Aerodynamics and Flight Mechanics

Aerodynamics and Flight Mechanics Principal Investigators: Mike Bragg Eric Loth Graduate Students: Holly Gurbacki (CRI support) Tim Hutchison Devesh Pokhariyal (CRI support) Ryan Oltman 3-1

SMART ICING SYSTEMS Research Organization Core Technologies Aerodynamics and Propulsion Flight Mechanics Controls and Sensor Integration Human Factors Aircraft Icing Technology IMS Functions Characterize Icing Effects Operate and Monitor IPS Envelope Protection Adaptive Control Flight Simulation Demonstration Safety and Economics Trade Study 3-2

Aerodynamics and Flight Mechanics Goal: Improve the safety of aircraft in icing conditions. Objective: Approach: 1) Develop a nonlinear iced aircraft model. 2) Develop steady state icing characterization methods and identify aerodynamic sensors. 3) Identify envelope protection needs and methods. First use Twin Otter and tunnel data to develop a linear clean and iced model. Then develop a nonlinear model with tunnel and CFD data. Use the models to develop characterization and envelope protection. 3-3

Smart Icing System Research Holly Gurbacki, Dr. Bragg Devesh Pokhariyal, Dr. Bragg Tim Hutchison, Dr. Bragg Ryan Oltman, Dr. Bragg Dr. Loth Aerodynamic Sensors Clean Aircraft Model Steady State Characterization Characterization Flight Mechanics Model Iced Aircraft Model Iced Aerodynamics Model Aircraft - Flight Mechanics Analysis Envelope Protection Wind Tunnel Data Computational Fluid Dynamics THE AERODYNAMICS AND FLIGHT MECHANICS GROUP Flight Simulation 3-4

Outline Flight Mechanics Model Development of Clean Aircraft Model Development of Iced Aircraft Model Flight Mechanics Analysis of Clean and Iced Aircraft Steady State Characterization Hinge-Moment Aerodynamic Sensor Summary and Conclusions Future Plans/CFD Analysis 3-5

Equations of Motion 6 DoF equations of motion : m (U& VR + WQ) = mg sinθ + F A + F x T x m (V& + UR WP) = mg sinφ cosθ + F A + F z y T y m (W& UQ + VP) = mg cos φ cos θ + F + F xx xz xz zz yy A A z T z I P& I R& I PQ + (I I )RQ = L + L & 2 2 I yyq (Ixx Izz )PR + Ixz(P R ) = MA + I R& I P& + (I I )PQ + I QR = N + N zz xz yy xx xz A M T T T 3-6

Equations of Motion (cont.) The longitudinal equations of motion are considered initially the forces along the aircraft body axes are resolved into lift and drag forces to yield: m(u VR + WQ) = mgsinθ + (L sinα Dcosα) + Tcosφ T m(w UQ + VP) = mgcosφ cosθ + ( Lcosα Dsinα) + T sinφ T 2 2 I yy Q (Ixx Izz )PR + Ixz(P R ) = MA + M T 3-7

Smart Icing System Research Holly Gurbacki, Dr. Bragg Devesh Pokhariyal, Dr. Bragg Tim Hutchison, Dr. Bragg Aerodynamic Sensors Steady State Characterization Characterization Ryan Oltman, Dr. Bragg Dr. Loth Clean Aircraft Model Flight Mechanics Model Iced Aircraft Model Iced Aerodynamics Model Aircraft - Flight Mechanics Analysis Envelope Protection Wind Tunnel Data Computational Fluid Dynamics THE AERODYNAMICS AND FLIGHT MECHANICS GROUP Flight Simulation 3-8

Twin Otter Clean Model (v1.0) Longitudinal model is derived from flight dynamics data in AIAA report 86-9758, AIAA report 89-0754 and AIAA 93-0754 Dimensional parameters: Parameter Value Units Wing Area 39.02 m2 Wing Span 19.81 m Aspect Ratio 10 Mean Aerodynamic Chord 1.981 m Mass 4150 kg Airspeed 61.73 m/s Altitude 1524 m Moments of Inertia: Ixx, Iyy, Izz, Ixz 21279, 30000,44986, 1432 kg.m2 Flap Deflection 0 deg 3-9

Clean Dimensional Derivatives (v1.0) Nondimensional Clean Dimensional Clean Parameter Value Parameter Value Units C L 0.5 M δ -10.45 /s 2 C Lo 0.2 M u 0 /ft-s C Lq 19.97 M q -3.06 /s C Lα 5.66 M αdot -0.804 /s C Lαdot 2.5 M Tu 0 /ft-s C LδE 0.608 M α -7.87 /s 2 C D0 0.0414 Z δ -40.33 ft/s 2 K 0.0518 Z α -379.03 ft/s 2 C m 0 Z u -0.31 /s C mo 0.15 Z αdot -2.446 ft/s C mq -34.2 Z q -19.7 ft/s C mα -1.31 X α 13.72 ft/s 2 C mαdot -9 X Tu 0.0149 /s C mδe -1.74 X u -0.033 /s X δ 0 ft/s 2 3-10

Empirical Clean Model Method The clean aircraft model is developed using methods outlined in NASA TN D-6800 for twin-engine, propeller-driven airplanes. Lift, pitching moment, drag and horizontal tail hinge moments are modeled. Method is based on theoretical and empirical methods (USAF Datcom handbook and NACA/NASA reports) Model requires mainly aircraft geometry and thus can be applied to different aircraft at minimal cost. Waiting for Twin Otter data 3-11

Empirical Clean Model (NASA TN D-6800) Representative equations: C L = CL + C ( C ) wfn L + h(hf ) L δe + ( C L ) power C M = CM + C ( C ) ( C ) ( C ) wfn M + h(hf ) M + e M + δ tab M power C D = C D + (C 0 D ) + (C i w D ) + (C ) (C ) (C ) ( C ) i h D + i f D + i n D + coolingsystem D power C h (x hinge h h = (C h ( f ) L ) + ( C ) ( C ) h( f ) tab 0 L + δ = δtab M δtab c h x ac ) (x hinge c h x c / 4 ) 3-12

Icing Effects Model Objective: To devise a simple, but physically representative, model of the effect of ice on aircraft flight mechanics for use in the characterization and simulation required for the Smart Icing System development research. 3-14

Linear Icing Effects Model C ( A )iced = (1+ ηice kc ) C(A) A C A = Arbitrary coefficient (C Lα, C mδe, etc.) ( ) η ice = icing severity factor k CA = coefficient icing factor 3-15

Icing Factors η = f ( n, A E) ice c η ice is the icing severity factor k CA where: n A c E = freezing fraction = accumulation parameter = collection efficiency is the coefficient icing factor k C A = f(a )(IPS, aircraft geometry and config., icing conditions) 3-16

η ice Formulation η ice = C d ref Cd( NACA 0012, c = 3',IRT data) ( NACA 0012, cont. max.conditions, t = 45min) C d fit as a function of n and A c E C d data obtained from NACA TM 83556 C dref calculated from C d equation using continuous maximum conditions η ice formulated such that η ice =0 at n=0 or A c E=0 3-17

C d Curve Fit of NASA TM 83556 Data 0.12 0.1 0.08 n=.33 Data n=.33 Curve Fit n=1 Data n=1 Curve Fit Cd 0.06 0.04 0.02 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 A c E 3-18

η ice Reference Value To nondimensionalize the C d equation, a reference condition was chosen based on FAA Appendix C Maximum Continuous conditions. NACA 0012 c = 3 ft. MVD = 20 µm V = 175 knots LWC = 0.65 g/m 3 t = 45 min T 0 = 25 F These conditions yielded a C d = 0.1259 at η ice =1 3-19

Final η ice Equation (v1.0) η ice 1 ( A E) Z ( A E) 2 = Z + c 2 c 2 3 4 an + bn + cn + dn Z 1 = 3.176n Z2 = 2 3 4 1+ en + fn + gn + hn a b c d = 4547.33 = 54370.52 = 248690.58 = 179810.26 e = 4.322 f = 33.295 g = 250.595 h = 36.697 3-20

Variation with n and A c E 1.00 0.80 AcE=.01 AcE=.02 AcE=.03 AcE=.04 Cont. Max. Case 0.60 ηice 0.40 0.20 0.00 0 0.2 0.4 0.6 0.8 1 Glaze Ice n Rime Ice 3-21

η ice Variation with A c E and n 1.60 1.40 1.20 1.00 n=0.1 n=0.2 n=0.4 n=0.6 n=1 ηice 0.80 0.60 0.40 0.20 0.00 0.000 0.010 0.020 0.030 0.040 0.050 A c E 3-22

Iced Model (v1.0) Equations: (CA ) ice ( CA ) = (CA ) (1+ kc ηice) k 1 ice clean A C η A ice = (C ) A clean C = C + KC D D0 2 L C L C Lo C Lq C Lα C Lαdot C LδE C D0 K clean 0.5 0.2 19.97 5.66 2.5 0.608 0.041 0.052 iced 0.5 0.2 19.7 5.094 2.5 0.55 0.062 0.057 k CA η ice 0 0-0.014-0.1 0-0.095 0.5 0.1 C m C mo C mq C mα C mαdot C mδe clean 0 0.15-34.2-1.31-9 -1.74 iced 0 0.15-33 -1.18-9 -1.566 k CA η ice 0 0-0.035-0.099 0-0.1 3-23

Comparison of Clean and Iced Model (v1.0) Parameter Clean Iced Units M δ -10.44-9.4 /s 2 M u 0 0 /ft-s M q -3.055-2.948 /s M αdot -0.804-0.804 /s M Tu 0 0 /ft-s M α -7.863-7.083 /s 2 Z δ -40.29-36.45 ft/s 2 Z α -378.72-342.67 ft/s 2 Z u -0.31-0.31 /s Z αdot -2.446-2.466 ft/s Z q -19.697-19.431 ft/s X α 13.706 13.898 ft/s 2 X Tu 0.0149 0.0266 /s X u -0.033-0.0463 /s X δ 0 0 ft/s 2 3-24

Flight Dynamics and Control Toolbox Flight Dynamics Code 1.3 FDC 1.3 is a free source code written by Marc Rauw (based in the Netherlands) Code developed using MATLAB and SIMULINK 6 DoF equations: Assumptions The body is assumed to be rigid during motions The mass of the aircraft is assumed to be constant during the time-interval in which its motions are studied Earth is assumed to be fixed in space & the curvature is neglected 12 - Nonlinear differential equations used to describe the motion 3-26

3-27 Velocity Alpha Beta Forces & Moments FDC Equations ( ) β α β β α β α β β α cos sin w qu pv sin v ru pw cos cos u rv qw sin sin F sin F cos cos F m 1 V w w w w w w w w w z y x + + + + + + = ],,,,,,,,,p,q,r,,,,,, [0, C S c V M ],,,,,,,,,p,q,r,,,,,, [0, C S V F 2 e a r f r a f e 3 2 3 2 L,M,N 2 2 1 L,M,N 2 e a r f r a f e 3 2 3 2 x,y,z 2 2 1 x,y,z β β δ αδ αδ αδ αδ αδ αδ δ δ δ δ β β β α α α ρ β β δ αδ αδ αδ αδ αδ αδ δ δ δ δ β β β α α α ρ & & = = ( ) ( ) β α α α α α α β α tan r sin pcos q sin u rv qw cos w qu pv cos F sin F m 1 V cos 1 w w w w w w z x + + + + + + = ( ) α α β α β β α β α β β α β cos r p sin sin sin w qu pv cos v ru pw sin cos u rv qw sin sin F cos F sin cos F m 1 V 1 w w w w w w w w w z y x + + + + + + + + =

Pitch, Roll & Yaw Rates p& = 2 ( Iyy Izz) Izz Jxz ) 2 ( Ixx Izz Jxz ) FDC Equations (cont.) r + (( Ixx Iyy + Izz) Jxz) p q + L + Jxz 2 2 2 ( Ixx Izz Jxz ) ( Ixx Izz Jxz ) ( Ixx Izz Jxz ) Izz N q& = ( Izz Ixx) Ixz 2 2 p r ( p r ) Iyy Iyy + M Iyy r& = 2 ( ( ) ) (( Ixx Iyy + Izz) Jxz) Ixx Ixx Iyy + Jxz p Jxz r q + L + ( Ixx Izz Jxz ) ( Ixx Izz Jxz ) ( Ixx Izz Jxz ) N 2 2 2 Ixx 3-28

Euler Angles qsinϕ + r cosϕ ψ& = cosθ θ& = qcosϕ r sinϕ ϕ& = p + Position x& y& z& e e e = = FDC Equations (cont.) ( qsinϕ + r cosϕ) tanθ = p + ψ& sinθ { ue cosθ + ( ve sinϕ + w e cosϕ) sinθ} cosψ ( ve cosϕ w e sinϕ) { ue cosθ + ( ve sinϕ + w e cosϕ) sinθ} sinψ ( ve cosϕ w e sinϕ) u sinθ + ( v sinϕ + w cosϕ) cosθ = e e e sinψ cosψ 3-29

FDC Equations (cont.) The current aircraft model (without turbulence) is using the following equations for the longitudinal mode: V = α = q& = 1 m ( F cosα cosβ F sinα sinβ) 1 V cos x + β 1 m z ( F sinα + F cosα) + q ( pcosα r sinα) tanβ ( Izz Ixx) Jxz 2 2 p r ( p r ) Iyy θ& = qcosϕ r sinϕ x z + Iyy + M Iyy x& z& e e = { ue cosθ + ( v e sinϕ + w e cosϕ) sinθ} cosψ ( ve cosϕ w e sinϕ) u sinθ + ( v sinϕ + w cosϕ) cosθ = e e e sinψ 3-30

Open Loop Analysis Tool for Nonlinear Twin Otter Model 3-31

Closed Loop Analysis Tool for Nonlinear Twin Otter Model 3-32

Validation of the FDC (TIP flight p5220) Code is validated by comparing the response of a doublet to published NASA data (AIAA 99-0636) for the Twin Otter aircraft. Flight conditions: V = 187 ft/s alt. = 5620 ft α = 3.53 deg δ F = 0 deg 3-33

Clean and Iced Model (v2.0 TIP) C X0 C Xα C Xα 2 C Xδe Clean -0.076 0.390 2.910 0.096 Iced -0.090 0.714 1.744 0.068 η ice.k C(A) 0.182 0.831-0.401-0.290 C Z0 C Zα C Zα 2 C Zq C Zδe Clean -0.311-7.019 4.111-3.182-0.234 Iced -0.318-7.510 6.573-7.395-0.3541 η ice.k C(A) 0.020 0.070 0.599 1.322 0.513248 C m0 C mα C mα 2 C mq C mδe Clean -0.011-0.879-3.852-19.509-1.8987 Iced -0.026-0.790-3.930-21.480-1.8629 η ice.k C(A) 1.361-0.101 0.020 0.101-0.01886 Ref: Robert Miller and W. Ribbens, AIAA 99-0636 3-34

Validation of FDC 1.3 Validation of the FDC (TIP flight p5220, no ice) q, deg/sec 10 8 6 4 2 0-2 -4 Flight Data FDC Alpha, deg 8 7 6 5 4 3 Flight Data FDC -6-8 -10 0 5 10 15 Time, sec 2 1 0 0 5 10 15 Time, sec 3-35

Validation of FDC 1.3 (cont.) Validation of the FDC (TIP flight p5220, no ice) Velocity, ft/sec 190 189 188 187 186 185 184 183 182 181 Flight Data FDC Altitude, ft 5655 5650 5645 5640 5635 5630 5625 5620 5615 5610 Flight Data FDC 0 5 10 15 Time, sec 0 5 10 15 Time, sec 3-36

Validation of FDC 1.3 (cont.) Validation of the FDC (TIP flight p4601, iced) 3-37

Clean and Iced Dynamic Comparison Initial trimmed flight conditions: Altitude = 5600 ft Velocity = 187.5 ft/sec Angle of Attack = 3.52 Aircraft Model v2.0 Clean: η ice = 0.0 Iced: η ice =.15 3-39

Dynamic Analysis, Clean & Iced 3-40

Dynamic Analysis, Clean & Iced (cont.) 3-41

Steady State Characterization Goal: Analyze quasi-steady data characterized by control inputs and disturbances insufficient to excite dynamic modes to characterize the icing encounter. Objectives: Determine onset of icing on an aircraft in real-time during flight. Estimate the severity of ice accretion in terms of its effect on performance, stability and control. Identify location of ice accretion on the A/C and the potential safety hazards. 3-43

Steady State Characterization (cont.) Approach: Acquire flight data, using onboard sensors. Process aircraft data to obtain nondimensional parameters in iced and equivalent clean conditions. Compare iced and clean models to back out useful flight parameters such as C L, δ E, C D, and C h. Set threshold values to determine onset of icing. Analyze the s and other sensor information to determine the type and location of ice accretion and the potential safety hazards. 3-44

S. S. Characterization Results Use FDC 1.3 auto-pilot configuration set at: constant altitude constant power Analyze the effects of icing on: angle of attack elevator deflection velocity and drag characteristics The clean and iced configurations have been compared for conditions with and without turbulence. The icing simulations are set at η ice =.15 and the simulations are run for 22 minutes. 3-45

Steady State Flight Conditions The initial conditions for the steady state analysis are: Altitude = 9000 ft Velocity = 268 ft/sec Angle of Attack = 0.5 Elevator Deflection = -0.6 η ice (t = 0) = 0 η ice (t = 22 min.) = 0.83 Clean and Iced Model v2.1 is used. 3-46

Turbulence Model The turbulence model used in the FDC 1.3 steady state analysis is based on the Dryden spectral density distribution. The turbulence intensity produces an aircraft z- acceleration of 0.13g RMS with typical variations of +/- 0.5g encountered over the 22 minute flight. 3-47

Comparison for α and δ E (No turbulence) η ice = 0.83 η ice = 0 η ice = 0 η ice = 0.83 3-48

Comparison for C D and V (No turbulence) η ice = 0.83 η ice = 0 ηice = 0 η ice = 0. 83 3-49

Comparison for α and δ E (turbulence) η ice = 0.83 η ice = 0 η ice = 0 η ice = 0.83 3-50

Comparison for C D and V (turbulence) η ice = 0.83 η ice = 0 η ice = 0 η ice = 0.83 3-51

Wind Tunnel Testing 3-53

Sensing Unsteady Hinge Moments Objective: Use unsteady hinge moment to sense potential control problems and nonlinearities due to ice-induced flow separation Approach: NACA 23012 airfoil model with simple flap and forward-facing quarter round simulated ice Steady-state C l, C d and C m from balance and pressures and C h from hinge-moment balance and pressures Time series and frequency spectra of unsteady C h from hingemoment balance Time series and frequency spectra of flow unsteadiness from hot-wire anemometer placed within and aft of separation bubble, in shear-layer, and over flap 3-54

Unsteady C h RMS 0.05 NACA 23012, Re = 1.8 million, δ f = 0 C l, max 0.04 Unsteady C h RMS 0.03 0.02 C l, max 0.01 0-10 -5 0 5 10 15 20 AOA (degrees) Clean x/c =.02 x/c =.10 x/c =.20 C l, max 3-55

Aerodynamics and Flight Mechanics Waterfall Chart Federal Fiscal Year 98 99 00 01 02 03 Linear Iced Aircraft Model CFD Wind Tunnel Testing Nonlinear Iced Aircraft Model Determine Need for and Select Aerodynamics Sensors Steady State Characterization of Icing Effects S. S. Char. Method 3-56

Summary and Conclusions Clean twin otter linear models developed. Method for including icing effects in linear model developed. Flight mechanics computational method available. Iced twin otter models for TIP studies available and performs well. Steady state characterization formulated and initial results promising. 3-57

Future Research Complete and refine linear models, icing effects model and perform icing accident analysis Complete steady state characterization method Study and develop envelop protection schemes Identify aerodynamic and other sensors Develop fully nonlinear model Experiment & CFD for AE data bases Neural Networks for AE interrogation Assess Feasibility of a VIFT (Year 4) 3-58

Fully Non-Linear APC Overview Holly Gurbacki, Dr. Bragg Devesh Pokhariyal, Dr. Bragg Tim Hutchison, Dr. Bragg Ryan Oltman, Dr. Bragg to be decided, Dr. Loth Aerodynamic Sensors Clean Aircraft Model Steady State Characterization Characterization Flight Mechanics Model Iced Aircraft Model AE Iced Aerodynamics Model Aircraft - Flight Mechanics Analysis Envelope Protection Wind Tunnel Data Computational Fluid Dynamics THE AERODYNAMICS AND FLIGHT MECHANICS GROUP Flight Simulation 3-59

Objective: Fully Non-Linear Model For flight mechanics, we would like non-linear Aero- Performance Curves (APC): C L, C D, C m, C h as a function of α, δ, etc. and environmental conditions Method: Use high-quality previous and new data sets (experimental and computational) to construct All- Encounters (AE) data bases Construct neural networks for use in interrogation of any condition atmospheric/flight condition Apply neural networks to flight mechanics 3-60

All Encounters Data Bases Method: Collect data of ice-shape characteristics (x/c ice, k/c ice ) as a function of flight conditions (α, d, LWC, T 0, Re, etc.): Icing Research Tunnel Shapes In-Flight Icing Shapes LEWICE shapes Collect data of 2-D APC (C l, C m,..) as a function of iceshape characteristics (x/c ice, k/c ice ) and α and δ: Icing Research Tunnel Aerodynamic Tests Wind Tunnel Tests for various Ice Shapes CFD for various Ice Shapes 3-61

Computational Fluid Dynamics NSU2D will be the primary code for CFD unstructured adaptive triangulated grid Can handle complex shapes & multi-element Spallart-Almaras turbulence model Employs e n transition model Unsteady capabilities for flow shedding To improve prediction fidelity To investigate unsteady aerodynamic sensing To be parallelized for SG Origin 2000 3-62

Sample CFD NSU2D LE ice-shape predictions 3-63

Neural Network Approach Construct Separate Neural Networks for: Ice-shape characteristics as a function of environmental conditions 2-D APC as a function of ice-shape characteristics and flight conditions Train Neural Networks with AE databases Use analytical methods to convert 2-D APC to C L,C D,C m, C h Replace Linear Model with Non-Linear Neural Networks for Flight Mechanics 3-64

Neural Network for Ice-Shape Sample neuron: Y= f(σ W i x i ) with x i = (α, d, LWC, etc.) W i are trained with data (f refers to a sigmoidal function) Y refers to output of a neuron; final output: x/c ice, k/c ice α δ Input Layer Hidden Layer 1 Hidden Layer 2 Output Layer d x/c ice, k/c ice LWC 3-65

Neural Network Interrogation Input are ice-shape characteristics & flight condition Final output are the 2-D APC: C l,c d,c m, or C h α δ Input Layer Hidden Layer 1 Hidden Layer 2 Output Layer x/c ice k/c ice C l,c d,c m,c h 3-66

Feasibility of a Virtual Icing Flight Test Objective: Assess Feasibility of a VIFT (for a follow-on study) which would simulate a complete icing encounter including temporal resolution of ice accretion, pilot input, IMS, etc. Goal: Consider requirements for integrating Ice Accretion (LEWICE) Aerodynamic Predictions (NSU2D) A/C Flight Dynamics Model (Selig) Pilot Input / Flight Simulator Output (Sarter/Selig) IMS Control (Basar/Perkins) 3-67

Virtual Icing Flight Test Configuration? Atmospheric model: real time conditions: pressure, temperature, humidity, LWC of clouds A/C dynamic state, IPS on? Send appropriate IMS output: see levels a)-d) listed below aero forces/moments, virtual ice sensor output A/C state, pilot input icing sensor data L IPS initiating t D t Dedicated NCSA Supercomputer t x H1 H0 pilot yoke "Aero Workstation" for simulated A/C performance Computes as function. of time a) ice shape from LEWICE b) instantaneous aero forces & moments as a function of angle-of-attack & flap defl. "A/C Workstation" for virtual airplane state & pilot I/O a) receive input from pilot, IMS, and aerodynamic performance b) computes A/C dynamic state c) displays cockpit view including IMS warnings/info "IMS Workstation" for icing ID and IMS decision making: modify display/ips/control From A/C state data can: a) issue warnings to pilot b) initiate IPS operation c) modify flight envelope d) institute control adaptation 3-68