Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical solution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Numerical solutions of forward-flight rotor flow using an upwind method

A finite-volume upwind algorithm for solving the 3-D Euler equations with a moving grid has been developed for computing helicopter forward-flight rotor flows. The computed pressure distributions and shock positions of high-speed rotor flow are compared with various experimental data as well as with other numerical results, and the agreement is encouraging. A comparison of quasi-steady solutions with unsteady solutions reveals that when a shock occurs in the flowfield, the assumption of quasi-steady flow may fail due to the time-lag of the shock motion. Similarly, three-dimensional effects cannot be neglected. Sufficient subiterations for each time step are required to avoid numerical lag effects in using the present method. The redistribution of the residual due to the coordinate transformation is discussed. For high-order MUSCL-type schemes, a coordinate-independent solution can be obtained by interpolating primitive variables.

Chen, C. L.↗
NASA NTRS1989

Numerical Solution Of Navier-Stokes Equations

Three-dimensional, incompressible flow simulated on computer. Report discusses mathematical basis of IN3SD computer code and application of code to several test problems. Relies heavily on use of pseudocompressibility to solve numerically three-dimensional Navier-Stokes equations of viscous, incompressible flow. With further study and some modification, valuable computational tool for solution of engineering problems in fluid dynamics.

Rogers, Stuart E.↗
NASA NTRS1981

Numerical solutions of atmospheric flow over semielliptical simulated hills

Atmospheric motion over obstacles on plane surfaces to compute simulated wind fields over terrain features was studied. Semielliptical, two dimensional geometry and numerical simulation of flow over rectangular geometries is also discussed. The partial differential equations for the vorticity, stream function, turbulence kinetic energy, and turbulence length scale were solved by a finite difference technique. The mechanism of flow separation induced by a semiellipse is the same as flow over a gradually sloping surface for which the flow separation is caused by the interaction between the viscous force, the pressure force, and the turbulence level. For flow over bluff bodies, a downstream recirculation bubble is created which increases the aspect ratio and/or the turbulence level results in flow reattachment close behind the obstacle.

Shieh, C. F.↗
NASA NTRS1978

On a numerical solution of the plastic buckling problem of structures

An automated digital computer procedure is presented for the accurate and efficient solution of the plastic buckling problem of structures. This is achieved by a Sturm sequence method employing a bisection strategy, which eliminates the need for having to solve the buckling eigenvalue problem at each incremental (decremental) loading stage that is associated with the usual solution techniques. The plastic buckling mode shape is determined by a simple inverse iteration process, once the buckling load has been established. Numerical results are presented for plate problems with various edge conditions. The resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 machine proves to be most economical in comparison with other existing methods of such analysis.

Gupta, K. K.↗
NASA NTRS1974

Steady simple shear flow past a circular cylinder at moderate Reynolds numbers - A numerical solution

The two-dimensional steady flow of an incompressible viscous fluid past a circular cylinder, placed symmetrically in a simple shear field, has been studied for both the stationary and the freely rotating case by solving numerically the Navier-Stokes equations for values of the Reynolds number R in the range from 0.047 to 70. At R = 0.047, the results obtained are in substantial agreement with the analytic small-R perturbation solution given by Robertson and Acrivos (1970). Inertia effects were found, however, to play a significant role even at R = 1, and hence the calculated flow pattern for R greater than or equal to 1 differs significantly from that of the creeping-flow solution. Specifically, for the freely rotating case, the region of closed streamlines decreases rapidly in extent with increasing R, two symmetrically placed wakes are formed on either side of the cylinder, and the dimensionless rotational speed of the freely suspended cylinder decreases as the reciprocal of the square root of R.

Kossack, C. A.↗
NASA NTRS1985

Numerical solution of strong radiation gasdynamic interactions in a hydrogen-seedant mixture

Theoretical and experimental results are provided for the absorption of laser energy by a gas flow. A two-dimensional numerical model described the temperature field, fluid dynamics, variable absorptivity and gas dynamics. The model was tested using a hydrogen-seedant mixture injected with 10.6 micron laser radiation. The laser mix was selected to allow reduced temperature gradients and energy source terms. It was found possible, by varying parameters such as the laser power and flash pressure, to precisely position the peak absorptance region in higher speed flows. More refined models are being tested to achieve accurate absorptance predictions in flows below Mach 0.0001.

Merkle, C. L.↗
NASA NTRS1977

Numerical solution of the viscous hypersonic flow past blunted cones at angle of attack

Hypersonic viscous flow over spherically blunted cones of large half angle is computed at small angles of attack in the plane of symmetry of the flow field. Time-dependent viscous shock-layer equations in body-oriented coordinates are used to describe the flow field. The shock wave is treated as a discontinuity, across which the Rankine-Hugoniot relations are used to compute the flow conditions behind the shock. A time-marching second-order finite-difference method is used to solve the equations for a perfect gas. The local CFL (Courant-Friedrich-Lewy) time increment is used to advance the solution in time at each grid point. A fourth-order damping is used to damp the oscillations in the flow quantities. The numerical results of the present analysis for quantities such as shock standoff distance, surface-pressure distribution, and heating rates compare well with the existing theoretical and experimental results.

Kumar, A.↗
NASA NTRS1989

A stable numerical solution method in-plane loading of nonlinear viscoelastic laminated orthotropic materials

In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.

Gramoll, K. C.↗
NASA NTRS1983

Numerical solutions for spin-up from rest in a cylinder

A set of three-dimensional flow-field data for the region around a cylinder impulsively spun-up from rest was derived with a numerical model based on the Navier-Stokes equations. Laser-Doppler anemometer data in the azimuthal direction was employed to test the model predictions, and data was developed for a flowfield with Ekman numbers from 9.18/1,000,000 to 9.18/10,000. The contributions of inviscid and viscous terms were determined as functions of radius and time. It was found that immediately after start-up viscous diffusion is the dominant factor, which is replaced by nonlinear radial advection. The Coriolis force dominates in the later stages of spin-up. The inward radial flow is a maximum near the front, where the vertical velocity is small, but features strong radial gradients, as it does at the edge of the Ekman layer.

Hyun, J. M.↗
NASA NTRS1999

Numerical Solution of Incompressible Navier-Stokes Equations Using a Fractional-Step Approach

A fractional step method for the solution of steady and unsteady incompressible Navier-Stokes equations is outlined. The method is based on a finite volume formulation and uses the pressure in the cell center and the mass fluxes across the faces of each cell as dependent variables. Implicit treatment of convective and viscous terms in the momentum equations enables the numerical stability restrictions to be relaxed. The linearization error in the implicit solution of momentum equations is reduced by using three subiterations in order to achieve second order temporal accuracy for time-accurate calculations. In spatial discretizations of the momentum equations, a high-order (3rd and 5th) flux-difference splitting for the convective terms and a second-order central difference for the viscous terms are used. The resulting algebraic equations are solved with a line-relaxation scheme which allows the use of large time step. A four color ZEBRA scheme is employed after the line-relaxation procedure in the solution of the Poisson equation for pressure. This procedure is applied to a Couette flow problem using a distorted computational grid to show that the method minimizes grid effects. Additional benchmark cases include the unsteady laminar flow over a circular cylinder for Reynolds Numbers of 200, and a 3-D, steady, turbulent wingtip vortex wake propagation study. The solution algorithm does a very good job in resolving the vortex core when 5th-order upwind differencing and a modified production term in the Baldwin-Barth one-equation turbulence model are used with adequate grid resolution.

Kiris, Cetin↗
NASA NTRS1980

Numerical solution techniques for unsteady transonic aerodynamics problems

Basic concepts of finite difference solution techniques for unsteady transonic flows are presented. The hierarchy of mathematical forumulations that approximate the Navier-Stokes equations are reviewed. The basic concepts involved in constructing numerical algorthms to solve these formulations are given. Semi-implicit and implicit schemes are constructed and analyzed. The discussion focuses primarily on techniques for solving the low frequency transonic small disturbance equation. This is the simplest formulation that contains the essence of inviscid unsteady transonic flow physics. The low frequency formulation is emphasized here because codes based on this theory can be run in minutes of processor time on currently available computers. Furthermore, numerical techniques involved in solving this simple formulation also apply to the more complicated formulations. Extensions to these formulations are briefly described. An indication of the present capability for solving unsteady transonic flows is provided. Important areas of future research for the advancement of computational unsteady transonic aerodynamics are described.

Ballhaus, W. F.↗
NASA NTRS1978

Numerical solution for supersonic flow near the trailing edge of a flat plate

In the present study, problems of laminar and turbulent two-dimensional flow of a viscous compressible fluid near the trailing edge of a thin flat plate are considered. The complete set of Navier-Stokes equations is solved by the finite-difference method of MacCormack (MacCormack and Baldwin, 1975). It is an explicit, predictor-corrector, time-splitting method of second order acuracy. The computational mesh employed has sufficient resolution for all the characteristic lengths suggested by theory. In the laminar case, the present results are compared with the triple deck solution of Daniels (1974). This comparison indicates that the asymptotic triple deck theory for supersonic trailing edge flow is accurate within five percent for Reynolds numbers greater than 1000. In the turbulent case, the Prandtl-Van Driest-Clauser algebraic eddy viscosity model is used. The numerical results show that the region of upstream influence is approximately of the order of the boundary layer thickness. The solutions for skin-friction, pressure and wake center-line velocity are presented.

Degani, D.↗
NASA NTRS1987

Numerical solutions of the compressible 3-D boundary-layer equations for aerospace configurations with emphasis on LFC

The application of stability theory in Laminar Flow Control (LFC) research requires that density and velocity profiles be specified throughout the viscous flow field of interest. These profile values must be as numerically accurate as possible and free of any numerically induced oscillations. Guidelines for the present research project are presented: develop an efficient and accurate procedure for solving the 3-D boundary layer equation for aerospace configurations; develop an interface program to couple selected 3-D inviscid programs that span the subsonic to hypersonic Mach number range; and document and release software to the LFC community. The interface program was found to be a dependable approach for developing a user friendly procedure for generating the boundary-layer grid and transforming an inviscid solution from a relatively coarse grid to a sufficiently fine boundary-layer grid. The boundary-layer program was shown to be fourth-order accurate in the direction normal to the wall boundary and second-order accurate in planes parallel to the boundary. The fourth-order accuracy allows accurate calculations with as few as one-fifth the number of grid points required for conventional second-order schemes.

Harris, Julius E.↗
NASA NTRS1991

Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems

Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.

Cerro, J. A.↗
NASA NTRS1989

A simple time-accurate turbomachinery algorithm with numerical solutions of an uneven blade count configuration

The present computer algorithm for the time-accurate flow analysis of rotating turbomachines is based on the finite-volume method and employs a high-resolution approximate Riemann solver for interface flux definitions and an implicit numerical scheme that possesses apparent unconditional stability. Block-block interfaces, including dynamic ones, are treated in such a way as to mimic interior block communication. The turbomachine configurations treated by way of illustration are 8-8-bladed and 11-9-bladed versions of a contrarotating unducted fan engine.

Janus, J. Mark↗
NASA NTRS1982

Numerical solution of transonic wing flow fields

A fast, fully implicit, approximate factorization algorithm designed to solve the conservative full-potential equation is used to compute lifting-wing flow fields with embedded transonic flow. The computer program (TWING - transonic wing analysis) uses an elliptic-solver numerical grid-generation routine and is capable of analyzing arbitrary wing geometries with sweep, twist, taper, and section variation. Computed flowfield results for several wing geometries are presented; they demonstrate substantial improvement in convergence speed relative to the FL028 computer code.

Holst, T. L.↗