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Über dieses Buch

This book covers the parameterization of entry capsules, including Apollo capsules and planetary probes, and winged entry vehicles such as the Space Shuttle and lifting bodies. The aerodynamic modelling is based on a variety of panel methods that take shadowing into account, and it has been validated with flight and wind tunnel data of Apollo and the Space Shuttle. The shape optimization is combined with constrained trajectory analysis, and the multi-objective approach provides the engineer with a Pareto front of optimal shapes.

The method detailed in Conceptual Shape Optimization of Entry Vehicles is straightforward, and the output gives the engineer insight in the effect of shape variations on trajectory performance. All applied models and algorithms used are explained in detail, allowing for reconstructing the design tool to the researcher’s requirements.

Conceptual Shape Optimization of Entry Vehicles will be of interest to both researchers and graduate students in the field of aerospace engineering, and to practitioners within the aerospace industry.

Inhaltsverzeichnis

Chapter 1. Introduction

Abstract
The design and analysis of atmospheric entry has been an integral part of the developments in space engineering. In this chapter, we start by giving a historical perspective of a selection of the development of hypersonic flight and re-entry technology, followed by a presentation of some recent and upcoming projects in this area. Subsequently, we focus our attention on key past efforts of the optimization of entry vehicle shapes. Finally, we provide an overview of the contents and structure of this book.
Dominic Dirkx, Erwin Mooij

Chapter 2. Flight Mechanics

Abstract
The numerical propagation of the dynamics of the re-entry vehicle is the core segment of the determination of the performance of the system. In this chapter, we review the models for the physical environment and the relevant aspects of the equations of motion for atmospheric entry. All relevant reference frames are discussed, and the transformation between these frames is clearly provided. Finally, we present the models that re used for the guidance of the capsule and winged vehicles. Both vehicles use similar bank angle modulation (designed to prevent skipping entry), but distinct angle of attack modulation.
Dominic Dirkx, Erwin Mooij

Chapter 3. Aerothermodynamics

Abstract
The shape of an entry vehicle influences its performance primarily through the aerothermodynamic interaction with the atmosphere. In particular, the aerodynamic forces and moments, and the heat flux are crucial parameters driving the vehicle performance. Modelling the aerothermodynamic properties of re-entry vehicles is a highly complicated and multidisciplinary problem. For conceptual design optimization, incorporating a high-fidelity analysis in-the-loop is not feasible. Instead, we use local inclination methods for the aerodynamic behaviour, and analyze the heating of the vehicles only at key areas using (semi-)empirical relations. In this chapter, physical background of relevant aspects of hypersonic flow is reviewed, and the mathematical modelling approach we take here is presented.
Dominic Dirkx, Erwin Mooij

Chapter 4. Numerical Interpolation

Abstract
To optimize the shape of a generic winged vehicle, we generate the exterior of the vehicle from a discrete number of points. Computing a continuous vehicle surface from these points requires an interpolation algorithm. In this work, we use cubic splines and spline surfaces as the interpolation scheme. In this chapter the basics of these methods, as well as some issues pertaining to their implementation, are discussed. The splines and spine surfaces are presented in both Hermite and Bézier formulation, and the link between the two is used to enforce that the spline surface net shows neither concavity nor self-intersection.
Dominic Dirkx, Erwin Mooij

Chapter 5. Vehicle Geometry

Abstract
We apply our shape optimization methodology to two types of vehicles: a capsule shape and a winged-fuselage shape. In this chapter, we present the methods by which we parameterize these vehicle shape, e.g. the manner in which we relate the shape parameters that are to be optimized to a continuous vehicle shape. The capsule is defined by a combination of basic geometric shapes: sphere segments, a torus segment and a conical frustum. The winged vehicle is defined more generically using cubic spline surfaces for both the fuselage and the wings. An algorithm to map shape parameters to surface points, while ensuring a physically realistic vehicle shape, is presented in detail.
Dominic Dirkx, Erwin Mooij

Chapter 6. Optimization

Abstract
The optimization of vehicle shapes is performed using the Particle Swarm Optimization (PSO) method, which is metaheuristic global optimization algorithm. In this chapter, we start by discussing the general problem of both single- and multi-objective global optimization, followed by a discussion of the PSO method, including the approach we use to for multi-objective optimality and constraint handling. Finally, we show how the optimization algorithm is applied to the design problem at hand by defining the objective and constraint functions for both the capsule and winged-vehicle shape.
Dominic Dirkx, Erwin Mooij

Chapter 7. Simulator Design

Abstract
In an optimization algorithm, the performance for each vehicle shape is independently assessed by generating the vehicle shape, generating an aerodynamic database, and numerically propagating the entry trajectory. In this chapter, we give a top-level overview of the implementation of the algorithm, with a focus on the interfaces between the various components. We perform a detailed validation of our aerodynamics modelling approach by comparing literature values of the hypersonic force and moment coefficients for the Apollo capsule and Space Shuttle with results obtained using our methodology. Subsequently, we propagate the entry trajectory using both our coefficients and the tabulated aerodynamic coefficients. Finally, we list the settings we use in our numerical simulations (initial conditions, environmental parameters, etc.).
Dominic Dirkx, Erwin Mooij

Chapter 8. Shape Analysis - Capsule

Abstract
Using the methods and models described in the previous chapters, we present the results of the shape optimization of the capsule vehicle in this chapter. We start by discussing the results of a Monte Carlo analysis of the search space, from which we draw preliminary conclusions on the influence of the various contraint functions. Subsequently, we show the optimization results for the following objective functions: optimal heat load, volumetric efficiency and ground track length. Both the double-objective results (for each combination) and the full triple-objective results are shown. By comparing these results, it is clear that full three-dimensional Pareto front could not have been reproduced or deduced from the three two-dimensional fronts, indicating the need for considering multiple competing objectives.
Dominic Dirkx, Erwin Mooij

Chapter 9. Shape Analysis - Winged Vehicle

Abstract
Using the methods and models described in the previous chapters, we present the results of the shape optimization of the winged vehicle in this chapter. We start by discussing the results of a Monte Carlo analysis of the search space, from which we draw preliminary conclusions on the influence of the various constraint functions, and their correlation with the shape parameters. Subsequently, we show the optimization results for the following objective functions: vehicle mass, fuselage volume and ground track length. Both the double-objective results (for each combination) and the full triple-objective results are shown. We perform two additional alternative optimizations, one for which the pitch stability constrain is imposed for all angles of attach (instead of $$\alpha > 20^{\circ }$$) and one where the range objective is replaced with a maximum time at reference heat flux objectives. The results of these optimizations provide insight into the influence of a change in vehicle and mission requirements, respectively.
Dominic Dirkx, Erwin Mooij

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