Aerodynamics Fundamentals and Principles
AERODYNAMICS
د. محمد خضير عباس
Contents
1.
Aerodynamics: Some Introductory Thoughts
2.
Aerodynamics: Some Fundamental Principles
and Equations
3.
Fundamentals of Inviscid, Incompressible Flow
4.
Incompressible Flows Over Airfoils
5.
Incompressible Flows Over Finite Wings
Flow similarity
Definition of dynamically similar for two
different flows
The streamline patterns are geometrically similar.
The distributions of V/V
, p/p
, etc. are the same
when plotted against common non-dimensional
coordinates.
The force coefficients are the same.
Criteria
The bodies and any other solid boundaries are
geometrically similar.
Same similarity parameters (Re and M
).
Example
Assume
Similar flows
Types of flow
Inviscid vs. viscous flow
Inviscid: assume no friction, thermal conduction and
diffusion.
viscous: consider effects of friction, thermal
conduction and diffusion.
Incompressible vs. compressible
Incompressible: density
is constant.
Compressible: density
is variable.
Mach number regimes
Subsonic flow: M<1 everywhere
Transonic flow: mixed regions where M<1 and M>1
Supersonic flow: M>1 everywhere
Hypersonic flow: very high supersonic speeds, usually
M
>5.
Chap.2
Aerodynamics: Some
Fundamental Principles and
Equations
OUTLINE
Review of vector relations
Control volumes and fluid elements
Continuity equation
Momentum equation
Pathlines and streamlines
Angular velocity, vorticity and circulation
Stream function and velocity potential
Review of vector relations
Vector algebra
Scalar product:
Vector product:
Orthogonal coordinate systems
Cartesian coordinate system
Cylindrical coordinate system
Spherical coordinate
system
Gradient of a scalar field
Definition of
gradient
of a scalar
p
Its magnitude is the
maximum rate of change
of
p
per unit
length.
Its direction is the
maximum rate of change
of
p
.
Isoline: a line of constant
p
values
Gradient line: a line along which
p
is tangent at
every point.
Directional derivative:
where
n
is the unit vector in the
s
direction.
Expression for
p
in Cartesian coordinate system
Divergence of a vector field
If
V
is the velocity of a flow, the divergence of
V
will
be the
time rate of volume change per unit volume
.
Expression for divergence of
V
,
V
, in Cartesian
coordinate system
Curl of a vector field
The angular velocity
of a fluid element translating
along a streamline is equal to
one-half of
the curl of
V
, denoted by
V
.
Expression for curl of
V
in Cartesian coordinate
system
Relations between line, surface and volume
integrals
Stokes
’
theorem
Divergence theorem
Gradient theorem
Delve into the world of aerodynamics with an exploration of fundamental principles, equations, flow types, Mach number regimes, and vector relations. Discover the distinctions between inviscid and viscous flows, incompressible and compressible flows, as well as the various Mach number regimes from subsonic to hypersonic speeds. Gain insights into dynamically similar flows and the significance of orthogonal coordinate systems in aerodynamics.
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Presentation Transcript
Contents Aerodynamics: Some Introductory Thoughts Aerodynamics: Some Fundamental Principles and Equations Fundamentals of Inviscid, Incompressible Flow Incompressible Flows Over Airfoils Incompressible Flows Over Finite Wings 1. 2. 3. 4. 5.
Flow similarity Definition of dynamically similar for two different flows The streamline patterns are geometrically similar. The distributions of V/V , p/p , etc. are the same when plotted against common non-dimensional coordinates. The force coefficients are the same. Criteria The bodies and any other solid boundaries are geometrically similar. Same similarity parameters (Re and M ).
Example , T a T Assume 4 T T T = = = 2 2 2 1 T 1 1 1 a T = = 2 2 2 a T 1 1 2 V V V = = = = M M 2 1 1 2 1 2 d a a a 2 1 1 ( 1 4 )( 2 )( 4 ) V V d = = Re 2 2 2 1 1 2 2 2 1 V d = = Similar flows Re 1 1 1 1 1
Types of flow Inviscid vs. viscous flow Inviscid: assume no friction, thermal conduction and diffusion. viscous: consider effects of friction, thermal conduction and diffusion. Incompressible vs. compressible Incompressible: density is constant. Compressible: density is variable.
Mach number regimes Subsonic flow: M<1 everywhere Transonic flow: mixed regions where M<1 and M>1 Supersonic flow: M>1 everywhere Hypersonic flow: very high supersonic speeds, usually M >5.
Chap.2 Aerodynamics: Some Fundamental Principles and Equations
OUTLINE Review of vector relations Control volumes and fluid elements Continuity equation Momentum equation Pathlines and streamlines Angular velocity, vorticity and circulation Stream function and velocity potential
Review of vector relations Vector algebra A A B B A ( B A cos B Scalar product: = e G sin ) Vector product:
Orthogonal coordinate systems Cartesian coordinate system + = + A i j k A A A x y z = + + B i j k B B B B x = y z + + A A B A B A B x x y y z z i j k = A B A A A x y z B B B x y z
Cylindrical coordinate system = + + A e e e A A A r r z z = + + B e e e B B B B r = r z z + e + A A e B A B A B r r z z e r z = A B A A A r z B B B r z
Spherical coordinate system = A r r e B + + A e e e A A = + + e e B B B B r r = + + A A B A B A B r r e e e r = A B A A A r B B B r
Gradient of a scalar field Definition of gradient of a scalar p Its magnitude is the maximum rate of changeof p per unit length. Its direction is the maximum rate of changeof p. Isoline: a line of constant p values Gradient line: a line along which p is tangent at every point. dp = n p Directional derivative: where n is the unit vector in the s direction. ds
Expression for p in Cartesian coordinate system p y x p p = + + i j k p z
Divergence of a vector field If V is the velocity of a flow, the divergence of V will be the time rate of volume change per unit volume. Expression for divergence of V, V, in Cartesian coordinate system = + + V i j k V V V x y z V V V y = + + V x z x y z
Curl of a vector field The angular velocity of a fluid element translating along a streamline is equal to one-half of the curl of V, denoted by V. Expression for curl of V in Cartesian coordinate system V V V + + = k j i V x y z i j k = V x y z V V V x y z
Relations between line, surface and volume integrals Stokes theorem c s = ( A ds A) dS Divergence theorem s V = ( A dS A) dV Gradient theorem s V = pdS pdV
