Ballistic range and aerothermodynamic testing
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Strawa, A. W.↗
Engineering topics
Chapman, G. T.
Publications and source records attributed to Chapman, G. T..
One-degree-of-freedom motion induced by modeled vortex shedding
The motion of an elastically supported cylinder forced by a nonlinear, quasi-static, aerodynamic model with the unusual feature of a motion-dependent forcing frequency was studied. Numerical solutions for the motion and the Lyapunov exponents are presented for three forcing amplitudes and two frequencies (1.0 and 1.1 times the Strouhal frequency). Initially, positive Lyapunov exponents occur and the motion can appear chaotic. After thousands of characteristic times, the motion changes to a motion (verified analytically) that is periodic and damped. This periodic, damped motion was not observed experimentally, thus raising questions concerning the modeling.
Yates, L. A.↗
The ballistic range and aerothermodynamic testing
A renewed interest in hypervelocity vehicles requires an increase in our knowledge of aerothermodynamic phenomena. Tests conducted in our ground-based facilities can be used both to better understand the physics of hypervelocity flight, and to calibrate and validate computer codes designed to predict vehicle performance in the hypervelocity environment. This paper reviews the requirements for aerothermodynamic testing and discusses the ballistic range and its capabilities. Examples of the kinds of testing performed in typical high-performance ballistic ranges are described; we draw heavily on experience obtained in the ballistics facilities at NASA Ames. Prospects for improving the capabilities of the ballistic range by using advanced instrumentation are discussed. Finally, recent developments in gun technology and their application to extend the capability of the ballistic range are summarized.
Strawa, A. W.↗
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.↗
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.↗
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.↗
Comparison of various drag coefficient expansions using polynomials and splines
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Sabot, S. M.↗
Topological classification of flow separation on three-dimensional bodies
In the study of three-dimensional, separated flows, a topological approach to separation and a phenomenological approach have been considered. The topological approach is based on ideas of Poincare (1928), while the phenomenological approach distinguishes between 'open' and 'closed' separation as posed by Wang (1974). In the present paper, the topological description provided by Legendre (1956, 1965, 1982) is considered, taking into account its utilization by Tobak and Peake (1979, 1982). An attempt is made to provide a more complete framework for the description of separated as well as attached flows. Nomenclature is introduced to describe the topology of the skin-friction-line portraits on a three-dimensional body. The topological ideas are illustrated by the use of hypothetical oil-flow experiments supplemented with actual flow-visualization data when possible.
Chapman, G. T.↗
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.↗
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.↗
A numerical investigation of the aerodynamics of biconic and non-circular flared configurations
Two families of biconic flares and three noncircular flares were studied at Mach numbers from 2 to 4 using a parabolized Navier-Stokes code. All configurations had cone-cyclinder forebodies. The biconic flares were examined to determine if drag could be reduced without significant loss of stability. Only slight drag reduction was found; however, meaningful volume increases were possible with negligible drag penalty. Significant decreases in drag were obtained with the noncircular flares. These configurations maintain considerable pitch stability but sacrifice nearly all yaw stability. The latter can be corrected with fold-out fins that could be readily accommodated on the noncircular flares.
Cottrell, C. J.↗
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.↗
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.↗
Comparison of various drag coefficient expansions using polynomials and splines
The longitudinal differential equation of motion has been used to investigate various aerodynamic expansion techniques. The total drag coefficient was expanded using conventional polynomials and splines with and without floating knot locations. This paper discusses the various techniques and approaches, compares results obtained from simultaneously fitting four separate flights (time vs distance measurements) and outlines the potential advantages and/or disadvantages of the various aerodynamic expansion techniques. It is believed that this is the first time splines have been used in the aerodynamic coefficient estimation process and that these results and techniques are germane to other applications.
Sabot, S. M.↗
An evaluation of a parabolized Navier-Stokes (PNS) code for cone-cylinder-flared configurations
A PNS code's capability to predict the onset of laminar and turbulent boundary layer separation, forces, moments, and pressure distributions was investigated. Predictions of incipient separation show good agreement with experimental results. Force and moment calculations were found to agree favorably with experimental data for a wide range of geometries for Mach numbers from 2 to 4 with turbulent boundary layers. Limited comparison of pressure distribution data also showed good agreement. Skin friction and Stanton number calculations are presented to indicate the code's capability to calculate this information and hence, provide a complete data base for attached flow conditions. The sensitivity of these calculations to smoothing and marching parameter variations was examined and found to be acceptable for most design work. The code was found to be suitable to complement or reduce wind tunnel experimentation for the design of this class of configuration with regard to accuracy, cost and usability.
Cottrell, C. J.↗
Aerodynamic design using numerical optimization
The procedure of using numerical optimization methods coupled with computational fluid dynamic (CFD) codes for the development of an aerodynamic design is examined. Several approaches that replace wind tunnel tests, develop pressure distributions and derive designs, or fulfill preset design criteria are presented. The method of Aerodynamic Design by Numerical Optimization (ADNO) is described and illustrated with examples.
Murman, E. M.↗
Flow visualization studies of bodies with square cross sections
A water-tunnel study was conducted of four bodies. A solution of sodium fluorescein coating the body provided visualization of vortices and feeding sheets and isolated dots of methyl blue dye provided visualization of stream lines. These data, along with published oil-flow photos, were analyzed to develop the topological representation of the flows in cross-flow planes. Presented are the development of the flow along the body at fixed angles of attack and at a fixed body station with changes in angle of attack. Effects of roll angle, body corner radius, and nose bluntness are illustrated.
Chapman, G. T.↗
Test section configuration for aerodynamic testing in shock tubes
This paper presents results of a study of the test section configuration required to minimize or alleviate interference effects on model flow produced by the presence of test section walls in the aerodynamic testing of two dimensional transonic airfoils in a shock tube. Tests at a nominal Mach number of 0.85 and a chord Reynolds number of 2,000,000 were carried out by means of schlieren photography and pressure measurements for several symmetric airfoil profiles using shock tube test sections with unmodified straight walls, contoured walls, and slotted walls with adjacent chambers. Results were compared with corresponding results from conventional wind tunnel tests of the airfoils. Results for the straight wall tests show major airfoil flow distortions. Results from contoured wall tests and those performed using a slotted wall test section developed in this study exhibit essential agreement with wind tunnel results. The collective results show that test sections for aerodynamic testing can be designed for shock tubes that will alleviate wall interference effects.
Cook, W. J.↗