Editing Atmospheric entry (section)

===Shock layer gas physics ===
At typical reentry temperatures, the air in the shock layer is both [[ionized]] and [[dissociation (chemistry)|dissociated]].{{citation needed |date=May 2021}}<ref>{{Cite web|url=https://www.icas.org/ICAS_ARCHIVE/ICAS2018/data/papers/ICAS2018_0837_paper.pdf|title=Ionization And Dissociation Effects On Hypersonic Boundary-Layer Stability|access-date=May 13, 2021|archive-date=October 1, 2021|archive-url=https://web.archive.org/web/20211001035258/https://www.icas.org/ICAS_ARCHIVE/ICAS2018/data/papers/ICAS2018_0837_paper.pdf|url-status=live}}</ref> This chemical dissociation necessitates various physical models to describe the shock layer's thermal and chemical properties. There are four basic physical models of a gas that are important to aeronautical engineers who design heat shields:

====Perfect gas model====
Almost all aeronautical engineers are taught the [[Ideal gas|perfect (ideal) gas model]] during their undergraduate education. Most of the important perfect gas equations along with their corresponding tables and graphs are shown in NACA Report 1135.<ref>{{cite journal |title=Equations, tables, and charts for compressible flow |publisher=NASA Technical Reports |issue=NACA-TR-1135 |year=1953 |url=http://www.nasa.gov/sites/default/files/734673main_Equations-Tables-Charts-CompressibleFlow-Report-1135.pdf |journal=NACA Annual Report |volume=39 |pages=613–681 |access-date=June 17, 2015 |archive-date=September 4, 2015 |archive-url=https://web.archive.org/web/20150904043857/http://www.nasa.gov/sites/default/files/734673main_Equations-Tables-Charts-CompressibleFlow-Report-1135.pdf |url-status=live }}</ref> Excerpts from NACA Report 1135 often appear in the appendices of thermodynamics textbooks and are familiar to most aeronautical engineers who design supersonic aircraft.

The perfect gas theory is elegant and extremely useful for designing aircraft but assumes that the gas is chemically inert. From the standpoint of aircraft design, air can be assumed to be inert for temperatures less than {{Convert|550|K}} at one atmosphere pressure. The perfect gas theory begins to break down at 550 K and is not usable at temperatures greater than {{Convert|2000|K}}. For temperatures greater than 2,000 K, a heat shield designer must use a ''real gas model''.

====Real (equilibrium) gas model====
An entry vehicle's pitching moment can be significantly influenced by real-gas effects. Both the Apollo command module and the Space Shuttle were designed using incorrect pitching moments determined through inaccurate real-gas modelling. The Apollo-CM's trim-angle angle of attack was higher than originally estimated, resulting in a narrower lunar return entry corridor. The actual aerodynamic center of the [[Space Shuttle Columbia|''Columbia'']] was upstream from the calculated value due to real-gas effects. On ''Columbia''{{'}}s maiden flight ([[STS-1]]), astronauts [[John Young (astronaut)|John Young]] and [[Robert Crippen]] had some anxious moments during reentry when there was concern about losing control of the vehicle.<ref>Kenneth Iliff and Mary Shafer, ''Space Shuttle Hypersonic Aerodynamic and Aerothermodynamic Flight Research and the Comparison to Ground Test Results'', pp. 5–6 {{ISBN?}}</ref>

An equilibrium real-gas model assumes that a gas is chemically reactive, but also assumes all chemical reactions have had time to complete and all components of the gas have the same temperature (this is called ''[[thermodynamic equilibrium]]''). When air is processed by a shock wave, it is superheated by compression and chemically dissociates through many different reactions. Direct friction upon the reentry object is not the main cause of shock-layer heating. It is caused mainly from [[isentropic process|isentropic]] heating of the air molecules within the compression wave. Friction based entropy increases of the molecules within the wave also account for some heating.{{original research inline|date=November 2013}} The distance from the shock wave to the [[stagnation point]] on the entry vehicle's leading edge is called ''shock wave stand off''. An approximate rule of thumb for shock wave standoff distance is 0.14 times the nose radius. One can estimate the time of travel for a gas molecule from the shock wave to the stagnation point by assuming a free stream velocity of 7.8&nbsp;km/s and a nose radius of 1 meter, i.e., time of travel is about 18 microseconds. This is roughly the time required for shock-wave-initiated chemical dissociation to approach [[chemical equilibrium]] in a shock layer for a 7.8&nbsp;km/s entry into air during peak heat flux. Consequently, as air approaches the entry vehicle's stagnation point, the air effectively reaches chemical equilibrium thus enabling an equilibrium model to be usable. For this case, most of the shock layer between the shock wave and leading edge of an entry vehicle is chemically reacting and ''not'' in a state of equilibrium. The [[wikt:Appendix:Glossary of atmospheric reentry#F|Fay–Riddell equation]],<ref name="Fay-Riddell"/> which is of extreme importance towards modeling heat flux, owes its validity to the stagnation point being in chemical equilibrium. The time required for the shock layer gas to reach equilibrium is strongly dependent upon the shock layer's pressure. For example, in the case of the [[Galileo (spacecraft)|''Galileo'']] probe's entry into Jupiter's atmosphere, the shock layer was mostly in equilibrium during peak heat flux due to the very high pressures experienced (this is counterintuitive given the free stream velocity was 39&nbsp;km/s during peak heat flux).

Determining the thermodynamic state of the stagnation point is more difficult under an equilibrium gas model than a perfect gas model. Under a perfect gas model, the ''ratio of specific heats'' (also called ''isentropic exponent'', [[adiabatic index]], ''gamma'', or ''kappa'') is assumed to be constant along with the [[gas constant]]. For a real gas, the ratio of specific heats can wildly oscillate as a function of temperature. Under a perfect gas model there is an elegant set of equations for determining thermodynamic state along a constant entropy stream line called the ''isentropic chain''. For a real gas, the isentropic chain is unusable and a ''Mollier diagram'' would be used instead for manual calculation. However, graphical solution with a Mollier diagram is now considered obsolete with modern heat shield designers using computer programs based upon a digital lookup table (another form of Mollier diagram) or a chemistry based thermodynamics program. The chemical composition of a gas in equilibrium with fixed pressure and temperature can be determined through the ''Gibbs free energy method''. [[Gibbs free energy]] is simply the total [[enthalpy]] of the gas minus its total [[entropy]] times temperature. A chemical equilibrium program normally does not require chemical formulas or reaction-rate equations. The program works by preserving the original elemental abundances specified for the gas and varying the different molecular combinations of the elements through numerical iteration until the lowest possible Gibbs free energy is calculated (a [[Newton–Raphson method]] is the usual numerical scheme). The data base for a Gibbs free energy program comes from spectroscopic data used in defining [[partition function (statistical mechanics)|partition functions]]. Among the best equilibrium codes in existence is the program ''Chemical Equilibrium with Applications'' (CEA) which was written by Bonnie J. McBride and Sanford Gordon at NASA Lewis (now renamed "NASA Glenn Research Center"). Other names for CEA are the "Gordon and McBride Code" and the "Lewis Code". CEA is quite accurate up to 10,000 K for planetary atmospheric gases, but unusable beyond 20,000 K ([[double ionization]] is not modelled). [https://web.archive.org/web/20200205195610/https://www.grc.nasa.gov/WWW/CEAWeb/ CEA can be downloaded from the Internet] along with full documentation and will compile on Linux under the [[GNU Fortran|G77 Fortran]] compiler.

====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}}

====Frozen gas model====
The frozen gas model describes a special case of a gas that is not in equilibrium. The name "frozen gas" can be misleading. A frozen gas is not "frozen" like ice is frozen water. Rather a frozen gas is "frozen" in time (all chemical reactions are assumed to have stopped). Chemical reactions are normally driven by collisions between molecules. If gas pressure is slowly reduced such that chemical reactions can continue then the gas can remain in equilibrium. However, it is possible for gas pressure to be so suddenly reduced that almost all chemical reactions stop. For that situation the gas is considered frozen.{{citation needed|date=August 2018}}

The distinction between equilibrium and frozen is important because it is possible for a gas such as air to have significantly different properties (speed-of-sound, [[viscosity]] etc.) for the same thermodynamic state; e.g., pressure and temperature. Frozen gas can be a significant issue in the wake behind an entry vehicle. During reentry, free stream air is compressed to high temperature and pressure by the entry vehicle's shock wave. Non-equilibrium air in the shock layer is then transported past the entry vehicle's leading side into a region of rapidly expanding flow that causes freezing. The frozen air can then be entrained into a trailing vortex behind the entry vehicle. Correctly modelling the flow in the wake of an entry vehicle is very difficult. [[Space Shuttle thermal protection system|Thermal protection shield]] (TPS) heating in the vehicle's afterbody is usually not very high, but the geometry and unsteadiness of the vehicle's wake can significantly influence aerodynamics (pitching moment) and particularly dynamic stability.{{citation needed|date=August 2018}}