EML 5714 & EAS 4132
Fall 2014
Homework # 3
Due: September 25, 2014
This assignment is to be turned no later than 5:00 pm (Gainesville time) electronically
through the assignment utility in elearning interface.
1. Do problem 5.1 in Oosthuizen and Carscalle
Consider one-dimensional flow in a jet ejector as shown below
e
i
Secondary Jet (S)
Primary Jet (P)
Secondary Jet (S)
Mixing tube
C.V.
x
In this application it could be typical to know properties at the inlet and you want to know properties
(velocity, pre
EML 5714/EAS4132 Fall 2015
Tools for Analysis
Material Derivative (Substantial or Particle)
Used to relate a fixed mass system to a control volume fixed in space with
mass flowing through it.
Consider a small fluid element of fixed mass moving through a f
EML 5714/EAS4132 Fall 2015
One-Dimensional Isentropic flow Concept
We have already introduced concepts of both one-dimensional (dominated by velocity in one direction)
and isentropic flows (adiabatic and reversible) but here we will go a little deeper.
Pl
EML 5714/EAS4132 Fall 2015
Mach Number
Definition = rate of local velocity to that of the local speed of sound.
At altitude T decreases therefore a decreases and the same velocity will
result in increase in M
M a=V thus if limited by Mach number on veh
EML 5714/EAS4132 Fall 2015
Relationships
Similar to what we previously discussed lets look at isentropic flow along a stream tube
V=V2=0
V=V1
Temperature first
But here the velocity at the end of the stream tube is zero.
For steady flow with no changes in
EXAMPLE 2: A blunt nosed missile is flying at Mach 2 at standard sea level.
Find the temperature and
pressure at the nose of the missile.
Soln: Nose of the missile is a stagnation point and the flow to get there passes through the
normal portion of the bo
EML 5714/EAS4132 Fall 2015
Intuitively what happens as increased
increases hence the shock strength increases therefore M2 is reduced
Intuitively if M1 increases with being constant
decreases but the shock becomes stronger
bottomline is anything that in
EML 5714/EAS4132 Fall 2015
Oblique Shock Waves
Normal shock waves are actually fairly rare (expect for portions of the bow shock) and oblique
shock waves are the more normal
By definition the study of oblique waves will force us to leave 1-D concepts
Exa
EML 5714/EAS4132 Fall 2015
Moving Normal Shocks
Examples: explosions, shock tubes, re-entry of blunt objects, valves shutting, etc .
We will examine this by considering a Normal Shock which we have already studied; but now the
reference frame is fixed to
EML 5714/EAS4132 Fall 2015
Example A normal shock wave propagates into stagnant air with T=300 K. The pressure ratio
across the shock is 10.
Find:
The shock velocity
The velocity of the induced mass behind the shock
The temperature ratio across the wa
EML 5714/EAS4132 Fall 2015
Now for a given value of M1 we can plot this curve as a function of and
Physical bounds on
90 > >
For a given M there is a max value of and
if is greater there is no solutions for an
attached straight shock
For any given <max
EML 5714/EAS4132 Fall 2014
Introduction
The study of Compressible Flow involves the combination of thermodynamic
principles with that of fluid motion.
Applicable from high speed aircraft to turbines to pipeline flows
A Fluid is defined as substance whi
EML 5714/EAS4132 Fall 2015
Conservation of Energy
Start with 1st Law of Thermodynamics for a fixed mass system.
(Energy can not be created or destroyed)
=
, , cfw_
and the implies a small amount
This equation can be written on a rate basis
=
LHS r
EML 5714 & EAS 4132
Fall 2014
Homework # 1
Due: September 10, 2014
This assignment is to be turned no later than 5:00 pm (Gainesville time) electronically
through the assignment utility in elearning interface.
1. Do problem 1.1 in Oosthuizen and Carscalle
EML 5714 & EAS 4132
Fall 2014
Homework # 2
Due: September 18, 2014
This assignment is to be turned no later than 5:00 pm (Gainesville time) electronically
through the assignment utility in elearning interface.
1. Do problem 3.1 in Oosthuizen and Carscalle
EML 5714/EAS4132 Fall 2015
Aspects of Compressible Flow
Wave Propagation in Compressible Media
Consider ideal flow (inviscid and incompressible) over and air foil as shown below
Ques: How does the flow upstream of the airfoil know of the obstacle and how
EML 5714/EAS4132 Fall 2015
So if every fluid is compressible (i.e., infinite speed of sound is not possible), Why is
compressibility more important in certain flows?
In a flow where entropy is constant it can be shown for a perfect gas
=
recall from Therm
EML 5714/EAS4132 Fall 2015
Conservation of Momentum
Newtons 2nd law of motion for a fixed mass
=
therefore
define linear momentum as =
=
from analogy with the RTT = and = so
+
(
) =
=
.
.
[
] + [ . .] = [
]
. .
. .
( )
typically