Efficient treatments of stationary free boundary problems

In the present paper we consider the efficient treatment of free boundary problems by shape optimization. We reformulate the free boundary problem as shape optimization problem. A second order shape calculus enables us to realize a Newton scheme to solve this problem. In particular, all evaluations of the underlying state function are required only on the boundary of the domain. We compute these data by boundary integral equations which are numerically solved by a fast wavelet Galerkin scheme. Numerical results prove that we succeeded in finding a fast and robust algorithm for solving the considered class of problems. Furthermore, the stability of the solutions is investigated by treating the second order sufficient optimality conditions of the underlying shape problem

Theoretical studies on flapped delta wings

The effects of leading edge flaps on the aerodynamic characteristics of a low aspect-ratio delta wing are studied theoretically. As an extension of the classical crossflow plane analysis and in order to include separated shear layers, an analogy between three dimensional steady conical and two dimensional unsteady self-similar flows is explored. This analogy provides a simple steady-unsteady relationship. The criteria for the validity of the steady-unsteady analogy are also examined. Two different theoretical techniques are used to represent the separated shear layers based on the steady-unsteady analogy, neglecting the trailing edge effect. In the first approach, each vortex system is represented by a pair of concentrated vortices connected to the separation points by straight feeding sheets. In the second approach, the vortex cloud method is adopted for simulating the flow field in the crossflow plane. The separated shear layers are replaced with a cloud of discrete vortices and the boundary element method is employed to represent the wing trace by a vorticity distribution. A simple merging scheme is used to model the core region of the vortical flow as a single vortex by imposing a restriction on the shear layer rotation angle. The results are compared with experiments and with results from 3-D panel calculations

Laboratory Simulation of the Effect of Rocket Thrust on a Precessing Space Vehicle

Ground tests of solid propellant rocket motors have shown that metal-containing propellants produce various amounts of slag (primarily aluminum oxide) which is trapped in the motor case, causing a loss of specific impulse. Although not yet definitely established, the presence of a liquid pool of slag also may contribute to nutational instabilities that have been observed with certain spin-stabilized, upper-stage vehicles. Because of the rocket's axial acceleration, absent in the ground tests, estimates of in-flight slag mass have been very uncertain. Yet such estimates are needed to determine the magnitude of the control authority of the systems required for eliminating the instability. A test rig with an eccentrically mounted hemispherical bowl was designed and built which incorporates a follower force that properly aligns the thrust vector along the axis of spin. A program that computes the motion of a point mass in the spinning and precessing bowl was written. Using various RPMs, friction factors, and initial starting conditions, plots were generated showing the trace of the point mass around the inside of the fuel tank. The apparatus will incorporate future design features such as a variable nutation angle and a film height measuring instrument. Data obtained on the nutational instability characteristics will be used to determine order of magnitude estimates of control authority needed to minimize the sloshing effect

Numerical simulation of a wawe generator: a case of study

The aim of present work is the numerical simulation of a linear generator, capable of directly converting the kinetic energy, available by the wave, into electrical energy, through the device linear motion (up and down). In this paper, we intend to propose a numerical simulation approach to immersed devices by applying the Immersed Boundary Method. The Theory of linear wave is used to study and reproduce sea conditions and the computational domain is created based on observations available for the site in which it is envisaged the positioning of the devic

Development and application of unified algorithms for problems in computational science

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting

Applied Mechanics Dynamics

The present edition incorporates a number of revisions and additions which should improve its usefulness as a textbook without changing the basic organization or the general philosophy of presentation of the subject matter. The experience of the past few years at the California Institute of Technology and other schools indicates that the book has been useful to engineering students who wish to prepare for more advanced studies and applications of dynamics, and hence a new edition was felt to be justified. Among the additions and modifications the following may be mentioned to indicate the scope of the revision. The section on dimensional analysis has been rewritten and a brief treatment of the theory of models has been added. The section on impact problems has been revised, and a more extensive treatment of variable mass systems has been included. A more general discussion of the moment of momentum equations for systems of particles has been added, and the general momentum and energy equations for rigid bodies have been more completely developed. The discussion of rotation about a fixed point and gyroscopic motion has been expanded and somewhat more complex systems have been considered, including problems on the stability of rolling motion. The problem of longitudinal waves in an elastic bar is discussed, and a comparison is made between wave propagation techniques and vibration methods for such problems. The discussion of generalized coordinates and Lagrange's equations has been revised, and a general treatment of the problem of small oscillations of a conservative system has been added. The sections on the Calculus of Variations and Hamilton's Principle have been rewritten with some expansion. Over one hundred new problems have been added to increase the total number to some four hundred. All of the new problems have been thoroughly tested in classroom use. The number of illustrative examples has been increased and many of the original examples have been modified. As in the first edition, the main emphasis of the book is on particle and rigid-body dynamics, although some other aspects of the subject have been included to show how the methods of classical mechanics are applied to the various branches of engineering science. Some of these topics, such as fluid dynamics and the kinetics of gases, have been treated in a very brief fashion. Although the student will make a more complete analysis of these subjects in specialized courses, it is believed that the brief discussions will help him to acquire a broader view of the applied sciences. In all such instances care has been taken to use methods that can be extended later for more complete treatments, and the student has been informed of the limitations of the analyses. As a textbook the main emphasis has been on method and on development of fundamental principles. The problems form an essential part of the presentation, and important conclusions are sometimes given in problems and illustrative examples. The student should examine such problems and note the results, even if the details of the proofs are not carried through