《Computation of Supersonic Flow over Flying Configurations》
《Computation of Supersonic Flow over Flying Configurations》飞行构型超音速流场的计算
作者：Adriana Nastase
出版社：Elsevier
出版时间：2008年
目录
About the Author xv
Preface xvii
Acknowledgments xix
Chapter 1 Zonal, Spectral Solutions for the Three-Dimensional,
Compressible Navier–Stokes Layer 1
1.1 Introduction 1
1.2 Three-dimensional, partial-differential equations of compressible
Navier–Stokes layer (NSL) 2
1.3 The spectral variable and the spectral forms of the velocity’s components
and of the physical entities 4
1.4 The first and second derivatives of the velocity’s components 5
1.5 The implicit and explicit forms of the boundary conditions at the
NSL’s edge 8
1.6 The dependence of the density function R versus the spectral velocity,
inside the NSL 10
1.7 Dependence of absolute temperature T versus the spectral velocity,
inside the NSL 11
1.8 The scalar forms of the NSL’s impulse’s partial-differential equations
and their equivalent quadratical algebraic equations 12
1.9 Determination of spectral coefficients of the velocity’s components by
solving an equivalent quadratical algebraic system, via the collocation
method 15
1.10 An original iterative method to solve a quadratical algebraic system 16
1.11 Conclusions 18
References 19
Chapter 2 Hyperbolical Potential Boundary Value Problems of the Axial
Disturbance Velocities of Outer Flow, at NSL’s Edge 20
2.1 Introduction 20
2.2 Basic equations 21
2.3 Full-linearized partial-differential equations of the flow over flattened,
flying configurations 26
v
vi Contents
2.4 The characteristic hypersurfaces of the partial-differential equations
of second order 28
2.4.1 The classification of quasi-linear partial-differential equations
of second order 28
2.4.2 The characteristic’s condition and the characteristic hypersurface 30
2.5 The linearized pressure coefficient Cp on flying configurations 33
2.6 The linearized boundary value problems for flying configurations,
at moderate angles of attack α 34
2.7 Definitions and properties of the thin and thick-symmetrical components
of the thick, lifting flying configurations 35
2.8 The disturbance regions produced by a moving point in subsonic and
supersonic flow 38
2.9 Disturbance regions and characteristic surfaces produced by triangular
wings, in supersonic flow 40
2.10 Disturbance regions and characteristic surfaces produced by trapezoidal
wings, in supersonic flow 49
2.11 Disturbance regions and characteristic surfaces produced by rectangular
wings, in supersonic flow 52
2.12 The boundary value problems for the axial disturbance velocities on thin and
thick-symmetrical wedged triangular wing components, in supersonic flow 53
2.13 Conclusions 56
References 57
Chapter 3 Computation of Axial Disturbance Velocities on Wedged Wings,
in Supersonic Flow, at NSL’s Edge 58
3.1 General considerations 58
3.2 The conical flow of first order 60
3.2.1 Definition of the conical flow 60
3.2.2 The Germain’s complex plane 61
3.2.3 The Germain’s compatibility conditions for the conical flow 63
3.2.4 The Carafoli’s hydrodynamic analogy for the conical flow 63
3.2.5 The principle of the minimal singularities for the wedged
triangular wings 65
3.3 The boundary conditions for the wedged triangular wings, in the
Germain’s plane 68
3.3.1 Introduction 68
3.3.2 The boundary conditions of the fictitious, complex potentials
U and U∗ on the real axis of the Germain’s complex plane 68
3.3.3 The wedged triangular wings with one subsonic and one
supersonic leading edge 72
3.3.4 The wedged triangular wings with two supersonic leading edges 73
3.4 The solutions of direct boundary value problems for U and U∗ on wedged
triangular wing components 78
3.4.1 The auxiliary plane χ=λ+iμ 78
Contents vii
3.4.2 The affine transformed wing and the transformed complex plane ˜x 78
3.4.3 The contribution of a subsonic leading edge on the thin wedged
triangular wing 80
3.4.4 The contributions of ridges of the thin and thick-symmetrical
wedged triangular wings 82
3.4.5 The contribution of the supersonic leading edge on the thin
wedged triangular wing 84
3.4.6 The contributions of the leading edges on the thick-symmetrical
wedged triangular wings 85
3.5 The complex axial disturbance velocities U and U∗ on the wedged
triangular wing components 85
3.5.1 Introduction 85
3.5.2 The complex axial disturbance velocity U on the thin wedged
triangular wing 86
3.5.3 The complex axial disturbance velocity U∗ on the thick-symmetrical
wedged triangular wing 88
3.6 The axial disturbance velocities u and u∗ on the wedged delta
wing components 91
3.7 The axial disturbance velocities u and u∗ on the wedged trapezoidal
wing components 95
3.8 The axial disturbance velocities u and u∗ on the wedged rectangular wing
components 101
3.9 Conclusions 102
References 103
Chapter 4 Computation of Axial Disturbance Velocities on Flying
Configurations with Arbitrary Shapes, in Supersonic Flow,
at NSL’s Edge 106
4.1 General considerations 106
4.2 The theory of high conical flow of nth order 107
4.2.1 Definition of the high conical flow of the nth order and the
homogeneity conditions 107
4.2.2 The Germain’s compatibility conditions for the high
conical flow of nth order 111
4.2.3 The Carafoli’s hydrodynamic analogy for the high
conical flow of nth order 112
4.2.4 The boundary conditions of the fictitious, complex potentials
Ff and F∗
f , on the real axis of the Germain’s complex plane 114
4.3 The principle of minimal singularities for the high conical flow of nth order 119
4.4 The solutions of boundary value problems of fictitious complex
potentials Ff and F∗
f , on triangular wings 121
4.5 The axial disturbance velocities on the thin and thick-symmetrical
triangular wings with arbitrary shapes 129
4.6 The axial disturbance velocities on delta wings with arbitrary shapes 135
viii Contents
4.7 The axial disturbance velocities on trapezoidal wings with arbitrary shapes 137
4.8 The axial disturbance velocities on rectangular wings with arbitrary shapes 140
4.9 The axial disturbance velocities on non-integrated or integrated delta
wing-fuselage configurations 142
4.10 The axial disturbance velocities on non-integrated or integrated delta
wing-fuselage configurations with movable leading edge flaps 147
4.11 Determination of the constants of axial disturbance velocities
on flying configurations 151
4.12 Conclusions 152
References 153
Chapter 5 The Aerodynamical Characteristics of Flying Configurations with
Arbitrary Shapes, in Supersonic Flow 156
5.1 General considerations 156
5.2 The computation of the aerodynamical characteristics of the delta wings 158
5.3 The computation of the aerodynamical characteristics of delta
wing-fuselage configurations 165
5.4 The computation of the aerodynamical characteristics of delta
wing-fuselage configurations, fitted with leading edge flaps, in
open positions 172
5.5 The computation of the lift, pitching moment and drag coefficients
of the rectangular wings 180
5.6 Conclusions 185
References 185
Chapter 6 The Visualizations of the Surfaces of Pressure Coefficients and
Aerodynamical Characteristics of Wedged Delta and Wedged
RectangularWings, in Supersonic Flow 188
6.1 Introduction 188
6.2 The three-dimensional visualizations of the Cp-surfaces on the LAF’s
wedged delta wing, in supersonic flow 189
6.3 Visualizations of the behaviors of the Cp-surfaces on a wedged
delta wing, by crossing of sonic lines 199
6.4 Visualizations of the surfaces of lift and pitching moment coefficients
of LAF’s wedged delta wing and of their asymptotical behaviors,
by crossing of sonic lines 201
6.5 The visualization of the inviscid drag coefficient’s surface of the
LAF’s wedged delta wing and of its asymptotical behavior, by
crossing of sonic lines 202
6.6 The polar surface of the LAF’s wedged delta wing and its asymptotical
behavior, by crossing of sonic lines 204
6.7 The visualizations of the Cp-surfaces on the LAF’s wedged
rectangular wing 207
Contents ix
6.8 The behaviors of the Cp-surfaces by changing of the LAF’s wedged
rectangular wing from long to short, at ν=1 213
6.9 The three-dimensional visualizations of surfaces of aerodynamical
characteristics of LAF’s wedged rectangular wing 215
6.10 The polar surface of the LAF’s wedged rectangular wing, in supersonic flow 219
6.11 Conclusions 220
References 222
Chapter 7 Qualitative Analysis of the NSL’s Asymptotical Behaviors in the
Vicinity of its Critical Zones 224
7.1 Introduction 224
7.2 Reduction of quadratical, elliptical and hyperbolical algebraic equations
to their canonical forms 226
7.3 The asymptotical behaviors of quadratical algebraic equations with
variable free term 228
7.3.1 General considerations 228
7.3.2 The qualitative analysis of the behaviors of quadratical, elliptical,
algebraic equations in the vicinity of their black points 229
7.3.3 The qualitative analysis of the behaviors of quadratical, hyperbolical,
algebraic equations in the vicinity of their saddle points 237
7.4 The qualitative analysis of elliptical and hyperbolical, quadratical, algebraic
equations with variable coefficients of free and linear terms 247
7.4.1 General considerations 247
7.4.2 The collapse of the elliptical QAEs along their critical parabola 248
7.4.3 The degeneration of the hyperbolical QAEs along their critical
parabola 250
7.5 The Jacobi determinant and the Jacobi hypersurface 251
7.6 The aerodynamical applications of the qualitative analysis of the QAEs 252
7.7 Conclusions 253
References 254
Chapter 8 Computation of the Friction Drag Coefficients of the Flying
Configurations 256
8.1 Introduction 256
8.2 Computation of the inviscid lateral velocity v, at the NSL’s edge 258
8.3 The coupling between the NSL’s slopes and the velocity field 263
8.4 Computation of friction and total drag coefficients of the delta wings 264
8.5 Conclusions 266
References 267
Chapter 9 Inviscid and Viscous Aerodynamical Global Optimal Design 269
9.1 Introduction 269
9.2 The optimum–optimorum theory 271
x Contents
9.3 Inviscid aerodynamical global optimal design, via optimum–optimorum
theory 273
9.4 Inviscid aerodynamic global optimal design of delta wing model ADELA,
via optimum–optimorum theory 277
9.5 Inviscid aerodynamic global optimal design of fully-integrated
wing/fuselage models FADET I and FADET II 279
9.6 The iterative optimum–optimorum theory and the viscous aerodynamical
optimal design 283
9.7 Proposal for a fully-optimized and fully-integrated Catamaran STA 285
9.8 Conclusions 287
References 288
Chapter 10 Comparison of the Theoretical Aerodynamical Characteristics
ofWing Models with Experimental-Determined Results 292
10.1 Introduction 292
10.2 The aims of the experimental program 293
10.3 Determination of experimental-correlated values of aerodynamical
characteristics and of interpolated values of pressure coefficient 297
10.4 Comparison of theoretical aerodynamical characteristics of LAF’s wedged
delta wing model with experimental results 299
10.4.1 The description of LAF’s wedged delta wing model 299
10.4.2 The computation of axial disturbance velocities on the
upper side of wedged delta wings 299
10.4.3 The comparison of the theoretical and experimentalcorrelated
values of C and Cm 304
10.5 Comparison of theoretical aerodynamical characteristics of LAF’s double
wedged delta wing model with experimental results 311
10.5.1 The description of LAF’s double wedged delta wing model 311
10.5.2 Computation of downwashes and of axial disturbance
velocities on double wedged delta wing 314
10.5.3 Comparison of theoretical and experimental-correlated
C and Cm of LAF’s double wedged delta wing 316
10.6 Comparison of theoretical aerodynamical characteristics of LAF’s wedged
delta wing model, fitted with a conical fuselage, with experimental results 319
10.6.1 Description of LAF’s delta wing-fuselage model 319
10.6.2 The computation of downwashes and of axial disturbance
velocities on the wedged delta wing model, fitted with
conical fuselage 320
10.6.3 Comparison of the theoretical and experimental-correlated
values C and Cm of LAF’s wedged delta wing model, fitted
with a conical fuselage 324
10.7 Comparison of theoretical aerodynamical characteristics of LAF’s fullyoptimized
delta wing model ADELA with experimental results 327
10.7.1 Description of LAF’s fully-optimized delta wing
model ADELA 327
Contents xi
10.7.2 The computation of downwashes and of axial disturbance
velocities on the fully-optimized delta wing model ADELA 330
10.7.3 Comparison of theoretical and experimental-correlated values of
C and Cm of LAF’s fully-optimized delta wing model ADELA 332
10.8 Comparison of theoretical aerodynamical characteristics of LAF’s
wedged rectangular wing model with experimental results 336
10.8.1 Description of LAF’s wedged rectangular wing model 336
10.8.2 The computation of axial disturbance velocities on wedged
rectangular wing model 339
10.8.3 The comparison of theoretical and experimental-correlated
values of C and Cm of LAF’s wedged rectangular wing 340
10.9 Comparison of theoretical aerodynamic characteristics of LAF’s cambered
rectangular wing model with experimental results 343
10.9.1 Description of LAF’s cambered rectangular wing model 343
10.9.2 Computation of the axial disturbance velocities on LAF’s
cambered rectangular wing model 344
10.9.3 The comparison of theoretical and experimental-correlated
values of C and Cm of LAF’s cambered rectangular wing 347
10.10 Conclusions 349
References 352
Final Remarks 354
Outlook 356
Author Index 357
Subject Index 361
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