THEORY OF PROPULSION 12' Special topics

1
THEORY OF PROPULSION12. Special topics

• P. M. SFORZA
• University of Florida

2
The Euler equations
continuity
3
Combined Euler and continuity equations
4
The perturbation potential
5
Transform to Laplaces equation
Transform the coordinates
fiLf
Introduce a new dependent variable
To obtain Laplaces equation
6
Relationships among the variables
compressible
incompressible
The angle of incidence
For geometrically similar airfoils
Therefore
7
The perturbation velocities and Cp
compressible
incompressible
The pressure coefficient in linearized flow
incompressible
8
The Prandtl-Glauert rule
spacing
solidity
9
Velocity distributions over airfoils
(v/V)2
(v/V)2
x/l
10
Critical Mach number as f(cL)
11
Limitation of the Prandtl-Glauert rule
is unbounded as Mm
0
The full plane inviscid subsonic flow potential
equation is
Karman and Tsien solved this using Chaplygins
hodograph method and an approximate equation of
state
12
The Karman-Tsien correction for Cp
It is still necessary that Mm2t ltlt1, that is,
thin airfoils
The Karman-Tsien correction is less than the
Prandtl-Glauert
13
Boundary layer effects
Curved streamlines initiate secondary flows
Pitch line streamline
R
dp/drrw2/R Slower regions have smaller R