9.4 High-temperature effects

High-temperature gas properties

As air temperatures climb to thousands of degrees Kelvin during hypersonic flight, the gas stops behaving the way it does at everyday conditions. Specific heat, thermal conductivity, and viscosity all shift significantly, which changes how the flow behaves, how heat transfers to the vehicle, and how aerodynamic forces develop. Accurate modeling of these changes is essential for hypersonic vehicle design.

Specific heat variation

Specific heat measures how much heat energy is needed to raise a substance's temperature by one degree. At low temperatures, air molecules store energy mainly in translational and rotational motion. But at high temperatures (roughly above 800 K for vibration, much higher for electronic modes), additional internal energy modes activate:

• Vibrational excitation causes molecules to vibrate along their bonds, absorbing extra energy
• Electronic excitation involves electrons jumping to higher energy states

Because these modes absorb additional energy, the specific heat increases with temperature. This matters because it changes key thermodynamic quantities like the speed of sound and the isentropic exponent ($\gamma$), both of which directly affect shock wave behavior and flow predictions.

Thermal conductivity changes

Thermal conductivity describes how well a material conducts heat. In high-temperature gas flows, thermal conductivity rises because the gas molecules carry more kinetic energy and collide more frequently, transferring energy more efficiently between collisions.

This increase is especially important in the boundary layer near the vehicle surface, where temperature gradients are steepest. Higher thermal conductivity means more heat conducted toward the wall, which directly affects how much thermal protection the vehicle needs.

Viscosity effects

Viscosity is a fluid's resistance to shearing motion. For gases, viscosity increases with temperature because faster-moving molecules collide more often and transfer more momentum across flow layers.

This temperature-dependent viscosity changes the boundary layer profile, affecting:

• Skin friction drag on the vehicle surface
• Flow separation behavior, which influences stability and control
• Heat transfer rates, since viscous dissipation adds thermal energy within the boundary layer

For approximate modeling, Sutherland's law is commonly used to relate gas viscosity to temperature.

Hypersonic flow regimes

Hypersonic flow occurs at Mach numbers typically greater than 5, where the flow velocity far exceeds the speed of sound. At these speeds, several distinct flow regimes emerge, each requiring different physical assumptions and modeling approaches.

Continuum vs rarefied flow

Continuum flow treats the gas as a smooth, continuous medium. This assumption holds when the mean free path (average distance a molecule travels between collisions) is much smaller than the vehicle's characteristic length.

Rarefied flow occurs when the mean free path becomes comparable to or larger than the characteristic length. This happens at high altitudes where the atmosphere is thin. In rarefied conditions, the continuum equations (Navier-Stokes) break down, and you need kinetic theory or particle-based methods like Direct Simulation Monte Carlo (DSMC).

The transition between these regimes is characterized by the Knudsen number:

$Kn = \frac{\lambda}{L}$

where $\lambda$ is the mean free path and $L$ is the characteristic length. When $Kn \ll 1$, continuum methods work. When $Kn \gtrsim 0.1$, rarefied effects become important.

Equilibrium vs nonequilibrium flow

Equilibrium flow assumes all internal energy modes (translational, rotational, vibrational, electronic) and chemical species have had time to reach their equilibrium values at the local temperature and pressure.

Nonequilibrium flow occurs when the flow changes conditions faster than the molecules can adjust. In hypersonic flight, the gas passes through a strong shock wave and is suddenly heated to thousands of Kelvin. The translational temperature jumps almost instantly, but vibrational modes take many more collisions to equilibrate. Chemical reactions (like dissociation) also have finite rates.

This mismatch means the gas behind the shock exists in a nonequilibrium state for some distance downstream. Nonequilibrium effects alter heat transfer rates, chemical composition, and radiative emission, making them critical to model accurately in high-enthalpy flows.

Inviscid vs viscous flow

• Inviscid flow neglects viscosity entirely and is governed by the Euler equations. It's a useful simplification for the outer flow away from surfaces.
• Viscous flow is governed by the full Navier-Stokes equations, which include shear stress and the no-slip condition at solid walls.

In hypersonic flight, viscous effects dominate inside the boundary layer, where they produce skin friction drag, promote flow separation, and significantly enhance heat transfer to the surface. The boundary layer can also be very thick relative to the shock layer at hypersonic speeds, meaning viscous and inviscid regions can interact strongly.

Thermodynamic and chemical effects

At the extreme temperatures behind hypersonic shock waves (often 3,000–10,000+ K), air is no longer a simple mixture of $N_2$ and $O_2$. Molecules break apart, atoms lose electrons, and the gas composition changes continuously. These thermodynamic and chemical processes profoundly affect flow behavior and vehicle loads.

Dissociation and recombination

Dissociation is the breaking of molecular bonds at high temperatures. Oxygen begins dissociating around 2,500 K, and nitrogen around 4,000 K:

$O_2 \rightarrow 2O$ $N_2 \rightarrow 2N$

Recombination is the reverse: atoms recombine into molecules when conditions (lower temperature, higher pressure) favor it.

These reactions are endothermic (dissociation absorbs energy) and exothermic (recombination releases energy), so they act as energy sinks and sources within the flow. Dissociation reduces the effective temperature rise behind a shock compared to what a calorically perfect gas model would predict. It also changes the specific heat, molecular weight, and speed of sound of the gas mixture.

Ionization and plasma formation

At even higher temperatures (above roughly 9,000 K), atoms begin losing electrons through ionization:

$N \rightarrow N^+ + e^-$

When a significant fraction of the gas is ionized, it forms a plasma, a mixture of ions, free electrons, and neutral species. Plasma formation has practical consequences:

• The electrically conductive plasma layer around a reentry vehicle can block radio signals, causing the well-known communications blackout during reentry
• Ionized species contribute to radiative heating
• Electromagnetic interactions may affect flow control strategies

Real gas effects on aerodynamics

At low speeds, air behaves close to an ideal gas. At hypersonic conditions, this assumption fails. Real gas effects include vibrational excitation, dissociation, ionization, and deviations from ideal compressibility.

These effects change the aerodynamic picture in measurable ways:

• The shock standoff distance increases compared to ideal gas predictions because the dissociated gas has a lower effective $\gamma$, making the shock layer thicker
• The shock angle decreases for a given wedge or cone
• Pressure distributions, lift, and drag all shift from ideal gas values

Real gas behavior can be modeled using advanced equations of state (such as Redlich-Kwong or Beattie-Bridgeman) or, more commonly in hypersonic CFD, through detailed thermochemical models that track individual species and energy modes.

Aerodynamic heating

Aerodynamic heating is one of the defining challenges of hypersonic flight. The kinetic energy of the high-speed flow converts into thermal energy near the vehicle surface, producing heat fluxes that can reach tens of MW/m² during planetary entry. Without proper thermal management, the vehicle structure will fail.

Stagnation point heating

The stagnation point, at the vehicle's leading edge where the flow comes to rest, experiences the highest heat transfer rates. All of the flow's kinetic energy converts to thermal energy here, producing extreme temperatures and pressures.

The Fay-Riddell correlation is a classic method for estimating stagnation point heat flux. It accounts for freestream conditions, gas properties, wall temperature, and nose radius. A key design takeaway: heat flux scales roughly as $1/\sqrt{R_n}$, where $R_n$ is the nose radius. This is why reentry vehicles use blunt noses rather than sharp ones.

Convective heat transfer

Convective heating occurs as the hot boundary layer gas transfers energy to the vehicle wall through molecular conduction and bulk fluid motion. In hypersonic flows, the boundary layer state (laminar vs. turbulent) has a huge effect: turbulent boundary layers produce heat transfer rates several times higher than laminar ones.

The Reynolds analogy provides a useful link between skin friction and heat transfer, relating the heat transfer coefficient to the skin friction coefficient and the Prandtl number. This allows engineers to estimate heating from friction data and vice versa, though the analogy has limitations in strongly nonequilibrium or chemically reacting flows.

Radiative heat transfer

At very high temperatures, the shock-heated gas emits thermal radiation that can contribute significantly to the total heat load on the vehicle. Radiative heating becomes especially important for:

• Planetary entry at high velocities (e.g., lunar or Mars return at 11+ km/s)
• High-altitude flight where the gas may be optically thin, allowing radiation to reach the surface from deep within the shock layer

The radiative transfer equation governs this process, accounting for emission, absorption, and scattering within the gas. For vehicles like the Apollo capsule during Earth reentry, radiative heating contributed a substantial fraction of the total heat load.

Thermal protection systems

Thermal protection systems (TPS) shield the vehicle structure from extreme heat loads. There are two main categories:

• Ablative TPS: Materials like carbon phenolic and silica phenolic decompose in a controlled way, absorbing heat through pyrolysis and forming a protective char layer. These are typically single-use and are favored for high-heat-flux missions like planetary entry (e.g., the Stardust sample return capsule used a PICA heat shield).
• Reusable TPS: Materials like ceramic tiles (used on the Space Shuttle) and metallic thermal protection provide insulation over multiple flights. They must withstand repeated thermal cycling without degrading.

TPS selection depends on mission-specific factors: peak heat flux, total integrated heat load, flight duration, and whether the vehicle needs to be reusable.

High-temperature materials

The structural and thermal components of hypersonic vehicles must survive extreme temperatures, oxidation, thermal shock, and mechanical loads simultaneously. Material selection is one of the most challenging aspects of hypersonic vehicle design.

Refractory metals and ceramics

Refractory metals like tungsten (melting point ~3,422°C), molybdenum, and tantalum offer high melting points and good strength at elevated temperatures. They're used for components like engine nozzles, leading edges, and control surfaces. Their main drawbacks are brittleness, high density, and susceptibility to oxidation without protective coatings.

Ceramics like silicon carbide (SiC), zirconia ($ZrO_2$), and hafnium carbide (HfC) provide high melting points, low thermal conductivity, and good oxidation resistance. They're used in thermal protection tiles and insulating blankets. However, ceramics are inherently brittle and have poor fracture toughness.

Advanced manufacturing methods, including chemical vapor deposition, powder metallurgy, and additive manufacturing, are being developed to improve the reliability and performance of both material classes.

Ablative materials

Ablative materials protect by sacrificing themselves. During heating, the resin matrix undergoes pyrolysis (thermal decomposition), absorbing large amounts of energy. The resulting char layer on the surface acts as an insulator, while pyrolysis gases blow outward and partially block convective heating (a phenomenon called blowing or transpiration cooling).

Common ablative systems include:

• Carbon phenolic: Carbon fiber reinforcement in a phenolic resin matrix, used for high heat flux applications
• Silica phenolic: Silica fiber reinforcement, used where heat fluxes are somewhat lower
• PICA (Phenolic Impregnated Carbon Ablator): A lightweight ablator developed by NASA, used on the Stardust and Mars Science Laboratory missions

Next-generation ablatives, including carbon-carbon composites and ultra-high-temperature ceramics (UHTCs like $ZrB_2$ and $HfB_2$), aim to improve thermal efficiency and potentially enable limited reusability.

Insulation and heat shields

Insulation materials reduce heat conduction from the hot exterior to the vehicle's internal structure. They need low thermal conductivity, high temperature stability, and resistance to vibration. Ceramic fiber blankets (alumina, silica, zirconia) are the most common, providing effective protection at low weight.

Heat shields protect external surfaces from both thermal and aerodynamic loads. They're typically made from ceramics, composites, or high-temperature metallic alloys, and are designed for the specific thermal and mechanical environment of the mission.

Emerging materials include aerogels (extremely low thermal conductivity), nanostructured ceramics, and multifunctional materials that combine structural load-bearing with thermal protection.

Experimental techniques

Studying high-temperature aerodynamic effects requires specialized facilities that can reproduce the extreme conditions of hypersonic flight. The temperatures, pressures, and velocities involved push the limits of both facility design and instrumentation.

High-enthalpy wind tunnels

High-enthalpy wind tunnels generate gas flows with very high thermal energy content (enthalpies up to several MJ/kg) to simulate real hypersonic flight conditions. The gas is heated using electric arc heaters, combustion heaters, or plasma torches, then accelerated through a converging-diverging nozzle to hypersonic speeds.

Test models in the test section are instrumented with pressure sensors, heat flux gauges, and temperature sensors to measure surface loads. These facilities are used to study aerodynamic heating, thermochemical effects, and TPS material performance.

Notable facilities include the NASA Ames Arc Jet Facility, the CUBRC LENS II Facility, and the DLR HEG Shock Tunnel in Germany.

Shock tubes and expansion tubes

Shock tubes and expansion tubes are impulse facilities that produce high-temperature, high-pressure test gas for very short durations. They work by suddenly rupturing a diaphragm between a high-pressure driver section and a low-pressure driven section. The resulting shock wave compresses and heats the driven gas to conditions representative of hypersonic flight.

• Shock tubes produce test times on the order of a few milliseconds
• Expansion tubes add a secondary expansion to achieve higher velocities, but with shorter test times (hundreds of microseconds)

The very short flow durations demand fast-response instrumentation, such as piezoelectric pressure transducers and thin-film heat flux gauges, capable of capturing data on microsecond timescales. Despite the brief test windows, these facilities are valuable for studying nonequilibrium chemistry, radiation, and shock layer physics at conditions that are difficult to achieve in continuous-flow tunnels.