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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

A new approximate LU factorization scheme is developed to solve the steady state Reynolds-averaged Navier-Stokes (NS) equations. Central differencing is used for both implicit and explicit operator and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two- and three-dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step the scheme can achieve. Supersonic and transonic three-dimensinal flows past a hemisphere cylinder are computed to demonstrate the convergence characteristics of the scheme. A good convergence rate is achieved for the inviscid case. Finally, an explicit eigenvector annihilation procedure is adopted successfully to remove the stiffness caused by the fine grid spacing for viscous flows.

Pan, D.↗
NASA NTRS1986

Gravity gradient torque for an arbitrary potential function

To permit investigation of the relative effects of higher-order terms in the potential function and allow computation of the gravity gradient torques consistent with the gravitational acceleration for a given potential function, a simple formula is derived for computing the gravity gradient torque on a vehicle in terms of the eigenvalues and eigenvectors of the gravity gradient matrix and the inertia properties of the vehicle. The formulation is applicable to any potential function for which the gravity matrix can be computed for a given point in the potential field.

Glandorf, D. R.↗
NASA NTRS1986

A shock capturing technique for hypersonic, chemically relaxing flows

A fully coupled, shock capturing technique is presented for chemically reacting flows at high Mach numbers. The technique makes use of a total variation diminishing (TVD) dissipation operator which results in sharp, crisp shocks. The eigenvalues and eigenvectors of the fully coupled system, which includes species conversion equations in addition to the gas dynamics equations, are analytically derived for a general reacting gas. Species production terms for a model dissociating gas are introduced and are included in the algorithm. The convective terms are solved using a first-order TVD scheme while the source terms are solved using a fourth-order Runge-Kutta scheme to enhance stability. Results from one-dimensional numerical experiments are shown for a two species and a three species gas.

Eberhardt, S.↗
NASA NTRS1985

Application of eigenspace techniques to design of aircraft control systems

Eigenspace techniques allow the control system designer to use feedback to place eigenvalues and shape eigenvectors so as to modify closed loop dynamic response characteristics to achieve performance objectives. In this paper the theory of eigenspace design is reviewed, extended and applied to several aircraft control problems.

Liebst, B. S.↗
NASA NTRS1985

Flight test trajectory controller synthesis with constrained eigenstructure assignment

The design of a maneuver autopilot for flight test trajectory control using constrained eigenvalue/eigenvector assignment is examined. The aircraft considered was a high-performance fighter with a command augmentation system engaged in all three axes. Attention is given to difficulties encountered in the generation of the desired eigenvalues and eigenvectors. It is found that this approach demands several iterations to converge to a satisfactory result, and does not appear to easily yield suitable insight for the output feedback design of high-order multivariable systems which will be used at other operating points. It is concluded that this technique could be made more attractive by generating gradients of the eigensystem between flight conditions, and including this information in the single-point design technique.

Menon, P. K. A.↗
NASA NTRS1985

AOTV bluff body flow - Relaxation algorithm

Preliminary investigations have led to the consideration of two classes of energy efficient aeroassisted orbital transfer vehicle (AOTV) concepts, with high and low L/D. The AOTV represent reentry space vehicles which are to fly hypersonically in the continuum upper reaches of the atmosphere. Problems arise in connection with convective and nonequilibrium radiative heating. As the possibilities for obtaining needed information by experimentation are limited, reliance must be placed on computational techniques to simulate testing of design concepts. A new relaxation algorithm for the compressible Navier-Stokes equations has been developed in the context of recent work with a conservative flux difference eigenvector split implicit upwind scheme CSCM (conservative supracharacteristics method). Attention is given to the CSCM implicit method, and early results for axisymmetric bluff body flow including complete forebody and base flow for a free flight range model drag brake AOTV.

Lombard, C. K.↗
NASA NTRS1986

Sensitivity analysis of discrete structural systems

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
NASA NTRS1986

Eigensystem synthesis for active flutter suppression on an oblique-wing aircraft

The application of the eigensystem synthesis technique to place the closed-loop eigenvalues and shape the closed-loop eigenvectors has not been practical for active flutter suppression, primarily because of the availability of only one control surface (aileron) for flutter suppression. The oblique-wing aircraft, because of its configuration, provides two independent surfaces (left and right ailerons), making the application of eigensystem synthesis practical. This paper presents the application of eigensystem synthesis using output feedback for the design of an active flutter suppression system for an oblique-wing aircraft. The results obtained are compared with those obtained by linear quadratic Gaussian techniques.

Alag, G. S.↗
NASA NTRS1986

Design of a multivariable flutter control/gust load alleviation system

This paper discusses the use of eigenspace techniques for the design of an active flutter control/gust load alleviation system for a hypothetical research drone. One leading edge and two trailing edge aerodynamic surfaces are available for control. Full state control laws are designed for two combinations of control surfaces by selecting feedback gains which place closed loop eigenvalues and shape closed loop eigenvectors so as to stabilize wing flutter and reduce gust loads at the wing root while yielding acceptable robustness and satisfying constraints on rms control surface activity. These controllers are realized by state estimators designed using an eigenvalue placement/eigenvector shaping technique which results in recovery of the loop transfer characteristics of the full state feedback systems. The resulting feedback compensators are shown to perform almost as well as the full state designs. They also exhibit acceptable performance in situations in which the failure of an actuator is simulated.

Liebst, B. S.↗
NASA NTRS1986

A numerical algorithm for optimal feedback gains in high dimensional LQR problems

A hybrid method for computing the feedback gains in linear quadratic regulator problems is proposed. The method, which combines the use of a Chandrasekhar type system with an iteration of the Newton-Kleinman form with variable acceleration parameter Smith schemes, is formulated so as to efficiently compute directly the feedback gains rather than solutions of an associated Riccati equation. The hybrid method is particularly appropriate when used with large dimensional systems such as those arising in approximating infinite dimensional (distributed parameter) control systems (e.g., those governed by delay-differential and partial differential equations). Computational advantage of the proposed algorithm over the standard eigenvector (Potter, Laub-Schur) based techniques are discussed and numerical evidence of the efficacy of our ideas presented.

Banks, H. T.↗
NASA NTRS1986

Semi-implicit and fully implicit shock-capturing methods for hyperbolic conservation laws with stiff source terms

Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogenous (source) terms are discussed. If the stiffness is entirely dominated by the source term, a semi-implicit shock-capturing method is proposed provided that the Jacobian of the soruce terms possesses certain properties. The proposed semi-implicit method can be viewed as a variant of the Bussing and Murman point-implicit scheme with a more appropriate numerical dissipation for the computation of strong shock waves. However, if the stiffness is not solely dominated by the source terms, a fully implicit method would be a better choice. The situation is complicated by problems that are higher than one dimension, and the presence of stiff source terms further complicates the solution procedures for alternating direction implicit (ADI) methods. Several alternatives are discussed. The primary motivation for constructing these schemes was to address thermally and chemically nonequilibrium flows in the hypersonic regime. Due to the unique structure of the eigenvalues and eigenvectors for fluid flows of this type, the computation can be simplified, thus providing a more efficient solution procedure than one might have anticipated.

Yee, H. C.↗
NASA NTRS1987

A parallel solution for the symmetric Eigenproblem

A completely parallel algorithm for the symmetric eigenproblem AX = Lambda BX is outlined. The algorithm is parallel in the sense that the numerical operations do not occur in a fixed sequence. Therefore, a large number of operations can be programmed to be performed concurrently on a computer with multiple central processing units. The standard symmetric eigenvalue problem AX = Lambda X has the property that the n eigenvalues of the principal submatrix of A of order n are separated by the (n-1) eignvalues of the principal submatrix of order (n-1). The separation property delineated n intervals containing one eigenvalue. Each eigenvalue and corresponding eigenvector can be computed independently. The n eigenproblem calculations can be divided among multiple processing units.

Thurston, Gaylen A.↗
NASA NTRS1987

Survey of methods for calculating sensitivity of general eigenproblems

A survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non-Hermitian matrices is presented. In addition, a modification of one method based on a better normalizing condition is proposed. Methods are classified as Direct or Adjoint and are evaluated for efficiency. Operation counts are presented in terms of matrix size, number of design variables and number of eigenvalues and eigenvectors of interest. The effect of the sparsity of the matrix and its derivatives is also considered, and typical solution times are given. General guidelines are established for the selection of the most efficient method.

Murthy, Durbha V.↗
NASA NTRS1987

Eigenspace techniques for active flutter suppression

The use of eigenspace techniques for the design of an active flutter suppression system for a hypothetical research drone is discussed. One leading edge and two trailing edge aerodynamic control surfaces and four sensors (accelerometers) are available for each wing. Full state control laws are designed by selecting feedback gains which place closed loop eigenvalues and shape closed loop eigenvectors so as to stabilize wing flutter and reduce gust loads at the wing root while yielding accepatable robustness and satisfying constrains on rms control surface activity. These controllers are realized by state estimators designed using an eigenvalue placement/eigenvector shaping technique which results in recovery of the full state loop transfer characteristics. The resulting feedback compensators are shown to perform almost as well as the full state designs. They also exhibit acceptable performance in situations in which the failure of an actuator is simulated.

Garrard, William L.↗
NASA NTRS1987

Discontinuous solutions to hyperbolic systems under operator splitting

Two-dimensional systems of linear hyperbolic equations are studied with regard to their behavior under a solution strategy that in alternate time-steps solves exactly the component one-dimensional operators. The initial data is a step function across an oblique discontinuity. The manner in which this discontinuity breaks up under repeated applications of the split operator is analyzed, and it is shown that the split solution will fail to match the true solution in any case where the two operators do not share all their eigenvectors. The special case of the fluid flow equations is analyzed in more detail, and it is shown that arbitrary initial data gives rise to pseudo acoustic waves and a non-physical stationary wave. The implications of these findings for the design of high-resolution computing schemes are discussed.

Roe, P. L.↗
NASA NTRS1987

Computational procedures for evaluating the sensitivity derivatives of vibration frequencies and Eigenmodes of framed structures

Computational procedures are presented for evaluating the sensitivity derivatives of the vibration frequencies and eigenmodes of framed structures. Both a displacement and a mixed formulation are used. The two key elements of the computational procedure are: (a) Use of dynamic reduction techniques to substantially reduce the number of degrees of freedom; and (b) Application of iterative techniques to improve the accuracy of the derivatives of the eigenmodes. The two reduction techniques considered are the static condensation and a generalized dynamic reduction technique. Error norms are introduced to assess the accuracy of the eigenvalue and eigenvector derivatives obtained by the reduction techniques. The effectiveness of the methods presented is demonstrated by three numerical examples.

Fetterman, Timothy L.↗
NASA NTRS1986

Automated tuning of airframe vibration by structural optimization

Numerical optimization techniques are used to modify the dynamic response at a specified point(s) of a helicopter airframe structure due to a steady state narrow band excitation. Calculation of steady state vibration amplitude is reduced to the solution of linear equations with complex coefficients. The sensitivity of the dynamic amplitudes with respect to the structural parameter perturbations can be computed with the same technique as the one used in the static displacement sensitivity without requiring eigenvector sensitivity. Approximate models for critical structural responses are created based on the sensitivity data to reduce the amount of computational effort and to enable the design of structures of practical scale and complexity. This approach is general in that it accommodates static, dynamic, and frequency constraints simultaneously as long as their computational models are available. It can be used in optimizing mass distribution as well as stiffness modifications of practical structures.

Miura, H.↗