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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

On the role of secondary instabilities in laminar-turbulent transition of 2D and 3D boundary layers

The accurate prediction of laminar/turbulent transition is one of the fundamental problems in engineering fluid mechanics. There is almost unanimous consent that such a transition criterion should come from stability theory. Linear primary stability theory describes the initial stage of transition, but falls short of predicting transition. Only in conjunction with empirical correlations, the widely used e(sup n) method is obtained, which, however, lacks a solid physical base. Three-dimensional secondary instabilities are known to play an important role in the transition process. However, no use has been made so far of secondary instabilities, instability interactions or wave resonances to define a 'transition location'. The paper summarizes new attempts to identify certain interaction and resonance phenomena within the laminar-turbulent transition regime in two and three-dimensional boundary layers which are associated with rapid structural and temporal changes of fluctuations beyond their exponential growths.

Dallman, Uwe↗
NASA NTRS1987

Boundary-layer receptivity and laminar-flow airfoil design

Boundary-layer receptivity examines the way in which external disturbances generate instability waves in boundary layers. Receptivity theory is complementary to stability theory, which studies the evolution of disturbances that are already present in the boundary layer. A transition prediction method which combines receptivity with linear stability theory would directly account for the influence of free-stream disturbances and also consider the characteristics of the boundary layer upstream of the neutral stability point. The current e sup N transition prediction methods require empirical correlations for the influence of environmental disturbances, and totally ignore the boundary layer characteristics upstream of the neutral stability point. The regions where boundary-layer receptivity occurs can be separated into two classes, one near the leading edges and the other at the downstream points where the boundary layer undergoes rapid streamwise adjustments. Analyses were developed for both types of regions, and parametric studies which examine the relative importance of different mechanisms were carried out. The work presented here has focused on the low Mach number case. Extensions to high subsonic and supersonic conditions are presently underway.

Kerschen, Edward J.↗
NASA NTRS1977

Transition and laminar instability

The linear stability theory was applied to the problem of boundary layer transition in incompressible flow. The theory was put into a form suitable for three-dimensional boundary layers; both the temporal and spatial theories were examined; and a generalized Gaster relation for three-dimensional boundary layers was derived. Numerical examples include the stability characteristics of Falkner-Skan boundary layers, the accuracy of the two-dimensional Gaster relation for these boundary layers, and the magnitude and direction of the group velocity for oblique waves in the Blasius boundary layer. Available experiments which bear on the validity of stability theory and its relation to transition are reviewed and the stability theory is applied to transition prediction. The amplitude method is described in which the wide band disturbance amplitude in the boundary layer is estimated from stability theory and an interaction relation for the initial amplitude density of the most unstable frequency.

Mack, L. M.↗
NASA NTRS1999

Development of a Three-Dimensional PSE Code for Compressible Flows: Stability of Three-Dimensional Compressible Boundary Layers

A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.

Balakumar, P.↗
NASA NTRS1994

A spectrally accurate boundary-layer code for infinite swept wings

This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

Pruett, C. David↗
NASA NTRS2008

Control Laws for a Dual-Spin Stabilized Platform

This paper describes two attitude control laws suitable for atmospheric flight vehicles with a steady angular momentum bias in the vehicle yaw axis. This bias is assumed to be provided by an internal flywheel, and is introduced to enhance roll and pitch stiffness. The first control law is based on Lyapunov stability theory, and stability proofs are given. The second control law, which assumes that the angular momentum bias is large, is based on a classical PID control. It is shown that the large yaw-axis bias requires that the PI feedback component on the roll and pitch angle errors be cross-fed. Both control laws are applied to a vehicle simulation in the presence of disturbances for several values of yaw-axis angular momentum bias. It is seen that both control laws provide a significant improvement in attitude performance when the bias is sufficiently large, but the nonlinear control law is also able to provide improved performance for a small value of bias. This is important because the smaller bias corresponds to a smaller requirement for mass to be dedicated to the flywheel.

Lim, K. B.↗
NASA NTRS1986

Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers

An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.

Berry, S. A.↗
NASA NTRS1995

Linear Wave Motion from Concentrated Harmonic Sources in Blasius Flow

The motion of individual linear instability waves in shear flows is well described by existing theoretical and numerical methods. However, naturally occuring sources produce coherent wave motions with broadband spanwise wavenumber and frequency spectra, and the different spectral components interact both linearly and nonlinearily. This paper describes a series of calculations for the parameters of three different experiments using locally parallel linear stability theory (LST), the Parabolized Stability Equations (PSE), and Direct Numerical Simulation (DNS). The calculations illustrate the strengths and weaknesses of the different methods, the extent to which the methods agree or disagree, and, finally the extent to which agreement with the measurements can be attained, given that the experiments also have their own difficulties.

linear↗
NASA NTRSDate not supplied

Exploring data-driven modeling of boundary layer transition

Prediction of laminar-turbulent transition in boundary layer flows is an important component of predicting the aerodynamic performance of a number of aerospace configurations. According to the CFD Vision 2030 [1], transition modeling represents acriticalarea in CFD simulation capability that will remain a pacing item for the foreseeable future. The fact thattransition can take placevia either one of a myriad possible paths adds to the challenges inreliable transition predictions, despite a limited knowledge of the relevant input parameters. In the low disturbance environments typical of flight applications, transition is often initiated by small amplitude disturbances in the form of linear instability waves of the laminar boundary layer. These disturbances amplify linearly at first and eventually undergo a sequence of nonlinear interactions that result in transition to turbulence. Because the nonlinear phase is rather rapid, the amplification of boundary layer instabilities is governed by the linearstability theory over a majority of the distance leading up to the onset of transition. Semi-empirical transition correlations based on the linear stability theory have been successful in explaining the observed trends in transition location within a broad class of flows. However, the application of stability theory is highly non-robust and often requires a significant domain expertise. Recent work at the NASA Langley Research Center has beenaimed at bridging the gap between physics based transition analyses such as those based on linear stability theory and practical applications that require transition prediction by users that may not be well versed in transition physics. The applications of deep learning have been at the center of these efforts. This presentation will focus on the progress achieved thus far, highlighting the applications of neural networks to selectedtransition scenarios across a range of Mach numbers and flow configuration, as well as the lessons learnedand remaining challengeswithrespect to the selection of training data and neural networks architectures, hyperparameter tuning, and the physical insights distilled from the otherwise black-box models.

M. R. Malik↗
NASA NTRS1979

On the stability of the boundary layer on a transonic swept wing

Both incompressible and compressible linear stability theory are applied to the three-dimensional compressible boundary layer on a particular transonic sweptback wing of infinite span. A spatial stability theory is used which identifies the growth direction with the real part of the complex angle of the group velocity. It is found that in the forward, but not the rear, crossflow instability region, the maximum amplification rates of the steady disturbances may be calculated to within about 10% by the incompressible stability theory. There is little difference between the sixth and eighth-order compressible theories. The maximum amplification rate of the steady disturbances at any chordwise station is closely related to the maximum crossflow at that station independent of the Reynolds number. For other than crossflow instability, there can be large differences between the incompressible and compressible theories, both as to the amplification rate and the angle of the wavenumber vector for maximum instability. Amplitude ratios of individual wave components are obtained by integrating the spatial amplification rate along the growth direction subject to the constraint that the wavenumber vector is irrotational. This procedure yields steady disturbances aligned with the local potential flow direction whose wavelengths are nearly independent of downstream distance.

Mack, L. M.↗
NASA NTRS1956

A Theory for Stability and Buzz Pulsation Amplitude in Ram Jets and an Experimental Investigation Including Scale Effects

From a theory developed on a quasi-one-dimensional-flow basis, it is found that the stability of the ram jet is dependent upon the instantaneous values of mass flow and total pressure recovery of the supersonic diffuser and immediate neighboring subsonic diffuser. Conditions for stable and unstable flow are presented. The theory developed in the report is in agreement with the experimental data of NACA-TN-3506 and NACA-RM-L50K30. A simple theory for predicting the approximate amplitude of small pressure pulsation in terms of mass-flow decrement from minimum-stable mass flow is developed and found to agree with experiments. Cold-flow tests at a Mach number of 1.94 of ram-jet models having scale factors of 3.15:1 and Reynolds number ratios of 4.75:1 with several supersonic diffuser configurations showed only small variations in performance between geometrically similar models. The predominant variation in steady-flow performance resulted from the larger boundary layer in the combustion chamber of the low Reynolds number models. The conditions at which buzz originated were nearly the same for the same supersonic diffuser (cowling-position angle) configurations in both large and small diameter models. There was no appreciable variation in stability limits of any of the models when the combustion-chamber length was increased by a factor of three. The unsteady-flow performance and wave patterns were also similar when considered on a reduced-frequency basis determined from the relative lengths of the model. The negligible effect of Reynolds number on stability of the off-design configurations was not anticipated in view of the importance of boundary layer to stability, and this result should not be construed to be generally applicable. (author)

Trimpi, Robert L↗
NASA NTRS1975

A numerical method for the prediction of high-speed boundary-layer transition using linear theory

A method is described of estimating the location of transition in an arbitrary laminar boundary layer on the basis of linear stability theory. After an examination of experimental evidence for the relation between linear stability theory and transition, a discussion is given of the three essential elements of a transition calculation: (1) the interaction of the external disturbances with the boundary layer; (2) the growth of the disturbances in the boundary layer; and (3) a transition criterion. The computer program which carried out these three calculations is described. The program is first tested by calculating the effect of free-stream turbulence on the transition of the Blasius boundary layer, and is then applied to the problem of transition in a supersonic wind tunnel. The effects of unit Reynolds number and Mach number on the transition of an insulated flat-plate boundary layer are calculated on the basis of experimental data on the intensity and spectrum of free-stream disturbances. Reasonable agreement with experiment is obtained in the Mach number range from 2 to 4.5.

Mack, L. M.↗
NASA NTRS1978

Relationships between digital signal processing and control and estimation theory

Research directions in the fields of digital signal processing and modern control and estimation theory are discussed. Stability theory, linear prediction and parameter identification, system synthesis and implementation, two-dimensional filtering, decentralized control and estimation, and image processing are considered in order to uncover some of the basic similarities and differences in the goals, techniques, and philosophy of the disciplines.

Willsky, A. S.↗
NASA NTRS1979

Algebraic methods for the solution of some linear matrix equations

The characterization of polynomials whose zeros lie in certain algebraic domains (and the unification of the ideas of Hermite and Lyapunov) is the basis for developing finite algorithms for the solution of linear matrix equations. Particular attention is given to equations PA + A'P = Q (the Lyapunov equation) and P - A'PA = Q the (discrete Lyapunov equation). The Lyapunov equation appears in several areas of control theory such as stability theory, optimal control (evaluation of quadratic integrals), stochastic control (evaluation of covariance matrices) and in the solution of the algebraic Riccati equation using Newton's method.

Djaferis, T. E.↗
NASA NTRS1983

Experimental and analytical studies of a true airspeed sensor

A true airspeed sensor based on the precession of a vortex whistle for sensing airspeeds up to 321.9 km/hr (200 mph). In an attempt to model the complicated fluid mechanics of the vortex precession, three dimensional, inviscid, unsteady, incompressible fluid flow was studied by using the hydrodynamical linearized stability theory. The temporal stability approach was used to derive the relationship between the true airspeed and frequency response. The results show that the frequency response is linearly proportional to the airspeed. A computer program was developed to obtain the numerical solution. Computational results for various parameters were obtained. The designed sensor basically consisted of a vortex tube, a swirler, and a transducer system. A microphone converted the audible tone to an electronic frequency signal. Measurements for both the closed conduit tests and wind tunnel tests were recorded. For a specific flow rate or airspeed, larger exit swirler angles produced higher frequencies. For a smaller cross sectional area in the precessional flow region, the frequency was higher. It was observed that as the airspeed was increased the Strouhal number remained constant.

Goglia, G. L.↗
NASA NTRS1992

Dynamics and control of coherent structure in turbulent jets

Current understanding of coherent structure dynamics in incompressible turbulent jets as explained by the nonlinear stability theory is reviewed, focusing on nonswirling turbulent jets. Topics addressed include hydrodynamic stability theory and coherent structures; dynamics of energy transfers among different scales of motion; nonlinear development of amplitude; development of single-frequency coherent mode; fundamental-subharmonic interaction and vortex pairing; and reversal of Reynolds stresses. Attention is also given to the effect of initial phase-difference angle between fundamental and subharmonic, conditions for resonance interaction, modulation of spreading rate by controlling coherent structure, turbulence enhancement or suppression due to excitation, 3D effects, jet noise, and swirling jets.

Mankbadi, Reda R.↗