Since the beginning of flight, every time we wanted to fly higher, faster or more efficiently, we needed to come up with higher fidelity aerodynamic theories. World War 1 airplanes were designed based on the thin airfoil theory. Improved potential flow and boundary layer theories allowed us to build much faster airplanes in WW2. The need to fly even faster under jet power led to the better compressibility theories. We now want to go even faster. In order to make flights to orbit routine and flights to/from Mars safe, we need to improve our understanding of gas dynamics once more.
Most of the vehicles designed to fly subsonically, supersonically or even hypersonically (but at sub orbital velocities,) assumed that air is a continuous medium that could be defined by temperature, pressure, density, and other simple gas dynamic properties. However, air is actually made up of individual particles that fly randomly while rotating and vibrating. Electrons flying around the air molecules can also store energy. Macroscopic parameters like temperature or pressure are actually derived based on microscopic configurations. When these particles collide, they exchange their translational, rotational and vibrational energy. Under equilibrium conditions, which dominate under most flight regimes, we can analytically calculate the distribution of gas internal energies and we don’t have to worry about the details of internal energy exchange. Unfortunately, the gas in the hypersonic shock layer is not in equilibrium and we need to improve our understanding of internal energy exchange processes to be able to better predict how the air responds to Mach 20+ vehicles.
At the most fundamental level, interaction between gas molecules could be described by the Schrodinger wave equation. However, this equation cannot be solved for complex aerodynamic flows. Instead, by applying a few approximations it is possible to solve the electronic part of the Schrodinger equation for fixed atomic coordinates to produce a potential energy surface. This surface could then be used to study millions of binary collisions and improve our understanding of fundamental gas interactions. Two collisions, between an O2 molecule an an O atom are shown below. In the first movie, the molecule was initially in the zeroth vibrational level while in the second movie it was in the 15th vibrational level. The initial vibrational level results in dramatically different collision dynamics.