Aerodynamic heating in large cavities in an array of RSI tiles

A large panel of reusable surface insulation (RSI) tiles including lost tile cavities was aerothermally tested in the Langley 8 foot high temperature structures tunnel to determine both the heat load within the cavities and the structural performance of the RSI surrounding the cavities. Tests were conducted with a turbulent boundary layer at a nominal free stream Mach number of 6.6, a total temperature of 1800 K, a Reynolds number per meter of 5 million, and a dynamic pressure of 62 kPa. The maximum aerodynamic heating to the floor of the cavity was two to three times the normal surface heating. The cavity heating rates agreed with data from other facilities and were successfully correlated with an empirical equation. A zippering failure occurred to a tile downstream of a double tile cavity when the separated flow attached to the floor of the cavity and forced the tile from its position

A canonical form for nonlinear systems

The conceptions of transformation and canonical form have been much used to analyze the structure of linear systems. A coordinate system and a corresponding canonical form are developed for general nonlinear control systems. Their usefulness is demonstrated by showing that every feedback linearizable system becomes a system with only feedback paths in the canonical form

Observability for two dimensional systems

Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no informaton is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problem, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability

Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation

Canonical coordinates for partial differential equations

Necessary and sufficient conditions are found under which operators of the form Sigma(m, j=1) X(2)sub j + X sub 0 can be made constant coefficient. In addition, necessary and sufficient conditions are derived which classify those linear partial differential operators that can be moved to the Kolmogorov type

Canonical forms for nonlinear systems

Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables

Aerodynamic force and moment characteristics of spheres and cones at mach 7.0 in methane-air combustion products

Aerodynamic force and moment characteristics of spheres and cones at hypersonic speeds in methane-air combustion product

Applications to aeronautics of the theory of transformations of nonlinear systems

The development of the transformation theory is discussed. Results and applications concerning the use of this design technique for automatic flight control of aircraft are presented. The theory examines the transformation of nonlinear systems to linear systems. The tracking of linear models by nonlinear plants is discussed. Results of manned simulation are also presented

Performance of LI-1542 reusable surface insulation system in a hypersonic stream

The thermal and structural performance LI-1542 reusable surface insulation (RSI) tiles was investigated. The test panel was designed to represent part of the surface structure on a space shuttle orbiter fuselage along a 1250 K isotherm. Aerothermal tests were conducted at a free-stream Mach number of 6.6, a total temperature of 1820 K, Reynolds numbers of 2 millon and 5 million per meter, and dynamic pressures of 26 and 65 kPa. The RSI tiles demonstrated good thermal protection and structural integrity. High temperatures were caused by misalinement in tile height, offset the tile longitudinal alinement, and leakage around thermal seals when differential pressure existed across the panel. The damage tolerance of LI-1542 RSI appeared high. The tile coating crazed early in the test program, but this did not effect the tile integrity. Erosion of the tile edges occurred at forward-facing steps and at the ends of longitudinal gaps because of particle impacts and flow shear

Effects of vertical vibration on hopper flows of granular material

This paper examines the flow of granular material through a wedge-shaped hopper subject to vertical, sinusoidal oscillations. Experiments and discrete element computer simulations were conducted to investigate particle trajectories within and mass discharge rates from the hopper. With the hopper exit closed, side wall convection cells are observed in both the experiments and simulations. The convection cells are oriented such that particles move up along the inclined walls of the hopper and down along the centerline. Results from the computer simulation indicate that the convection cells are a result of the dilation of the granular bed during free fall and interaction with hopper walls. Measurements of the mean mass discharge rate for various vibration parameters were also made in both the experiments and simulations. The ratio of the mass discharge rate for a vibrating hopper to the mass discharge rate for a non-vibrating hopper scales with the oscillation velocity amplitude and exhibits a maximum value just greater than one for oscillation velocity amplitudes less than 0.5. The ratio is less than one for larger velocity amplitudes. A simple model taking into account the change in the effective gravity acting on the granular material over an oscillation cycle is examined. A significant deficiency in the model is that is assumes no material discharges from the hopper during part of each oscillation cycle for acceleration amplitudes greater than gravitational acceleration. Data from the simulations indicate that although the discharge rate from the hopper varies throughout an oscillation cycle, it never equals zero. The simulation was also used to examine particle horizontal position and velocity profiles at the hopper exit. Lastly, preliminary observations of the effects of localized vibration on a granular material in a closed hopper are presented