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Tobak, M.

Publications and source records attributed to Tobak, M..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Flow Quality and Boundary Layer Transition

The widely held view is that transition to turbulence in the Blasius boundary layer occurs via amplification and eventual nonlinear breakdown of initially small amplitude instabilities i.e. Tollmien-Schlichting (TS) waves. However this scenario is only observed for low amplitude free-stream turbulence levels, i.e. u/U < 0.1%. Bypass of linear TS instability mechanism occurs for higher EST levels, yet considerable differences exist between the few experiments carefully designed to assess the effect of EST on transition. The consensus is that EST leads to longitudinal streaks that form near the leading edge in the boundary layer . These streaks appeal to be regions of concentrated streamwise vorticity and they are often referred to as Klebanoff modes. The importance of mean flow free-stream nonuniformity (FSN) is not as widely appreciated as EST for characterizing wind tunnel flow quality. Here it is shown that, although the v like generated by a d=50micron wire located upstream of the contraction (Re(sub d)=6.6, x/d=45,000) is immeasurably small by the time it interacts with the leading edge in the test section, it is responsible for generation of a pair of weak streamwise vortices in the boundary layer downstream. The characteristics of these wake-induced vortices and their effect on TS waves are demonstrated. Small remnant FSN variations are also shown to exist downstream of a turbulence grid. The question arises Are the adverse effects introduced by the turbulence grid caused by FST or by small remnant FSN variations?

Watmuff, Jonathan H↗
NASA NTRS1993

Deriving Indicial Response From Navier-Stokes Equations

Report discusses research directed toward recasting indicial-response approach into form appropriate to study of vortex-induced oscillations and related aerodynamic and aeroelastic phenomena. Serves two purposes: to show how deficiencies of prior mathematical model overcome to include effects of memory necessary for modeling of oscillatory but otherwise equilibrium state; and using method developed to analyze particular case of flow past cylinder in periodic forced transverse motion.

Truong, K. V.↗
NASA NTRS1990

Indicial response approach derived from Navier-Stokes equations. Part 1: Time-invariant equilibrium state

The indicial response approach is recast in a form appropriate to the study of vortex induced oscillations phenomena. An appropriate form is demonstrated for the indicial response of the velocity field which may be derived directly from the Navier-Stokes equations. On the basis of the Navier-Stokes equations, it is demonstrated how a form of the velocity response to an arbitrary motion may be determined. To establish its connection with the previous work, the new approach is applied first to the simple situation wherein the indicial response has a time invariant equilibrium state. Results for the aerodynamic response to an arbitrary motion are shown to confirm to the form obtained previously.

Truong, K. V.↗
NASA NTRS1990

Asymmetric vortices on a slender body of revolution

The symmetric and asymmetric leeward-side flow fields on an inclined ogive-cylinder have been investigated using a number of experimental techniques. Naturally occurring and perturbed flow fields were studied at a moderate Reynolds number and at many incidence angles. By close examination of the steady side force behavior at different roll orientations of the tip, it has been established that micro-variations in the tip geometry of the model have a large influence on the downstream development of the flow field. Under certain conditions, a bistable flow field was observed.

Zilliac, G. G.↗
NASA NTRS1987

Nonlinear stability of a flow with bound eddies

Kovasznay (1948) obtained an exact solution of the Navier-Stokes equations that describes a flow with periodic bound eddies. The stability of this nonparallel flow with respect to three-dimensional finite amplitude disturbances is analyzed by use of the energy method. A sufficient condition for global stability is obtained. It is shown that the additional nonhomogeneity in shear stress distribution in a nonparallel flow is a destabilizing factor.

Lin, S. P.↗
NASA NTRS1987

An algebraic criterion for the onset of chaos in nonlinear dynamic systems

The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one.

Unal, A.↗
NASA NTRS1987

Modeling aerodynamic discontinuities and onset of chaos in flight dynamical systems

Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiability are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equations of motion, and then at the level of the equations of motion themselves.

Tobak, M.↗
NASA NTRS1987

Nonlinear stability of Taylor's vortex array

It is proved that the two-dimensional Taylor vortex array, which is an exact unsteady solution of the Navier-Stokes equation, is globally and asymptotically stable in the mean with respect to three-dimensional periodic disturbances. A time-dependent bound on the decay rate of the kinetic energy of disturbances is obtained.

Lin, S. P.↗
NASA NTRS1987

Bifurcations in unsteady aerodynamics

Nonlinear algebraic functional expansions are used to create a form for the unsteady aerodynamic response that is consistent with solutions of the time dependent Navier-Stokes equations. An enumeration of means of invalidating Frechet differentiability of the aerodynamic response, one of which is aerodynamic bifurcation, is proposed as a way of classifying steady and unsteady aerodynamic phenomena that are important in flight dynamics applications. Accommodating bifurcation phenomena involving time dependent equilibrium states within a mathematical model of the aerodynamic response raises an issue of memory effects that becomes more important with each successive bifurcation.

Tobak, M.↗
NASA NTRS1986

Modeling aerodynamic discontinuities and the onset of chaos in flight dynamical systems

Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiality are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equation of motion, and then at the level of the equations of motion themselves.

Tobak, M.↗
NASA NTRS1986

Migration of the separation point on a deforming cylinder

An iterative scheme of solving the Navier-Stokes equations for unsteady two-dimensional flow about a deforming and translating cylinder is given. In the kth iteration, the convected vorticity appears as the source term in an equation of transient diffusion of vorticity. A novel integral transform is used to reduce this transient vorticity equation to a k-dimensional heat equation. The bounded solution of this equation is obtained with a general method of superposition for problems involving a moving boundary. An equation describing the migration of the separation point on a deforming cylinder in unsteady cross flows is derived from the analytically obtained velocity field. The radial expansion of the cylinder surface is shown to hasten the separation time and to increase the separation angle. The results imply that in the steady flow past a body that is moving forward and sinking at constant rates, the locus of points at which the azimuthal component of skin friction changes sign originates on the leeward ray at a point downstream of the front tip.

Lin, S. P.↗
NASA NTRS1986

Spectral stability of Taylor's vortex array

In a global sense it is shown that the two-dimensional Taylor vortex array, an exact solution of the Navier-Stokes equation, is absolutely and monotonically stable with respect to infinitesimal disturbances of all discrete frequencies as long as the viscosity is positive. It is suggested that the Taylor vortex array may also be stable with respect to finite amplitude disturbances.

Lin, S. P.↗
NASA NTRS1986

Bifurcations in unsteady aerodynamics

Nonlinear algebraic functional expansions are used to create a form for the unsteady aerodynamic response that is consistent with solutions of the time dependent Navier-Stokes equations. An enumeration of means of invalidating Frechet differentiability of the aerodynamic response, one of which is aerodynamic bifurcation, is proposed as a way of classifying steady and unsteady aerodynamic phenomena that are important in flight dynamics applications. Accomodating bifurcation phenomena involving time dependent equilibrium states within a mathematical model of the aerodynamic response raises an issue of memory effects that becomes more important with each successive bifurcation.

Tobak, M.↗
NASA NTRS1986

Reversed flow above a plate with suction

A minor extension is developed for Kovasznay's (1948) solution, and an exact solution is presented for Navier-Stokes equations that may represent the reversed flow about a flat plate with suction. This exact solution is the result of a search for a solution that may serve as an exact basic flow for a model stability analysis of nonparallel flows involving flow reversal.

Lin, S. P.↗
NASA NTRS1985

Bifurcation theory applied to aircraft motions

The bifurcation theory is used to analyze the nonlinear dynamic stability characteristics of single-degree-of-freedom motions of an aircraft or a flap about a trim position. The bifurcation theory analysis reveals that when the bifurcation parameter, e.g., the angle of attack, is increased beyond a critical value at which the aerodynamic damping vanishes, a new solution representing finite-amplitude periodic motion bifurcates from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solution is stable (supercritical) or unstable (critical). For the pitching motion of a flap-plate airfoil flying at supersonic/hypersonic speed, and for oscillation of a flap at transonic speed, the bifurcation is subcritical, implying either that exchanges of stability between steady and periodic motion are accompanied by hysteresis phenomena, or that potentially large aperiodic departures from steady motion may develop. On the other hand, for the rolling oscillation of a slender delta wing in subsonic flight (wing rock), the bifurcation is found to be supercritical. This and the predicted amplitude of the bifurcation periodic motion are in good agreement with the experiments.

Hui, W. H.↗
NASA NTRS1985

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

Chapman, G. T.↗