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Introduction to Gas Dynamics
All Lecture Slides
Teknillinen Korkeakoulu / Helsinki University of Technology
Autumn 2009
Gasdynamics — Lecture Slides
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Compressible flow
Zeroth law of thermodynamics
First law of thermodynamics
Equation of state — ideal gas
Specific heats
The “perfect” gas
Second law of thermodynamics
Adiabatic, reversible process
The free energy and free enthalpy
Entropy and real gas flows
One-dimensional gas dynamics
Conservation of mass — continuity equation
Conservation of energy — energy equation
Reservoir conditions
On isentropic flows
Gasdynamics — Lecture Slides

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Euler’s equation
Momentum equation
A review of equations of conservation
Isentropic condition
Speed of sound — Mach number
Results from the energy equation
The area-velocity relationship
On the equations of state
Bernoulli equation — dynamic pressure
Constant area flows
Shock relations for perfect gas — Part I
Shock relations for perfect gas — Part II
Shock relations for perfect gas — Part III
The area-velocity relationship — revisited
Nozzle flow — converging nozzle
Gasdynamics — Lecture Slides
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Nozzle flow — converging-diverging nozzle
Normal shock recovery — diffuser
Flow with wall roughness — Fanno flow
Flow with heat addition — Rayleigh flow
Normal shock, Fanno flow and Rayleigh flow
Waves in supersonic flow
Multi-dimensional equations of the flow
Oblique shocks
Relationship between wedge angle and wave angle
Small angle approximation
Mach lines
Weak oblique shocks
Supersonic compression by turning
Supersonic expansion by turning
The Prandtl-Meyer function
Gasdynamics — Lecture Slides

46 Detached shocks
47 Shock-expansion theory
48 Reflection and intersection of oblique shocks
49 Cones in supersonic flow
50 Derivation of perturbation equation
51 Irrotational flow
52 Governing equations for small perturbation flows — Part I
53 Governing equations for small perturbation flows — Part II
54 Pressure coefficient
55 Boundary conditions
56 Flow past a wave-shaped wall — an example
57 Flow past a wave-shaped wall — subsonic case
58 Flow past a wave-shaped wall — supersonic case
Gasdynamics — Lecture Slides
Compressible flow
In a nutshell, the term compressible flow refers to the fluids of
which there can be found significant variation of density in the flow
under consideration.
Compressibility is strongly related to the speed of the flow itself and
the thermodynamics of the fluid. A good grasp of thermodynamics
is imperative for the study of compressible flow.
For low-speed flow, the kinetic energy is often much smaller than
the heat content of the fluid, such that temperature remains more or
less constant.
On the other hand, the magnitude of the kinetic energy in a
high-speed flow can be very large, able to cause a large variation in
the temperature.
Some important phenomena strongly associated with compressibility
are the flow discontinuity and choking of the flow.
Gasdynamics — Lecture Slides

Compressible flow
To illustrate, consider a car at sea-level, 1 atm and 15 ◦ C, going at a
speed of 90 km/h. The density is 1.225 kg/m3 . At a stagnation
point, the density there is found to be 1.228 kg/m3 , a mere 0.27 %
difference. The temperature rises by 0.311 ◦ C and the pressure
changes by 0.38 %. Here, the incompressible assumption can be
applied.
Now, consider a typical air flow around a cruising jetliner at 10 km
altitude. The speed is now 810 km/h, while the ambient conditions
are 0.413 kg/m3 , 0.261 atm and −50 ◦ C. At the stagnation point the
temperature rises by over 25 ◦ C, while density and pressure changes
by more than 30 % and 45 %, respectively. It is clear that
compressibility must now be taken into account.
Gasdynamics — Lecture Slides
Compressible flow
Figure 1: Breaking the sound
barrier. . . ?
An extreme example of
compressible flow in action is the
re-entry flow. Another is shown
here on the left as a jet fighter
seemingly punches through the
“sound barrier”. However, more
daily mundane applications can
also be found in flows through jet
engines, or around a transport
aircraft.
Gasdynamics — Lecture Slides

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