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At least 217 records · Page 12
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NASA NTRS1977

Computation of viscous transonic flow about a lifting airfoil

The Reynolds averaged Navier-Stokes equations are solved numerically for the viscous transonic flow about a stationary NACA 64A010 airfoil in free air. This paper presents descriptions of the numerical method, turbulence models employed, and boundary conditions appropriate to simulation of free-air flight. Computed results are presented for the airfoil at a free-stream Mach number of 0.8, angles of attack of 0 and 2 deg, and a Reynolds number based on a chord of 4 x 10 to the 6th. For the lifting case, unsteady periodic motion was calculated along the aft portion of the airfoil and in its wake. Recent experimental results obtained by Johnson indicate periodicity aft of the shock closely approximates the computed frequency, but the amplitude of the disturbances was significantly less than the calculated amplitude.

Walitt, L.↗
NASA NTRS1982

Experiences in using the CYBER 203 for three-dimensional transonic flow calculations

In this paper, the authors report on some of their experiences modifying two three-dimensional transonic flow programs (FLO22 and FLO27) for use on the NASA Langley Research Center CYBER 203. Both of the programs discussed were originally written for use on serial machines. Several methods were attempted to optimize the execution of the two programs on the vector machine, including: (1) leaving the program in a scalar form (i.e., serial computation) with compiler software used to optimize and vectorize the program, (2) vectorizing parts of the existing algorithm in the program, and (3) incorporating a new vectorizable algorithm (ZEBRA I or ZEBRA II) in the program.

Melson, N. D.↗
NASA NTRS1983

Interactions of airfoils with gusts and concentrated vortices in unsteady transonic flow

Unsteady interactions of concentrated vortices and distributed free-stream gusts with a stationary airfoil have been analyzed in two-dimensional transonic flow. A simple method of introducing such disturbances has been implemented numerically in the well-known transonic small-disturbance code LTRAN2, and calculations have been performed for two important classes of current aerodynamic problems. The first, which demonstrates many of the essential features of the interactions between helicopter rotor blades and their trailing-vortex wakes, is that of a discrete potential vortex convecting past an airfoil. The second is the response of a transonic airfoil to a transverse periodic gust, with and without the alleviation that can be achieved by the proper active control motion of a trailing-edge flap. In both cases, unsteady effects are found to play important roles in the shock-wave motion, in the overall flow-field development, and consequently, in the air loads on the airfoil.

Mccroskey, W. J.↗
NASA NTRS1977

Investigations related to the inviscid-viscous interaction in transonic flows about finite 3-D wings

Inviscid small-disturbance theory has been shown to predict three-dimensional transonic flows about finite wings reasonably well as long as viscous effects are negligible. In order to include these effects, the inviscid small-disturbance solution of Bailey and Ballhaus (1975) has been combined with a finite-difference solution for Prandtl's boundary-layer equations. This solution employs the conditionally stable Krause (1968) scheme, implicit in the direction normal to the wall, to cope with the domain-of-dependence problem that arises for reverse cross flow. To be consistent with the inviscid-flow solution, the boundary layer is computed in the representative wing planform plane which is transformed into rectangular shape in the computational domain. The flow has been assumed turbulent, and a scalar eddy-viscosity model is adopted. The interaction between inviscid and viscous flow is modeled with the help of the displacement surface which is added to the geometric wing shape. Sample distributions of displacement thickness for swept wings are presented for weak and strong interaction cases.

Kordulla, W.↗
NASA NTRS1978

Numerical study of transonic flow over oscillating airfoils using the full potential equation

The behavior of unsteady aerodynamic loadings on airfoils oscillating in transonic flow has been investigated numerically with particular attention given to supercritical airfoil sections. A previously developed finite difference method, which is based on the full potential equation and which uses a quasi-conservative scheme for proper capture of a shock wave motion, was employed for the present study. The unsteady aerodynamic pressure and load distributions on several different airfoil sections are presented with particular emphasis on the effects of free-stream Mach number, reduced frequency, and mean angle of attack. These parameters are demonstrated to have a significant effect on the behavior of the unsteady aerodynamic loadings. Comparisons of the present calculations with the exact inviscid solution and with the experimental results are also presented.

Isogai, K.↗
NASA NTRS1978

Numerical computation of transonic flows by finite-element and finite-difference methods

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

Hafez, M. M.↗
NASA NTRS1978

Transonic flow over the NACA 64A006 with an oscillating flap-calculations based on the Euler equations

Exploratory calculations of transonic flows over the airfoil with a quarter-chord oscillating flap were made using a program which obtains approximate solutions to the Euler equations with an explicit, shock-capturing, finite-difference scheme. The calculations, essentially inviscid and for the airfoil at zero angle-of-attack in a free-stream, are at Mach numbers and reduced frequencies which were tested in experiments by Tijdeman. The oscillatory lifts from analogus calculations by various investigators generally agree with one another better than they agree with Tijdeman's data. Inclusion in the calculations of an approximate modelling of boundary conditions expected at slotted wind tunnel walls tends to shift some of the results closer to the experimental values.

Magnus, R. J.↗
NASA NTRS1993

Navier-Stokes simulation of external/internal transonic flow on the forebody/inlet of the AV-8B Harrier II

In this work, the computation of combined external/internal transonic flow on the complex forebody/inlet configuration of the AV-8B Harrier II is performed. The actual aircraft has been measured and its surface and surrounding domain, in which the fuselage and inlet have a common wall, have been described using structured grids. The 'thin-layer' Navier-Stokes equations were used to model the flow along with the Chimera embedded multi-block technique. A fully conservative, alternating direction implicit (ADI), approximately factored, partially fluxsplit algorithm was employed to perform the computation. Comparisons to some experimental wind tunnel data yielded good agreement for flow at zero incidence and angle of attack. The aim of this paper is to provide a methodology or computational tool for the numerical solution of complex external/internal flows.

Mysko, Stephen J.↗
NASA NTRS1980

Implicit computations of unsteady transonic flow governed by the full-potential equation in conservation form

An alternating-direction implicit algorithm is presented for solving the conservative, full-potential equation for unsteady, transonic flow. A new development is the time-linearization of the density function. This linearization reduces the solution process from one of solving a system of two equations at each mesh point to one of solving a single equation. Two sample cases are computed. First, a one-dimensional traveling shock wave is computed and compared with the analytic solution. Second, a two-dimensional case is computed of a flow field that results from a thickening and subsequently thinning airfoil. The resulting flow field, which includes a traveling shock wave, is compared to the flow field obtained from the low-frequency, small-disturbance, transonic equation.

Goorjian, P. M.↗
NASA NTRS1975

Inviscid transonic flow computations with shock fitting

First-and second-order numerical procedures are presented for calculating two-dimensional transonic flows that treat shock waves as discontinuities. Their application to a simple but nontrivial problem for which there are limited theoretical results is discussed.

Yu, N. J.↗
NASA NTRS1977

A simplified theory of oscillating airfoils in transonic flow - Review and extension

Significant old and new results are presented to show to what extent a simplified theory for transonic flow may be used. Solutions are obtained by classical techniques and compared with experiment. Results are given for two-dimensional, steady and unsteady flow and three-dimensional, steady flow. The effects of flow separation and improvements in Bernoulli's equations and the surface boundary condition are also briefly discussed.

Dowell, E. H.↗
NASA NTRS1982

Rotor tip clearance effects on overall and blade-element performance of axial-flow transonic fan stage

The effects of tip clearance on the overall and blade-element performance of an axial-flow transonic fan stage are presented. The 50-centimeter-diameter fan was tested at four tip clearances (nonrotating) from 0.061 to 0.178 centimeter. The calculated radial growth of the blades was 0.040 centimeter at design conditions. The decrease in overall stage performance with increasing clearance is attributed to the loss in rotor performance. For the rotor the effects of clearance on performance parameters extended to about 70 percent of blade span from the tip. The stage still margin based on an assumed operating line decreased from 15.3 to 0 percent as the clearance increased from 0.061 to 0.178 centimeter.

Moore, R. D.↗
NASA NTRS1981

Calculation of Unsteady Transonic Flow over an Airfoil

An implicit finite-difference solver for either the Euler equations or the "thin-layer" Navier-Stokes equations was used to calculate a transonic flow over the NACA 64A010 airfoil pitching about its one-quarter chord. An unsteady automatic grid-generation procedure that will improve significantly the computational efficiency of various unsteady flow problems is described. The calculated results for both inviscid and viscous flows at Much number 0.8 over the airfoil oscillating with reduced frequency referenced to one-half chord, 0.2, are compared with experimental data measured in the Ames 11 x 11-ft Transonic Wind Tunnel. Nonlinear, unsteady effects of the flow on the surface pressure variations, shock-wave excursions, and overall airloads are examined. Good agreements between the results of computations and experiments were obtained. In the shock-wave region, however, the results of the viscous-flow computations showed closer agreement with the experimental data.

Chyu, W. J.↗
NASA NTRS1981

Calculation of Unsteady Transonic Flow Over an Airfoil

An implicit finite-difference solver for either the Euler equations or the "thin-layer" Navier-Stokes equations was used to calculate a transonic flow over the NACA 64A010 airfoil pitching about its one-quarter chord. An unsteady automatic grid-generation procedure that will improve significantly the computational efficiency of various unsteady flow problems is described. The calculated results for both inviscid and viscous flows at Mach number 0.8 over the airfoil oscillating with reduced frequency referenced to one-half chord, 0.2, are compared with experimental data measured in the Ames 11 x 11 ft Transonic Wind Tunnel. Nonlinear, unsteady effects of the flow on the surface pressure variations, shock-wave excursions, and overall airloads are examined. Good agreements between the results of computations and experiments were obtained. In the shock-wave region, however, the results of the viscous-flow computations showed closer agreement with the experimental data.

Chyu, W. J.↗
NASA NTRS1972

Computation of transonic flow about finite lifting wings.

The results of Murman and Krupp (1971) are used to develop a procedure for computing a transonic flow about a finite lifting wing. A small disturbance equation describing the velocity potential of three-dimensional wings is solved in the process. The procedure is applied to a wing with a symmetric biconvex airfoil section in a zero-incidence subsonic flow, to a supersonic rectangular lifting wing with a sharp leading edge and to a subcritical nonlifting rectangular wing with a blunt leading edge.

Newman, P. A.↗
NASA NTRS1977

Unsteady linearized transonic flow analysis for slender bodies

An unsteady linearized formulation based on Oswatitsch-Keune's parabolic method is developed to analyze transonic flow past oscillating slender bodies. In contrast to the widely used integral transform method, it is shown that all solutions can be derived by a simpler method directly in the physical plane. By various expansion procedures, low-frequency solutions then are derived according to two clearly defined frequency ranges. Adams-Sears' iteration is employed to account for the second-order effects. Stability derivatives are compared with available theories and data. It is found that the derivatives depend more sensitively on thickness than on the reduced frequency. Finally, a critical assessment of the present method is given.

Liu, D. D.↗
NASA NTRS1981

Finite element analysis of transonic flows in highly staggered cascades

Finite element method is employed in the solution of full-potential equation for analyzing steady, transonic flows through a series of highly staggered cascades. Convergence characteristics and efficiency of the developed numerical procedure are discussed. Accuracy of the mathematical model is investigated in terms of the employed computational grid. In particular, the importance of accurate representation of the trailing edge together with the shock on the obtained flow results are studied. Numerical results include choked flows, for a cascade of NACA 0012 airfoils with pitch/chord length = 1, and stagger angle of 45 deg.

Akay, H. U.↗
NASA NTRS1979

Implicit finite-difference simulations of steady and unsteady transonic flows

Implicit methods for several fluid dynamic formulations have been developed and applied to steady-state and low-frequency transonic flows. The basic steps involved in the construction of implicit schemes include: selection of linearly stable accurate implicit difference operators, time-linearization of nonlinear terms, and approximate factorization of the implicit operators into easily solved systems of equations. The proposed schemes are found very efficient for the simpler formulations.

Ballhaus, W. F.↗