Representative Post-Stall Modeling of T-tailed Regional Jets and Turboprops for Upset Recovery Training by Tianhang Teng A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Aerospace Science and Engineering University of Toronto c Copyright 2016 by Tianhang Teng Abstract Representative Post-Stall Modeling of T-tailed Regional Jets and Turboprops for Upset Recovery Training Tianhang Teng Master of Applied Science Graduate Department of Aerospace Science and Engineering University of Toronto 2016 Loss-of-control resulting from airplane upset is a leading cause of worldwide commer- cial aircraft accidents. In order to provide pilots with sufficient stall recovery training using ground simulators, flight models will need to be improved. In this thesis, a methodology for generating a generic representative post-stall aircraft model is developed. Current type specific post-stall models are too expensive to generate, and are not practical for routine training. The representative model offers a much cheaper way to train crew for upset conditions, at the same time providing sufficiently realistic cues seen in an upset condition. The methodology provides a foundation for generating full scale representative models using wind tunnel data and physics-based approaches. An example of applying the methodology to predict stall regime aircraft behavior is provided for one aerodynamic coefficient. ii Acknowledgements First, I would like to express my sincere gratitude to my thesis supervisor Professor Peter Grant for the continuous support of my MASc study and related research, for his patience, motivation, and immense knowledge. His guidance helped me throughout the entire research and writing portions of this thesis. I could not have imagined having a better advisor and mentor for my MASc study. I would like to thank Stacey Liu for her tremendous support in the lab, for help on technical knowledge, as well as moral support at difficult times. Thanks also go out to the Plane of Sky (POS) group, Tony Zhang, Zane Luo, and Jacek Khan for their feedback on some of the issues related to this study, for the sleepless nights we were working together before deadlines, and for all the fun we have had in the last few years. Finally, I would like to thank my parents and my girlfriend for their constant support during the course of my studies. iii Contents 1 Introduction1 1.1 Background..................................1 1.2 Upset Recovery Training...........................2 1.3 Post Stall Modeling..............................3 1.4 Project Definition...............................4 1.5 Organization.................................5 2 Literature Review6 2.1 Existing Post-Stall Model..........................6 2.2 Semi-Analytical Methods...........................9 2.2.1 Linear Methods............................9 2.2.2 Non-Linear Methods......................... 11 2.3 Stall Aerodynamics.............................. 13 2.3.1 G Break/Pitch Non-Linearity.................... 14 2.3.2 Roll-Off................................ 15 2.3.3 Reduced Lateral/Directional Stability................ 15 2.3.4 Reduced Control Effectiveness.................... 15 2.4 Configuration Effects............................. 16 2.4.1 Tail Effects.............................. 16 2.4.2 Nacelle Effects............................ 19 2.4.3 Wing Effects............................. 19 2.4.4 Fuselage Effects............................ 21 2.4.5 Engine/Power Effects......................... 21 2.5 Published Wind Tunnel Data........................ 22 3 Basic Methodology 26 3.1 Model Structure................................ 26 3.2 Modeling Approach.............................. 28 iv 3.3 Configuration Deltas (∆)........................... 30 4 Generation of Configuration ∆'s 32 4.1 Overview.................................... 32 4.2 Semi-Analytical Approach.......................... 33 4.2.1 Coefficient of Lift CL ......................... 39 4.2.2 Coefficient of Pitching Moment Cm ................. 42 4.2.3 Coefficient of Rolling Moment Cφ due to β ............. 43 4.2.4 Flap Effects.............................. 46 4.2.5 Engine Power Effects CT ....................... 48 4.2.6 Dynamic Effects Clp and Clr ..................... 51 4.3 Empirical Approach.............................. 53 4.3.1 Effects of Nacelle-Tail Interaction on Pitching Moment...... 54 4.3.2 Effects of Wing-Tail Interaction on Pitching Moment....... 58 4.3.3 Effects of Tail Location on Pitching Moment............ 59 4.3.4 Effects of Tail Size and Incidence on Pitching Moment...... 59 4.3.5 Effects of Fuselage on Pitching Moment............... 60 5 Full Scale Example 62 6 Conclusions 67 6.1 Summary of Work.............................. 67 6.2 Future Research Needs............................ 69 References 70 v List of Figures 2.1 Enhanced post stall model developed by NASA LaRC [1].........7 2.2 Blending method used on merging post stall model onto existing pre-stall model [2]....................................8 2.3 Classical vortex-lattice method....................... 11 2.4 Pitching moment for conventional tailed aircraft versus T-tailed aircraft. Reprinted from [3].............................. 14 2.5 Schematic of Tail Effect on Cm for T-Tail (Data adapted from NASA technical report [4]).............................. 17 2.6 Effect of horizontal tail size on Cm. Adapted from Ray [4]........ 18 2.7 Effect of horizontal tail incidence angle on Cm. Adapted from Ray [4].. 18 2.8 Nacelle Location effect on Cm(α), dashed lines are nacelle off condition (Reprinted from Ray [4])........................... 19 2.9 Sweep effect on Cm(α) (Reprinted from NASA technical report [4])... 20 2.10 Effect of fuselage shape and size on Cm. Adapted from Ray [4]...... 21 2.11 Effect of fuselage length on Cm. Adapted from Ray [4].......... 21 2.12 Wind tunnel data of CT effect on a straight wing turboprop aircraft... 22 3.1 Example Pitch Moment Coefficients for Target pre-stall (T P ), Target es- timated pre-stall/stall/post-stall (T E), and Target Stretched/offset pre- stall/stall/post-stall ( T M )......................... 29 3.2 Example Pitch Moment Coefficients for Target pre-stall (T P ), Target Stretched/offset stall (T M ) and Target stall model (T S). Blending occurs between two dashed vertical lines............................. 30 4.1 Spanwise lift distribution for angle of attack ranging from 0◦ to 25◦ at 5◦ interval..................................... 34 4.2 Viscous remapping procedure for a generic swept wing using a generic cambered airfoil................................ 35 4.3 Schematic of the de-α process........................ 37 vi 4.4 Prediction of CL after every iteration of de-α ................ 38 4.5 Comparison between α-correction method and crude direct remap method 38 4.6 3-D effect on the spanwise lift distribution. Reprinted from [5]...... 38 4.7 Example of spanwise lift after correcting for 3-D effect.......... 38 4.8 Comparison of de-α method vs. wind tunnel data using wing modeled from Ostawari [6]............................... 41 4.9 2-D lift curve of NACA 4415 airfoil..................... 41 4.10 Comparison between the potential flow and corrected span-wise lift distri- bution..................................... 41 4.11 2-D lift curve of the artificially generated NACA 0024 airfoil....... 42 4.12 Comparison of wing configuration from Shortal [7] with wind tunnel data 42 4.13 Comparison of wing configuration from Shortal [7] with wind tunnel data 43 4.14 2-D pitching moment curve of the artificially generated NACA 0024 airfoil 43 4.15 Spanwise lift distribution for straight wing at α = 15◦ β = −10◦ ..... 44 4.16 Comparison of the spanwise lift of wings under sideslip for higher α ... 45 4.17 Comparison of Cr vs. β for wing configuration from Ray [8]....... 45 4.18 Comparison of Crβ for wing configuration from Ray [8].......... 45 4.19 Definition of the three parameters. Plot shows two-dimensional trailing- edge flap effects................................ 46 4.20 2-D lift curve of clean airfoil versus predicted flap 35 configuration.... 47 4.21 Comparison of predicted CL and Cm against wind tunnel data for flap 35 48 4.22 Augment spanwise lift distribution to capture accelerated flow...... 49 4.23 Comparing predicted CT effects against wind tunnel data for high and low CT ....................................... 50 4.24 A schematic showing the two side of the wing at non-zero rolling rate.. 51 4.25 Spanwise lift distribution under non-zero p or r .............. 52 4.26 Spanwise lift distribution of an already stalled wing under non-zero p .. 52 4.27 Predicted Clp for a straight wing....................... 52 4.28 Predicted Clr for a straight wing....................... 52 4.29 Isolation of nacelle-tail interaction N ⊗ VH ................ 56 4.30 N ⊗ VH effect for various tail shadow angles................ 56 4.31 Spline points on the interpolation curve................... 56 4.32 Extrapolation of nacelle-tail interaction from tail shadowing angle.... 56 4.33 ∆ term subtracted from the two interoplated curves............ 57 4.34 Comparison of wind tunnel data between target configuration and baseline + ∆...................................... 57 vii 4.35 Isolation of wing-tail interaction W ⊗ VH ................. 58 4.36 W ⊗ VH effect for various tail shadow angles............... 58 4.37 Look-up graph for horizontal tail size.................... 60 4.38 Look-up graph for horizontal tail incidence angle.............. 60 4.39 Look-up graph for fuselage cross-section size................ 60 4.40 Look-up