Mathematical methods of airfoil design: inverse boundary value problems of aerohydrodynamics
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | German Russian |
| Veröffentlicht: |
Berlin
Akad.-Verl.
1997
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 292 S. Ill. |
| ISBN: | 3055017013 |
Internformat
MARC
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| 100 | 1 | |a Elizarov, Aleksandr M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematical methods of airfoil design |b inverse boundary value problems of aerohydrodynamics |c A. M. Elizarov ; N. B. Il'inskiy ; A. V. Potashev |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1997 | |
| 300 | |a 292 S. |b Ill. | ||
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| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Aerofoils |x Design and construction |x Mathematical models | |
| 650 | 4 | |a Boundary value problems |x Mathematical models | |
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| 700 | 1 | |a Ilʹinskij, Nikolaj Borisovič |d 1932- |e Verfasser |0 (DE-588)115651241 |4 aut | |
| 700 | 1 | |a Potašev, Andrej V. |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804126056789049344 |
|---|---|
| adam_text | A. M. ELIZAROV
N
. B
. IL INSKI
Y
A. V. POTASHEV
MATHEMATICAL METHODS
OF AIRFOIL DESIGN
INVERSE BOUNDARY-VALUE PROBLEMS
OF AEROHYDRODYNAMICS
AKADEMIE VERLAG
CONTENTS
INTRODUCTIO
N 1
5
ABBREVIATION
S AN
D NOMENCLATUR
E 1
9
1 ISOLATE
D AIRFOI
L I
N IDEA
L FLOW O
F A
N INCOMPRESSIBL
E FLUID - PRINCIPA
L
IBVP
A 2
3
1.1 FORMULATIO
N OF TH
E PROBLEM
. SOLUTION METHOD
S 24
1.1.1 FORMULATIO
N OF TH
E PROBLE
M . .
V
24
1.1.2 SOLUTIO
N METHOD
S 26
1.1.3 ON METHOD
S OF CALCULATIO
N OF INTEGRA
L WIT
H HILBER
T KERNEL ..
. 30
1.1.4 EXAMPLE
S OF NUMERICA
L SOLUTIO
N 34
1.2 SOLVABILITY CONDITION
S AN
D SIMPLE METHOD
S OF SATISFYING THE
M 35
1.2.1 SOLVABILIT
Y CONDITION
S 35
1.2.2 SIMPL
E METHOD
S OF SATISFYING TH
E SOLVABILITY CONDITION
S 37
1.2.3 AN EXAMPL
E OF TH
E SIMPLE APPROAC
H FOR SATISFYING TH
E SOLVABILIT
Y
CONDITION
S 38
1.3 UNIVALENCE CONDITION
S 39
1.3.1 SUFFICIENT CONDITION
S OF UNIVALENCE 40
1.3.2 NECESSARY CONDITION
S OF UNIVALENCE 42
1.4 QUASISOLUTION
S 43
1.4.1 CORRECTNES
S SET 43
1.4.2 DEFINITION OF A QUASISOLUTIO
N OF TH
E PRINCIPA
L IBVP
A 45
1.4.3 METHOD
S OF CONSTRUCTIO
N OF QUASISOLUTIO
N 46
1.4.4 EXAMPLE
S OF QUASISOLUTIO
N 48
1.5 INVERSE PROBLE
M BY MEAN
S OF VELOCITY CHORD DIAGRA
M 49
1.5.1 FORMULATIO
N OF TH
E PROBLE
M 50
1.5.2 DEDUCTIO
N OF INTEGRA
L EQUATIO
N 51
1.5.3 ITERATIV
E PROCEDURE
53
1.5.4 EXAMPLE
S 55
1.6 CALCULATIO
N OF AERODYNAMI
C CHARACTERISTIC
S 57
1.6.1 DISTRIBUTE
D CHARACTERISTIC
S 57
10 CONTENTS
1.6.2 INTEGRAL AERODYNAMIC CHARACTERISTICS 58
1.6.3 CHAPLYGIN FORMULA 59
1.6.4 RECALCULATION FOR OTHER FREESTREAM FLOW CONDITIONS 61
VISCOSIT
Y AN
D COMPRESSIBILIT
Y O
F FLOW 6
3
2.1 SIMPL
E MODEL
S T
O ACCOUN
T FOR COMPRESSIBILIT
Y IN SUBSONI
C FLOW 65
2.1.1 CHAPLYGI
N EQUATION
S 65
2.1.2 CHAPLYGI
N GAS MODE
L 66
2.1.3 KARMAN-TSIE
N AN
D PRANDTL-GLAUER
T FORMULAE 68
2.2 DESIGN OF AIRFOIL FOR A SUBSONIC FLOW 69
2.2.1 PROBLE
M FORMULATIO
N 69
2.2.2 SIMPLE METHO
D OF SOLUTIO
N 69
2.2.3 SOLUTION USING TH
E CHAPLYGI
N GAS MODE
L 70
2.2.4 SOLVABILITY CONDITION
S AN
D QUASISOLUTION
S 71
2.2.5 RESULT
S OF CALCULATION
S
. . . . 11
2.3 TAKIN
G VISCOSITY INT
O ACCOUN
T FOR NONSEPARATIN
G FLOW AROUN
D AN AIRFOIL 74
2.3.1 PROBLE
M FORMULATIO
N 74
2.3.2 METHO
D OF SOLUTION 75
2.3.3 SOLVABILITY CONDITION
S AN
D QUASISOLUTION
S 76
2.3.4 AERODYNAMI
C FORCES AN
D CALCULATIO
N OF MOMENT
S 78
2.3.5 EXAMPLE
S 79
2.4 TAKIN
G VISCOSITY INT
O ACCOUN
T FOR SEPARATIN
G FLOW AROUN
D A
N AIRFOIL..
. 81
2.4.1 MODEL OF SEPARATIN
G FLOW AROUN
D AIRFOIL 81
2.4.2 SOLUTIO
N WIT
H PRESENCE OF SEPARATIO
N ZONE. SYMMETRICA
L CASE . 83
2.4.3 SOLUTION WIT
H PRESENCE OF SEPARATIO
N ZONE. NONSYMMETRICA
L CASE 86
2.5 COMBINE
D ANALYSI
S OF COMPRESSIBILIT
Y AN
D VISCOSITY 89
2.5.1 SIMPLE METHO
D 90
2.5.2 NONSEPARATIN
G FLOW 90
2.5.3
- SEPARATIO
N FLOW 92
2.6 ANALYSIS OF COMPRESSIBILIT
Y IN TH
E DESIGN PROBLE
M USIN
G TH
E VELOCITY
CHORD DIAGRA
M 93
2.6.1 PROBLE
M FORMULATIO
N 93
2.6.2 SIMPL
E METHO
D OF SOLUTIO
N 93
2.6.3 CHAPLYGI
N GAS MODE
L 94
2.6.4 RESULT
S OF CALCULATION
S 94
HYDRODYNAMICALL
Y EXPEDIEN
T VELOCIT
Y DISTRIBUTION
S 95
3.1 INCOMPRESSIBLE FLOW INSEPARATION CONDITIONS 96
3.1.1 GENERAL FORM OF INSEPARATION CONDITIONS 96
3.1.2 TURBULENT BL INSEPARATION 97
3.1.3 LAMINAR-TURBULENT BL TRANSITION 98
3.2 NONSEPARATING VELOCITY DISTRIBUTIONS 99
3.2.1 ROOF-TOP DISTRIBUTIONS 99
CONTENTS 11
3.2.2 PRESCRIBED FORM-PARAMETER DISTRIBUTION 100
3.3 OPTIMIZED HEVD 103
3.3.1 PRESCRIBED DISTRIBUTION OF FORM-PARAMETER 104
3.3.2 ROOF-TOP DISTRIBUTIONS 109
3.4 EXAMPLE OF AIRFOIL DESIGN 118
4 INVERS
E BOUNDARY-VALU
E PROBLEM
S OF AEROHYDRODYNAMIC
S FOR A RANG
E
OF ANGLE
S OF ATTAC
K 12
1
4.1 PRINCIPAL PROBLEM 122
4.1.1 FORMULATION OF THE PRINCIPAL PROBLEM 122
4.1.2 INTEGRAL REPRESENTATION OF SOLUTION 123
4.1.3 CONDITIONS OF COMPATIBILITY OF INITIAL DAT
A AND SOLVABILITY CON
DITIONS 125
4.2 INITIAL DAT
A SCHEMES AND QUASISOLUTIONS 128
4.2.1 PARAMETER ANALYSIS 128
4.2.2 EXAMPLES OF THE QUASISOLUTIONS 129
4.2.3 LIFT MAXIMIZATION 131
4.3 HYDRODYNAMICALLY EXPEDIENT VELOCITY DISTRIBUTIONS 133
4.3.1 NONSEPARATING FLOW CONDITIONS 133
4.3.2 PROOF OF TH
E MAIN ASSERTION 135
4.4 LIFT MAXIMIZATION 136
4.4.1 OPTIMIZED HEVD 136
4.4.2 OPTIMAL AIRFOIL DESIGN 138
4.5 FLOW COMPRESSIBILITY 144
4.5.1 PRINCIPAL PROBLEM 144
4.5.2 PROBLEM FOR GIVEN CHORD DIAGRAM . 145
5 PERMEABL
E AIRFOILS 147
5.1 NORMAJ SUCTION OF EXTERNAL FLOW 148
5.1.1 PROBLEM FORMULATION 148
5.1.2 SCHEME OF SOLUTION 149
5.1.3 RESULTS OF CALCULATIONS 152
5.2 TANGENTIAL SUCTION OF THE EXTERNAL FLOW 152
5.2.1 FIRST APPROACH 153
5.2.2 SECOND APPROACH 155
5.2.3 THIRD APPROACH 157
5.3 DISTRIBUTED SUCTION OF THE EXTERNAL FLOW 161
5.3.1 PROBLEM FORMULATION 161
5.3.2 ANALYTICAL SOLUTION 162
5.3.3 EXAMPLES 164
5.4 SUCTION OF BOUNDARY LAYER THROUGH A SLOT 164
5.4.1 PROBLEM FORMULATION 165
5.4.2 BL CALCULATION 166
12 CONTENTS
5.4.3 SOLUTION OF THE INVERSE PROBLEM 167
5.4.4 EXAMPLE OF AIRFOIL DESIGN 168
6 DESIG
N OF AIRFOILS FOR FLOW SINGULARITIE
S 169
6.1 FLAP MODELLED BY POINT VORTEX 169
6.1.1 PROBLEM FORMULATION 169
6.1.2 ANALYTICAL SOLUTION 170
6.1.3 RESULTS OF CALCULATIONS 174
6.2 INFINITELY THIN FLAP 177
6.2.1 PROBLEM FORMULATION 177
6.2.2 ANALYTICAL SOLUTION 178
6.2.3 RESULTS OF CALCULATIONS 181
6.3 THICK FLAP 183
6.3.1 ANALYTICAL SOLUTION 183
6.3.2 RESULTS OF CALCULATIONS
_,
185
6.4 AIRFOIL IN DOUBLE-LAYER FLOW OF WEIGHTLESS LIQUID 185
6.4.1 PROBLEM FORMULATION ^ . . 185
6.4.2 ANALYTICAL SOLUTION 185
6.4.3 ITERATION PROCESS 187
6.4.4 RESULTS OF CALCULATIONS 188
6.5 TAKING THE BOUNDARY LAYER INTO ACCOUNT 190
6.5.1 METHOD OF SOLUTION 190
6.5.2 RESULTS OF CALCULATIONS FOR AIRFOIL ABOVE INTERFACE 190
7 MIXE
D INVERS
E BOUNDARY-VALU
E PROBLEM
S OF AEROHYDRODYNAMIC
S 195
7.1 LEADING CRITICAL POINT ON THE GIVEN PART OF AN AIRFOIL CONTOUR 196
7.1.1 PROBLEM FORMULATION 196
7.1.2 SOLUTION OF THE PROBLEM 197
7.1.3
, SOLVABILITY CONDITIONS AND QUASISOLUTION 200
7.1.4 NUMERICAL EXAMPLES 200
7.2 ITERATIVE METHOD OF SOLUTION 203
7.2.1 PROBLEM FORMULATION 203
7.2.2 METHOD OF SOLUTION 205
7.2.3 SOLVABILITY CONDITIONS 207
7.2.4 EXAMPLES 207
7.3 SOLVABILITY OF THE MIXED IBVPA 212
7.3.1 SOLVABILITY OF THE EXTERNAL MIXED IBVP FOR ANALYTICAL FUNCTIONS
212
7.3.2 GENERALISED LERAY RESTRICTION 215
8 AIRFOIL CASCADES 219
8.1 IDEAL INCOMPRESSIBLE FLOW 219
8.1.1 PROBLEM FORMULATION 219
8.1.2 ANALYTICAL SOLUTION 220
CONTENTS 13
8.1.3 RESULT
S OF TES
T CALCULATIO
N 223
8.2 SOLVABILITY CONDITION
S AN
D METHOD
S OF SATISFYING THE
M 224
8.2.1 SOLVABILITY CONDITION
S 225
8.2.2 QUASISOLUTION
S 227
8.2.3 EXAMPLE
S OF CALCULATION
S 231
8.3 PECULIARITIE
S OF NUMERICA
L REALIZATIO
N FOR DENSE CASCADES 233
8.3.1 CONFORMA
L MAPPIN
G PARAMETER
S 233
8.3.2 DEPENDENC
E
-Y(S)
234
8.3.3 DEPENDENCE %
) 235
8.3.4 SOLVABILITY CONDITION
S 237
8.3.5 QUASISOLUTION
S 238
8.4 COMPRESSIBILIT
Y OF SUBSONIC FLOW 240
8.4.1 PROBLE
M FORMULATIO
N 240
8.4.2 SIMPLE METHO
D OF SOLUTIO
N 241
8.4.3 TH
E CHAPLYGI
N GAS MODE
L . . . . / 241
8.4.4 SOLVABILITY CONDITION
S 241
8.4.5 RESULT
S OF CALCULATION
S 243
8.5 ACCOUNTIN
G FOR TH
E BL 244
8.5.1 FORMULATIO
N OF PROBLE
M 244
8.5.2 SCHEME OF SOLUTIO
N 244
8.5.3 SOLVABILITY CONDITION
S 245
8.5.4 COMBINE
D ACCOUNT OF VISCOSITY AN
D COMPRESSIBILIT
Y OF FLOW . . . 246
8.5.5 NUMERICA
L RESULT
S 246
8.6 GIVEN RANG
E OF FLOW PARAMETER
S 247
8.6.1 PROBLE
M FORMULATIO
N 247
8.6.2 SOLUTIO
N OF TH
E PROBLE
M 248
8.6.3 EXAMPL
E 251
8.7 ROTATIN
G AIRFOIL CASCADE ON AXISYMMETRICA
L STREA
M SURFACE 252
8.7.1 BASIC ASSUMPTION
S 252
8.7.2 PROBLE
M FORMULATIO
N 254
8.7.3 IDE
A BEHIN
D SOLUTIO
N METHO
D 254
8.7.4 SECOND FORMULATIO
N OF TH
E PROBLE
M ...............
. 255
8.7.5 EXAMPL
E OF COMPRESSOR IMPELLER DESIGN 255
9
CORRECTNES
S
O
F FORMULATIO
N O
F PRINCIPA
L IBV
P 26
1
9.1 FORMULATIO
N OF QUASISOLUTIO
N PROBLEMS
. SOME PARTICULA
R CASES ...
. 261
9.1.1 DEFINITION OF QUASISOLUTIO
N 261
9.1.2 CORRECTNES
S OF TH
E PROBLE
M OF FINDING A QUASISOLUTIO
N 266
9.1.3 SOME PARTICULA
R CASES 270
9.2 MINIMIZIN
G SEQUENCES ...:-
, 273
9.2.1 FINIT
E DIMENSIO
N APPROXIMATION
. ANALYTICA
L FORMULAE 273
9.2.2 CONTRACTIO
N OF TH
E CORRECTNESS SET . 276
9.3 SCALES OF QUASISOLUTION
S , 277
14 CONTENTS
9.3.1 THE QUASISOLUTION FOR FUNCTIONAL
J
277
9.3.2 QUASISOLUTIONS FOR FUNCTIONAL
J
T
280
BIBLIOGRAPH
Y 285
|
| any_adam_object | 1 |
| author | Elizarov, Aleksandr M. Ilʹinskij, Nikolaj Borisovič 1932- Potašev, Andrej V. |
| author_GND | (DE-588)115651241 |
| author_facet | Elizarov, Aleksandr M. Ilʹinskij, Nikolaj Borisovič 1932- Potašev, Andrej V. |
| author_role | aut aut aut |
| author_sort | Elizarov, Aleksandr M. |
| author_variant | a m e am ame n b i nb nbi a v p av avp |
| building | Verbundindex |
| bvnumber | BV011534761 |
| callnumber-first | T - Technology |
| callnumber-label | TL574 |
| callnumber-raw | TL574.A4 |
| callnumber-search | TL574.A4 |
| callnumber-sort | TL 3574 A4 |
| callnumber-subject | TL - Motor Vehicles and Aeronautics |
| classification_rvk | UF 4500 |
| classification_tum | MAS 569f |
| ctrlnum | (OCoLC)38069175 (DE-599)BVBBV011534761 |
| dewey-full | 629.134320151 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.134320151 |
| dewey-search | 629.134320151 |
| dewey-sort | 3629.134320151 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Physik Verkehr / Transport Maschinenbau |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV011534761 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:23Z |
| institution | BVB |
| isbn | 3055017013 |
| language | German Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007763878 |
| oclc_num | 38069175 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-634 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-634 DE-83 |
| physical | 292 S. Ill. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Akad.-Verl. |
| record_format | marc |
| spelling | Elizarov, Aleksandr M. Verfasser aut Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics A. M. Elizarov ; N. B. Il'inskiy ; A. V. Potashev 1. ed. Berlin Akad.-Verl. 1997 292 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematisches Modell Aerofoils Design and construction Mathematical models Boundary value problems Mathematical models Hydrodynamics Mathematical models Bemessung (DE-588)4005461-5 gnd rswk-swf Turbinenschaufel (DE-588)4128173-1 gnd rswk-swf Aerodynamik (DE-588)4000589-6 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Inverses Problem (DE-588)4125161-1 gnd rswk-swf Flugzeugaerodynamik (DE-588)4135410-2 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Flugzeugaerodynamik (DE-588)4135410-2 s Randwertproblem (DE-588)4048395-2 s Inverses Problem (DE-588)4125161-1 s DE-604 Turbinenschaufel (DE-588)4128173-1 s Bemessung (DE-588)4005461-5 s Aerodynamik (DE-588)4000589-6 s 1\p DE-604 Hydrodynamik (DE-588)4026302-2 s 2\p DE-604 Ilʹinskij, Nikolaj Borisovič 1932- Verfasser (DE-588)115651241 aut Potašev, Andrej V. Verfasser aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007763878&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Elizarov, Aleksandr M. Ilʹinskij, Nikolaj Borisovič 1932- Potašev, Andrej V. Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics Mathematisches Modell Aerofoils Design and construction Mathematical models Boundary value problems Mathematical models Hydrodynamics Mathematical models Bemessung (DE-588)4005461-5 gnd Turbinenschaufel (DE-588)4128173-1 gnd Aerodynamik (DE-588)4000589-6 gnd Hydrodynamik (DE-588)4026302-2 gnd Inverses Problem (DE-588)4125161-1 gnd Flugzeugaerodynamik (DE-588)4135410-2 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4005461-5 (DE-588)4128173-1 (DE-588)4000589-6 (DE-588)4026302-2 (DE-588)4125161-1 (DE-588)4135410-2 (DE-588)4048395-2 |
| title | Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics |
| title_auth | Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics |
| title_exact_search | Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics |
| title_full | Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics A. M. Elizarov ; N. B. Il'inskiy ; A. V. Potashev |
| title_fullStr | Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics A. M. Elizarov ; N. B. Il'inskiy ; A. V. Potashev |
| title_full_unstemmed | Mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics A. M. Elizarov ; N. B. Il'inskiy ; A. V. Potashev |
| title_short | Mathematical methods of airfoil design |
| title_sort | mathematical methods of airfoil design inverse boundary value problems of aerohydrodynamics |
| title_sub | inverse boundary value problems of aerohydrodynamics |
| topic | Mathematisches Modell Aerofoils Design and construction Mathematical models Boundary value problems Mathematical models Hydrodynamics Mathematical models Bemessung (DE-588)4005461-5 gnd Turbinenschaufel (DE-588)4128173-1 gnd Aerodynamik (DE-588)4000589-6 gnd Hydrodynamik (DE-588)4026302-2 gnd Inverses Problem (DE-588)4125161-1 gnd Flugzeugaerodynamik (DE-588)4135410-2 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Mathematisches Modell Aerofoils Design and construction Mathematical models Boundary value problems Mathematical models Hydrodynamics Mathematical models Bemessung Turbinenschaufel Aerodynamik Hydrodynamik Inverses Problem Flugzeugaerodynamik Randwertproblem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007763878&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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