Error estimation and control are critical ingredients for improving the reliability of computational simulations Adjoint-based techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjoint-weighted residual method for error estimation Assumptions and approximations made in the calculations are discussed Presentation of the discrete and variational formulations enables a side-by-side comparison of recent work in output-error estimation using the finite volume method and the finite element method Techniques for adapting meshes using output-error indicators are also reviewed Recent adaptive results from a variety of laminar and Reynolds-averaged Navier-Stokes applications show the power of output-based adaptive methods for improving the robustness of computational fluid dynamics computations However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics

/pdf/review-of-output-based-error-estimation-and-mesh-adaptation-gx0exr3453.pdf

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

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

Chaos-based image encryption using a hybrid genetic algorithm and a DNA sequence

https://crd.lbl.gov/assets/pubs_presos/AMCS/ANAG/A131.pdf

An Adaptive Cartesian Grid Method for Unsteady Compressible Flow in Irregular Regions

A finite volume formulation for the Euler equations using Cartesian grids is presented and used to study complex two-dimensional configurations. The formulation extends methods developed for the potential equation to the Euler equations. Results using this approach for single element airfoils are shown to be competitive with and as accurate as other methods that employ mapped grids. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.

Euler calculations for multielement airfoils using Cartesian grids

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.

/pdf/design-optimization-of-a-space-launch-vehicle-using-a-2podpgy9vf.pdf

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

Aerospace design optimization using a steady state real-coded genetic algorithm

The aerodynamic analysis of grid fin configurations has been extended to generic cruciform configurations oriented at any azimuthal angle. The generality of grid fin designs has been retained providing orientations for up to four fins as mounted on or near the surface of a missile airframe. The theoretical analysis is based on a vortex lattice overlay of the lifting elements and includes appropriate body upwash terms as well as wing-body carry over load prediction. This basic approach produces adequate modeling for small angles of attack and small fin incidence angles for any grid fin located at any azimuthal position around the body. For higher angles of attack, empirical equations have been developed for fin coefficients and for the body aerodynamic coefficients. Entire four fin configurations are generically modeled and solutions are obtained in an iterative manner. Excellent agreement between experimental data and theoretical predictions have been obtained for the configuration considered up to angles of attack of twenty degrees and fin incidence angles of thirty degrees. For other grid fin designs other than the one considered in the wind tunnel test and for higher angles of attack, the agreement between the theory and experimental results has not been established.

Nonlinear Aerodynamic Analysis of Grid Fin Configurations

A methodology for developing optimized designs for symmetric - centerbody ramjet powered missiles, using genetic algorithms as the central driver for the system optimization process, has been developed. This paper contains discussion of that methodology and shows results for a typical design scenario.

Ramjet Powered Missile Design Using a Genetic Algorithm

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