Elsevier

Advances in Space Research

Volume 60, Issue 5, 1 September 2017, Pages 893-906
Advances in Space Research

Reentry trajectory and survivability estimation of small space debris with catalytic recombination

https://doi.org/10.1016/j.asr.2017.05.004Get rights and content

Abstract

A code has been developed to analyze reentry trajectories and survivability of space debris. In particular, an attention was given to small sizes. Based on simple shapes such as a sphere, a cylinder, and a box with sizes of 12.5–50 cm, reentry trajectories were calculated. Materials considered were graphite epoxy, aluminum, and titanium. In total, 120 different cases were examined. The results were compared and validated with various existing codes. Good agreement was found. In the heat transfer calculation, all of the existing codes used the well known Lees’ and Fay and Riddell’s formulae which assume an equilibrium boundary layer flow with a super-catalytic wall where the surface recombination efficiency is regarded infinity. In the case of small space debris having sizes of 2.5–10 cm, however, the flow residence time behind a shock wave is far too short, so that the super-catalytic assumption leads to over-estimation of surface heat transfer rates. Assuming a frozen boundary layer, a finite catalytic recombination can be considered and the results were compared with that of the super-catalytic cases. Both hollow and solid spheres were considered with different sizes and materials. In total, 24 different cases were examined. The results showed that, 16 out of 24 cases survived, while only 8 cases for the super-catalytic and 19 cases for the non-catalytic walls survived, implying the importance of catalytic wall effects for the study of small space debris.

Introduction

Over the years, survivability and hazard analysis of reentry space debris have been investigated by various researchers (see for example, (Lips and Fritsche, 2005, Ziniu et al., 2011)). Recently, South Korea showed an attention on space debris research because of the threat to the survivability of Korean satellites, such as the Science and Technology Satellite-3 and the Arirang Satellite.

To date, the reentry trajectory and survivability analysis codes have been developed by some research centers and space agencies. The codes Object Reentry Survival Analysis Tool (ORSAT) from NASA and Spacecraft Atmospheric Reentry and Aerothermal Breakup (SCARAB) from HTG under ESA/ESOC contracts are the most representative ones (Lips and Fritsche, 2005). Even though the two codes use different approaches for the analysis of the trajectory, heating rates, drag coefficient, thermal analysis, etc., both are known to show excellent agreement for simple-shaped objects (Lips et al., 2005). South Korea has developed the Survivability Analysis Program for Atmospheric Reentry (SAPAR) based on the ORSAT code. The SAPAR is a modified version for cylindrical objects with a revised equation for re-radiation heat loss (Sim and Kim, 2011).

As seen in Fig. 1, the reentry of solid objects such as space debris experiences ablation, non-equilibrium surface heat transfer, and breakup. The ORSAT and the SAPAR cannot predict a break-up process, and they simulate the reentry process from an assumed break-up point; although the SCARAB incorporates a break-up process, it predefines the breaking parts in the reentry object and these parts are separated due to melting or if the analyzed stress of the separated part exceeds the maximum stress (Lips and Fritsche, 2005). The analyzed heat transfer and stress were obtained using the shadow analysis and the local panel method in which pressure, shear stress and heat transfer were calculated for each elementary surface and integrated over all surface elements (Koppenwallner et al., 2005). Ablation usually consists of four mechanisms namely, pyrolysis, chemical erosion, mechanical ablation such as spallation, and melting, but the existing codes only take into account the melting. This simplification seems understandable since space debris is usually made of stainless steel, titanium, aluminum, and/or graphite. For the heat transfer calculation, all the existing codes use Lees’ and Fay and Riddell’s formulae, which assume an equilibrium flow in the boundary layer and the surface is super-catalytic (Fay and Riddell, 1958, Lees, 1956). Fig. 1 shows a schematic of the reentry process with an illustration of non-equilibrium heat transfer at the surface.

When the space debris re-enter at high Mach number hypersonic speeds, the flow behind the shock wave in the stagnation region becomes subsonic, and high temperature and pressure are generated in this region. Consequently, the high temperature provokes a chemical process of dissociation and leads to excitation of vibration and rotation. Towards the surface, the flow speed increases and some recombination may occur (Park et al., 2010). Because of the recombination of oxygen and/or nitrogen, more heat is released in the boundary layer, and it increases the wall temperature eventually leading to ablation. Aerodynamic load and centrifugal stress can break the space debris into many pieces and fragments. All these phenomena make the trajectory and the survivability very difficult to predict.

For the precise estimation of the reentry trajectory and survivability, an accurate heat transfer rate calculation at the surface is essential. To the authors’ knowledge, all the existing codes calculate the stagnation-point heat transfer rates using the well known Lees’ and Fay and Riddell’s formulae. The formulae assume an equilibrium boundary layer flow with a super-catalytic wall where the surface recombination efficiency is regarded infinity. In other words, all the impinging atoms recombine at the wall and therefore release all of their energy of dissociation to the surface (Bertin et al., 1992). For the case of large debris in the size of meters, the super-catalytic assumption seems a viable approach because the stagnation line is sufficiently long leading to enough flow residence time (Damköhler number, Da  1). In the case of small debris having sizes of centimeters, it is expected that the flow reaches thermochemical equilibrium at the edge of the boundary layer, but the residence time is far too short compared to chemical reaction times (Da  1) to sustain equilibrium in the boundary layer in which the flow becomes almost chemically frozen.

It is known that, at altitudes above 61 km, the boundary layer thickness at the hypersonic blunt body stagnation-point becomes almost comparable with the shock layer thickness. In this region, the flow between the shock wave and the body is considered viscous throughout (Park, 1964). On the other extreme, when the objects are having a meter size scale, the boundary layer is so thin compared to the model (for example, meteoroids) such that the flowfield behaves almost inviscid throughout (Park, 2014). In this respect, the region of interest of the present study is usually confined to somewhere in between the two extremes leading to the assumption of two layers: inviscid shock layer with thermochemical equilibrium at the boundary layer edge and chemically frozen inside of the boundary layer. In this case, the non-equilibrium gas-surface interaction needs to be considered. The level of the interaction is known to be a function of partial pressure of impinging atoms, wall temperature, energy accommodation coefficient, and to a certain degree of surface roughness; all of which serve further complication to the debris trajectory estimation. To date, the implementation of the non-equilibrium heat transfer approach to the reentry trajectory estimation and survivability study of space debris, especially with the small sizes that form a large percentage in number out of the total, has not yet been conducted nor documented. This serves as the motivation for this work.

Section snippets

Existing codes

The SAPAR code in South Korea has been developed and has been partly extended based on the ORSAT code by NASA (Sim and Kim, 2011). In line with the code structure of ORSAT and SAPAR, the code developed in this study consists of six modules, namely, trajectory, atmosphere, aerodynamics, aerothermodynamics, thermal analysis, and ablation. Detailed information and formulation of the six modules can be found in literature (Sim and Kim, 2011). So, only a brief description is given herein.

In the

General mechanism

There are four types of surface catalytic models which are defined as super-catalytic, fully-catalytic, partially-catalytic, and non-catalytic. Fig. 2 illustrates the catalytic models.

In the figure, γ is catalytic recombination efficiency, kw is catalytic reaction rate constant, and k is Boltzmann’s constant. The fully-catalytic wall is the wall where all dissociated atoms are recombined, unrelated to the mass fraction of atoms which are allowed to exist at the states of local chemical

Flow condition

The ORSAT and the SCARAB codes provide high accuracy reentry simulation results, and have been widely used over the years. There are various flight observation campaigns for the reentry space debris. To name a few, the representative ones are ATV-1, WT1190F, and Cygnus OA6 (Löhle et al., 2011, Jenniskens et al., 2016). The reentry was observed and documented through imaging and using spectroscopic instruments that measure a break-up scenario and radiation. Surface temperature was determined and

Conclusions

A reentry trajectory and survivability estimation code was developed in this work. Particular emphasis was placed on the small size debris with catalytic recombination at the surface. Based on simple shapes such as cylinders, spheres, and boxes, the present results show good agreement with the various existing codes when the debris have a super-catalytic wall with sizes of 12.5–50 cm. For smaller sizes of 2.5–10 cm, the existing codes based on the super-catalytic approach overestimate the heat

Acknowledgements

This work was supported by the National Research Foundation of Korea Grant, funded by the South Korean government (NRF-2015R1C1A1A02036694). The first author wish to express his sincere gratitude to Dr. Hyung-Seok Sim for his valuable advice and the SAPAR results.

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