Vaughn College of Aeronautics and Technology

About: Vaughn College of Aeronautics and Technology is a education organization based out in New York, New York, United States. It is known for research contribution in the topics: Gravitational microlensing & Planetary system. The organization has 727 authors who have published 708 publications receiving 14082 citations. The organization is also known as: College of Aeronautics.

Computation of Rarefied Hypersonic Flows Using Modified Form of Conventional Burnett Equations

Abstract: This paper describes the computations of hypersonic flows in a diatomic gas in rotational nonequilibrium using a newly developed simplified set of Burnett equations designated as simplified conventional Burnett equations. Since the original formulation by Burnett, a number of variations to the original Burnett equations have been proposed, and the differences among these variants and their merits/shortcomings have been described in the literature. A new variant is created based on the conventional Burnett equations for hypersonic flows by neglecting higher-order terms that are inversely proportional to the Mach number. This set of simplified conventional Burnett equations is linearly stable for small disturbances in contrast to the conventional Burnett equations that suffer from Bobylev instability. To simulate the rotational nonequilibrium effect in a diatomic gas, both the Navier–Stokes and the simplified conventional Burnett equations are modified by including a rotational nonequilibrium relaxation mod...

Design considerations in advanced gas turbine combustion chambers

Abstract: Publisher Summary This chapter discusses design considerations in advanced gas-turbine combustion chambers. The basic geometry of a combustion chamber is largely dictated by the need to achieve efficient combustion with the minimum of pressure loss and at overall mixture strengths that lie well outside the inflammability limits of kerosine air mixtures. However, within the limits imposed by these considerations, appreciable variations can be made in the amount of air participating in primary combustion, the size of the eddies created in the primary zone, and the degree of mixing achieved between the fuel and air. Small changes in any one of these variables can have a marked effect on combustor characteristics, and their combined effect is to allow considerable scope and flexibility in chamber design. As designers gain more confidence in exploiting these variables, the all-purpose type of combustion unit that is prevalent today will gradually disappear to be replaced by combustors that are tailor-made to meet a few specific combustion requirements.

$L_{1}$ -Norm Low-Rank Matrix Decomposition by Neural Networks and Mollifiers

Abstract: The $L_{1}$ -norm cost function of the low-rank approximation of the matrix with missing entries is not smooth, and also cannot be transformed into a standard linear or quadratic programming problem, and thus, the optimization of this cost function is still not well solved. To tackle this problem, first, a mollifier is used to smooth the cost function. High closeness of the smoothed function to the original one can be obtained by tuning the parameters contained in the mollifier. Next, a recurrent neural network is proposed to optimize the mollified function, which will converge to a local minimum. In addition, to boost the speed of the system, the mollifying process is implemented by a filtering procedure. The influence of two mollifier parameters is theoretically analyzed and experimentally confirmed, showing that one of the parameters is critical to computational efficiency and accuracy, while the other not. A large number of experiments on synthetic data show that the proposed method is competitive to the state-of-the-art methods. In particular, the experiments on large matrices and a real application in the structure from motion indicate that the memory requirement of the proposed algorithm is mild, making it suitable for real applications that often involve large-scale matrix decomposition.

Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation

Abstract: This work presents a novel approach combining radial basis function (RBF) interpolation with Galerkin projection to efficiently solve general optimal control problems. The goal is to develop a highly flexible solution to optimal control problems, especially nonsmooth problems involving discontinuities, while accounting for trajectory accuracy and computational efficiency simultaneously. The proposed solution, called the RBF-Galerkin method, offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points. The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker (KKT) conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem, if a set of discrete conditions holds. The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem. In addition, the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.

Systems of Axes and Notation

Abstract: This chapter explores various systems of axes and notation. By making the appropriate choice of axis, systems order and consistency may be introduced to the process of model building. The order and consistency play an important role in the definition of the mathematical framework. Only the most basic commonly used axes systems appropriate to aircraft are discussed in the chapter. It gives a description of the earth axes and various kinds of aircraft body fixed axes. It is not important which axis system is chosen provided it models the flight condition to be investigated, the end-result does not depend on the choice of axis system. However, when compiling data for use in the equations of motion of an aircraft it is quite common for some data to be referred. Further, euler angles and aircraft attitude is explained. The angles defined by the right handed rotation about the three axes of a right handed system of axes are called Euler angles. The chapter also defines controls notion, wherein aerodynamic controls and engine controls are explained. The last section mentions the aerodynamic reference centers.