# 再入

（重定向自返回式

## 再入飞行器形状

### 球形或球形部分

1950年代到1960年代，易于从理论上用Fay-Riddell方程建模分析。[1] 当时没有高速计算机，高速空气动力学还处于萌芽阶段。苏联的东方飞船上升飞船、以及火星、金星探测器的下降舱；美国的都采用了球形防热大底。阿波罗飞船再入时的攻角−27°，升阻比0.368[2]联盟飞船月球取样返回探测器双子座飞船水星号飞船都是如此设计。即使这少量的升力也使得从弹道式再入8-9g的峰值加速度减小到4-5g，同时大大减少了峰值气动加热。

LGM-30民兵洲际导弹的再入段

Mk-6 再入舱

"发现者"侦察卫星的胶片返回舱

## 激波层气体物理

### Real (equilibrium) gas model

An entry vehicle's pitching moment can be significantly influenced by real-gas effects. Both the Apollo-CM and the Space Shuttle were designed using incorrect pitching moments determined through inaccurate real-gas modeling. 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 Columbia was upstream from the calculated value due to real-gas effects. On Columbia’s maiden flight (STS-1), astronauts John W. Young and Robert Crippen had some anxious moments during reentry when there was concern about losing control of the vehicle.[4]

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 heating of the air molecules within the compression wave. Friction based entropy increases of the molecules within the wave also account for some heating.[原創研究？] 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 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 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 Fay-Riddell equation,[1] 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 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 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 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 modeled). CEA can be downloaded from the Internet along with full documentation and will compile on Linux under the 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.[5][6] 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., N2 → N + N and N + N → N2 (dissociation and recombination). Because of its simplicity, the Lighthill-Freeman model is a useful pedagogical tool, but is unfortunately too simple for modeling 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 N2, O2, 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, 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. Because the 5 ordinary differential equations are loosely 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 7.8 km/s. For lunar return entry of 11 km/s, 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. High speed Mars entry which involves a carbon dioxide, nitrogen and argon atmosphere is even more complex requiring a 19 species model.

### 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.

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, et cetera) 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 modeling the flow in the wake of an entry vehicle is very difficult. 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.

## 参考文献

1. ^ 1.0 1.1 Fay, J. A.; Riddell, F. R. Theory of Stagnation Point Heat Transfer in Dissociated Air (PDF Reprint). Journal of the Aeronautical Sciences. February 1958, 25 (2): 73–85 [2009-06-29]. doi:10.2514/8.7517.
2. ^ Hillje, Ernest R., "Entry Aerodynamics at Lunar Return Conditions Obtained from the Flight of Apollo 4 (AS-501)," NASA TN D-5399, (1969).
3. ^ Equations, tables, and charts for compressible flow. NACA Annual Report (NASA Technical Reports). 1953, 39 (NACA-TR-1135): 611–681.
4. ^ Kenneth Iliff and Mary Shafer, Space Shuttle Hypersonic Aerodynamic and Aerothermodynamic Flight Research and the Comparison to Ground Test Results, Page 5-6
5. ^ Lighthill, M.J. Dynamics of a Dissociating Gas. Part I. Equilibrium Flow. Journal of Fluid Mechanics. Jan 1957, 2 (1): 1–32. Bibcode:1957JFM.....2....1L. doi:10.1017/S0022112057000713.
6. ^ Freeman, N.C. Non-equilibrium Flow of an Ideal Dissociating Gas. Journal of Fluid Mechanics. Aug 1958, 4 (4): 407–425. Bibcode:1958JFM.....4..407F. doi:10.1017/S0022112058000549.