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At least 433 records · Page 24

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NASA NTRS1981

Study of the development of natural instabilities in a laminar boundary layer in incompressible flow

Natural instabilities which are created in a laminar boundary layer and which consist of intermittent wave trains were studied. The spectral analysis of these fluctuations makes it possible to localize them in terms of frequency and to isolate their spectrum of amplitude modulation. The variation in terms of abscissa value and ordinate value of these instabilities is compared with the results derived from the solution of the Orr-Sommerfeld equation.

Burnel, S.↗

NASA NTRS1981

Instability and transition in rotating disk flow

The stability of three-dimensional rotating disk flow is investigated, including the effects of Coriolis forces and streamline curvature. The numerical results show that the critical Reynolds number for establishment of stationary vortex flow is 287. These vortices spiral outward at an angle of about 11.2 deg, and transition to turbulence occurs when their total amplification is about e to the 11th. New experimental results are also reported on the spatial growth rates of the stationary vortices. It is shown that the analysis gives growth rates that compare much better with the experimental results than do results obtained using the Orr-Sommerfeld equation. The experimental results tend to support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number. The calculations also indicate the existence of weakly unstable propagating (type II) modes at low Reynolds numbers (Critical Reynolds Number being approximately equal to 49).

Malik, M. R.↗

NASA NTRS1981

Amplified crossflow disturbances in the laminar boundary layer on swept wings with suction

Solution charts of the Orr-Sommerfeld equation for stationary crossflow disturbances are presented for 10 typical velocity profiles on a swept laminar flow control wing. The critical crossflow Reynolds number is shown to be a function of a boundary layer shape factor. Amplification rates for crossflow disturbances are shown to be proportional to the maximum crossflow velocity. A computer stability program called MARIA, employing the amplification rate data for the 10 crossflow velocity profiles, is constructed. This code is shown to adequately approximate more involved computer stability codes using less than two percent as much computer time while retaining the essential physical disturbance growth model.

Dagenhart, J. R.↗

NASA NTRS1982

Laminar flow transition: A large-eddy simulation approach

A vectorized, semi-implicit code was developed for the solution of the time-dependent, three dimensional equations of motion in plane Poiseuille flow by the large-eddy simulation technique. The code is tested by comparing results with those obtained from the solutions of the Orr-Sommerfeld equation. Comparisons indicate that finite-differences employed along the cross-stream direction act as an implicit filter. This removes the necessity of explicit filtering along this direction (where a nonhomogeneous mesh is used) for the simulation of laminar flow transition into turbulence in which small scale turbulence will be accounted for by a subgrid scale turbulence model.

Biringen, S.↗

NASA NTRS1983

Viscous, resistive MHD stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗

NASA NTRS1981

On the OLP prediction of the unstable modes of the flat plate turbulent boundary layer

The Orr et al. (OLP) stability analysis is reformulated to yield profiles from hot-wire velocity covariance data in the boundary layer of a flow over a flat plate. The proper orthogonal decomposition theorem (PODT) is used to maximize the mean square of the inner product of the velocity vector with a deterministic candidate vector function in Hilbert space. The OLP formulation couples the PODT for the eddy viscosity with a global extremum principle for the disturbance kinetic energy. Derivation of the governing equations is described analytically, as are the extraction of the mean velocity profile and the eddy viscosity. Finally, techniques for characterizing the dominant mode of the velocity field are introduced and applied to three-dimensional flow over a flat plate. Good agreement is found between the predictions, using laboratory data, and the measured energy and three-dimensional structures of the dominant eddies.

Wadia, A. R.↗

NASA NTRS1984

Applications of spectral methods to turbulent magnetofluids in space and fusion research

Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas.

Montgomery, D.↗

NASA NTRS1984

Numerical simulation of boundary-layer transition

The transition to turbulence in boundary layers was investigated by direct numerical solution of the nonlinear, three-dimensional, incompressible Navier-Stokes equations in the half-infinite domain over a flat plate. Periodicity was imposed in the streamwise and spanwise directions. A body force was applied to approximate the effect of a nonparallel mean flow. The numerical method was spectra, based on Fourier series and Jacobi polynomials, and used divergence-free basis functions. Extremely rapid convergence was obtained when solving the linear Orr-Sommerfeld equation. The early nonlinear and three-dimensional stages of transition, in a boundary layer disturbed by a vibrating ribbon, were successfully simulated. Excellent qualitative agreement was observed with either experiments or weakly nonlinear theories. In particular, the breakdown pattern was staggered or nonstaggered depending on the disturbance amplitude.

Spalart, P. R.↗

NASA NTRS1983

Viscous, resistive magnetohydrodynamic stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one-dimensional magnetohydrodynamic quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds-like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds-like numbers. Marginal stability curves, growth rates versus Reynolds-like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result that appears general is that instability has been found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three-dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗

NASA NTRS1984

On the stability of the decelerating laminar boundary layer

The stability of a decelerating boundary-layer flow is investigated experimentally and numerically. Experimentally, a flat plate having a Blasius boundary layer is decelerated in an 18 m towing tank. The boundary layer becomes unstable to two-dimensional waves, which break down into three-dimensional patterns, hairpin vortices, and finally turbulent bursts when the vortices lift off the wall. The unsteady boundary-layer equations are solved numerically to generate instantaneous velocity profiles for a range of boundary and initial conditions. A quasi-steady approximation is invoked and the stability of local velocity profiles is determined by solving the Orr-Sommerfeld equation using Chebyshev matrix methods. Comparisons are made between the numerical predictions and the experimentally observed instabilities.

Gad-El-hak, M.↗

NASA NTRS1984

Differential eigenvalue problems in which the parameter appears nonlinearly

Several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly. The equations are the result of the discretization of differential eigenvalue problems using a finite Chebyshev series. Two global methods are considered which determine the spectrum of eigenvalues without an initial estimate. A local iteration scheme with cubic convergence is presented. Calculations are performed for a model second order differential problem and the Orr-Sommerfeld problem for plane Poiseuille flow.

Bridges, T. J.↗

NASA NTRS1985

Hydrodynamic stability problem formulated by numerical solutions of the Navier-Stokes equations

The problem of hydrodynamic stability and the transition from laminar to turbulent flows are reformulated by seeking numerical solutions of the full, unapproximated Navier-Stokes equations. This method differs significantly from the well known Orr-Sommerfeld equation approach. The oncoming laminar flow is disturbed by forced, time dependent perturbations. The magnitudes of these perturbations are arbitrary. Then, the ensuing spatial and temporal development of the imposed perturbations on the basic flow is calculated by direct numerical solutions of the time dependent Navier-Stokes equations. One of the main advantages of this method is its ability to simulate nonlinear processes. As a specific application of this technique to SSME (Space Shuttle Main Engine) flow configurations, computer programs have been written for the two dimensional flow over a backward facing step. This numerical code will be tested for operational use as part of a continued research collaboration effort with the NASA/MSFC counterparts.

Hyun, J. M.↗

NASA NTRS1986

A study of over-reflection in viscous Poiseuille flow

It is shown that viscous Poiseuille flow sustains wave propagation in its center region for waves whose phase speed is less than the maximum flow speed. When, moreover, there are critical levels, there exists a range of phase speeds for which over-reflection occurs, and this range corresponds exactly to the range for which unstable eigenmodes exist. Consistent with the conjecture of Lindzen and Barker (1985), it is found that viscous boundary layers around the critical level and at the wall replace the exponential regions and wave sinks required for inviscid over-reflection. It is found that over-relection is confined to phase speeds for which these two boundary layers are in close proximity, rather than widely separated or substantially overlapping. Over-reflection is inevitably associated with a wave phase tilt opposite in direction to the shear at the critical level. All other cases yield a phase tilt in the direction of the shear. The former is consistent with the condition for the Orr (1977) mechanism to produce amplification (Boyd 1983).

Lindzen, R. S.↗

NASA NTRS1986

Interactions of coupled acoustic and vortical instability

In the past, the acoustic combustion instability was studied independently of the hydrodynamic instability induced by vortex motions. This paper is intended to combine the two different sources of energy everywhere within the spatial domain and determine the effect of one upon the other. This can be achieved by calculating the mean flow velocities and vorticities and their fluctuating parts of velocities and vortices, as well as the fluctuating pressure. The Orr-Sommerfeld equation is utilized to determine the wavenumbers and unsteady stream functions from which vortically coupled acoustic instability growth constants are calculated. This process demonstrates that there are two different frequencies, acoustic and hydrodynamic, various combinations of which contribute to either damping or amplification. It is found that stability boundaries for coupled acoustic and vortical oscillations are somewhat similar to the classical hydrodynamic stability boundaries, but they occur in the form of multiple islands.

Chung, T. J.↗

NASA NTRS1987

On the spatial instability of piecewise linear free shear layers

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. This is done by obtaining numerical solutions to the Orr-Sommerfeld equation of high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. It is found that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qwalitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. It is concluded that there is nothing wrong with the inviscid spatial instability of piecewise linear shear flows.

Balsa, T. F.↗

NASA NTRS1987

Removal of spurious modes encountered in solving stability problems by spectral methods

A technique based on the Galerkin approximation is developed to remove spurious roots arising when Chebyshev spectral methods are used to solve eigenvalue problems in hydrodynamic stability. The derivation of Galerkin-Chebyshev approximations is explained, and numerical results for the Orr-Sommerfeld equations of plane Poiseuille flow and a Blasius profile are presented in tables and compared with those obtained by the method of Zebib (1984). It is pointed out that the present method does not increase the size of the algebraic system to be solved.

Zebib, Abdelfattah↗

NASA NTRS1987

A note on the generation of Tollmien-Schlichting waves by sudden surface-curvature change

This note is primarily concerned with the generation of spatially growing Tollmien-Schlichting waves by the interaction of very long-wavelength free-stream disturbances with a discontinuity in the curvature of a bounding surface (whose slope may or may not be continuous). The theory is combined with a numerical solution of the local Orr-Sommerfeld equation, and the result is used to predict the Tollmien-Schlichting amplitude in a relevant experiment carried out by Leehey and Shapiro (1980). The calculated results are in satisfactory agreement with their observations.

Goldstein, M. E.↗

NASA NTRS1986

Numerical simulation of a controlled boundary layer

The problem of interest is the boundary layer over a flat plate. The three standard laminar flow control (LFC) techniques are pressure gradient, suction, and heating. The parameters used to describe the amount of control in the context of the boundary layer equations are introduced. The numerical method required to find the mean flow, the linear eigenvalues of the Orr-Sommerfeld equation, and the full, nonlinear, 3-D solution of the Navier-Stokes equations are outlined. A secondary instability exists for the parallel boundary subject to uniform pressure gradient, suction, or heating. Selective control of the spanwise mode reduces the secondary instability in the parallel boundary layer at low Reynolds number.

Zang, Thomas A.↗