1) the ice-induced unsteady flow field and (2) the unsteady structural acceleration of the aircraft, is present. A wind tunnel study is employed to investigate the lock-in mechanism of the structural acceleration and the unsteady flow field induced by ice accumulation that is only present on the elevator horn balance leading edges (in general not equipped with an anti-icing device in the class of small general aviation aircraft), as schematically indicated in Figure 6-1.

A B C

ice accumulation ice-induced unsteady flow aircraft

elevator horn balance

Figure 6-1: Schematic overview of research. Copy of Figure 1-3.

The ice accumulation (block A) on the leading edges of the elevator horn balances, cause un- steady flow fields (block B) that can trigger the aircrafts stability (block C). An experimental data set has been obtained where the unsteady, ice-induced, flow field and the acceleration of a 1:10 scale aircraft model is synchronously acquired using pressure transducers and accelerom- eters, respectively. Statistical signal processing techniques, that are able to compute linear and quadratic coherence spectra, have been presented in this thesis work and have been ap- plied in the pressure-acceleration coherence study. The first-order processing technique, based on the well-known linear coherence spectrum, revealed a low-frequency lock-in region in the f, αp-plane for the case where ice accumulation was simulated on the leading edges of the horn balances, while no lock-in was observed without ice simulations. This indicates that violent aircraft motions can indeed be a result from the ice-induced flow field over the horn balances.

M.Sc. Thesis Woutijn J. Baars, BSc. 6-2 Recommendations 65

The lock-in occured for the reduced-stiffness model at a frequency of 6Hz and for αp > 7◦. Although a reduced-stiffness aircraft model was used in the experimental setup, and thus the quantitative results are not translatable to the real-size case, the identification of this linear lock-in mechanism indicates that their is a significant chance that similar lock-in mechanisms occur in full-scale flight applications. The actual pressure-acceleration coupling appears to be mainly non-linear according to the literature by Tate & Stearman (1986); Kruger et al. (2005); Park et al. (2008), therefore, an HOS statistical signal processing technique, based on a second-order, non-orthogonal, Volterra model, has been introduced. A quadratic interaction occurs when harmonics, sum, and differ- ence combinations of input spectral peaks, at frequencies f1 and f2 with associated phases φ1 and φ2, result in a spectral peak at frequency f with phase φ in the output signal according to the selection rules f = f1 + f2 and φ = φ1 + φ2. The Volterra model technique, a low- dimensional identification technique, is able to quantify the quadratic coupling by presenting a quadratic coherence spectrum, similar to the linear coherence spectrum, as function of that output frequency, f. The source frequencies (and phases) in the input signal, f1 and f2, causing the output excitation frequency f, can be obtained from bispectrum analysis. Next to the linear and quadratic terms in the power spectrum of the model output, two cross terms are present. These cross terms, resulting in an interference coherence spectrum, can cause an error in the linear and quadratic coherence spectra if the amplitude of the interference spectrum is relatively large. Due to computational power and memory limitations of conventional desktop computers, the higher-order results that have been presented were created using a relative low number of Discrete Fourier Transform (DFT) coefficients, N. The small value of N resulted in a coherence spectrum frequency resolution, ∆f, that was too small to identify second-order lock- in phenomena in the pressure-acceleration study. The amplitudes of the quadratic coherence spectra were non-unique, since variations in the amplitudes have been observed when more or less data was used in the process of ensemble averaging. This implies convergence issues concerning this method. Thus, a correct interpretation of the physics, related to the quadratic coherence, was not possible yet, due to the current limitations related to the implementation of this technique.

6-2 Recommendations

The recommendations are given to perform further research on the ice-induced upsets of aircraft and to further develop the higher-order system identification tool that can be used throughout the entire field of (experimental) fluid dynamics. The future research will eventually result in a better understanding of the fluid-structure interaction mechanisms that inititate the stability and control upsets of small general aviation aircraft, as discussed in this thesis work. Future work involves:

Theoretical Background The proposed ice-induced destabilizing mechanisms have been identified based on NTSB-, FAA-, and pilot-reports. The written reports provide a lot of know-how about the experiences of the pilots. However, interviews with pilots, who recently experienced an ice-induced

M.Sc. Thesis Woutijn J. Baars, BSc. 6-2 Recommendations 66 upset, provide more detail about how they identified the upset and in what way they have responded to it. Furthermore, interviews with the engineers that built the aircraft can provide a lot of extra knowledge about the features of the aircraft and the trade-off’s that were made in the design process that resulted in, for example, the exclusion of anti-icing protection systems on the horn balances.

Experimental Study The two proposed ice-induced destabilizing mechanisms can be verified using experimental techniques in future work. All the mechanisms that in a combined form result in the up- set mechanism can be studied individually. For example, the wind tunnel study conducted by Dearman & et al. (2007) to investigate the loss of elevator pitch down authority was inves- tigated using pressure contours downstream. This experiment can be improved by mounting the horizontal stabilizer on a balance system, which can actually quantify the loss of ele- vator pitch down control. The next step is to investigate the destabilizing mechanisms on the entire aircraft. To investigate the ice-induced aeroelatic stability and control upsets of the entire aircraft, a model that exactly represents the dynamics of the full-scale aircraft is preferred. In that case, the quantitative results can be scaled to the full-scale aircraft ap- plication. Cable-mounted models, or free-flying models, which are dynamically scaled, are suitable for this, since they do not have the interference with a support system, the asso- ciated lock-in phenomena during aeroelastic experiments, and they are not limited in their motions. Another alternative is flight testing, however, the associated dangers with flying the aircraft with unknown changes in the performance might result in failure. The sting mounted, reduced-stiffness, model that was used in the current experimental investigation can still be used for a better understanding (using PIV) of the flow characteristics initiated by aircraft features, such as the wing root trailing vortices. The sampling criteria that were used to quantify the acquisition of the data in the current experimental investigation were based on acceptable errors in the mean of the estimators. Since coherence studies were performed in the after processing phase, the sampling criteria were not fully representative. During the design of an experiment, one should already take the after processing phase into account, therefore, sampling criteria should be developed based on the higher-order system identification techniques such that the data sets are suitable to be processed by the higher-order system identification tool afterwards.

Higher-Order System Identification Tool Quantification of the non-linear interactions will result in a better understanding of the fluid- structure interaction mechanism that initiate aircraft stability upsets. Therefore, the current implementation of the higher-order system identification tool should be expanded. This in- volves:

Implementation of the code on a supercomputer, available at UT Austin at the → Texas Advanced Computing Center (TACC), will provide the capability of producing results with higher frequency ranges and resolutions (larger number of DFT coefficients N).

The amplitude of the quadratic coherence spectrum, in the application to the turbulent → mixing layer and current experimental investigation, decreases when more ensemble

M.Sc. Thesis Woutijn J. Baars, BSc. 6-2 Recommendations 67

averages are taken. An investigation in this convergence issue and the uniqueness of this spectral QSE technique should be among the topics of future research.

Higher-order terms can be included, such as cubic terms (Nam & Powers, 1994; → Im & Powers, 1996; Powers et al., 1993), to increase the prediction performance of the Volterra model technique, and thereby, to increase the power of finding coupling mech- anisms in a single-I/O system.

The identification tool can be expanded by using an orthogonal Volterra → model (Im & Powers, 1996; Powers et al., 1993; S. B. Kim & Powers, 1993; Im et al., 1993) to eliminate the interference term in the auto power spectrum of the model out- put, Eq. (4-18), and general model coherence, Eq. (4-19). This will result in purely linear and higher-order coherence spectra that can be interpreted correctly at all times.

Although HOS techniques are insensitive to independent Gaussian noise, due to the → fact that bispectrum terms are zero for Gaussian functions (Tick, 1961), advanced filter techniques can be applied as well in order to extract physical interpretations of data with a low signal-to-noise ratio.

As was proposed in the ’experimental study’ paragraph, sampling criteria for an exper- → iment should be developed based on the higher-order system identification technique.

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M.Sc. Thesis Woutijn J. Baars, BSc. Appendix A

Volterra Technique - Linear Algebra

Note: For a complete overview of the linear algebra approach in the Volterra model technique, the interested reader is referred to the work presented by K. I. Kim & Powers (1988); Nam et al. (1989); Nam & Powers (1994).

The linear algebra system, presented by Eq. (A-1), consists of vector p, vector h and the measured physical output of the system, A(f). Vector p is called the polyspectral input vector and consists of all the pressure input terms, P (..), present in Eq. (4-8). Vector h consists of all the discrete transfer function coefficients, H(..). For an even discrete frequency, f, the transfer function vector h and polyspectral input vector p are given by Eq. (A-2) and Eq. (A-3), respectively. Matrix E p pT is presented on the next page. { ∗ }

T E p∗p h = E p∗A(f) . (A-1) { } { }

hT = H (f) ,H f , f , 2H f + 1, f 1 ,..., 2H (f, 0) ,..., 2H N , 0 (A-2) L Q 2 2 Q 2 2 − Q Q 2 h    
i

pT = P (f) , P f P f , P f + 1 P f 1 ,...,P (f) P (0) ,...,P N P (0) (A-3) 2 2 2 2 − 2 h        
i

M.Sc. Thesis Woutijn J. Baars, BSc. 75                     } 2 | ) N − f ( P ...... | 2 | ) N ( P | { E } ) N − f ( P ) . N . ··· ··· ··· ( . P ) f ( ∗ P { E } ) 1 −  2 2 f | ( ) 1 P ) − 2 f +1 ( 2 f P ( | 2 . . . P ··· ··· | ) ) 2 f ( +1 ∗ 2 f P ( ) P 2 f | (  ∗ E P { E } ) 2 f } ( ) P 1 ) − 2 f 2 f ( (  P 4 P ) | 1 ) ) − 2 f +1 . . . 2 f ··· ( 2 f ( P ( ∗ | P  P ) ) E f ( +1 ∗ 2 f P ( { ∗ E P { E } ) } 2 f ) ( f } } ( ) P ) f P ) f ( ( ) 2 f P 1 P ) ( ) − N P 2 2 f f ) − f ( ( f ( ∗ ∗ ( . . . ∗ ∗ P P P ) ) P ) { 2 f +1 E N ( ( 2 f } ∗ ∗ 2 ( P | P ) ∗ { { f P ( E E { P | E { E                    

M.Sc. Thesis Woutijn J. Baars, BSc.