Space traffic hazards from orbital debris mitigation

Acta Astronautica 109 (2015) 144–152

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Space traffic hazards from orbital debris mitigation strategies N.N. Smirnov a,b, A.B. Kiselev b, M.N. Smirnova b,c,n, V.F. Nikitin a,b a

Scientific Research Institute for System Studies of Russian Academy of Sciences, Moscow 117218, Russia Moscow M.V. Lomonosov State University, Leninskie Gory, 1, Moscow 119992, Russia c Saint Petersburg State Polytechnical University, 29 Politechnicheskaya Str., St. Petersburg 195251, Russia b

a r t i c l e in f o

abstract

Article history: Received 22 September 2014 Accepted 23 September 2014 Available online 2 October 2014

The paper gives coverage of recent advances in mathematical modeling of long term orbital debris evolution within the frames of continua approach. Under the approach the evolution equations contain a number of source terms responsible for the variations of quantities of different fractions of orbital debris population due to fragmentations and collisions. Mechanisms of hypervelocity collisions of debris fragments with pressurized vessels are investigated. The spacecraft shield honeycomb concept is suggested based on principles of impact energy conversion and redistribution and consumption by destroyable structures. The paper is devoted to the 100th anniversary of the founder of space debris research in Moscow State University Prof. G.A. Tyulin. & 2014 IAA. Published by Elsevier Ltd. All rights reserved.

Keywords: Space debris Population Collisions Fragmentation Hypervelocity Impact Vessel Shield Concept

1. Introduction The rapid growth of the orbital debris population in Low Earth Orbits results in an increase in collision probability of space vehicles with debris particles, especially with those sizing less than 1 cm [1–3]. The continua approach to space debris evolution modeling was first developed at the end of 1980s in Moscow M.V. Lomonosov State University in the Laboratory under the direction of Georgy Tyulin (1914–1990), whose 100th anniversary is celebrated this year (Fig. 1). After completing graduation from the University in 1940, Georgy Tyulin was in the Second World War from 1941 to 1945 as a commander of ram artillery troops units. After the War he was working in the team of pioneers of Russian cosmonautics (Figs. 2 and 3) serving as a state commission chairman for many space programs. After his retirement from military service in the grade of two stars general he returned to his Alma Mater n Corresponding author at: Moscow M.V. Lomonosov State University, Leninskie Gory, 1, Moscow 119992, Russia. Tel./fax: þ7 495 9393754. E-mail address: [email protected] (M.N. Smirnova).

http://dx.doi.org/10.1016/j.actaastro.2014.09.014 0094-5765/& 2014 IAA. Published by Elsevier Ltd. All rights reserved.

Moscow M.V. Lomonosov State University in 1977 and became the head of Wave Processes Laboratory in 1978. The main topic of research was numerical investigation of irreversible wave processes relevant to space applications. The suggested continua method for orbital debris evolution modeling [2,4] has the following peculiarities:

making use of a statistical approach describing the

current debris environment in the form of distribution functions for the main elements of debris orbits; applying the averaged description for the sources of space debris production; taking into account collisions of debris fragments of different sizes (including non-cataloged ones) that could lead not only to debris self-production but also to self-cleaning of the Low Earth Orbits; developing numerical methods for integration of the governing system of evolution equations in partial derivatives.

Examples of long-term forecasts of the space debris environment were studied and the role of collisions of

N.N. Smirnov et al. / Acta Astronautica 109 (2015) 144–152

Fig. 1. Space debris research in Moscow M.V. Lomonosov State University was launched in 1980s by Prof. G.A. Tyulin.

Fig. 2. S.P. Korolev and G.A. Tyulin. Final instructions to the cosmonaut P. Belyaev at a launch site Baikonur, March 18, 1965.

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The number of objects with size from 10 to 20 cm will increase 3.2 times, whereas predicted increase in smallersized fragments is 13–20 times [6,7]. The number of smallsize, non-cataloged objects will grow exponentially in mutual collisions. The shield should meet the following requirements: providing an effective protection for the spacecraft in collisions with small size debris at relative velocities up to 12 km/s, and having a relatively low mass. The double bumper and multi-shock shield concepts [8–10] suggested at the end of 20th century proved their effectiveness. A new concept suggested in the beginning of the 21st century [2,11,12] states that protecting the spacecraft by a honeycomb of small gas-filled containments could form a much more efficient shield with lower mass. As multi-sheet shielding concept uses thin shield elements to repeatedly shock the impacting projectile to cause its melting and vaporization, the new gas-filled containment shield concept uses continuous effect of pressurized gas to cause fragments slowing down, heating, melting, atomization and evaporation. Besides, using gas-filled bumpers makes it possible to increase the area of the zone of impact energy redistribution including the side and front walls due to the property of gas to transmit pressure in all directions. This is a considerable advantage of the present concept. The gas-filled bumper shields could be reusable, as the rate of gas phase leakage on depressurization is rather low and the loss of mass is negligible during the characteristic time of impact. The influence of molar mass of the gas phase and other parameters on the rate of impact energy consumption and transformation is important. This principle could be used for effective shielding of space vehicles. 2. Shielding concepts in hypervelocity collisions

Fig. 3. G.A. Tyulin and first cosmonauts team members. From left to right: Yu Gagarin, G. Tyulin, G. Titov, A. Nikolaev, A. Kuklin.

debris fragments of different sizes in the overall processes of space contamination and self-cleaning of the low orbits was evaluated [4–7]. The growth of collision probability with debris fragments brought spacecraft designers to the necessity of shielding the space vehicles. For the scenario business as usual without explosions and disposal following our prediction model the number of fragments larger than 20 cm in size will increase 1.5 times during 200 years.

Developing a concept for spacecraft elements shielding needs answering the main question: which characteristic determines effective shield or shielding failure? This characteristic is, usually, penetration of a projectile behind the shield, or perforation. The impacting projectile carries definite momentum and energy. In spite of different breakup criteria used in engineering practice the most detailed examination of accumulation of damages and fragmentation shows that energetic criteria reflect the true physics. Methods avoiding perforation are similar for all shields, which means that redistribution of momentum and energy on a larger area is needed to provide lower local loading. However, the momentum conservation law is that of a vector type, which means that, despite all efforts, momentum carried by the projectile would be transmitted to the target plus projectile agglomeration in case of inelastic collision. From this point of view impact momentum of 1000 kilo body at velocity 1 m/s is equivalent to impact momentum of 1 kilo bullet at velocity 1 km/ s. However the probability of shield perforation in the second case is much higher because damages in the target are determined using delivered energy. And the delivered energy in the second example surpasses three orders of magnitude impact energy in the first example. Thus in developing the shield concept it seems more profitable to

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reduce the impact energy due to its absorption by the shield. The energy conservation law has a scalar formulation, and it is feasible to reduce the impact energy by its redistribution in all directions.

Fig. 4. The crater shape developed in high-speed collision of the steel ball and steel obstacle. The scale is in millimeters.

In the case of hypervelocity impact on solid structures for low velocities all the impact energies are applied in the direction of impact. On increasing impact velocity stresses in the projectile and target surpass plasticity limit and deformations look like fluid flow [13]. A typical crater is shown in Fig. 4. This illustrates onset of a different scenario for projectile–target interaction, under which impact energy is redistributed in all directions. The depth of penetration being a function of impact velocity based on the data developed in [13] is shown in Fig. 5. For small impact velocity there is a linear dependence of crater depth on velocity. On approaching critical value the mechanism of projectile–target interaction changes; impact energy is redistributed in all directions and crater depth drastically decreases. On further increasing velocity crater depth again grows. Analysis shows that natural material flow restructuring in hypervelocity impact results in a decrease in perforation

Fig. 5. The crater depth to cubic root of impactor mass ratio (10 m/kg1/3 ) versus impact velocity (m/s).

Fig. 6. Honeycomb fluid-gas filled shield providing 3-D impact energy dissipation: a) general view of the shield; b) compressible gas flow and shock wave formation on impactor penetrating a single cell.


depth. The aim of effective shield concept development should be in creating structures aimed at redistribution of impact energy and its absorption by the shield. The multisheet shielding concept uses thin shield elements to repeatedly shock the impacting projectile to cause its melting and vaporization [8–10]. Besides, the momentum and energy delivered to the target by the impactor are redistributed on a larger area of the wall thus making local pressure in collision much less. The new concept [2,11,12] states that protecting the spacecraft by a honeycomb of small gas-filled containments could form a much more efficient shield with lower mass (Fig. 6a). The new gas-filled containment shield concept makes use of continuous effect of pressurized gas causing fragments slowing down, heating, melting, atomization and evaporation. On the other hand, using gas-filled bumpers makes it possible to increase the area of the zone of impact energy redistribution including the side and front walls due to the property of gas to transmit pressure in all directions (Fig. 6b). This is a considerable advantage of the present concept. Fragmentation of a gas-filled or fluid-filled containment in hypervelocity collision (Fig. 7) has several characteristic stages [2,11,12]. The first stage is fragmentation of the impactor and the front wall in the collision zone and formation of a hypervelocity jet of small fragments penetrating inside the containment (Fig. 8a and b). Formation of cracks (and petals) in the collision zone of the front wall does not usually result in the breakup of the containment at the present stage. The hypervelocity fragments cloud forms a shock wave in the media, filling the containment. This results in the transformation of impact kinetic energy into the energy of compressed and heated fluid, which redistributes this energy in all directions by means of diverging spherical shock wave (Fig. 6b).

Fig. 7. Schematic picture for fluid-filled containment perforation.

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In case of a fluid-filled containment an overheated expanding gaseous cloud is formed in the zone of fragments deceleration due to the concentrated energy release Fig. 7. The expansion of the gas-vapor cloud results in the formation of a diverging shock wave. Reflections of shock waves in fluids from elastic walls take place in the form of the rarefaction waves that result in the formation of the cavitation zones near the walls. The collapse of these zones usually results in pressure increase. The succession of the processes of internal loading of the fluid-filled containment: energy release in deceleration of fragments, gasvapor cloud formation and expansion, blast wave propagation, reflection from an elastic shell, cavitation and collapse of cavities. Deceleration of fragment cloud takes place much faster in fluid than in gas, thus releasing energy more close to the front wall, which could cause its irreversible deformations and breakup [14–16]. The formation of a strong blast wave can take place more close to the front wall [16] thus causing its intense loading and breakup, while the rear wall receives only widely distributed impact momentum and very few of impact energy. This could result in damage in the front wall of the shield rather than the rear one [14–16] thus protecting space structure. The breakup of the wall causes the pressure drop due to a jet outflow, and formation of rarefaction waves, which go inside the containment, overtaking the blast wave and lowering down its intensity [17,18]. Thus the far wall will be much less loaded. Shock wave could have high intensity; however, propagating at a supersonic speed in the medium filling the containment, it always propagates with a subsonic speed with respect to the compressed medium behind the shock wave. Rarefaction wave being a continuous pressure drop propagates at a sonic speed with respect to the compressed by the shock wave medium. Due to this reason overtaking of the impact induced shock wave by the rarefaction wave is inevitable. The overtaking distance, however, should be less than the length of containment to guarantee sufficient interaction time for the effective suppression of the shock wave. Fig. 9 shows the pictures of fluid filled containment front wall after the impact. Fig. 9 shows the circular bulging part of the wall, which appeared due to internal loading by shock wave formed in fluid after absorption of impactor energy. The ejected mass in perforation makes crater walls on both sides of the plate. The crater diameter is 3 mm. The experiment testifies our concept of transmitting

Fig. 8. Experimental (a) and theoretical (b) modeling of fragmentation in particle impact on metallic wall.

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Fig. 9. Perforated 2 mm thick wall of the water-filled containment after impact of spherical steel element mass 0.2 g at a relative velocity 2 km/s: 1 – front view, 2 – back view.

Fig. 10. Model fragments location inside the gas-filled containment (p0 ¼ 0.01 MPa) at a time t ¼ 76 μs (a) and t ¼ 214 μs after a hypervelocity impact.

the impact energy mostly to the front wall rather than to the back wall behind which the spacecraft structure being protected is located. 3. Numerical modeling of fragments cloud deceleration in a gas-filled honeycomb section of a shield The mathematical model for multiphase fragment cloud interaction with gaseous atmosphere was used for performing numerical simulations [2,11]. Numerical modeling of hypervelocity cloud of fragments propagation in a gas-filled cylindrical containment after perforation of the bottom wall near the axis being the result of a hypervelocity impact was performed based on the developed mathematical models. A cylindrical containment of 0.1 m radius and 0.2 m height was considered, wall thickness 2 mm. A hole 10 mm in diameter was formed as a result of the impact, and the material of the wall formed a cloud of small fragments, characterized by the average diameter 0.3 mm and stochastic deviations 0.05 mm. The fragments initial temperature was 700 K with stochastic deviations 750 K; maximal velocity in the axial direction was assumed to be 1900 m/s, average velocity 1500 m/s with stochastic deviations 400 m/s both in axial and radial directions. The average density of the material was assumed

to be ρ¼2000 kg/m3, the melting temperature was 800 K, and viscosity and surface tension in the liquid state were 10 3 N s and 10 2 N/m respectively. The gas pressure inside the containment was varied from 0.01 MPa up to 1.5 MPa, initial temperature T0 ¼ 300 K, and molar mass 0.028 kg/mol. The adopted initial data corresponds to a cloud that could be formed by impact of a 5 mm particle at a velocity 5 km/s. Fig. 10 shows the model particles location and temperature distribution inside the containment for two successive times. The initial pressure of gas inside the containment was rather low: p0 ¼0.01 MPa (0.1 atm). The size of circles showing model particles is much larger than their real size, but is directly proportional to it. The intensity of color reflects particles temperature in K as shown in the tables in the right hand side of figures. Fig. 10 shows that the velocity of the axial propagation of the cloud is too high and could not be essentially slowed down by the rarefied gas atmosphere. The shock wave and the cloud both collide with the upper wall of the containment practically simultaneously in the present case of rather low initial pressure of gas filling the containment. Nevertheless, due to the dispersion of fragments in the cloud the total momentum is distributed on a larger area of the upper wall in collision.


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Fig. 11. Model fragments location (a) and gas pressure distribution (b) inside the gas-filled containment (p0 ¼1 MPa) at a time t ¼ 76 μs after a hypervelocity impact.

Fig. 12. Model fragments location (a) and gas pressure distribution (b) inside the gas-filled containment (p0 ¼ 1 MPa) at a time t ¼ 473 μs after a hypervelocity impact.

Fig. 13. Model fragments location (a) and gas pressure distribution (b) inside the gas-filled containment (p0 ¼ 1 MPa) at a time t ¼ 1100 μs after a hypervelocity impact.

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The average pressure on the walls of the containment (taking into account the momentum of fragments in impact) is illustrated in Fig. 14a (curve 0.1 atm). The maximal loading still takes place at the axis of symmetry. Figs. 11–13 illustrate the model particles locations (a) and gas pressures (b) for the case of a relatively high gas pressure inside the containment (p0 ¼1 MPa). The aerodynamic drag and heating of the particles are much more essential for the present case. On entering the containment the front particles of the cloud are heated above the melting temperature. Fragmentation of liquid droplets due to their interaction with the atmosphere results in the formation of very fine droplets in the front part of the cloud (Fig. 11a). A strong shock wave is formed ahead of

the cloud (Fig. 11b). The particles, representing smaller fragments, are illustrated by dots in Fig. 11a. Nevertheless, the major mass of the cloud is represented by these dots, and only a smaller number of low velocity particles keeps its initial size. Rapid slowing down of fragments in a dense atmosphere results in the following situation: when the shock wave overtakes the cloud and reflects from the upper and side walls the fragments are still in the center of the vessel (Fig. 12). The small droplets slow down very rapidly and lose their kinetic energy much faster than the large ones. Thus the large fragments, that had initially much lower velocity, try to overtake the small ones (Fig. 10a). Those fragments are, actually, the first to collide with the upper

Fig. 14. Average wall overpressure distribution accounting for the momentum of impacting fragments for different initial gas pressures: 0.1 bar, 0.5 bar, 5 bar, 10 bar, 15 bar.


wall (Fig. 11a). The reflected shock wave prevents the small droplets from colliding the upper wall for some time (Fig. 11b). The average wall overpressure profile for the corresponding time (t ¼1.1 ms) is shown in Fig. 14b (curve 10 atm). It is seen that contrary to the previous case, the overpressure is distributed rather uniformly along the top, bottom and side walls of the containment. Its maximal value could be still found on the top wall at the axis of symmetry. But the maximal average overpressure for the present case is more than an order of magnitude lower.

4. Internal wall loading in hypervelocity collisions of debris particles with pressurized vessels Hypervelocity collision of a debris particle with a thinwalled containment results in the formation of a cloud of fragments penetrating the containment and expanding in a radial direction (Fig. 8). On reaching the opposite wall the cloud impacts a wider zone thus reducing the specific kinetic energy of the impact per square unit. If the kinetic energy is still large enough perforation of the opposite wall takes place. Thus in the absence of any filling substance inside the containment hypervelocity collision could result in the formation of maximum two holes in the opposite walls. In case the containment is filled in with some atmosphere a definite part of the kinetic energy of fragments would be transformed into the energy of the surrounding gas giving birth to shock waves propagating in all the directions, reflecting from the walls and resulting in an overpressurization under certain conditions. Thus internal loading of the walls would be the sum of momentum of particles colliding the walls and pressure growth due to reflections of shock waves. Under these conditions loading is exercised not only by a limited zone on the opposite wall of the containment but by all its internal surface. This results in a much wider spectrum of possible breakup scenario. Depending on the loading and strength of material three different scenarios are possible. The intense nonuniform internal loading could result in a breakup of the whole containment as if in an explosion and formation of fragments of a definite distribution versus mass. The coupled non-uniform internal loading by impacting particles and shock waves could result in the perforation of the opposite wall only due to maximal values of the cumulative load. The loaded zone and loads distribution will naturally depend on the density of the atmosphere inside the containment. And the third possible scenario illustrates the conditions under which the redistribution of loading on all the internal surface of the containment and rapid slowing down of debris particles due to aerodynamic drag forces lowers down the cumulative loads below the breakup limit and the rear wall remains undamaged. To determine the conditions under which all these scenarios could take place it is necessary to investigate the internal loading for the considered cases. The local overpressure on the shell can be determined by the

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following formula: Nðτn Þ !! AvðpÞ ¼ p p0 þ ∑ mi V i n =τn ; i¼1

2h τn ¼ ; cs

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E ; cs ¼ ð1 ν2 Þρs0

ð1Þ

ð2Þ

where E and v are Young's modulus and Poisson coefficient of the material of the shell, ρs0 is the density of the material in the initial undisturbed state, τn is the characteristic time for dynamical deforming of the shell, h is the thickness, mi and V i are the mass and velocity of the ! ith fragment colliding the wall, n is the external normal vector, Nðt; τn Þ is the number of particles colliding the wall during the time interval ðt; t þ τn Þ. The results of analysis show that for homogeneous clouds of fragments N is proportional to τn . Then, as shown in formula (1), the dependence of AvðpÞ on the value of characteristic time is not very strong. Fig. 14a–c illustrates average wall overpressures Av(p) for one and the same fragments cloud propagating inside the containment, but for different initial gas pressures in the containment. The coordinate axis “s” starts at the center of the bottom part of the cylinder and following the wall reaches the center of the top plate. Vertical lines in Fig. 14 mark the connections of the side wall of the cylinder with the top and bottom plates. The results show that on increasing the initial pressure (and density) of the gas filling the containment the maximal overpressures decrease. For the case p0 ¼1.5 MPa the overpressures are negligible (Fig. 14c) and present only on the bottom and side walls. All the fragments are split into small droplets and slowed down. 5. Conclusions

A concept for spacecrafts shielding from space debris

environment is discussed based on the effects of energy dissipation in hypervelocity collisions of particles with vessels filled in by compressible fluid accumulating and transforming the kinetic energy of the impact into the energy of blast wave propagation in all directions from the perforation zone. Using gas-filled bumpers makes it possible to increase the area of the zone of impact energy redistribution including the side and front walls due to the property of gas to transmit pressure in all directions. This is a considerable advantage of the present concept.

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