WE found, on experimental grounds in Article I, that the field of air‐flow past a short body of low resistance shape, such as an aerofoil, comprises two dissimilar parts: (a) a thin boundary layer enveloping the body and dominated by viscous effects, and (b) a motion outside the boundary layer in which viscosity is much less important. It will be remembered that in the external motion occur the large pressure changes, which, transmitted through the boundary layer, account for nearly all the lift and for part of the drag. These pressures we observed to be calculable from the velocities without appreciable error by Bernoulli's equation. In the present Article we confine attention to this external flow, assuming it to be steady, incompressible, and inviscid. Its dependence upon (a), already discussed to some extent, we ignore; the boundary layer is conceived to be everywhere very thin, so that the only role it plays is to allow of relative velocity at the surface of the body. The assumptions made, excepting that of incompressibility, will appear drastic, and it will not be surprising if some of our deductions prove discordant with experimental fact. Nevertheless, they lead to a theory which finds many applications and uses in real fluid motion, and, in particular, gives an intimate view of aerofoil flow that is very close to the truth. It is convenient to develop our reasoning in analytical terms and for simplicity to restrict the flow to two dimensions (Article 1, §5). But the engineer will find special scope in this part of aerodynamics for graphical methods in the solution of particular problems.

Aerodynamics for Engineers

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners.

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State-of-the-art in aerodynamic shape optimisation methods

Optimal design of launch vehicles is a complex problem which requires the use of specific techniques called Multidisciplinary Design Optimization (MDO) methods. MDO methodologies are applied in various domains and are an interesting strategy to solve such an optimization problem. This paper surveys the different MDO methods and their applications to launch vehicle design. The paper is focused on the analysis of the launch vehicle design problem and brings out the advantages and the drawbacks of the main MDO methods in this specific problem. Some characteristics such as the robustness, the calculation costs, the flexibility, the convergence speed or the implementation difficulty are considered in order to determine the methods which are the most appropriate in the launch vehicle design framework. From this analysis, several ways of improvement of the MDO methods are proposed to take into account the specificities of the launch vehicle design problem in order to improve the efficiency of the optimization process.

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A survey of multidisciplinary design optimization methods in launch vehicle design

A combined approach of inverse method and direct flow analysis is presented for the hydrodynamic design of gas-liquid two-phase flow rotodynamic pump impeller. The geometry of impeller blades is designed for a specified velocity torque distribution by treating the two-phase mixture as a homogeneous fluid under the design condition. The three-dimensional flow in the designed impeller is verified by direct turbulent flow analysis, and the design specification is further modified to optimize the flow distribution. A helical axial pump of high specific speed has been developed. To obtain a favorable pressure distribution the impeller blade was back-loaded at the hub side compared to the tip side

Hydrodynamic design of rotodynamic pump impeller for multiphase pumping by combined approach of inverse design and CFD analysis

This paper describes an effort to optimize the design of an entire space launch vehicle to lowEarth (circular) orbit, consisting of multiple stages using a genetic algorithm with the goal of minimizing vehicle weight and ultimately vehicle cost. The entire launch vehicle system is analyzed using various multistage configurations to reach low Earth orbit. Specifically, threeand four-stage solid propellant vehicles have been analyzed. The vehicle performance modeling requires that analysis from four separate disciplines be integrated into the design optimization process. The disciplines of propulsion characteristics, aerodynamics,mass properties, andflight dynamics have been integrated to produce a high-fidelity systemmodel of the entire vehicle. In addition, the systemmodel has been validated using the existing launch vehicle data. The cost model is mass based and uses extensive historical data to produce a cost estimating relationship for a solid propellant vehicle. For the design optimization, the goal is for the genetic algorithm tominimize the differences between thedesired andactual orbital parameters. This ensures that thepayload achieves the desired orbit. One final goal is to minimize the overall vehicle mass, thus minimizing the system cost per launch. This paper will represent the first effort of its kind to minimize the solid propellant launch vehicle cost at the preliminary design level using a genetic algorithm.

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Design Optimization of a Space Launch Vehicle Using a Genetic Algorithm

Analytical methods for solid rocket motor grain design are proving to be tremendously beneficial to some recent efforts to optimize solid-rocket propelled missiles. The analytical approach has fallen out of favor in recent decades; however, for some classes of grains, the analytical methods are much more efficient than grid-based techniques. This paper provides a review of analytical methods for calculating burn area and port area for a variety of cylindrically perforated solid rocket motor grains. The equations for the star, long spoke wagon wheel, and dendrite grains are summarized and the development of the burn-back equations for the short spoke wagon wheel and the truncated star configurations are included. This set of geometries and combinations of these geometries represent a very wide range of possibilities for two-dimensional grain design. Introduction In many practical solid rocket motor design efforts, final geometric designs for grains are arrived at using numerical layering techniques. This process is geometrically versatile and imminently practical for cases in which small numbers of final geometries are to be considered. However, for a grain design optimization process in which large numbers of grain configurations are to be considered, generating grids for each candidate design is often prohibitive. For such optimization processes, analytical developments of burn perimeter and port area for two-dimensional grains are critically important. Most modern texts on solid rocket propulsion do not provide geometric details for grain design. This paper will offer a review of analytical methods for determining burn area and port area as a function of burn distance for a selection of common grain designs. Analytical developments for solid rocket motor grains were much more prevalent in the decades before widespread use of microcomputers. A summary of one version of the burn back equations for the star grain and for part of one type of wagon wheel can be found in Barrere. Analytical methods have also been developed for the truncated star and for the dendrite. Other potential grain configurations are described in NASA publications but very few geometric details are given in such publications. 1 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 20-23 July 2003, Huntsville, Alabama AIAA 2003-4506 Copyright © 2003 by Roy Hartfield. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Star Grain Geometry Grain geometries are generally described using lengths and angles defined in the cross section. A sample burn back diagram is shown in Figure 1 and the geometric definition diagram for the familiar star grain geometry is shown in Figure 2. Since some of the geometric equations for the burn perimeter and port area for the star grain have been developed and published, only a summary of this geometry is included here. Figure.1 Sample Star Grain Figure 2. Star Grain Geometry The geometric relationship between the two primary angles in the geometry definition can be written as:

A Review of Analytical Methods for Solid Rocket Motor Grain Analysis

The use of computer programs driven by genetic algorithms has become an increasingly popular method for optimizing engineering designs. This paper focuses on the modeling and optimization of liquid-rocket-enginepropelled missiles with a computer program that is composed of a series of codes that simulate the performance of liquid-propelled rockets andare controlledby a genetic algorithm.Because the entiremissile design is considered, the complete system performance must be modeled accurately and efficiently. The methodology described in this paper has been extended to both the preliminary design and reverse-engineering of liquid-propelled missiles. The performance model has been validated against the performance of a liquid-propelled missile and the results are provided. Two different fast-aerodynamic-prediction codes are used and their results are compared. A complete preliminary design of a liquid-propelled missile system is considered with a variety of goals and constraints. Results from the preliminary design optimization are also shown and discussed in detail.

Genetic-Algorithm Optimization of Liquid-Propellant Missile Systems

For this preliminary design study an apportioned pareto genetic algorithm, unique to the software package IMPROVE?“‘, was used to manipulate a solid rocket design code, an aerodynamic design code, and a three-loop autopilot to produce interceptor designs capable of accurately engaging a target. Twenty-nine design variables were required to define the optimization problem, and four primary goals were established to access the’performance of the interceptor designs. Design goals included 1) minimize miss distance, 2) minimize intercept time, 3) minimize takeoff weight, and 4) minimize maximum G-loading. In 100 generations the genetic algorithm was able to develop several basic types of external aerodynamic designs that ,performed nearly the same, with miss distances less than 10.0 feet. The solid rocket motors that propelled these external shapes shared one common characteristic: a large initial burning area. Initial combustion chamber volumes varied significantly, but the fastest interceptors generally had less fuel than would have been expected. The genetic algorithm did not prefer maximizing the amount of fuel within the rocket motor case (high fuel volume ratio). Introduction With the addition of guidance, an autopilot, and an airframe with movable control surfaces, basic rocketry expands into a more lethal and much more precise means of waging war. Rather than increasing the size of the warhead being delivered (to make-up for a loss in delivery accuracy), modem weaponeering has tended to use a small warhead coupled with an accurate control system. For ground launched systems, ideas such as “smart rocks” and “brilliant pebbles” that sprang from early Strategic Defense Initiative (SDI) research were based on the belief that the energy delivered by a small fast moving projectile without an explosive could be as lethal as a less accurate system with an explosive warhead. Similarly for air-launched ground attack weapons, Vietnam proved that delivery accuracy was paramount to defeating tough targets, and the Air Force devoted billions of dollars to the development of precise warhead delivery systems. Certainly the Persian Gulf War showed the benefit of the highly accurate weapon systems the Air Force developed. In more human terms, increased delivery accuracy means less collateral damage to nonmilitary facilities and less civilian casualties. While it is difficult to argue with .the success of the air-launched ground attack weapons that have been demonstrated in combat, these systems, and air-to-air missile systems, share a common design ‘philosophy with the less successful ground launch interceptors. When a system has a guidance system and autopilot, there is a tendency to compensate for less than stellar aerodynamic designs by shifting more and more of the delivery problems over to the autopilot. As a result, autopilots are typically very good and very robust, but the airframe and aerodynamics of the overall system are almost an afterthought. Overall system performance and system capability, therefore, suffers because of the overreliance on the autopilot to compensate for weaknesses in the aerodynamic performance of the weapon, system’. The goal of this research is to let an artificial intelligence tool, a genetic algorithm, design the aerodynamic shape while at the same time designing the propulsion system and key autopilot variables. This all-at-once approach to missile design is intended to provide a system capable of producing good aerodynamic shapes in addition to the good performance expected from an autopilot. Previous Work Rather than discuss the historical development of the autopilot, propulsion system, or’aerodynamics used for this research, it is more pertinent to discuss previous applications of genetic algorithms to autopilot and control systems. Norris and Crossleyz recently used a genetic algorithm to find gains to control a standard pedagogical two-disk torsional spring system. The approach used a very simple two-loop proportional-integral control system with velocity feedback. The two loop controller had three gains that needed to be determined as a function of variable spring stiffness. The objective functions were defined such that good gain values produce little error between the commanded and achieved disk rotation angles. Since two separate disks were being commanded in twist, a pareto genetic algorithm was used to try to minimize the rotational errors in both disks simultaneously. At the conclusion of 80 .generations, the resulting family (i.e. population of 80 members) of three controller gains were hybrid performers that would work reasonably well for both disks. Two points worth noting from this study was that the crossover * Deputy Director, Development Test Department, Senior Member, AIAA ’ Professor, Auburn University, Associate Fellow, AIAA * Associate Professor, Auburn University, Senior Member, AIAA Copyright@ 19!$lby Murray B. Anderson. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission.

Rhonald M. Jenkins

Papers

Design Optimization of a Space Launch Vehicle Using a Genetic Algorithm

A Review of Analytical Methods for Solid Rocket Motor Grain Analysis

Design Optimization of a Space Launch Vehicle Using a Genetic Algorithm

Genetic-Algorithm Optimization of Liquid-Propellant Missile Systems

Design of an air to air interceptor using genetic algorithms