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Tobak, M.

Publications and source records attributed to Tobak, M..

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Bifurcation theory applied to aircraft motions

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 (subcritical). 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 experiments.

Hui, W. H.↗
NASA NTRS1985

Nonlinear problems in flight dynamics involving aerodynamic bifurcations

Aerodynamic bifurcation is defined as the replacement of an unstable equilibrium flow by a new stable equilibrium flow at a critical value of a parameter. A mathematical model of the aerodynamic contribution to the aircraft's equations of motion is amended to accommodate aerodynamic bifurcations. Important bifurcations such as, the onset of large-scale vortex-shedding are defined. The amended mathematical model is capable of incorporating various forms of aerodynamic responses, including those associated with dynamic stall of airfoils.

Tobak, M.↗
NASA NTRS1984

Nonlinear problems in flight dynamics

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Chapman, G. T.↗
NASA NTRS1984

Bifurcation analysis of aircraft pitching motions near the stability boundary

Bifuraction theory is used to analyze the nonlinear dynamic stability characteristics of an aircraft subject to single degree of freedom pitching-motion perturbations about a large mean angle of attack. The requisite aerodynamic information in the equations of motion is represented in a form equivalent to the response to finite-amplitude pitching oscillations about the mean angle of attack. This information is deduced from the case of infinitesimal-amplitude oscillations. The bifurcation theory analysis reveals that when the mean angle of attack is increased beyond a critical value at which the aerodynamic damping vanishes, new solutions representing finite-amplitude periodic motions bifurcate from the previously stable steady motion. The sign of a simple criterion, cast in terms of aerodynamic properties, determines whether the bifurcating solutions are stable (supercritical) or unstable (subcritical). For flat-plate airfoils flying at supersonic/hypersonic 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.

Hui, W. H.↗
NASA NTRS1984

Mathematical modeling of the aerodynamic characteristics in flight dynamics

Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.

Tobak, M.↗
NASA NTRS1983

On issues concerning flow separation and vortical flows in 3 dimensions

This review provides an illustrated introduction laying the knowledge base for vortical flows about three dimensional configurations that are of typical interest to aerodynamicists and researchers in fluid mechanics. The paper then compiles a list of ten issues, again in illustrative format, that the authors deem important to the understanding of complex vortical flows. These issues and our responses to them provide, it is hoped, a skeletal framework on which to hang the ensuing conference proceedings.

Peake, D. J.↗
NASA NTRS1982

Three-dimensional separation and reattachment

The separation of three dimensional turbulent boundary layers from the lee of flight vehicles at high angles of attack is investigated. The separation results in dominant, large scale, coiled vortex motions that pass along the body in the general direction of the free stream. In all cases of three dimensional flow separation and reattachment, the assumption of continuous vector fields of skin friction lines and external flow streamlines, coupled with simple laws of topology, provides a flow grammar whose elemental constituents are the singular points: the nodes, spiral nodes (foci), and saddles. The phenomenon of three dimensional separation may be constrained as either a local or a global event, depending on whether the skin friction line that becomes a line of separation originates at a node or a saddle point.

Peake, D. J.↗
NASA NTRS1982

Three-dimensional flows about simple components at angle of attack

The structures of three dimensional separated flow about some chosen aerodynamic components at angle of attack are synthesized, holding strictly to the notion that streamlines in the external flow (viscous plus inviscid) and skin friction lines on the body surface may be considered as trajectories having properties consistent with those of continuous vector fields. Singular points in the fields are of limited number and are classified as simple nodes and saddles. Analogous flow structures at high angles of attack about blunt and pointed bodies, straight and swept wings, etc., are discussed, highlighting the formation of spiral nodes (foci) in the pattern of the skin friction lines. How local and global three dimensional separation lines originate and form is addressed, and the characteristics of both symmetric and asymmetric leeward wakes are described.

Peake, D. J.↗
NASA NTRS1982

Three-dimensional separation and reattachment

The separation of three dimensional turbulent boundary layers from the lee of flight vehicles at high angles of attack is investigated. The separation results in dominant, large scale, coiled vortex motions that pass along the body in the general direction of the free stream. In all cases of three dimensional flow separation and reattachment, the assumption of continuous vector fields of skin friction lines and external flow streamlines, coupled with simple laws of topology, provides a flow grammar whose elemental constituents are the singular points: the nodes, spiral nodes (foci), and saddles. The phenomenon of three dimensional separation may be construed as either a local or a global event, depending on whether the skin friction line that becomes a line of separation originates at a node or a saddle point.

Peake, D. J.↗
NASA NTRS1982

Three-dimensional flows about simple components at angle of attack

The structures of three dimensional separated flow about some chosen aerodynamic components at angle of attack are synthesized, holding strictly to the notion that streamlines in the external flow (viscous plus inviscid) and skin friction lines on the body surface may be considered as trajectories having properties consistent with those of continuous vector fields. Singular points in the fields are of limited number and are classified as simple nodes and saddles. Analogous flow structures at high angles of attack about blunt and pointed bodies, straight and swept wings, etc., are discussed, highlighting the formation of spiral nodes (foci) in the pattern of the skin friction lines. How local and global three dimensional separation lines originate and form is addressed, and the characteristics of both symmetric and asymmetric leeward wakes are described.

Peake, D. J.↗
NASA NTRS1982

Bifurcation analysis of nonlinear stability of aircraft at high angles of attack

The problem of stability of steady flight of an aircraft flying at high angles of attack subject to finite-amplitude disturbances in pitch is studied using bifurcation theory, taking account of the interactions between the pitching motion and the unsteady flow. The aerodynamic responses to large-amplitude slow oscillations of the aircraft are obtained from that of infinitesimal amplitude case. Increasing the angle of attack past some critical angle for which the damping vanishes, the steady flight becomes unstable and Hopf bifurcation sets in, resulting in a periodic motion. A simple criterion in terms of the aerodynamic coefficients is given for determining the stability of the bifurcating period motion. For supersonic/hypersonic flat plate airfoils the bifurcating periodic motion is found to be unstable. This implies that when the angle of attack is increased past that of neutral damping, there will be drastic changes of the motion of the aircraft from its steady flight condition at the critical angle, including, e.g. hysteresis.

Hui, W. H.↗
NASA NTRS1982

Topology of three-dimensional separated flows

A Legendre formulation for a pattern of streamlines adjacent to a surface considered as trajectories with properties consistent with those of a constant vector field is used to develop a mathematical framework for three-dimensional separated flows. Convergence of skin-friction lines onto a particular skin-friction line originating from a particular saddle point is defined as a necessary condition for flow separation. Steady, three-dimensional flow is considered, and singular points occurring in the skin-friction lines are shown to happen where the skin friction or the surface vorticity become zero, and become nodal or saddle points. The separation initiates and continues only globally, as a mixture of an infinite set of friction lines, or locally, with one line. The topography of streamlines in two-dimensional sections of three-dimensional flows is discussed, and examples are provided of a round-nosed body of revolution at varying angles of attack.

Tobak, M.↗
NASA NTRS1981

Unsteady Newton-Busemann flow theory. II - Bodies of revolution

A complete Newtonian flow theory is presented for unsteady flow past oscillating bodies of revolution of general shape at very high Mach numbers, consideration being given to a centrifugal force correction to the impact pressures. Expressions are obtained for the unsteady pressure and the stability derivatives are presented in closed form. It is stressed that the correction for the centrifugal force, which arises because of the curved trajectories that fluid particles follow along the surface subsequent to their impact, must not be neglected. If the correction is included, the theory is shown to be in excellent agreement with experimental results for relatively sharp cones. Theoretical results are in poor agreement with experimental results in air for bodies having moderate or large-nose bluntness.

Hui, W. H.↗
NASA NTRS1981

Some applications of aerodynamic formulations to problems in aircraft dynamics

Two applications of mathematical modeling to aerodynamic problems are cussed. The first application is an investigation of the capacity of a nonlinear aerodynamic mathematical model to describe the aerodynamic reactions on an airfoil with a deflecting flap in transonic flow. Flow field computational methods are used to evaluate the nonlinear, unsteady aerodynamic data in terms of characteristic motions called for by the model. Histories of unconstrained motions of the flap are generated from the flap equations of motion, with the aerodynamic reactions specified by the mathematical model. In the second application wing rock is investigated. The most recent model accommodates experimental results wing rock by admitting the existence of aerodynamic hysteresis in the variation of the steady state rolling moment coefficient with roll angle is described.

Schiff, L. B.↗
NASA NTRS1981

Topology of three-dimensional separated flows

Based on the hypothesis that patterns of skin-friction lines and external streamlines reflect the properties of continuous vector fields, topology rules define a small number of singular points (nodes, saddle points, and foci) that characterize the patterns on the surface and on particular projections of the flow (e.g., the crossflow plane). The restricted number of singular points and the rules that they obey are considered as an organizing principle whose finite number of elements can be combined in various ways to connect together the properties common to all steady three dimensional viscous flows. Introduction of a distinction between local and global properties of the flow resolves an ambiguity in the proper definition of a three dimensional separated flow. Adoption of the notions of topological structure, structural stability, and bifurcation provides a framework to describe how three dimensional separated flows originate and succeed each other as the relevant parameters of the problem are varied.

Tobak, M.↗
NASA NTRS1981

Unsteady Newton-Busemann flow theory. Part 2: Bodies of revolution

Newtonian flow theory for unsteady flow past oscillating bodies of revolution at very high Mach numbers is completed by adding a centrifugal force correction to the impact pressures. Exact formulas for the unsteady pressure and the stability derivatives are obtained in closed form and are applicable to bodies of revolution that have arbitrary shapes, arbitrary thicknesses, and either sharp or blunt noses. The centrifugal force correction arising from the curved trajectories followed by the fluid particles in unsteady flow cannot be neglected even for the case of a circular cone. With this correction, the present theory is in excellent agreement with experimental results for sharp cones and for cones with small nose bluntness; gives poor agreement with the results of experiments in air for bodies with moderate or large nose bluntness. The pitching motions of slender power-law bodies of revulution are shown to be always dynamically stable according to Newton-Busemann theory.

Hui, W. H.↗