# High Speed Aero

## EAS 4134

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### Lecture 1

Instructor: Dr Chen

Midterm, Final and Quizes. Quizes come from homework.

Chap 1-10;

1. ThermoDynamics
Wave and isentrophic
2. Flows in variable
3. Normal Shock waves
Stationary/Moving chap4-5
4. Oblique Shockwaves
5. Prandtl-meyers flows
6. Applications
Airfoils and tunnels inlets
7. Fanno-line
8. Rayleigh-line
9. Other Topics
MultidymentionalFlow

Low speed aero - numbers less than Mach 3:
Density is no longer constant faster than mach 3.
$\rho=\frac{m}{v}$
ideal gas law
$P=\rho R T$

Variables in Incompressible
Bernuli equation does not work in compressible

In Compressible flow

• P
• v
• $\rho$
• T
Read section 1.1 - 1.2 - and 1.5

#### 1.3 - Viscosity and Boundary

invisid flow is easy to resolute
asume inviside outside of boundary layer
flow separation after breakup of boundary layer, causes thermodynamic interaction. causes skin-friction drag

Thermodynamics important concepts:
compute density:$\rho$
Equation of state: $P,T,\rho$
$P=\rho R T$ where $Pv=m R T$
$R=gasconstant$
$R=R_u/(\mu m)$

From definition
specific heat constant
$C_v=(\frac{du}{dt})_v$ and $C_p=\frac{dh}{dt}$
perfect gas
$du=C_v dt$ and $dh=C_p dt$
$h=u\frac{P}{\rho}$
$dh=du+d*\frac{P}{\rho}$
$C_p*dt=C_v*dt+d*\frac{P}{\rho}$
$R=C_p-C_v$
du=C_v*dt -> $u_2-u_1=integral C_v*dt= C_v*(T_2-T_1)$ dh=C_p*dt -> $C_p*(T_2 -T_1)$

#### 1.7 Control Volume

Substantial Derivative
$D/DT=d/dt + \hat{v}\nabla$ time rate of change
Reynolds Transport theorem for any property
$DX/DT=d/dt(integral (cv cs xpdv and pvda$
due to unsteady flow for cv
net flow across control surface which gives us three equations of motion

#### 1.8 Mass Continuity equation

X is mass $Dm/Dt=d/dt*triple integral pdv + double integral pv*da = 0$3d equation unsteady or invicid/viscous compressible

Puting the right equations and asumptions gives you most points on test

#### example 1.1 Tank air cilinder, that punctured

$\rho v a=\dot{m}$
$me=0.040418*\frac{P}{\sqrt{T}}*A_e$
find amount of time for mass to be half
$P=\rho*R*T$

Not unsteady, assume that everything is constant.
$0=\frac{dm}{dt}+\dot{m}_{out}-\dot{m}_{in}$
$\frac{dm}{dt}=0.040418*\frac{P}{\sqrt{T}}*A_e$
write P in terms of mass
P*v=m*r*T -> P = 287mt/v (N*m/kgK)

HW:1.8 1.9 1.12 1.16 1.17 2.1.2.2 2.3 2.4 2.5 2.6 2.12

### Lecture 2

08/27/15

Out mass flow is + and in mass flow is -
$\dot{m}=\rho v A$
Uniform flow v1 constant v2 constant

#### Conservation of momentum

EX1.3

find thrust transmitted to test stand:given

• $\dot{m}=10kg/s$
• $v_e=800m/s$
• $A_e=0.01m^2$
• $P_e=50kpa$
Assume steady and uniform

Right side: $P_eA_e$
Left Side: $P_aA_e$

X -> E
x -> e=E/m