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At least 397 records · Page 22

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NASA NTRS1979

Comparative study of solar optics for paraboloidal concentrators

Different analytical methods for computing the flux distribution on the focal plane of a paraboloidal solar concentrator are reviewed. An analytical solution in algebraic form is also derived for an idealized model. The effects resulting from using different assumptions in the definition of optical parameters used in these methodologies are compared and discussed in detail. These parameters include solar irradiance distribution (limb darkening and circumsolar), reflector surface specular spreading, surface slope error, and concentrator pointing inaccuracy. The type of computational method selected for use depends on the maturity of the design and the data available at the time the analysis is made.

Wen, L.↗

NASA NTRS1974

A finite element method for potential aerodynamics around complex configurations

A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flow around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of the flow field around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with a hyperboloidal surface. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, intrinsically general and flexible, is also fast, accurate and in excellent agreement with existing results.

Chen, L.-T.↗

NASA NTRS1985

Relative control effectiveness technique with application to airplane control coordination

A method to select optimal combinations of the control variables of a linear system is reported. The combinations are chosen so that the control channels have their principal influences on selected fundamental modes of the system. A series of algebraic maximization problems is used to maximize the effects of the control channels on selected modes while simultaneously minimizing the effects on the remaining modes. The method is applied to the lateral and directional control of a linearized airplane model having ailerons, a rudder, and differential tail surfaces. Integration of these control eliminates oscillations present in the roll rate for a step lateral-control input and improves the sideslip response with reduced rolling motions for a step directional-control input. Inclusion of thrust-vectoring engine nozzles improves the roll rate capability of the airplane.

Lallman, F. J.↗

NASA NTRS1949

Response of a Rotating Propeller to Aerodynamic Excitation

The flexural vibration of a rotating propeller blade with clamped shank is analyzed with the object of presenting, in matrix form, equations for the elastic bending moments in forced vibration resulting from aerodynamic forces applied at a fixed multiple of rotational speed. Matrix equations are also derived which define the critical speeds end mode shapes for any excitation order and the relation between critical speed and blade angle. Reference is given to standard works on the numerical solution of matrix equations of the forms derived. The use of a segmented blade as an approximation to a continuous blade provides a simple means for obtaining the matrix solution from the integral equation of equilibrium, so that, in the numerical application of the method presented, the several matrix arrays of the basic physical characteristics of the propeller blade are of simple form, end their simplicity is preserved until, with the solution in sight, numerical manipulations well-known in matrix algebra yield the desired critical speeds and mode shapes frame which the vibration at any operating condition may be synthesized. A close correspondence between the familiar Stodola method and the matrix method is pointed out, indicating that any features of novelty are characteristic not of the analytical procedure but only of the abbreviation, condensation, and efficient organization of the numerical procedure made possible by the use of classical matrix theory.

Arnoldi, Walter E.↗

NASA NTRS1973

Prediction of free turbulent mixing using a turbulent kinetic energy method

Free turbulent mixing of two-dimensional and axisymmetric one- and two-stream flows is analyzed by a relatively simple turbulent kinetic energy method. This method incorporates a linear relationship between the turbulent shear and the turbulent kinetic energy and an algebraic relationship for the length scale appearing in the turbulent kinetic energy equation. Good results are obtained for a wide variety of flows. The technique is shown to be especially applicable to flows with heat and mass transfer, for which nonunity Prandtl and Schmidt numbers may be assumed.

Harsha, P. T.↗

NASA NTRS1976

Low temperature simulation of subliming boundary layer flow in Jupiter atmosphere

A low-temperature approximate simulation for the sublimation of a graphite heat shield under Jovian entry conditions is studied. A set of algebraic equations is derived to approximate the governing equation and boundary conditions, based on order-of-magnitude analysis. Characteristic quantities such as the wall temperature and the subliming velocity are predicted. Similarity parameters that are needed to simulate the most dominant phenomena of the Jovian entry flow are also given. An approximate simulation of the sublimation of the graphite heat shield is performed with an air-dry-ice model. The simulation with the air-dry-ice model may be carried out experimentally at a lower temperature of 3000 to 6000 K instead of the entry temperature of 14,000 K. The rate of graphite sublimation predicted by the present algebraic approximation agrees to the order of magnitude with extrapolated data. The limitations of the simulation method and its utility are discussed.

Chen, C. J.↗

NASA NTRS1982

Research on numerical algorithms for large space structures

Numerical algorithms for large space structures were investigated with particular emphasis on decoupling method for analysis and design. Numerous aspects of the analysis of large systems ranging from the algebraic theory to lambda matrices to identification algorithms were considered. A general treatment of the algebraic theory of lambda matrices is presented and the theory is applied to second order lambda matrices.

Denman, E. D.↗

NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chambers of a motored rotary engine

A numerical study was performed to investigate the unsteady, multidimensional flow inside the combustion chambers of an idealized, two-dimensional, rotary engine under motored conditions. The numerical study was based on the time-dependent, two-dimensional, density-weighted, ensemble-averaged conservation equations of mass, species, momentum, and total energy valid for two-component ideal gas mixtures. The ensemble-averaged conservation equations were closed by a K-epsilon model of turbulence. This K-epsilon model of turbulence was modified to account for some of the effects of compressibility, streamline curvature, low-Reynolds number, and preferential stress dissipation. Numerical solutions to the conservation equations were obtained by the highly efficient implicit-factored method of Beam and Warming. The grid system needed to obtain solutions were generated by an algebraic grid generation technique based on transfinite interpolation. Results of the numerical study are presented in graphical form illustrating the flow patterns during intake, compression, gaseous fuel injection, expansion, and exhaust.

Shih, T. I. P.↗

NASA NTRS1986

Three-dimensional vibrations of twisted cantilevered parallelepipeds

A large number of references dealing with the vibrations of twisted, cantilevered beams and plates exist in the literature. These works show considerable disagreement concerning the effect of twist angle upon frequencies. The present work is the first three-dimensional study of the problem. Displacement components are assumed in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete. The Ritz method is then applied. Accurate frequencies are calculated for twisted thick plates and are compared with ones obtained recently by others using beam, shell, and finite element theory.

Leissa, A.↗

NASA NTRS1986

A two-dimensional numerical study of the flow inside the combustion chamber of a motored rotary engine

Shih, T. I-P.↗

NASA NTRS1988

Spectral element multigrid. Part 2: Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from tha approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗

NASA NTRS1989

Numerical computation of shock wave-turbulent boundary layer interaction in transonic flow over an axisymmetric curved hill

A control-volume based finite difference computation of a turbulent transonic flow over an axisymmetric curved hill is presented. The numerical method is based on the SIMPLE algorithm, and hence the conservation of mass equation is replaced by a pressure correction equation for compressible flows. The turbulence is described by a k-epsilon turbulence model supplemented by a near-wall turbulence model. In the method, the dissipation rate in the region very close to the wall is obtained from an algebraic equation and that for the rest of the flow domain is obtained by solving a partial differential equation for the dissipation rate. The other flow equations are integrated up to the wall. It is shown that the present turbulence model yields the correct location of the compression shock. The other computational results are also in good agreement with experimental data.

Kim, S.-W.↗

NASA NTRS1989

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Numerical calculations of turbulent reattaching shear layers in a divergent channel are presented. The turbulence is described by a multiple-time-scale turbulence model. The turbulent flow equations are solved by a control-volume based finite difference method. The computational results are compared with those obtained using k-epsilon turbulence models and algebraic Reynolds stress turbulence models. It is shown that the multiple-time-scale turbulence model yields significantly improved computational results than the other turbulence models in the region where the turbulence is in a strongly inequilibrium state.

Kim, S.-W.↗

NASA NTRS1988

Spectral element miltigrid. II - Theoretical justification

A multigrid algorithm is analyzed which is used for solving iteratively the algebraic system resulting from the approximation of a second order problem by spectral or spectral element methods. The analysis, performed here in the one-dimensional case, justifies the good smoothing properties of the Jacobi preconditioner that was presented in Part 1 of this paper.

Maday, Yvon↗

NASA NTRS1990

Calculation of reattaching shear layers in divergent channel with a multiple-time-scale turbulence model

Kim, S.-W.↗

NASA NTRS1995

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗

NASA NTRS1996

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

Lin, Shu↗

NASA NTRSDate not supplied

Efficient and Singularity-Aware Inverse Kinematics for 6-DOF and 7-DOF Revolute Manipulators

Inverse kinematics (IK) for 6-DOF and 7-DOF revolute robot manipulators may be decomposed into canonical subproblems which find the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems. We demonstrate significant performance improvements over existing IK methods. 7-DOF manipulators have one redundant DOF to parameterize, so we introduce the general SEW angle, which generalizes the conventional SEW angle but with an arbitrary reference direction function. One special choice, the stereographic SEW angle, has a singularity when the wrist is on a half-line instead of a full line.

Computational Geometry↗