Abstract ...................................................... vii
Preface ........................................................ ix
Acknowledgments ................................................ xi
List of Acronyms ............................................. xiii
List of Symbols ................................................ xv
Greek symbols .................................................. xx
Mathematical symbols ............................................ 1
1 Introduction ................................................. 3
1.1 Literature review ....................................... 4
1.1.1 Aircraft trim simulations ........................ 4
1.1.2 Surrogate modeling ............................... 6
1.1.3 Mesh deformation ................................. 7
1.2 Contributions of this thesis ............................ 9
1.3 Thesis outline ......................................... 11
2 Flight Mechanics ............................................ 15
2.1 Coordinate frames and transformations .................. 15
2.2 Atmospheric model ...................................... 16
2.3 Governing equations .................................... 18
3 Fluid Mechanics ............................................. 21
3.1 Governing equations .................................... 21
3.2 Solution method ........................................ 22
3.3 Aerodynamic forces and moments ......................... 23
4 Interpolation by Radial Basis Functions ..................... 25
4.1 Theory of RBF interpolation ............................ 25
4.1.1 Solution ........................................ 25
4.1.2 Evaluation ...................................... 26
5 Control Surface Deflection .................................. 27
5.1 Specifics of RBF interpolation pertaining to mesh
deformation for control surface deflection ............. 29
5.2 Prescription of surface displacements and surface
mesh deformation ....................................... 30
5.2.1 Surface mesh deformation for the ailerons and
the rudder ...................................... 32
5.2.2 Surface mesh deformation for the horizontal
tail ............................................ 34
5.3 Enhancements of volume mesh deformation ................ 38
5.3.1 Point reduction ................................. 39
5.3.2 Center adaptation ............................... 41
5.3.3 Prescription of additional data sites;
constraining mesh deformation and enabling
large deformations .............................. 42
5.4 Automation aspects ..................................... 45
6 Surrogate Modeling .......................................... 47
6.1 Specifics of RBF interpolation pertaining to
surrogate modeling ..................................... 48
6.2 Sampling via multi-dimensional Halton points ........... 50
6.3 Derivative calculation for surrogate-based trim
simulations ............................................ 51
6.3.1 Finite difference approximations ................ 52
6.3.2 Complex-step derivative approximations .......... 52
7 Trim Procedure .............................................. 55
7.1 Description of the trim problem ........................ 55
7.2 Barebones trim procedure ............................... 56
7.3 Selected solution methods .............................. 57
7.3.1 Newton method ................................... 57
7.3.2 Genetic algorithm ............................... 59
7.4 Trim strategy .......................................... 59
8 Applications ................................................ 61
8.1 Preliminaries .......................................... 62
8.2 Mesh deformation ....................................... 64
8.2.1 Deflection of the aileron with chord-and
spanwise blending ............................... 64
8.2.2 Deflection of the aileron with chordwise
blending and spanwise gap ....................... 68
8.2.3 Deflection of the horizontal tail ............... 76
8.3 Calculation of derivatives ............................. 80
8.4 Trim simulations ....................................... 82
8.4.1 Steady level flight ............................. 82
8.4.2 Steady level flight with jammed rudder .......... 85
8.4.3 Steady level coordinated turn ................... 90
9 Conclusions and Outlook ..................................... 95
A Projection of a Point onto a Cylindrical Surface ............ 99
A.1 Projection in radial direction ......................... 99
A.2 Projection in the direction of a vector ............... 100
В Illustration of the Point Reduction Method ................. 101
С Mesh Quality Assessment .................................... 105
D Assessment of CSD for a Thin-plate Spline Radial Basis
Function ................................................... 107
E Comparison of the Newton and the Broyden method ............ 109
F Publications Written in the Course of this Thesis .......... 113
Bibliography .................................................. 117
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