THE SECRET OF FLIGHT

Report
INTRODUCTION TO
NEW THEORY OF FLIGHT
REVEALING
THE SECRET OF FLIGHT
UNDERSTANDING
WHY IT IS POSSIBLE TO FLY
JOHAN HOFFMAN JOHAN JANSSON
CLAES JOHNSON
WEB SITE: THE SECRET OF FLIGHT
http://secretofflight.wordpress.com/
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MATHEMATICS
FLUID MECHANICS
COMPUTATION
MEASUREMENT
APPLICATIONS
HISTORY
NEW THEORY SUBMITTED TO AIAA
• MAIN JOURNAL OF AERONAUTICS
• NOW UNDER SCRUTINY OF EXPERTS
• FOLLOW THE REVIEW PROCESS ON WEB SITE
• FIRST VERSION PRESENTED IN NORMAT 2009
OLD THEORY
• KUTTA-ZHUKOVSKY 1904
• FATHERS OF MODERN AERONAUTICS
• PRANDTL 1904
• FATHER OF MODERN FLUID MECHANICS
• KZP THEORY
SCIENTIFIC MATHEMATICAL THEORIES
FOR UNEDUCATED:
1. TRIVIAL AND CORRECT
2. TRIVIAL AND INCORRECT
FOR EDUCATED:
3. NON-TRIVIAL AND INCORRECT: OLD
4. NON-TRIVIAL AND CORRECT: NEW
NEW THEORY
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PHYSICAL
MATHEMATICAL
CORRECT
DOES REVEAL THE SECRET
USEFUL
OLD THEORY
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UNPHYSICAL
UNMATHEMATICAL
INCORRECT
DOES NOT REVEAL THE SECRET
DANGEROUS
WHAT TO EXPLAIN:
LIFT / DRAG =L/D = 10 - 70
AIRBUS L/D=20 GLIDER L/D=70
THE SECRET: L/D = 10 - 70
• SURPRISING
• INGENIOUS
• ELEGANT
• INCOMPRESSIBLE FLOW
• SLIGHTLY VISCOUS FLOW
IS THEORY NEEDED?
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BIRDS HAVE LEARNED TO FLY WITHOUT
THEORY OF FLIGHT
BUT IT TOOK 100 MILLION YEARS
FROM DINOSAUR TO ARCHAEOPETRYX
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HUMANS HAVE LEARNED TO FLY WITHOUT
THEORY OF FLIGHT
BUT IT TOOK 500 YEARS
FROM DA VINCI TO SUCCESS: GOSSAMER CONDOR 1978
• BECAUSE OF LACK OF THEORY!!
DA VINCI FLYING MACHINE 1500
GOSSAMER CONDOR 1978
FIRST HUMAN POWERED FLIGHT
CONFESSIONS ABOUT OLD THEORY
NEW YORK TIMES 2003 (CHANG)
To those who fear flying, it is
probably disconcerting that
physicists and aeronautical
engineers still passionately debate
the fundamental issue underlying
this endeavor:
WHAT KEEPS PLANES IN THE AIR?
NASA LISTS INCORRECT THEORIES
• LONGER DISTANCE
• SKIPPING STONE
• VENTURI
• BUT NO THEORY CLAIMED TO BE CORRECT!!
• NASA DOES NOT SEEM TO KNOW WHAT KEEPS
PLANES IN THE AIR!!
LONGER PATH THEORY INCORRECT
SKIPPING STONE THEORY: NEWTON
VENTURI THEORY: BERNOULLI
HOFFREN 2001 AIAA
• A SATISFACTORY THEORY OF LIFT IS STILL
LACKING
• THERE IS A GENUINE NEED FOR ONE
WHAT KEEPS PLANES IN THE AIR?
• INCORRECT THEORY OK AS LONG
AS YOU DON’T USE IT
• NOT USEFUL
• NEW THEORY: CORRECT: USEFUL
WHY CORRECT THEORY ONLY 2009?
• COMPUTE TURBULENT SOLUTIONS OF
• NAVIER-STOKES EQUATIONS + SLIP BC
• DIRECT SIMULATION WITHOUT TURBULENCE
MODELING
• POSSIBLE WITH ~ 1 MILLION MESH POINTS
• COMPUTATION TELLS THE TRUTH
• STUDY REVEALS THE SECRET
DRAG CAR COMPUTABLE
LIFT DRAG WING COMPUTABLE
VELOCITY
PRESSURE
PRESSURE DISTRIBUTION C_P
UPPER LOWER SURFACE
LIFT DRAG OF WING COMPUTABLE
MAX L = 1.5 L/D = 50 AOA = 16
TO UNDERSTAND: STABILITY
• STABILITY - INSTABILITY OF FLUID MOTION
• STABLE COMPUTABLE ASPECTS OF
TURBULENT FLOW
• LIFT DRAG MOMENTS..: COMPUTABLE
• ALL YOU MAY WANT TO KNOW: COMPUTABLE
OPPOSING FLOW INSTABILITY
STABLE ATTACHMENT
UNSTABLE SEPARATION:
OPPOSING FLOW
FROM CYLINDER TO AIRFOIL:
ROUNDED LEADING + TRAILING EDGE
UNDERST CYL = UNDERSTAND AIRFOIL
SHORT STORY: THEORIES OF FLIGHT
• NEWTON 17H MATH: IMPOSSIBLE: WRONG
• D’ALEMBERT 18TH MATH: IMPOSSIBLE: WRONG
• WRIGHT BROTHERS 1903 REAL EXP : POSSIBLE
• KUTTA-ZHUKOVSKY 1904 MATH: POSSIBLE:
WRONG: OLD THEORY OF FLIGHT
• HOFFMAN-JOHNSON 2009 MATH: POSSIBLE:
RIGHT: NEW THEORY OF FLIGHT
NEW VS OLD THEORY
• NEW THEORY REVEALS THE SECRET OF FLIGHT
• OLD THEORY HIDES THE SECRET OF FLIGHT
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OLD: RULING PARADIGM
OLD: NOT FUNCTIONAL
NEW INCOMPATIBLE WITH OLD
SCIENTIFIC REVOLUTION A LA KUHN
LIFT AND DRAG OF LONG WING
• SUCTION ON UPPER LEADING EDGE/SURFACE:
• LIFT + NEGATIVE DRAG
• PUSH ON LOWER LEADING EDGE/SURFACE:
• LIFT + POSITIVE DRAG
• FLOW SEPARATES AT TRAILING EDGE WITHOUT
PRESSURE RISE/DROP: ELEGANT SEPARATION
AIRFOIL – AIRPLANE WING
OBSERVATION WIND TUNNEL
OBSERVATION: 2D SECTION OF 3D
OBSERVATION
LIFT
• UPPER LEADING EDGE SUCTION
• LOWER LEADING EDGE PUSH
DRAG
• LEADING EDGE PUSH/SUCTION
• SEPARATION WITHOUT PRESSURE RISE/DROP
• DOWNWASH
RECALL C_P UPPER LOWER
NAVIER-STOKES
PRESSURE AOA = 5
VELOCITY AOA = 10
VELOCITY AOA = 10
VELOCITY AOA = 15
UNDERSTANDING: THEORY
• MATHEMATICAL MODEL OF PHYSICS
• ASSUMPTIONS
MATHEMATICAL MODEL = EQUATION:
1. NAVIER-STOKES + BC: GENERAL
2. LAPLACE + BC: SPECIAL
• MATHEMATICAL THEORY: SOLVE EQUATION
LAPLACE EQN: POTENTIAL FLOW
1.
2.
3.
INCOMPRESSIBLE: CORRECT FOR SUBSONIC FLIGHT
INVISCID - SMALL VISCOSITY: CORRECT
SLIP BOUNDARY CONDITION: SMALL SKIN FRICTION: CORRECT
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5.
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IRROTATIONAL?? NO VORTICES
STATIONARY??
2D??
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V = GRADIENT OF HARMONIC FUNCTION
2D FOR CYLINDER LONG WING
• 1 + 2 + 3 VALID!! EVERYWHERE!! NAVIER-STOKES
• 4 + 5 +6 VALID?? SOMEWHERE BUT NOT EVERYWHERE!! LAPLACE??
1- 4 : LAPLACE’S EQN: POTENTIAL:
HARMONIC FUNCTION + SLIP
LAPLACE VS NAVIER-STOKES
LAPLACE SIMPLIFIED VERSION OF NAVIER-STOKES
POTENTIAL SOLUTION:
• 2D
• STATIONARY
• IRROTATIONAL
• LAPLACE SOLUTIONS NOT TURBULENT
• NAVIER-STOKES SOLUTIONS TURBULENT
CIRC CYLINDER: POTENTIAL FLOW:
P=0 P=1 P=-3
V= 1 V=0 V=2
POTENTIAL FLOW: BERNOULLI’S LAW
½ V2 + P = CONSTANT
• HIGH PRESSURE P – LOW VELOCITY V
• LOW PRESSURE P – HIGH VELOCITY V
CIRC CYLINDER: POTENTIAL FLOW:
ZERO LIFT + ZERO DRAG
(L/D = 3)
LIFT OF HALF CYLINDER
THEORY: POTENTIAL FLOW:
D’ALEMBERT’S PARADOX 1752:
ZERO LIFT AND DRAG
POTENTIAL FLOW VS OBSERVATION
POTENTIAL FLOW
• SEPARATION BEFORE TRAILING EDGE
• HIGH PRESSURE AT SEPARATION REQUIRED TO
BRING FLOW TO STAGNATION
• NO DOWNWASH
• MATHEMATICAL SOLUTION
• BUT NOT OBSERVED IN REALITY
• UNPHYSICAL!! WHY??
WHAT’S WRONG WITH POTENTIAL
FLOW??
D’ALEMBERT
COULD NOT
UNDERSTAND
1752
D’ALEMBERT’S PARADOX 1752
It seems to me that the theory
(potential flow), developed in all
possible rigor, gives, at least in
several cases, a strictly vanishing
resistance, a singular paradox which
I leave to future Geometers to
elucidate”.
WHAT’S WRONG WITH POTENTIAL
FLOW??
EULER COULD NOT
UNDERSTAND
???? 18TH
POTENTIAL FLOW
SOLVES
EULER’S EQNS
WHAT’S WRONG WITH POTENTIAL
FLOW??
LAPLACE COULD
NOT UNDERSTAND
???? 19TH
POTENTIAL FLOW
SOLVES
LAPLACE’S EQN
WHAT’S WRONG WITH POTENTIAL
FLOW??
CAUCHY COULD
NOT UNDERSTAND
???? 19TH
MASTER OF
HARMONIC FCNS
WHAT’S WRONG WITH POTENTIAL
FLOW??
POISSON
COULD NOT
UNDERSTAN
D
??? 19TH
NOBODY
COULD
UNDERSTAN
WILBUR + ORWILLE WRIGHT: FLYER
DEC 17 1903
KUTTA-ZHUKOVSKY 1904
• SEPARATION AT TRAILING EDGE BY ADDING
CIRCULATION
• LIFT BUT NO DRAG
FATHERS OF MODERN AERODYNAMICS
CIRCULATION: LIFT BUT NO DRAG
FATHER OF MODERN FLUID
MECHANICS
LUDWIG PRANDTL 1904
• SLIP BOUNDARY CONDITION IS WRONG
• NO-SLIP IS RIGHT:
• THIN BOUNDARY LAYER
• DRAG BUT NO LIFT
TURBULENT WAKE: DRAG BUT NO LIFT
INCORRECT + INCORRECT = CORRECT?
• (-1) x (-1) = 1
• NO!!
• PRANDTL INCORRECT
• KUTTA-ZHUKOVSKY INCORRECT
• WHAT IS THEN CORRECT?
RESOLUTION OF D’ALEMBERT’S
PARADOX
• JOHAN HOFFMAN AND CLAES JOHNSON
• J MATHEMATICAL FLUID MECHANICS 2008
• FINALLY AFTER 256 YEARS
• SPIN-OFF: SECRET OF FLIGHT 2012
POTENTIAL FLOW:
STABLE ATTACHMENT
UNSTABLE SEPARATION:
OPPOSING FLOW
POTENTIAL FLOW SEPARATION
INSTABILITY
TROUBLE: TRAILING EDGE
• POTENTIAL FLOW SEPARATION:
• UNPHYSICAL UNSTABLE: OPPOSING FLOW
• POTENTIAL FLOW ATTACHMENT:
• PHYSICAL STABLE
• NON-POTENTIAL FLOW SEPARATION??
• 3D ROTATIONAL SEPARATION: PHYSICAL STABLE:
AVOIDS OPPOSING FLOW
CIRC CYLINDER: POTENTIAL FLOW:
P=0 P=1 P=-3
V= 1 V=0 V=2
ZERO LIFT DRAG
CIRCULAR CYLINDER: 3D ROTATIONAL
SEPARATION: LOW MEAN PRESSURE
3D ROTATIONAL SEPARATION
KUTTA-ZHUKOVSKY CIRCULATION
THEORY VS NEW THEORY
STREAMWISE VORTICITY
3D SEPARATION AT TRAILING EDGE
• 3D ROTATIONAL SEPARATION:
• WITHOUT PRESSURE RISE
• WITHOUT PRESSURE DROP: WAKE
• ELEGANT SEPARATION
• PRESSURE RISE:
• 2D IRROTATIONAL POTEN. FLOW SEPARATION
• PRESSURE DROP: WAKE SEPARATION
THE SECRET
• POTENTIAL FLOW:
• BEFORE SEPARATION
• NON-POTENTIAL AT SEPARATION:
• 3D ROTATIONAL SLIP SEPARATION WITH POINT
STAGNATION
• 256 YEARS: 1752 - 2008 TO UNDERSTAND
FROM CYLINDER TO AIRFOIL:
ROUNDED LEADING + TRAILING EDGE
UNDERST CYL = UNDERSTAND AIRFOIL
THE SECRET: L/D = 10
THE SECRET
• INCOMPRESSIBLE
• SLIGHTLY VISCOUS FLOW
• POTENTIAL FLOW BEFORE SEPARATION
• 3D TRAILING EDGE SEPARATION WITHOUT
PRESSURE RISE/DROP
SECRET OF FLIGHT
• HOW TO SEPARATE IN AN ELEGANT WAY:
• WITHOUT PRESSURE RISE/DROP
• ENGAGEMENT: EASY
• DIVORCE: DIFFICULT
• THE TRICK: ELEGANT DIVORCE
NEW THEORY: NEW WING DESIGN
HUMPBACK WHALE LEADING EDGE
NEW THEORY: NEW DESIGN
ROUNDED TRAILING EDGE WIND
TURBIN BLADE
THE SECRET OF FLIGHT WEB SITE
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FULL STORY
MATHEMATICS
PHYSICS
COMPUTATION
APPLICATIONS: SAILING, SWIMMING,….
BACKGROUND
HISTORY INCORRECT THEORY…

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