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NASA NTRS1981

Efficient computation of the stability of three-dimensional compressible boundary layers

Methods for the computer analysis of the stability of three-dimensional compressible boundary layers are discussed and the user-oriented Compressible Stability Analysis (COSAL) computer code is described. The COSAL code uses a matrix finite-difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, M. R.↗

NASA NTRS1982

Finite-difference solution of the compressible stability eigenvalue problem

A compressible stability analysis computer code is developed. The code uses a matrix finite difference method for local eigenvalue solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used initial value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed which may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black box stability code. Sample stability calculations are presented for the boundary layer profiles of a Laminar Flow Control (LFC) swept wing.

Malik, M. R.↗

NASA NTRS1983

The inner edge of Saturn's B ring

The sharp, 90-km wide transition from an optical depth of 0.2 in the C ring to 1 in the B ring begins at 91,970 km from Saturn's center. This radius is found to be almost exactly at the inward stability limit of charged particles launched in the ring plane at the local Kepler velocity, provided these particles have large charge to mass ratio. The zonal harmonic models of Saturn's magnetic field from the Voyager data and the gravitational field model from Pioneer data are essential to get the very close agreement between theory and observation. The theoretical stability limits are 91,973 + or - 145 km from Voyager 1 magnetic field data and 91,991 + or 145 km from Voyager 2 magnetic data. The zonal harmonic magnetic field lines are not perpendicular to the ring plane. Therefore, in addition to the magnetic mirror, gravitational, and centrifugal forces, an unknown force must be postulated to produce equilibrium in the ring plane and make the stability calculation meaningful.

Northrop, T. G.↗

NASA NTRS1985

Experiments on the stability of crossflow vortices in swept-wing flows

Experiments are conducted which demonstrate the feasibility of creating crossflow vortices in a flat-plate flow. A swept leading edge and contoured wind-tunnel walls produce a strong pressure gradient and a typical swept-wing flow on the plate. Detailed three-dimensional measurements, made within the boundary layer using hot-wire anemometry, are supplemented with different flow-visualization techniques. Data are presented on the mean flow characteristics as well as on the behavior of the crossflow vortices. Comparisons are made with theoretical flow-field and stability calculations.

Saric, W. S.↗

NASA NTRS1986

Applications of potential theory computations to transonic aeroelasticity

Unsteady aerodynamic and aeroelastic stability calculations based upon transonic small disturbance (TSD) potential theory are presented. Results from the two-dimensional XTRAN2L code and the three-dimensional XTRAN3S code are compared with experiment to demonstrate the ability of TSD codes to treat transonic effects. The necessity of nonisentropic corrections to transonic potential theory is demonstrated. Dynamic computational effects resulting from the choice of grid and boundary conditions are illustrated. Unsteady airloads for a number of parameter variations including airfoil shape and thickness, Mach number, frequency, and amplitude are given. Finally, samples of transonic aeroelastic calculations are given. A key observation is the extent to which unsteady transonic airloads calculated by inviscid potential theory may be treated in a locally linear manner.

Edwards, J. W.↗

NASA NTRS1987

Some observations of a sheared Rayleigh-Taylor/Benard instability

An account is provided of preliminary flow visualization observations made in an unstably stratified flow with shear superimposed. The structures observed appear to be the superposition of a Rayleigh-Taylor/Benard instability and a Kelvin-Helmholtz instability. Aside from its intrinsic fundamental value, the study of these structures is of special interest to theoreticians developing nonlinear stability calculation methodologies.

Humphrey, J. A. C.↗

NASA NTRS1987

Linear stability analysis of three-dimensional compressible boundary layers

A compressible stability analysis computer code is developed. The code uses a matrix finite-difference method for local eigenvale solution when a good guess for the eigenvalue is available and is significantly more computationally efficient than the commonly used inital-value approach. The local eigenvalue search procedure also results in eigenfunctions and, at little extra work, group velocities. A globally convergent eigenvalue procedure is also developed that may be used when no guess for the eigenvalue is available. The global problem is formulated in such a way that no unstable spurious modes appear so that the method is suitable for use in a black-box stability code. Sample stability calculations are presented for the boundary layer profiles of an LFC swept wing.

Malik, Mujeeb R.↗

NASA NTRS1988

Unsteady Flow In A Supersonic Cascade With Shocks

Operating range of turbomachinery for which stability calculated extended. TIPS (Two In-Passage Shocks) calculates unsteady lifts and moments on compressor blade if relative mach number supersonic and if two shock waves in blade passage. Written in FORTRAN IV and run on IBM 3033 with 370TSS operating system.

Molls, Frank B.↗

NASA NTRS1986

Variable Sweep Transition Flight Experiment (VSTFE)-Parametric Pressure Distribution Boundary Layer Stability Study and Wing Glove Design Task

The Variable Sweep Transition Flight Experiment (VSTFE) was initiated to establish a boundary-layer transition data base for laminar flow wing design. For this experiment, full-span upper-surface gloves will be fitted to a variable sweep F-14 aircraft. The results of two initial tasks are documented: a parametric pressure distribution/boundary-layer stability study and the design of an upper-surface glove for Mach 0.8. The first task was conducted to provide a data base from which wing-glove pressure distributions could be selected for glove designs. Boundary-layer stability analyses were conducted on a set of pressure distributions for various wing sweep angles, Mach numbers, and Reynolds number in the range of those anticipated for the flight-test program. The design procedure for the Mach 0.8 glove is described, and boundary-layer stability calculations and pressure distributions are presented both at design and off-design conditions. Also included is the analysis of the clean-up glove (smoothed basic wing) that will be flight-tested initially and the analysis of a Mach 0.7 glove designed at the NASA Langley Research Center.

Rozendaal, Rodger A.↗

NASA NTRS1987

Boundary-layer instability mechanisms on a swept-leading edge at Mach 3.5

Correlations have been made in NASA Langley's Mach 3.5 Pilot Quiet Tunnel for the transitions occurring from laminar to turbulent flow, in the cases of 45-deg and 60-deg swept cylinders. While freestream noise variations had no effect on boundary layer transition, the addition of boundary layer trips to the leading edges led to transition at lower Re numbers, depending on both trip height and wind tunnel noise level. Also presented are the results of compressible linear stability calculations for the boundary layer of an infinite swept cylinder; Tollmien-Schlichting waves are found to be amplified in the attachment line boundary layer.

Creel, T. R., Jr.↗

NASA NTRS1988

Boundary-layer control for drag reduction

Although the number of possible applications of boundary-layer control is large, a discussion is given only of those that have received the most attention recently at NASA Langley Research Center to improve airfoil drag characteristics. This research concerns stabilizing the laminar boundary layer through geometric shaping (natural laminar flow, NLF) and active control involving the removal of a portion of the laminar boundary layer (laminar flow control, LFC) either through discrete slots or a perforated surface. At low Reynolds numbers, a combination of shaping and forced transition has been used to achieve the desired run of laminar flow and control of laminar separation. In the design of both natural laminar flow and laminar flow control airfoils and wings, boundary layer stability codes play an important role. A discussion of some recent stability calculations using both incompressible and compressible codes is given.

Harvey, William D.↗

NASA NTRS1989

Elimination of spurious eigenvalues in the Chebyshev tau spectral method

Spectral methods have been used to great advantage in hydrodynamic stability calculations; the concepts are described in Orszag's seminal application of the Chebyshev tau method to the Orr-Sommerfeld equation for plane Poiseuille flow in 1971. Orszag discusses both the Chebyshev Galerkin and the Chebyshev tau methods, but presents results for the tau method, which is easier to implement than the Galerkin method. The tau method has the disadvantage that two unstable eigenvalues are produced that are artifacts of the discretization. An extremely simple modification to the Chebyshev tau method is presented which eliminates the spurious eigenvalues. First a simplified model of the Orr-Sommerfeld equation discussed by Gottlieb and Orszag was studied. Then the Chebyshev tau method is considered, which has two spurious eigenvalues, and then a modification which eliminates them is described. Finally, results for the Orr-Sommerfeld equation are considered where the modified tau method also eliminates the spurious eigenvalues. The simplicity of the modification makes it a convenient alternative to other approaches to the problem.

Mcfadden, G. B.↗

NASA NTRS1990

Transition in high-speed free shear layers

The laminar free-shear layers considered in the study are formed by combinations of the velocities and momentum thicknesses of two adjacent parallel flows. Transition in wakes, pure free-shear layers of the Chapman type, and separate and partition flows are discussed. A stability-transition connection is emphasized, and it is suggested that a recurring deficiency in some stability calculations is the use of overly simplified laminar profiles. It is also noted that physical principles can be used for estimating the transition location or providing the factors affecting it. One such approach, a threshold theory, is discussed by way of example.

Demetriades, A.↗

NASA NTRS1991

Numerical simulations of the nonlinear kink modes in linearly stable supersonic slip surfaces

High-resolution numerical simulations of supersonic slip surfaces were performed using the Cray 2 at the Minnesota Supercomputer Center to confirm earlier analytic nonlinear stability calculations of such structures. The present study presents a numerical solution for the problem solved analytically by Artola and Majda (1987) and follows growing modes well into the large-amplitude regime. The response of an equal-density Mach-4 slip surface to a variety of impinging nonlinear sound wave trains is computed using the piecewise-parabolic method (PPM). The nature of the nonlinear kink modes observed in the simulations was found to be similar to that discussed by Artola and Majda. Most of the speeds moved in either direction, with speeds near the predicted value. It is suggested that the stationary modes will eventually dominate the flow at much later times, and it is argued that the stationary modes are more disruptive than the propagating kink modes.

Pedelty, Jeffrey A.↗

NASA NTRS1992

Design of a hybrid laminar flow control nacelle

Consideration is given to the potential application of hybrid-laminar-flow control to the external surface of a modern, high-bypass-ratio (HBR) turbofan engine nacelle. With the advent of advanced ultra-HBR fans (with bypass ratios of 10-15), the wetted areas of these nacelles approach 10 percent of the total wetted area of future commercial transports. A hybrid-laminar-flow-control pressure distribution is specified and the corresponding nacelle geometry is computed utilizing a predictor/corrector design method. Linear stability calculations are conducted to provide predictions of the extent of the laminar boundary layer. Performance studies on an advanced twin-engine transport configuration are presented to determine potential benefits in terms of reduced fuel consumption.

Wie, Yong-Sun↗

NASA NTRS1991

Application of laminar flow control to high-bypass-ratio turbofan engine nacelles

Recently, the concept of the application of hybrid laminar flow to modern commercial transport aircraft was successfully flight tested on a Boeing 757 aircraft. In this limited demonstration, in which only part of the upper surface of the swept wing was designed for the attainment of laminar flow, significant local drag reduction was measured. This paper addresses the potential application of this technology to laminarize the external surface of large, modern turbofan engine nacelles which may comprise as much as 5-10 percent of the total wetted area of future commercial transports. A hybrid-laminar-flow-control (HLFC) pressure distribution is specified and the corresponding nacelle geometry is computed utilizing a predictor/corrector design method. Linear stability calculations are conducted to provide predictions of the extent of the laminar boundary layer. Performance studies are presented to determine potential benefits in terms of reduced fuel consumption.

Wie, Y. S.↗

NASA NTRS1992

The linear stability of a flat plate boundary-layer approaching a cylindrical obstacle

The linear stability of the low-speed three-dimensional flow over a flat plate with an attached cylinder is studied. The region of interest is upstream of the initial separation point and includes the effects of both adverse and favorable pressure gradients, as well as crossflow. The resulting boundary-layer is subject to both the Tollmien-Schlichting (TS) and crossflow instabilities. Linear stability calculations, using N-factor correlations, indicate that the transition process would be dominated by TS instabilities, although for low frequencies crossflow-type disturbances are important.

Spall, R. E.↗

NASA NTRS1993

Multigrid time-accurate integration of Navier-Stokes equations

Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.

Arnone, Andrea↗