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At least 73 records · Page 4

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NASA NTRS1975

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.↗

NASA NTRS1975

Numerical study of supersonic turbulent flow over small protuberances

Supersonic turbulent boundary layers over two-dimensional protuberances are investigated, using the numerical finite difference alternating direction implicit (ADI) method. The turbulence is modeled mathematically. The turbulence is represented here by the eddy viscosity approach. The turbulent boundary layer structure as well as an interest in thick boundary layers and much larger protuberance heights than in the laminar case lead to new difficulties. The problems encountered and the means to remove them are discussed.

Polak, A.↗

NASA NTRS1977

Implicit finite-difference computations of unsteady transonic flows about airfoils, including the treatment of irregular shock-wave motions

A computer code, LTRAN2, has been constructed that efficiently computes low-frequency unsteady transonic flows about airfoils in motion. The code solves the two-dimensional, nonlinear, low-frequency, small-disturbance equation by an alternating-direction implicit (ADI) algorithm. First, as a check on the code, LTRAN2 is used to solve the linear, low-frequency, small-disturbance equation. The results are compared with known answers from linear theory. Then nonlinear results are presented. Tijdeman's experimental observations of shock wave motions resulting from airfoil flap oscillations are qualitatively reproduced by LTRAN2. These computations compare favorably with those of Magnus and Yoshihara and are obtained in substantially less computer time. Also the underlying theory of the governing equation and the construction of the algorithm are discussed.

Ballhaus, W. F.↗

NASA NTRS1979

A viscous flow analysis for the tip vortex generation process

A three dimensional, forward-marching, viscous flow analysis is applied to the tip vortex generation problem. The equations include a streamwise momentum equation, a streamwise vorticity equation, a continuity equation, and a secondary flow stream function equation. The numerical method used combines a consistently split linearized scheme for parabolic equations with a scalar iterative ADI scheme for elliptic equations. The analysis is used to identify the source of the tip vortex generation process, as well as to obtain detailed flow results for a rectangular planform wing immersed in a high Reynolds number free stream at 6 degree incidence.

Shamroth, S. J.↗

NASA NTRS1979

Artificial compressibility methods for numerical solutions of transonic full potential equation

New methods for transonic flow computations based on the full potential equation in conservation form are presented. The idea is to modify slightly the density (due to the artificial viscosity in the supersonic region), and solve the resulting elliptic-like problem iteratively. It is shown that standard discretization techniques (central differencing) as well as some standard iterative procedures (SOR, ADI, and explicit methods) are applicable to the modified transonic mixed-type equation. Calculations of transonic flows around cylinders and airfoils are discussed with special emphasis on the explicit methods that are suitable for vector processing on the STAR 100 computer.

Hafez, M.↗

NASA NTRS1979

A viscous flow analysis of the tip vortex generation process

A viscous primary-secondary flow analysis designed for numerical solution by forward marching integration is applied to the tip vortex generation problem. Equations governing streamwise momentum, streamwise vorticity, and a gas law are solved in conjunction with equations governing scalar and vector surface potentials for the secondary velocities. The numerical method used combines a consistently split linearized block implicit (LBI) scheme for parabolic equations and a scalar iterative ADI scheme for elliptic equations. Computed results are presented for a wing of rectangular planform immersed in a high Reynolds number stream at 6 degrees incidence. The physical mechanism for generation of the tip vortex, as revealed by the analysis and computations, is discussed. Detailed flow results for the case of 6 degree incidence are included.

Shamroth, S. J.↗

NASA NTRS1980

Pilot assessment of two computer-generated display formats for helicopter instrument approach

Two computer generated display formats were evaluated as primary displays by six research pilots in a fixed base simulator. One of the computer generated display formats was an electronic attitude director indicator (EADI) which featured three cue flight director, command information, superimposed on true perspective runway symbology. The other computer generated display format featured separate horizontal and vertical situation information with vector predictors. A baseline display, consisting of an electromechanical attitude director indicator (ADI) with a three cue flight director and a moving map, was used as a reference for the pilot evaluations.

Niessen, F. R.↗

NASA NTRS1980

Generation of C-type cascade grids for viscous flow computation

A rapid procedure for generating C-type cascade grids suitable for viscous flow computations in turbomachinery blade rows is presented. The resulting mesh is periodic from one blade passage to the next, nearly orthogonal, and continuous across the wake downstream of a blade. The procedure employs a pair of conformal mappings that take the exterior of the cascade into the interior of an infinite strip with curved boundaries. The final transformation to a rectangular computational domain is accomplished numerically. The boundary values are obtained from a panel solution of an integral equation and the interior values by a rapid ADI solution of Laplace's equation. Examples of C-type grids are presented for both compressor and turbine blades and the extension of the procedure to three dimensions is briefly outlined.

Sockol, P. M.↗

NASA NTRS1978

Preliminary study of head-up assessment techniques. 1: Viewing duration of instrument panel and HUD symbology using a recall methodology

Eight commercial pilots were shown 50 colored, high fidelity slides of a standard instrument panel (IP) with the needle positions of each instrument varying from slide to slide and then 50 slides of a head-up display (HUD) symbology format which contained an equivalent amount of flight-related information as the instrument panel slides. All stimuli were presented under controlled, static viewing conditions that allowed the measurement of the speed and accuracy with which one randomly selected flight parameter on each slide could be read. The subject did not know which parameter would be requested and, therefore, had to remember the total set of information in order to answer the question correctly. The results showed that from 6.6 - 8.7 sec total viewing time was required to correctly extract altitude, airspeed, heading, VSI, or ADI from the IP slides and from 6.1 to 7.4 sec for the HUD slides.

Haines, R. F.↗

NASA NTRS1978

A preliminary study of head-up display assessment techniques. 2: HUD symbology and panel information search time

Twelve commercial pilots were shown 50 high-fidelity slides of a standard aircraft instrument panel with the airspeed, altitude, ADI, VSI, and RMI needles in various realistic orientations. Fifty slides showing an integrated head-up display (HUD) symbology containing an equivalent number of flight parameters as above (with flight path replacing VSI) were also shown. Each subject was told what flight parameter to search for just before each slide was exposed and was given as long as needed (12 sec maximum) to respond by verbalizing the parameter's displayed value. The results for the 100-percent correct data indicated that: there was no significant difference in mean reaction time (averaged across all five flight parameters) between the instrument panel and HUD slides; and a statistically significant difference in mean reaction time was found in responding to different flight parameters.

Guercio, J. G.↗

NASA NTRS1981

A simplified model for the viscous crossflow in a slotted test section

A simplified physical model is constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two-dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, are obtained. Fairly general slot geometry is incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters is employed to solve a finite difference analog of the stream function equation. The vorticity equation is numerically solved with a modified version of the classical alternating direction implicit (ADI) scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slot are at least qualitatively similar to some experimental results of Berndt and Sorenson.

Cooke, C. H.↗

NASA NTRS1979

Calculation of three-dimensional turbulent subsonic flows in transition ducts

A method for computing three-dimensional turbulent subsonic flow in curved ducts is being developed. A set of tube-like surface oriented coordinates is employed for a general class of geometries applicable to subsonic diffusers with offset bends. The geometric formulation is complex and no previous treatment of this class of viscous flow problems is known to the authors. The duct centerline is a space curve specified by piecewise polynomials. A Frenet frame is located on the centerline at each axial location. The cross sections are described by superellipses imbedded in the Frenet frame. Duct surfaces are also coordinate surfaces, which greatly simplifies the boundary conditions. The resulting coordinates are nonorthogonal. An approximate set of governing equations is employed for viscous flows having strong flow in a primary flow direction. The derivation is coordinate invariant and the resulting equations are expressed in tensor form. These equations are solved by an efficient alternating direction implicit (ADI) method. This numerical method is generally stable and permits solution in difficult geometries using the general tensor formulation.

Levy, R.↗

NASA NTRS1981

Recent advances in the development of implicit schemes for the equations of fluid dynamics

Innovations and extensions of implicit schemes for equations of fluid dynamics are presented. The notation and theory for linear multistep methods are reviewed, and extensions of work by Beam and Warming (1979) include the implementation of one-leg methods, ADI methods for equations with mixed derivatives, flux vector splitting, the P-dimensional wave equation, and boundary conditions. Numerical experiments indicate that implicit treatment of the boundary conditions is necessary for unconditional stability, and the improvement and implementation of the boundary condition theory should improve the implicit algorithms for gas dynamic equations.

Warming, R. F.↗

NASA NTRS1982

Implicit unsteady transonic airfoil calculations at supersonic freestreams

The computer code LTRAN2 has been extended to compute unsteady transonic flows about oscillating airfoils with supersonic freestreams. The LTRAN2 code uses an alternating direction implicit (ADI) algorithm to solve the two-dimensional, nonlinear, low-frequency, transonic small-disturbance (LF-TSD) equation. The modified code, LTRAN2-SS, includes a 'high-frequency' option. Steady solutions are checked against those computed by the steady TSD code, TSFOIL; unsteady computations of the linear LF-TSD equation are compared with known linear theory solutions; and new unsteady nonlinear solutions are presented. These cases include standard AGARD test cases for the NLR 7301, MBB-A3, and DO Al supercritical airfoils, as well as several NACA airfoils. The modified code enables aerodynamicists to quickly and efficiently compute transonic flows for both subsonic and supersonic freestreams, and thus resolve flutter boundaries through the full extent of the transonic dip phenomenon.

Chow, L. J.↗

NASA NTRS1982

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Bridgeman, J. O.↗

NASA NTRS1983

On a finite-difference method for solving transient viscous flow problems

A method has been developed to solve the unsteady, compressible Navier-Stokes equation with the property of consistency and the ability of minimizing the equation stiffness. It relies on innovative extensions of the state-of-the-art finite-difference techniques and is composed of: (1) the upwind scheme for split-flux and the central scheme for conventional flux terms in the inviscid and viscous regions, respectively; (2) the characteristic treatment of both inviscid and viscous boundaries; (3) an ADI procedure compatible with interior and boundary points; and (4) a scalar matrix coefficient including viscous terms. The performance of this method is assessed with four sample problems; namely, a standing shock in the Laval duct, a shock reflected from the wall, the shock-induced boundary-layer separation, and a transient internal nozzle flow. The results from the present method, an existing hybrid block method, and a well-known two-step explicit method are compared and discussed. It is concluded that this method has an optimal trade-off between the solution accuracy and computational economy, and other desirable properties for analyzing transient viscous flow problems.

Li, C. P.↗

NASA NTRS1983

Calculation of unsteady small disturbance transonic flow at arbitrary reduced frequency using an extended integral equation method.

A novel analytical-numerical method for calculating unsteady small disturbance transonic flow over airfoils has been developed. The method uses an extended integral equation technique, based on both the velocity potential and the acceleration potential, to predict unsteady aerodynamic loading on airfoils oscillating in subcritical transonic free stream conditions. The formulation is an extension of the work of Sivaneri and Harris (1980) for steady, non-lifting flows and utilizes the linear theory of Landahl (1961) for decoupling of steady and unsteady components. The analytical-numerical procedure involves several intnegrating schemes and applies to general frequencies of oscillations. The technique is illustrated by computing the transonic flow about parabolic arc airfoils. Specific unsteady results for reduced frequencies based on semi-chord of 0.01, 0.1, 0.3, 0.4 and 0.6 are given. Comparison of results with those obtained by an ADI finite difference scheme is made.

Lamah, C. A.↗

NASA NTRS1983

Numerical simulation of the leading-edge separation vortex for a wing and strake-wing configuration

In the present investigation, the 'thin layer' Navier-Stokes equations are used to compute the flow about a delta wing and a strake-delta wing configuration. Both configurations possess blunt noses and rounded leading edges. The computational grid about these configurations is generated using a newly developed three-dimensional grid-generation code which solves a set of Poisson equations with spherical coordinate variables using an alternating direction implicit (ADI) scheme. Computational results are obtained for an isolated wing with 60 deg sweep and a strake-wing configuration with 80-60 deg sweep. Computations for angles of attack in the range from 6 to 30 deg are presented. Attention is given to the effect of the angle of attack, the Mach number, and the Reynolds number. Theoretical results are compared with experimental data.

Fujii, K.↗