Aerothermodynamic Heating
Summary
Aero-thermodynamic heating is a severe limit at high speeds and concerns jet engines,
ramjets, scramjets, rockets, ballistic missiles and combustors. The simplest
explanation of heating is derived from the concept of stagnation value, that
is the value of the temperature reached in an adiabatic flow slowed down to zero
The heating problem consists in evaluating all the relevant terms in the energy
equations at the body surface, in order to establish the correct heat transfer
rates.
Calculations at cruise conditions (aircraft, spacecraft, scramjet) can be
performed, while for cases in unsteady conditions during the flight (ballistic
missiles, rockets) the analysis is more difficult, because of non isentropic shocks,
energy radiation, convection and diffusion, boundary layer transition and non
equilibrium phenomena.
At high speeds the flow is at stagnation at several points of a supersonic object and
the shock is detached from the vehicle. The compression region between the shock wave
and the stagnation regions is a major cause of aero-thermodynamic heating, with large
temperature gradients in the boundary layers. Heat from the boundary layers is
transferred onto the vehicle surface, Fig. 1. Heating occurs also in the hypersonic wakes
(jets at the base of the vehicle).
Figure 1: Bow shock and heating process
Figure 2: Bow shock in front of wedge at M = 1.8
The current limit is above 1300 °K. The skin of the vehicle can be covered by
material (for exemple, silicon), that melts and evaporates (ablation process),
thus absorbing part of the heat.
1. Supersonic Vehicles
2. Hypersonic Vehicles
See Table of Skin Temperatures for more data.
The temperature and the pressure field are useful to identify the similitude
conditions at supersonic and hypersonic speeds for simulation in
hyper-velocity tunnels.
In most of the cases listed in Table 1 the heating is
so strong that cooling is made necessary to protect the structure. The maximum
temperature that the skin of a space vehicle or ballistic missile can reach is a
technological limit, which may move upward with further progress in material science
and configuration design.
Blunt Nose.
An important parameter is the geometry of the nose. A basic result of hypersonic
theory shows that the heat transfer at the nose is inversely proportional to the
radius of the nose, Fig. 1.
Another case, though not technological, is the atmospheric penetration of
meteors, which occurs as speeds estimated between 20 km/h and 70 Km/s. The meteors
look as luminous objects (shooting stars) because of the high temperature
reached. Their vaporization starts at temperatures around 3500 °K. Small meteors
disintegrate before reaching the lower atmosphere.
The Heating Problem
Stagnation Temperatures
Temperature Limits
Thermodynamic heating in supersonic jet transport
(Concorde, M=2.0÷2.4) is estimated at about 700 °K. Maximum heating rates
are reported for ballistic missiles, because of their steep flight path toward the
lower atmosphere.
The atmospheric entry of a spacecraft has instead the maximum total heat load because
of its longer trajectory in the high temperature corridor. Some interesting data are
the following: 1600 °K for the Space Shuttle in atmospheric re-entry; over 7000
°K for the Apollo capsule and intercontinental ballistic missiles (ICBM) in
atmospheric re-entry.
Cooling Requirements
Shooting Stars
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