Gas Dynamics

date2025-07-24tags:meche:

Steal from this URL and attribute it. https://kyleniemeyer.github.io/gas-dynamics-notes/intro/review-thermo.html#law Kyle Niemeyer took a more textbook approach to gas dynamics.

Labview stuff https://www.halvorsen.blog/documents/hardware/level_tank/Level%20Tank%20System.pdf

Add in this stuff too https://www.halvorsen.blog/documents/hardware/level_tank/Level%20Tank%20System.pdf https://kyleniemeyer.github.io/gas-dynamics-notes/intro/review-thermo.html#law https://github.com/kyleniemeyer/rocket-propulsion https://kyleniemeyer.github.io/dynamics-book/intro.html https://kyleniemeyer.github.io/space-systems-notes/orbital-mechanics/orbit-transfers.html https://github.com/kyleniemeyer/finite-difference-course

He uses openfoam too! https://github.com/kyleniemeyer/directChillFoam

Introduction and review

Review of thermodynamics

This section reviews thermodynamics concepts: definitions, laws, and useful property relationships.

%matplotlib inline
from matplotlib import pyplot as plt
import numpy as np

# these lines are only for helping improve the display
import matplotlib_inline.backend_inline
matplotlib_inline.backend_inline.set_matplotlib_formats('pdf', 'png')
plt.rcParams['figure.dpi']= 300
plt.rcParams['savefig.dpi'] = 300
plt.rcParams['mathtext.fontset'] = 'cm'

Our study of gas dynamics will focus on a handful of important fluid properties:

density: $\rho = \frac{m}{V} = \frac{1}{\nu}$
pressure: p = force/unit area. We work with absolute pressure, and I suggest sticking to Pa
temperature: T, which also must be absolute temperature.

Equations of state

For a fluid in general, the pressure, density, and temperature are not fully independent, and we can find one property given the other two. When dealing with liquids, we will frequently assume that they are incompressible and thus the density is constant.

For gases, we can frequently use the perfect, or ideal, gas equation of state:

$$ p = \rho R T $$

where R is the specific gas constant:

$$ R = \frac{8314 \frac{J}{kmol K}}{MW} $$

and MW is the molecular weight of the gas. For air, R = 287 J/(kg K).

The ideal gas equation of state applies best for relatively low densities, or at relatively low pressures or high temperatures.

Thermodynamics definitions

Properties describe the state of a system.

intensive properties depend only on the state, and not how much stuff is in the system. Examples include temperature, density, and pressure

extensive properties depend on the amount of stuff (i.e., the mass) of the system. Examples include total internal energy (U) and volume (V)

We can also break down properties into type:

observable properties are directly measureable ($p$, $T$, $V$, mass)
mathematical properties come from combinations of other properties ($\rho$, $c_p$, $h$)
derived properties we arrive at from some analysis (internal energy from the First Law of thermodynamics, entropy from the Second Law)

Path/process: a series of consecutive states that define a unique journey from one state to another. Common features of processes that we will encounter or assume include:

adiabatic: no heat transfer ($\dot{Q} = 0$)
isothermal: constant temperature
isobaric: constant pressure
isentropic: constant entropy
isochoric: constant specific volume / density

Cycle: a sequence of processes that returns a system to its original state. point function: a property, that depends only on the state of a system. path function: not just a function of the state, but of the path/journey taken. Examples include heat and work.

Laws of Thermodynamics

Pressure - absolute pressure as a key gas property
Vacuum - ideal gas law in vacuum systems
Pump - pumping compressible gases and fluids
Propeller - compressible flow over propellers
Microfluidics - fluid flow and equations of state
Units - SI units for thermodynamic quantities
Reynolds Number Calculator - laminar vs turbulent transition
Compressible Flow Calculator - isentropic and shock tables