High-fidelity Numerical Simulations for Destructive Re-entry of Upper Stages

In order to keep our space activity sustainable, comprehensive research effort should be taken for the space debris problem. Improvement in the destructive re-entry risk analysis methodology is one of the important research areas to reduce the uncertainties on the expected casualty predictions and to realize the design-for-demise. Uncertainty quantification strategy was proposed, and the role of the high-fidelity numerical simulations was discussed. Based on the detailed investigation of the computed results, selection of the reference length to predict the stagnation heat flux, considerations on the local curvature and the shockinteraction effect were found to be the key factors to achieve high-order accurate heat flux predictions. 1 BACKGROUND AND OBJECTIVES Space debris problem is a growing concern to be tackled internationally to keep our space activity sustainable. Numerous pieces of debris are tracked on the orbit around the Earth, those number will be rapidly increased due to the growing satellite demands such as mega-constellations. The increasing number of space debris directly results in the increasing potential risk to all spacecraft. Therefore, a comprehensive research and development (R&D) efforts should be made to understand the space debris environment, assess its risk, mitigate its number growth, and control the risk. An importance to ensure a sustainable space environment has been firstly stated in space basic act of Japan in 2008. One of the major plans on the space policy is to address the R&D activities for the space debris problems. Reorganizations of the regulation issues and R&D activities for space debris of Japan Aerospace Exploration Agency (JAXA) were initiated in 2016. Four major activities were identified and re-organized, those are 1) formulation of space debris international standards and guidelines, 2) debris situational awareness and defense, 3) low cost active debris removal, and 4) debris mitigation [1, 2]. Space debris mitigation is the most efficient strategy to reduce the number of orbital debris in the critical orbital zones for long term sustainability. There are two mitigation approaches to remove the derelict spacecraft from the protected regions, the one is transfer to the non-protected orbit and the other is the destructive atmospheric re-entry. Risk should be minimized as much as possible by the comprehensive consideration on the design and the disposal operation based on the mission analysis and the risk assessment. The destructive re-entry of satellites and rockets and the related ground risk due to the fragments reaching the ground are getting increased interest in recent years. Survived fragments derived from the launch vehicle’s ascent and the spacecraft’s re-entry have been found and retrieved in many places all over the world. Fatal accident due to artificial space debris has not been happened yet, however, the survived fragments have been found at the place near the human living area. It is apparently the strong reason to emphasize the importance to predict the risk quantitatively, and minimize the risk by the detailed consideration on the design and the end of mission disposal operations. Therefore, focus of this study lies in the significant uncertainty reduction of the destructive re-entry safety analysis to realize the detailed design and operation considerations. The uncertainty quantification factors are identified, and effective uncertainty quantification strategy mainly based on the high-fidelity numerical simulations is proposed. Finally, an effectiveness of the high-fidelity numerical simulations is shown. Based on the investigation of the numerical results, the key findings to improve the accuracy of empirical model are discussed. 2 STRATEGY FOR UNCERTAINTY QUANTIFICATION There are mainly two approaches for the re-entry safety analysis, the one is object-oriented approach [3] [4] and the spacecraft-oriented approach [5] [6]. Comparison and the description of these approaches can be found in present author’s study [1]. There exist various uncertainty factors in the re-entry risk analysis. Major un-certainty factors identified in this study are shown in Fig. 1, those are 1) model accuracy, 2) attitude stability mode, 3) shape complexity, 4) shape change in time, and 5) initial conditions. The uncertainties on the aerodynamic and the heat flux models have significant influences on the resulting expected casualty. The empirical correlation models are used in the re-entry safety analysis [5-7]. Those models should be validated for the various geometries under the wide range of flow conditions. High-fidelity numerical simulations such as Proc. 7th European Conference on Space Debris, Darmstadt, Germany, 18–21 April 2017, published by the ESA Space Debris Office Ed. T. Flohrer & F. Schmitz, (http://spacedebris2017.sdo.esoc.esa.int, June 2017) computational fluid dynamics (CFD) analysis and the direct simulation Monte Carlo (DSMC) analysis tools are validated by the comparison with the experiments under the specific flow conditions. To cover the wide range of geometries and flow conditions, the predicted results by the empirical correlation models are compared with those by CFD and DSMC. An attitude stability mode has significant effect on the time variation of the heat flux distributions, and thus heating amount. As already been clarified in the present author’s previous study [1], the rocket upper stage has the possibility to have the aerodynamic stability at the pitch angle conditions where the heavier components such as engines are in the wind-ward side. As a result, the heating amount to the heavier components would be increased. Effects of the shape complexity and the shape change in time are also dominant factor. If the realistic complicated geometry can be considered in the re-entry safety analysis, it is generally resulting in the surface heating area increase. In addition, the mass, the moment of inertia, and the aerodynamic shape are also changed during the destructive re-entry of the fragments. These effects should be modelled appropriately to achieve the high-order accurate re-entry safety analysis. Furthermore, in order to realize the design-for-demise, the consideration of the realistic complicated shape is essential. Therefore, the spacecraft-oriented re-entry safety analysis method is under the development at JAXA. Initial conditions such as the temperature level, induced velocity of the components at the primary break-up are also one of the dominant factors. Those uncertainties are quantified by the flight data acquisition and the high-fidelity numerical simulations [1]. Overview of the uncertainty quantification strategy is also shown in Figure 2. Based on the correct understanding of the mechanism of the destructive reentry, and the investigations on the uncertainty factors as described above, the physics-based models are validated on a step-by-step basis. As will be shown in the following sections, the high-fidelity numerical simulation plays important roles for the significant uncertainty reduction. Fig. 1. Uncertainty factors for the destructive re-entry risk analysis. Fig.2 Uncertainty quantification strategy for destructive re-entry risk analysis. 3 HIGH-FIDELITY NUMERICAL SIMULATIONS High-fidelity numerical simulation is the essential technology to achieve high-order accuracy in the reentry risk analysis. Alghough the high-fidelity numerical simulations does not used in the re-entry risk analysis, it is essential to under stand destructive reentry mechanisms and to validate the empirical correlation models used in the re-entry risk analysis. If the physical models used in the simulation are validated by comparing with the experimental data throughout the possible environmental condtions, the significant uncertainty reduction can be achieved. Based on the detailed investigation of the computed results, the mechanism of the destruction process can be understood, and the empirical correlation models used in the re-entry risk analysis can be improved by comparing with the high-fidelity numerical simulation results. Since the accuracy of the aerodynamics and the heat flux model has significant influence on the expected casualty, the establishemnt of CFD method for the destructive re-entry analysis is essential. In the last two decades, the comprehensive and intensive research efforts have been made in order to improve CFD schemes and the computational speed especially for the aerodynamic design of the aircrafts, rockets, re-entry vehicles. Consequently, the aerodynamic and the heat flux analysis for the complicated geometry have been matured and available. However, there are still technological gaps to establish an accurate CFD for the destructive re-entry, those are 1) model validation and accuracy improvements for the non-smooth bodies, 2) development of the capability to handle deforming complicated bodies, and 3) development of the heat flux model including important effects such as the surface chemical reactions and the shape deformations. In this study, two state-of-the-art in-house CFD codes, named as UNITED and LS-FLOW have been employed. Those codes have superior advantages such as the capability to handle complicated geometry, and the capability of the solution adaptive mesh refinement (AMR). Furthermore, these two codes have been employed various types of the aerodynamic characteristics and the heat flux predictions, and intensive research efforts for the accuracy validaton studies have been made. Technical details on the computational fluid dynamics are described as follows respectively. 3.1 Rarefied Flow Solver (UNITED) At the high altitude roughly over 90 km, the effecs of the rarefied gas dynamics such as non-equilibrium of thermodynamics and chemical reacions are significant. For the prediction of the surface pressure and heat flux distributions, the Boltzmann equation of kinetic theory is solved by direct simulation