Elsevier

Acta Astronautica

Volume 179, February 2021, Pages 105-121
Acta Astronautica

Research paper
Drag reduction through shape optimisation for satellites in Very Low Earth Orbit

https://doi.org/10.1016/j.actaastro.2020.09.018Get rights and content

Highlights

  • Bi-conic Aeroshell profiles can be used to reduces aerodynamic drag in VLEO.

  • A reduction in the aerodynamic drag can be achieved by adjusting the tail profile.

  • For equal reduction in volume and drag, blunter Aeroshell profiles are preferable.

  • An application of a Radial Basis Function-based surrogate model trained using DSMC.

Abstract

Operating satellites at altitudes in Very Low Earth Orbit (VLEO) has many advantages. However, due to the higher atmospheric density of this region, satellites encounter significantly higher atmospheric drag. Depending on the mission, this may require a propulsive system to maintain the orbit which costs both fuel mass and volume. It is therefore desirable to reduce the drag in order to either reduce these costs or to extend the operational life. In this paper a series of viable aeroshell profiles are identified for satellites operating in VLEO using a Radial Basis Function-based surrogate model with data generated using both Panel Methods and Discrete Simulation Monte Carlo simulations. It was demonstrated that a maximum drag reduction of between 21% and 35% was achievable for the profiles when optimising a bi-conic profile for minimum drag based on Discreet Simulation Monte Carlo simulations with an energy accommodation coefficient of 0.95. Accounting for the loss of internal volume and assuming the reduction in fuel mass results in an equally proportioned reduction in fuel system volume it was observed that only a 13% to 27% reduction was achieved.

Introduction

There is increasing interest in improving the capabilities and reducing the cost of Earth observation platforms by operating in orbits with much lower altitudes in a region commonly referred to as Very Low Earth Orbit (VLEO) [1]. VLEO provides a number of advantages over higher altitude orbits, such as reduced payload size and mass [1], [2] as well as reduction in the payload power requirements, and improvements in the data rate [3], [4]. It therefore provides the opportunity to reduce the overall cost of a platform for a given mission as compared to similar platforms at more common higher altitudes.

There are many different definitions for the upper extent of VLEO with common definitions including 300 km [5] and 450 km [6]. The defining characteristic of VLEO is the increased effects of the Earth’s atmosphere on the satellite design. One of the key challenges is combating the higher levels of atmospheric drag that are experienced which would otherwise limit the operational life of satellites [1], [7], [8].

In some case a shorter operational life can be desirable, such as the US Keyhole and USSR Zenit reconnaissance satellites during the cold war. In other cases a longer operational life maybe necessary. To achieve this could require regular orbit-raising manoeuvres or to adopt a low thrust drag compensation scheme in order to maintain altitude. An example of such a satellite is ESA’s Gravity Field and Steady-State Ocean Circulation Explorer (GOCE), a 1077 kg Earth observation satellite launched in 2009 to examine the Earth’s gravitational field [9]. Operating at an altitude of 260 km, it employed an ion propulsion system to provide the necessary thrust to compensate for the drag it experienced. Under this regime it was able to maintain orbit for 55 months using 40 kg Xenon fuel, before deorbiting within 2 weeks of fuel depletion. JAXA have also sent a satellite to this region of orbit called the Super Low Altitude Test Satellite (SLATS) with the aim to studying the effects of atomic oxygen in VLEO. Launched in late 2017, this 400 kg satellite descended to its research orbit between 180–250 km where it employed a hybrid chemical and electrical propulsion system to remain there for 90 days [10], [11].

Due to their high specific impulse (Isp), electrical propulsion systems are the ideal choice for supporting long duration drag compensation. However, they still require fuel which becomes the limiting factor on the operational life of the platform [12] as was the case of with both GOCE and SLATS. The fuel required is proportional to the thrust and by extension the drag that the satellite experiences [2], therefore it is desirable to minimise the drag as much as practicable in order to reduce the fuel mass fraction or to extend the life of the platform. Since the drag a satellite experiences is linked to its geometry [13], it is necessary to identify configurations that may prove beneficial within the rarefied gas of the thermosphere of VLEO. Reducing the drag is important for extending the operational life, but this does not guarantee the usability of the geometry selected. It is therefore also important to consider other factors such as the internal volume of the bodies.

The atmospheric density in VLEO, while sufficient to deorbit a satellite within days, is also sufficiently rarefied that the gas flow the satellite experiences can be described as a molecular flow (Knudsen number > 10). As summarised by Vallado & Finkleman [8] there are a number of methods available for calculating the aerodynamic forces for this regime. Analytical methods such as those presented by Sentman [14] and Fujita [10] can provide estimates of the aerodynamic forces a body might experience within a rarefied flow. However, while suitable to simple convex geometries they have limited value with more complex shapes, especially where secondary particle–surface interactions may occur [8]. Additionally, the lower the altitude at which the analysis is performed the less accurate analytical methods become as non-linear aspects of the flow begin to dominate [15]. Alternatively, particle simulators such as the Direct simulation Monte Carlo (DSMC) methods pioneered by Bird [16], [17] can provide a more accurate assessment of the aerodynamic forces, as they endeavour to replicate the physics behind molecular flow, however, this comes at the cost of longer simulation time. Examples of the DSMC codes available for this application included ‘SPARTA’ (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) [18], [19], the ‘dsmcFoam’ part of the openFOAM CFD toolkit [20], and DS2V and DS3Vl, the original DSMC codes developed by Bird [16], [17]. For the wider work being performed, the ability to capture the non-linear aspects of the flow around complex bodies was highly desirable. As such developing a framework in which DSMC simulations could be used to assess the viability of satellite geometries was necessary.

Performing the simulations using DSMC methods can be time intensive and computationally expensive. This would normally make it prohibitive to explore an entire design space with sufficient fidelity. As outlined by Forrester et al. [21], this problem can be effectively managed by employing a surrogate model framework. This reduces the number of simulations required through careful selection of the sample points and effective interpolation of the data. Much of the current development in surrogate based modelling builds on the work of Sacks et al. [22] and there have been a number of advances in the field as reported in the review papers Queipo et al. [23] and Simpson et al. [24].

The work presented here forms part of a larger body of work assessing the effectiveness of altering the geometry of the satellite in order to reduce its drag in an effort to either prolong its operational life or increase its payload capacity. The novelty of the work lies in identifying viable aeroshell profiles for satellites operating in VLEO using a Radial Basis Function-based surrogate model with data generated using DSMC. To test and verify the methodology, the results were compared with a similar model created using panel methods. The set-up for both methods are described in Section 4 and will be used to generate samples to train a set of surrogate models as described in Section 5. The aeroshell profiles and their associate design space are described in Sections Section 3. The optimisation strategy will be described in Section 7 with the resulting optimised profiles presented and explored in Section 8.

Section snippets

Workflow

The work presented in this paper focuses on how the geometry of the satellite can be altered to minimise the aerodynamic drag it experiences in VLEO, thereby saving fuel mass or extending the system’s operational life while not limiting the internal volume. An overview of how this was achieved is provided in Fig. 1. As can be seen on the right of Fig. 1, to explore how the geometry affected the drag it was first necessary to identify what profiles are to be used in the analysis. This required

Satellite geometry

When designing a satellite, the aerodynamic effectiveness of its geometry is not usually considered since the atmospheric density at the more common higher LEO orbits is low enough that it can be effectively ignored during the early design. The structural/geometric design of the satellite is primarily driven by the considerations of launch and the various constraints of its subsystems. At the time of writing, GOCE and SLATS are the only none-military platforms that have sustained circular

Atmosphere

VLEO sits within the lower portion of the Earth’s thermosphere. As shown in Fig. 3, this region has higher air density than higher orbits. This has the effect of limiting the life of satellites in VLEO to the order of weeks or days without active drag compensation. There are multiple models available to approximate the fluid properties of this region, namely the density, temperature and chemical composition. For the work performed here the atmospheric model NRLMSISE-00 was used follows the

Overview

There are three aspects to a successful surrogate model: the interpolation method, the sampling strategy, and the data source. Perhaps the two most common forms of interpolation method are Radial Basis Function (RBF) [34] and Kriging [35]. Both methods share similar model formulations, with key differences arising from the different branches of mathematics used for their derivation. Simpson et al. [36] demonstrated that RBF and Kriging performed well over a range of sampling strategies and

The surrogate model

A surrogate model was generated for the design space outlined in Section 3 using the method outlined in Section 5 for each body. The design space consisted of the 4 variables representing the nose length, nose radius, tail length and tail radius. The outputs of the surrogate model are the coefficient of drag CD and internal volume of the geometry represented by the evaluation point. The coefficient of drag for each sample point was acquired using the DSMC software SPARTA as outlined in Section 4

The cost function

As outlined at the beginning of the paper there are two key objectives here: to minimise the drag on the satellite body, and to maximise the internal volume of the satellite. The cost function for this is given by fc=αfCDA(G)(1α)fV(G)The objective function for the atmospheric drag fCDA(G) will take the satellite geometry and return the coefficient of drag (CD) for the orbital environment by interrogating the surrogate model. The objective function for the internal volume fV(G) takes the

Nose profile

This section will focus on the impact the nose profile will have on the atmospheric drag on the body. The nose profile is described by the nose radius and the nose length, as described in Section 3. Fig. 7, Fig. 8 show the minimum drag achievable when the nose radius and length are fixed respectively for both panel methods (Left) and DSMC (right). In both figures, the other element was allowed to vary to achieve the lowest drag, while the rear of the body was held in a blunt configuration. As

Future work

In order to carry out the work for this paper a number of assumptions where made about the design space and in particular the geometries of the satellite. First and foremost, the profiles examined here were all two dimensions. As a first step it would be useful to extend the analysis to three dimensional geometries to see if the relationships identified in this paper hold. This would also allow the examination of the choice of cross-section and its impact on the nose and tail profiles.

Another

Conclusion

The work presented here forms part of a larger body of work assessing the effectiveness of altering the geometry of the satellite in order to reduce its drag in an effort to either prolong its operational life or increase its payload capacity. In this paper a series of satellite aeroshell profiles were presented that will reduce the drag experienced in VLEO while ensuring the usability of the geometries. This was achieved by first creating a RBF-based surrogate model which could be interrogated

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to thank Simon Chalkley and Andrew Bacon from Thales Alenia Space UK for their advice throughout this work. The views expressed in this paper do not represent those of Thales Alenia Space UK.

This work was supported by an Engineering and Physical Sciences Research Council iCASE grant number 15220191.

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