Debris re-entry: THE multiphysics-multiscale application
Debris re-entry involves a large quantity of different physical phenomena, each of which has to be captured or modelled adequately by a computer-aided simulation to ensure the fidelity of the results.
Let us take a close look at what is happening as the debris is coming down to the planet !
Artist view of the demise of a re-entering debris. Multiple broken-away pieces are shown along with the shockwaves and the flames caused by ablation of the diverse materials at the surface of the debris. Courtesy of ESA.
Stage 1:
The first part of the debris life that has to be simulated is its orbiting around the planet. This falls in the purview of astrodynamics, or orbital mechanics, which applies Newton’s laws of motion and the law of universal gravitation to the motion of rockets and other spacecrafts.
Illustration by Security Management, iStock
In layman’s terms, the debris is then only submitted to the gravitational pull of nearby celestial bodies - there are no aerodynamic forces since there is no atmosphere - and at first order the predominant contribution comes from the planet itself.
This kind of motion is referred to as “3 degrees of freedom” as the object trajectory can only be modified by translational effects (in the three directions of space, that is). The interested reader can refer to the treaty written by Vallado [1].
At this stage, regarding thermal behavior, the debris is exposed to solar radiation which will act as a source of heat depending on the material properties and surface reflectivity. While the solar radiation will tend to heat up the debris, it will also have a cooling rate depending on its own thermal radiation - again, there is no extra heat flux brought by the atmosphere.
Stage 2:
As the debris goes down towards the surface of the planet, it will eventually encounter a thickening atmosphere, and the number of complex physical phenomena it is exposed to suddenly skyrockets. The translational motion of the debris is now driven by the gravitational pull of the planet and by the aerodynamic forces the debris is subjected to because of the surrounding atmospheric pressure. Those forces tend to oppose the debris motion.
Another direct consequence of the atmosphere is related to how the debris is shaped. Because of the irregularities in its shape, the aerodynamic forces can apply more on one side than on another, similarly to how the wind pushes on a sail but barely on the mast. This imbalance in force distribution causes the debris to rotate and in addition to its translational motion, the debris gains a rotational motion -
it thus enters the world of “6 degrees of freedom” motion, counting the translation in the three directions of space, and the rotation around each of them. This is another domain of mechanics, namely flight mechanics and more specifically ballistic flight mechanics since the debris has no thrust-production system. The interested reader can refer to the textbook by Phillips [2].
Now it is interesting to note that the atmosphere state is not independent of the altitude. On the contrary, while the atmosphere is really thin close to space, where only a few molecules of air cohabit, it gets thicker as the altitude decreases. In technical terms, the air surrounding the debris is said to be in a:
free molecular regime at very high altitudes, and
continuum regime at low altitudes close to the ground.
The limit between the two regimes is not a single altitude but rather an interval wherein the atmosphere starts to have enough molecules per unit volume that the debris meets more than one molecule here and there; it is the transition regime.
These regimes surely have an influence on the magnitude of the aerodynamic forces applied onto the debris - they are least at high altitudes and strongest as the debris descends.
Yet another domain of mechanics involved in debris re-entry is fluid mechanics. As soon as the debris re-enters the atmosphere, a flow of air forms around it.
At very high altitudes, in the free molecular regime, the debris is seldom hit by an air molecule, and the flow is driven by the laws of molecular dynamics. The interested reader is referred to the treaty of Bird [3], the forefather of numerical molecular dynamics simulations.
As the debris continues its descent, it enters ever denser layers of the atmosphere and the flow is driven by the laws of continuous viscous fluid mechanics.
In the transition regime, the flow starts by being very coherent and “smooth”, exhibiting very little disturbances: it is said to be laminar.
At lower altitudes, the air gets denser and it gets all the more disturbed by the debris passing through; vortices start forming and the flow becomes random, akin to the flow of rapids in a river: it is said to be turbulent.
The interested reader is referred here to two different treaties, one by White [4] and the other one by Anderson [5] - the fluid mechanics involved in the debris re-entry is indeed even more specialized due to the sheer velocity of the debris that is much higher than the speed of sound: it flies at hypersonic speeds.
An interesting note about these speeds is that the fluid mechanics involved becomes really multiscale, from the pinhead-sized vortices to the debris-sized shockwaves - and all those scales have to be resolved and/or modelled adequately in a numerical simulation software to obtain high-fidelity results.
Numerical simulation of the turbulent flow around a re-entering debris. Courtesy of NASA.
The thermodynamics also becomes more complex because of the presence of the atmosphere around the debris. The solar radiation effects become negligible before the heating induced by the friction of the very-high-speed flow on the debris. The heat flux brought by the friction on the air can reach values as high as ten thousand to a million times the heat flux brought by the Sun on the ground in a sunny afternoon. Such heat can cause the temperature of the outer shell of the debris to reach thousands of degrees Celsius. Aside from the macroscopic heat transfer that is challenging in itself because of the large heat fluxes and temperatures involved, the material, i.e. the debris, will also get damaged and modified as the descent continues.
Depending on the material properties, it is susceptible to undergo pyrolysis, which is basically a change of chemical composition due to the extreme heat - in a more familiar setting, the wood burning in a hearth also undergoes pyrolysis which is characterized by the transition from complex, fibrous, wood to homogeneous char.
In the case of the re-entering debris, the pyrolysis will cause
the escape of gasses from the material to the nearby air, thus changing its chemical composition and the nature of the flow,
and the “inflation” of the material, as its density is going to drastically decrease in some places.
The second major heat- (and high-speed-) related phenomenon that the re-entering debris will encounter is ablation. Because of the intense heat flux and the overall friction, some pieces of the debris will be destructed by vaporization and/or chipping, a.k.a. the debris will get eroded and its shape will change.
Ablation of a cork heat shield under re-entry heat flux conditions: by design, it burns up and flakes away to carry away excess heat and protect the payload behind it. Courtesy of ESA.
Together, pyrolysis and ablation make it necessary, to ensure the proper characterization of the debris re-entry, to add structural dynamics to the long list of involved physical domains. Indeed, the degradation of the debris will eventually trigger its breaking apart into smaller debris - this is a critical aspect of the lifecycle of the debris if one wants to evaluate the probability of the debris hitting the ground.
Hypersonic fluid dynamics, turbulence, shockwaves, thermodynamics, chemical degradation, destructive analysis, structural dynamics … it takes a lot of ingredients to run the computer simulation of a debris re-entry that will help determine with confidence whether it will reach the ground and cause damages.
But between them, Re.Propagate, Re.Entry and Re.CFD have them all !
[1] Vallado, D. A. (2001). Fundamentals of astrodynamics and applications (Vol. 12). Springer Science & Business Media.
[2] Phillips, W. F. (2004). Mechanics of flight. John Wiley & Sons.
[3] G. A. Bird, Molecular Gas Dynamics, Clarendon Press, Oxford (1976)
[4] White, F. M., & Majdalani, J. (2006). Viscous fluid flow (Vol. 3, pp. 433-434). New York: McGraw-Hill
[5] Anderson, J. D. (2000). Hypersonic and high temperature gas dynamics. AIAA.
