Editing Atmospheric entry (section)

====Real (non-equilibrium) gas model====
A non-equilibrium real gas model is the most accurate model of a shock layer's gas physics, but is more difficult to solve than an equilibrium model. The simplest non-equilibrium model is the ''Lighthill-Freeman model'' developed in 1958.<ref>{{cite journal |last=Lighthill |first=M.J. |title=Dynamics of a Dissociating Gas. Part I. Equilibrium Flow |journal=Journal of Fluid Mechanics |volume=2 |pages=1–32 |date=Jan 1957 |doi=10.1017/S0022112057000713 |issue=1|bibcode = 1957JFM.....2....1L |s2cid=120442951 }}</ref><ref>{{cite journal |last=Freeman |first=N.C. |title=Non-equilibrium Flow of an Ideal Dissociating Gas |journal=Journal of Fluid Mechanics |volume=4 |pages=407–425 |date=Aug 1958 |doi=10.1017/S0022112058000549 |issue=04|doi-broken-date=November 1, 2024 |bibcode = 1958JFM.....4..407F |s2cid=122671767 }}</ref> The Lighthill-Freeman model initially assumes a gas made up of a single diatomic species susceptible to only one chemical formula and its reverse; e.g., N<sub>2</sub> = N + N and N + N = N<sub>2</sub> (dissociation and recombination). Because of its simplicity, the Lighthill-Freeman model is a useful pedagogical tool, but is too simple for modelling non-equilibrium air. Air is typically assumed to have a mole fraction composition of 0.7812 molecular nitrogen, 0.2095 molecular oxygen and 0.0093 argon. The simplest real gas model for air is the ''five species model'', which is based upon N<sub>2</sub>, O<sub>2</sub>, NO, N, and O. The five species model assumes no ionization and ignores trace species like carbon dioxide.

When running a Gibbs free energy equilibrium program,{{clarify|date=August 2018}} the iterative process from the originally specified molecular composition to the final calculated equilibrium composition is essentially random and not time accurate. With a non-equilibrium program, the computation process is time accurate and follows a solution path dictated by chemical and reaction rate formulas. The five species model has 17 chemical formulas (34 when counting reverse formulas). The Lighthill-Freeman model is based upon a single ordinary differential equation and one algebraic equation. The five species model is based upon 5 ordinary differential equations and 17 algebraic equations.{{Citation needed|date=December 2017}} Because the 5 ordinary differential equations are tightly coupled, the system is numerically "stiff" and difficult to solve. The five species model is only usable for entry from [[low Earth orbit]] where entry velocity is approximately {{cvt|7.8|km/s|km/h mph}}. For lunar return entry of 11&nbsp;km/s<!-- 36545 ft/s in NASA 1960s units -->,<ref>[https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690029435.pdf Entry Aerodynamics at Lunar Return Conditions Obtained from the Fliigh of Apollo 4] {{Webarchive|url=https://web.archive.org/web/20190411091352/https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690029435.pdf |date=April 11, 2019 }}, Ernest R. Hillje, NASA, TN: D-5399, accessed 29 December 2018.</ref> the shock layer contains a significant amount of ionized nitrogen and oxygen. The five-species model is no longer accurate and a twelve-species model must be used instead.
Atmospheric entry interface velocities on a Mars–Earth [[orbital trajectory|trajectory]] are on the order of {{Cvt|12|km/s|km/h mph}}.<ref>[https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080023907.pdf Overview of the Mars Sample Return Earth Entry Vehicle] {{Webarchive|url=https://web.archive.org/web/20191201012539/https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080023907.pdf |date=December 1, 2019 }}, NASA, accessed 29 December 2018.</ref>
Modeling high-speed Mars atmospheric entry—which involves a carbon dioxide, nitrogen and argon atmosphere—is even more complex requiring a 19-species model.{{citation needed|date=August 2018}}

An important aspect of modelling non-equilibrium real gas effects is radiative heat flux. If a vehicle is entering an atmosphere at very high speed (hyperbolic trajectory, lunar return) and has a large nose radius then radiative heat flux can dominate TPS heating. Radiative heat flux during entry into an air or carbon dioxide atmosphere typically comes from asymmetric diatomic molecules; e.g., [[cyanogen]] (CN), [[carbon monoxide]], [[nitric oxide]] (NO), single ionized molecular nitrogen etc. These molecules are formed by the shock wave dissociating ambient atmospheric gas followed by recombination within the shock layer into new molecular species. The newly formed [[diatomic]] molecules initially have a very high vibrational temperature that efficiently transforms the [[Quantum harmonic oscillator|vibrational energy]] into [[radiant energy]]; i.e., radiative heat flux. The whole process takes place in less than a millisecond which makes modelling a challenge. The experimental measurement of radiative heat flux (typically done with shock tubes) along with theoretical calculation through the unsteady [[Schrödinger equation]] are among the more esoteric aspects of aerospace engineering. Most of the aerospace research work related to understanding radiative heat flux was done in the 1960s, but largely discontinued after conclusion of the Apollo Program. Radiative heat flux in air was just sufficiently understood to ensure Apollo's success. However, radiative heat flux in carbon dioxide (Mars entry) is still barely understood and will require major research.{{citation needed|date=August 2018}}