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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Forward marching procedure for separated boundary-layer flows

A forward-marching procedure for separated boundary-layer flows which permits the rapid and accurate solution of flows of limited extent is presented. The streamwise convection of vorticity in the reversed flow region is neglected, and this approximation is incorporated into a previously developed (Carter, 1974) inverse boundary-layer procedure. The equations are solved by the Crank-Nicolson finite-difference scheme in which column iteration is carried out at each streamwise station. Instabilities encountered in the column iterations are removed by introducing timelike terms in the finite-difference equations. This provides both unconditional diagonal dominance and a column iterative scheme, found to be stable using the von Neumann stability analysis.

Carter, J. E.↗
NASA NTRS1977

Interactive LORAN-C to geographic and geographic-to-LORAN-C computation

The LORAN program is stored in CMS disk files for use by Avionics Engineering Center terminal users. A CMS EXEC file named LORAN controls program operation. The user types LORAN and the program then prompts for data input and produces output on the terminal. The FORTRAN program refers to a disk file of LORAN master data giving station locations, coding delays, repetition rate and station pair identification letters. For Geographic-to-LORAN conversion, no iterative computations are required; the program is a straightforward coordinate conversion based upon the techniques described by the Navy. For LORAN-to-Geographic conversion, the original Navy program required a dead-reckoned position, near the actual unknown fix, to begin computations. No iteration was performed to obtain the LORAN fix, but internal program errors occurred at execution time if the dead-reckoned fix were displaced from the actual fix by more than a few minutes of latitude or longitude. In order to enhance usefulness of the program for the terminal user, an iterative routine was added which allows a single dead-reckoned position to be entered from the master data file for each LORAN chain. The results compare exactly with the LORAN-C navigation chart, and provide adequate benchmark data for general aviation flight planning and data analysis.

Piecuch, L. M.↗
NASA NTRS1979

Improvements in surface singularity analysis and design methods

The coupling of the combined source vortex distribution of Green's potential flow function with contemporary numerical techniques is shown to provide accurate, efficient, and stable solutions to subsonic inviscid analysis and design problems for multi-element airfoils. The analysis problem is solved by direct calculation of the surface singularity distribution required to satisfy the flow tangency boundary condition. The design or inverse problem is solved by an iteration process. In this process, the geometry and the associated pressure distribution are iterated until the pressure distribution most nearly corresponding to the prescribed design distribution is obtained. Typically, five iteration cycles are required for convergence. A description of the analysis and design method is presented, along with supporting examples.

Bristow, D. R.↗
NASA NTRS1979

Numerical computation of aeroelastically corrected transonic loads

A numerical scheme is presented for the computation of transonic aerodynamic loads on flexible wings. The method consists of iteratively applying the loads computed by a 3D transonic aerodynamics code to a structural model to obtain elastic twist, and then recomputing the loads. Because this iteration is performed concurrently with the iterations performed in computing the aerodynamics, flexible loads are obtained in roughly the same amount of computing time as required to obtain rigid loads. Applications of this method to a flexible supercritical transonic transport wing are presented and compared with model test data.

Chipman, R.↗
NASA NTRS1979

Flight test of a VTOL digital autoland system along complex trajectories

The objective of this research is the development and flight test of a digital multi-rate VTOL autoland system. This autoland system provided the NASA/Army Fly-by-Wire CH-47 helicopter with an automatic 4-D trajectory following and landing capability. Flight tests were conducted along complex trajectories with descending, turning, and decelerating segments. The flight software consists of a trajectory generator and guidance algorithm operating at two iterations per second and a set of sensor filters and an advanced controller operating at 10 iterations per second. This low iteration rate digital controller has a proportional-integral structure that provides an autotrim function. The control gains, scheduled as a function of flight condition, are updated every two seconds. All flight software, except input/output routines, are coded in FORTRAN using floating point arithmetic and are exercised in a ROLM 1664 flight computer. The flight software, the ground and flight hardware, the autoland system's position tracking performance, and the controller's velocity and heading tracking performance are presented.

Downing, D. R.↗
NASA NTRS1980

Newton's method: A link between continuous and discrete solutions of nonlinear problems

Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

Thurston, G. A.↗
NASA NTRS1979

A general algorithm for the solution of Kepler's equation for elliptic orbits

An efficient algorithm is presented for the solution of Kepler's equation f(E)=E-M-e sin E=0, where e is the eccentricity, M the mean anomaly and E the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics in M, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20,000 pairs of values of e and M show that for single precision, 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision one additional iteration is required.

Ng, E. W.↗
NASA NTRS1981

A preliminary study of relaxation methods for the inviscid conservative gasdynamics equations using flux splitting

Plus minus flux vector split schemes are combined with the multigrid relaxation method to obtain fast rates of iterative (or steady state) convergence. On model nonlifting biconvex airfoil flow, steady state convergence is obtained using multigrid in 40 iteractions for subsonic cases and in 120 iterations for transonic cases. A 65 x 33 stretched grid is used. However, the multigrid scheme used here (and there are numerous variations) sometimes could not be made to work for transonic cases with a large number of supersonic points. Moreover, the multigrid method is only several times faster than the conventional algorithm which itself could perhaps be accelerated by other means. Nethertheless, with proper adjustment the multigrid method will ultimately lead to very fast rates of iterative convergence.

Steger, J. L.↗
NASA NTRS1981

Self-adaptive predictor-corrector algorithm for static nonlinear structural analysis

A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.

Padovan, J.↗
NASA NTRS1980

The solution of variable-step implicit difference equations for dynamic systems analysis

A semi-implicit iterative technique is given for the solution of implicit matrix difference equations which arise in variable-step direct time integration of dynamic systems equations. For all practical purposes, the technique avoids repeated refactoring of the stepsize-dependent solution matrix and achieves the solution convergence for engineering accuracy requirements within a permissible number of iterations. Extension of the present method to nonlinear problems treated by the pseudo-force procedure is straightforward. For nonlinear solution procedures based on the tangent modulus formulation, the technique requires modification to make use of the tangent stiffness matrix. It is noted that the question of whether to include the nonlinear terms within the iteration loop has not yet been resolved.

Park, K. C.↗
NASA NTRS1983

Experimental and finite element study of a standing torus under normal and tangential loads

The effect of a combined external load consisting of a normal component and a tangential braking force applied to an inflated torus is addressed. Experimental results obtained by photographic study of the contact area between the torus and load plate are presented as well as measurements of the vertical and horizontal displacement of the torus under load. A numerical procedure for displacement analysis is developed in which the finite element program STAGS (Structural Analysis of General Shells) is used in an iterative manner to produce a flat, horizontal footprint surface under force loading. The redistributed force distribution obtained by the iterative process is displayed along with computed meridional and circumferential stresses. Finally, an extension of the iterative method is introduced which eliminates the need to experimentally determine the footprint area.

Flugrad, D. R.↗
NASA NTRS1983

Convergence characteristics of nonlinear vortex-lattice methods for configuration aerodynamics

Nonlinear panel methods have no proof for the existence and uniqueness of their solutions. The convergence characteristics of an iterative, nonlinear vortex-lattice method are, therefore, carefully investigated. The effects of several parameters, including (1) the surface-paneling method, (2) an integration method of the trajectories of the wake vortices, (3) vortex-grid refinement, and (4) the initial conditions for the first iteration on the computed aerodynamic coefficients and on the flow-field details are presented. The convergence of the iterative-solution procedure is usually rapid. The solution converges with grid refinement to a constant value, but the final value is not unique and varies with the wing surface-paneling and wake-discretization methods within some range in the vicinity of the experimental result.

Seginer, A.↗
NASA NTRS1983

Subsonic panel method for designing wing surfaces from pressure distribution

An iterative method has been developed for designing wing section contours corresponding to a prescribed subcritical distribution of pressure. The calculations are initialized by using a surface panel method to analyze a baseline wing or wing-fuselage configuration. A first-order expansion to the baseline panel method equations is then used to calculate a matrix containing the partial derivative of potential at each control point with respect to each unknown geometry parameter. In every iteration cycle, the matrix is used both to calculate the geometry perturbation and to analyze the perturbed geometry. The distribution of potential on the perturbed geometry is established by simple linear extrapolation from the baseline solution. The extrapolated potential is converted to pressure by Bernoulli's equation. Not only is the accuracy of the approach good for very large perturbations, but the computing cost of each complete iteration cycle is substantially less than one analysis solution by a conventional panel method.

Bristow, D. R.↗
NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗
NASA NTRS1983

A new approach to optimization for aerodynamic applications

A new approach to solving optimization problems that involve nonlinear partial differential equations is presented. The approach eliminates the need for an inner-outer iterative procedure, solving the partial differential equation only once, thereby reducing the cost of computation to an extent which would allow its use as a practical tool in optimization problems. The approach is tested on a single design parameter problem through the use of a specially developed scheme. The results indicate comparable convergence properties for the present iterative process and the standard iterative scheme. The presented ideas are also applicable to multidesign parameter problems.

Rizk, M. H.↗
NASA NTRS1983

Parallel solution of finite element equations

The paper examines several parallel processing solution algorithms for finite element equations arising in linear equilibrium problems. Two basic groups of algorithms, direct and iterative, are investigated with respect to a number of parallel computer architectures and associated selection criteria. The direct algorithms include: LR-Gauss, Crout, Cholesky, Cyclic Reduction and WZ-factorization. The iterative methods examined are: Accelerated Gauss-Seidel, Surrogate Stiffness, Jacobi, Series Expansion, and Energy Monte Carlo. For real-time applications, where the object is to minimize the execution time, Cyclic Reduction appears to be best suited. This assumes a computer with an unlimited number of parallel processors. However, for computers with a limited number of parallel processors that must be used efficiently, both Gauss factorization and Jacobi-like iterative methods rank favorably.

Salama, M.↗
NASA NTRS1983

Convergence characteristics of nonlinear vortex-lattice methods for configuration aerodynamics

Nonlinear panel methods have no proof for the existence and uniqueness of their solutions. The convergence characteristics of an iterative, nonlinear vortex-lattice method are, therefore, carefully investigated. The effects of several parameters, including 1) the surface-paneling method, 2) the integration method of the trajectories of the wake vortices, 3) vortex-grid refinement , and 4) the initial conditions for the first iteration on the computed aerodynamic coefficients and on the flow field details are presented. The convergence of the iterative-solution procedure is usually rapid. The solution converges with grid refinement to a constant value, but the final value is not unique and varies with the wing surface-paneling and wake-discretization methods within some range in the vicinity of the experimental result.

Seginer, A.↗
NASA NTRS1983

Computational technique for three-dimensional compressible flow past wings at high angles of attack

A computational technique, based on the integral solution of the full potential equation, has been developed for the solution of three-dimensional high-subsonic flows past wings at high angles of attack. The problem includes two sources of nonlinearities: a boundary oriented nonlinearity (separated flow roll up) and a region oriented nonlinearity (flow compressibility). The former is represented by a nonlinear vortex lattice while the latter is represented by a source distribution inside a finite volume. The solution is obtained by using double iteration cycles; a separated flow (wake) iteration cycle and a compressibility iteration cycle. The computational technique is applied to a delta wing. The results show that the technique is very promising and efficient.

Kandil, O. A.↗