Aerodynamic heating

Aerodynamic heating is the heating of a solid body produced by its high-speed passage through air (or by the passage of air past a static body), whereby its kinetic energy is converted to heat by adiabatic heating,[1] and by skin friction on the surface of the object at a rate that depends on the viscosity and speed of the air. In science and engineering, it is most frequently a concern regarding meteors, atmospheric reentry of spacecraft, and the design of high-speed aircraft.

Physics

When moving through air at high speeds, an object's kinetic energy is converted to heat through compression of and friction with the air. At low speeds, the object also loses heat to the air if the air is cooler. The combined temperature effect of heat from the air and from passage through it is called the stagnation temperature; the actual temperature is called the recovery temperature.[2] These viscous dissipative effects to neighboring sub-layers make the boundary layer slow down via a non-isentropic process. Heat then conducts into the surface material from the higher temperature air. The result is an increase in the temperature of the material and a loss of energy from the flow. The forced convection ensures that other material replenishes the gases that have cooled to continue the process.

The stagnation and the recovery temperature of a flow increases with the speed of the flow and are greater at high speeds. The total thermal loading of the object is a function of both the recovery temperature and the mass flow rate of the flow. Aerodynamic heating is greatest at high speeds and in the lower atmosphere where the density is greater. In addition to the convective process described above, there is also thermal radiation from the flow to the body and vice versa, with the net direction governed by their temperatures relative to each other.

Aerodynamic heating increases with the speed of the vehicle. Its effects are minimal at subsonic speeds, but are significant enough at supersonic speeds beyond about Mach 2.2 that they affect design and material considerations for the vehicle's structure and internal systems. The heating effects are greatest at leading edges, but the whole vehicle heats up to a stable temperature if its speed remains constant. Aerodynamic heating is dealt with by the use of alloys that can withstand high temperatures, insulation of the exterior of the vehicle, or the use of ablative material.

Aircraft

Aerodynamic heating is a concern for supersonic and hypersonic aircraft.

One of the main concerns caused by aerodynamic heating arises in the design of the wing. For subsonic speeds, two main goals of wing design are minimizing weight and maximizing strength. Aerodynamic heating, which occurs at supersonic and hypersonic speeds, adds an additional consideration in wing structure analysis. An idealized wing structure is made up of spars, stringers, and skin segments. In a wing that normally experiences subsonic speeds, there must be a sufficient number of stringers to withstand the axial and bending stresses induced by the lift force acting on the wing. In addition, the distance between the stringers must be small enough that the skin panels do not buckle, and the panels must be thick enough to withstand the shear stress and shear flow present in the panels due to the lifting force on the wing. However, the weight of the wing must be made as small as possible, so the choice of material for the stringers and the skin is an important factor.

At supersonic speeds, aerodynamic heating adds another element to this structural analysis. At normal speeds, spars and stringers experience a load called Delta P, which is a function of the lift force, first and second moments of inertia, and length of the spar. When there are more spars and stringers, the Delta P in each member is reduced, and the area of the stringer can be reduced to meet critical stress requirements. However, the increase in temperature caused by energy flowing from the air (heated by skin friction at these high speeds) adds another load factor, called a thermal load, to the spars. This thermal load increases the net force felt by the stringers, and thus the area of the stringers must be increased in order for the critical stress requirement to be met.

Another issue that aerodynamic heating causes for aircraft design is the effect of high temperatures on common material properties. Common materials used in aircraft wing design, such as aluminum and steel, experience a decrease in strength as temperatures get extremely high. The Young's Modulus of the material, defined as the ratio between stress and strain experienced by the material, decreases as the temperature increases. Young's Modulus is critical in the selection of materials for wing, as a higher value lets the material resist the yield and shear stress caused by the lift and thermal loads. This is because Young's Modulus is an important factor in the equations for calculating the critical buckling load for axial members and the critical buckling shear stress for skin panels. If the Young's Modulus of the material decreases at high temperatures caused by aerodynamic heating, then the wing design will call for larger spars and thicker skin segments in order to account for this decrease in strength as the aircraft goes supersonic. There are some materials that retain their strength at the high temperatures that aerodynamic heating induces. For example, Inconel X-750 was used on parts of the airframe of the X-15, a North American aircraft that flew at hypersonic speeds in 1958.[3][4] Titanium is another high-strength material, even at high temperatures, and is often used for wing frames of supersonic aircraft. The SR-71 used titanium skin panels painted black to reduce the temperature[5] and corrugated to accommodate expansion.[6] Another important design concept for early supersonic aircraft wings was using a small thickness-to-chord ratio, so that the speed of the flow over the airfoil does not increase too much from the free stream speed. As the flow is already supersonic, increasing the speed even more would not be beneficial for the wing structure. Reducing the thickness of the wing brings the top and bottom stringers closer together, reducing the total moment of inertia of the structure. This increases is axial load in the stringers, and thus the area, and weight, of the stringers must be increased. Some designs for hypersonic missiles have used liquid cooling of the leading edges (usually the fuel en route to the engine). The Sprint missile's heat shield needed several design iterations for Mach 10 temperatures.[7]

Reentry vehicles

Heating caused by the very high reentry speeds (greater than Mach 20) is sufficient to destroy the vehicle unless special techniques are used. The early space capsules such as used on Mercury, Gemini, and Apollo were given blunt shapes to produce a stand-off bow shock, allowing most of the heat to dissipate into the surrounding air. Additionally, these vehicles had ablative material that sublimates into a gas at high temperature. The act of sublimation absorbs the thermal energy from the aerodynamic heating and erodes the material away as opposed to heating the capsule. The surface of the heat shield for the Mercury spacecraft had a coating of aluminum with glassfiber in many layers. As the temperature rose to 1,100 °C (1,400 K) the layers would evaporate and take the heat with it. The spacecraft would become hot but not harmfully so.[8] The Space Shuttle used insulating tiles on its lower surface to absorb and radiate heat while preventing conduction to the aluminum airframe. The damage to the heat shield during liftoff of Space Shuttle Columbia contributed to its destruction upon reentry.

References
  1. "NASA – Spacecraft Design". Archived from the original on July 9, 2009. Retrieved January 7, 2013.
  2. Kurganov, V.A. (3 February 2011), "Adiabatic Wall Temperature", A-to-Z Guide to Thermodynamics, Heat and Mass Transfer, and Fluids Engineering, Thermopedia, doi:10.1615/AtoZ.a.adiabatic_wall_temperature, retrieved 2015-10-03
  3. Käsmann, Ferdinand C. W. (1999). Die schnellsten Jets der Welt: Weltrekord-Flugzeuge [The Fastest Jets in the World: World Record Aircraft] (in German). Kolpingring, Germany: Aviatic Verlag. p. 105. ISBN 3-925505-26-1.
  4. Weisshaar, Dr. Terry A. (2011). Aerospace Structures- an Introduction to Fundamental Problems. Purdue University. p. 18.
  5. Rich, Ben R.; Janos, Leo (1994). Skunk works: a personal memoir of my years at Lockheed. Warner Books. p. 218. ISBN 0751515035.
  6. Johnson, Clarence L.; Smith, Maggie (1985). Kelly: more than my share of it all. Washington, D.C.: Smithsonian Institution Press. p. 141. ISBN 0874744911.
  7. Bell Labs 1974, 9-17
  8. "How Project Mercury Worked". How Stuff Works. Retrieved 2011-10-04.
  • Moore, F.G., Approximate Methods for Weapon Aerodynamics, AIAA Progress in Astronautics and Aeronautics, Volume 186
  • Chapman, A.J., Heat Transfer, Third Edition, Macmillan Publishing Company, 1974
  • Bell Laboratories R&D, ABM Research and Development At Bell Laboratories, 1974. Stanley R. Mickelsen Safeguard Complex
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