Oblique Shock Wave
LEC 12-13
Oblique Shock Wave
We have discussed normal shock wave in previous lectures. In general, a shock wave is
not necessarily perpendicular to the flow. Consider a 2-D supersonic flow along a corner.
If the corner is bended toward

AE 439 Homework 9, assigned Nov. 9, due on Nov. 16 (Before class)
1. In Lecture 25, we considered elliptic lift distribution with ( )
consider the case with a parabolic lift distribution with ( )
(
( ) . Now
). For the
same wing span , what is the relatio

Introduction
LEC 1
What is Aerodynamics
Branch of fluid mechanics, specifically focused on air flow.
In AE439, we mainly focus on invicid air flow. Both incompressible and compressible
flow will be covered. Spend one week on viscous flow (boundary layer t

AE 439 Homework 5, assigned Oct. 12, due on Oct. 19 (Before class)
1. A uniform supersonic air flow of Mach number 3.0, pressure of 100kPa and temperature of
280K flows over a geometries as shown in the figure below. Determine the downstream static
pressu

AE 439 Homework 5, assigned Oct. 3, due on Oct. 12 (before class)
1. Uniform airflow at Mach 3 passes into a concave corner of angle 15, as shown in the figure
below. The pressure and temperature in the supersonic flow are, respectively, 72kPa and 290K.
D

AE 439 Homework 3, assigned Sep. 14, due on Sep. 21 (at 10:29am)
1. Air at
,
enters a compressor
with negligible velocity and is discharged
at a gauge pressure of
,
through a pipe with 0.1
area (here the
velocity is not negligible). The flow rate
is 10
.

AE 439 Homework 2, assigned Sep. 7, due on Sep. 14 @ 10:30AM
1. Velocity in a certain 2-D flow field is given by:
, where the velocity is in
m/s when
and in the units of and second. Determine the expression for local,
convective and substantial accelerat

AE439 Homework 1, assigned Aug. 31, due on Sep. 7 (10:30 AM)
1. Two air tanks have the same temperature. One has air pressure of
and volume of 21
; the other one has air pressure of
and
volume of
. Now the two tanks are connected together, assuming the te

AE 439 Homework 7, assigned Oct. 19, due on Oct. 26 (Before class)
1. Air is drawn into an insulated pipe of constant area through a smoothly contoured
converging nozzle. Room conditions are
and
(abs). The pipe inner
diameter is 20 mm. The pressure at the

AE 439 Homework 8, assigned Oct. 31, due on Nov. 9 at 10:30AM
1. A crude model of a tornado is formed by combining a sink with strength of
and a free vortex of strength
. (a) Obtain the stream
function and velocity potential of this flow. (b) Calculate th

Shock-expansion theory on supersonic airfoil
LEC 15
The lift coefficients ( ) of airfoils in incompressible flows are usually determined using
Kutta-Joukowski theory. However, this theory cannot be used directly for compressible
flow case. Especially, whe

Prandtle-Meyer Expansion Waves
LEC 14
As we learn from the previous lectures, when supersonic flow makes turn into itself, an
oblique shock will be generated to make the turn. In contrast, when supersonic pass over
a convexed corner, the flow will bend aw

Normal Shock Wave and Pitot tube
LEC 9-11
Shock Wave
Shock wave is an extremely thin layer, typically with a thickness in the order
of
. Across the shock wave flow properties can change drastically,
and they are considered to be discontinuous across the s

Reference Conditions
LEC 8
Reference state
For incompressible flow, integration of Eulers equation for frictionless flow along the
streamline led to the Bernoulli equation (gravitational force is usually neglected for air
flow):
The frictionless decelerat

Speed of sound
LEC 7
Speed of Sound
Supersonic and subsonic are terms refer to speeds that are respectively greater than or
less than the speed of sound. The speed of sound is the speed of a pressure wave of
infinitesimal strength. It is a very important

Governing equations
LEC 4-6
Number of equations needed to solve in compressible flow
For incompressible flow, we are usually only interested in the flow velocity and pressure
distribution, the density is assumed to be constant and the temperature is usual

Vector calculus brief review
LEC 3
This section provides some brief review on vector calculus. Mathematics is a very
important tool in this class. Students at this stage should have already taken the required
classes. As many of you mentioned, some classe

Thermodynamics (Review)
LEC 2
Equation of State
Equation of state describes the relation between various properties of a substance. In this
class, we only consider simple compressible systems, which means electrical, magnetic,
surface tension, gravitation

Finite wing theory (incompressible)
LEC 25
In the previous lectures, we talked about the philosophy of the way dealing a finite wing:
1, we start from easier 2-D airfoil case, 2, then modify the 2-D results to account for 3-D
effects of a real finite wing

Incompressible airfoil theory
LEC 22-23
In the previous lectures, we reviewed potential flow, Kutta-Joukowski theorem and Kutta
condition. Now we have everything required to introduce the thin airfoil theory. This
theory can be used to calculate lift and

Airfoils and the Kutta condition
LEC 22
On any air craft, wings are used to generate lift. How and how much lift is
generated is the topic of the following lectures. We will start with incompressible flow
situation, which is when the Mach number is less t

Potential flow (review)
LEC 21
Since you all take the AE339 class, you should already be familiar with potential
flow. In this lecture, I am just going to give a very brief review of 2-D potential flow.
For steady incompressible and invicid flow, if the f

Frictionless Internal Flow With Heat Transfer
LEC 20
Frictionless flow with heat exchange
Frictionless flow with heat exchange in a constant area duct is analyzed in this lecture. To
explore the effects of heat exchange on a compressible flow, we apply th