1. Gas Dynamics ESA 341 Chapter 2
Dr Kamarul Arifin B. Ahmad
PPK Aeroangkasa

2. Isentropic Flow Introduction Derivation Stagnation properties
IF in a converging and converging-diverging nozzle
Application

3. Introduction
Consider a gas in horizontal sealed cylinder with a piston at one end. The gas expands outwards moving the piston and performing work. The walls of the piston are insulated and no heat transfer takes place.
Is this an isentropic process?
q=0
P  T
The mathematical relationships between pressure, density, and temperature are known as the isentropic flow relations.

4. Introduction Isentropic core flow
Examples of isentropic flows: Jet or rocket nozzles, diffusers. Airfoils.
Isentropic
core flow
But in reality there is no real flow is entirely isentropic!!

5. Derivation For isentropic flow: And: So:
Applying energy eqn to get relation between T & M:

6. Derivation cont.
But:
And:
So:

7. Derivation cont. To find relation between A & M:
Using relation r-M and T-M
Where:

8. Stagnation Properties
Stagnation condition is a condition that would
exist if the flow at any point was isentropically
brought to or come from rest (V =M= 0).
Stagnation values:

9. Stagnation Properties cont.
Examples 1 2
Stagnation point is point 0.
Stagnation point is inside the chamber.

10. Isentropic Relations in Tabular Form – Appendix B:
Example:
M T0/T P0/P r0/r a0/a A/A* q -
2.40

11. Pitot Probe Measurement for Compressible Flow:
V = 0 P0 P
Incompressible flow (Bernoulli eqn):
Compressible flow:

12. Critical Conditions: A=A* M=1 M<1 M>1 Mach number A/A* 5
Critical condition is a condition
that would exist if the flow was
isentropically accelerated
or decelerated until M = 1.
M*=1  T*, P*, r*, A*, a* = 1 2 3 4

13. Group exercises 2
Calculate the Mach number of two aircraft both travelling with an airspeed of 300m/s. One is traveling at sea level (T=250C); the other at an altitude of 11km (T=-160C.)
A perfect gas with is traveling at Mach 3 with a static temperature of 250K, a static pressure of 101kPa, and a static density of kg/m3. Determine the stagnation temperature, pressure, and density values.
An aircraft is flying at 80m/s at sea level where the temperature is 200C, density is 1.225kg/m3 and pressure is mbar. Assuming R=287 J/kgK what Mach number is the aircraft flying? Air stagnates near the leading edge. Assuming isentropic compressible flow calculate the stagnation pressure. Assuming incompressible flow, use Bernoulli’s equation to calculate the stagnation pressure. What is the error in assuming incompressible flow at this Mach number?
Mach number equations
Use the po/p, to/t, and rho0/rho equations
M,P0/P,bernoulli equations