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

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

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

The impulsive motion of a liquid resulting from a particle collision

When two particles collide in a liquid, the impulsive acceleration due to the rebound produces a pressure pulse that is transmitted through the fluid. Detailed measurements were made of the pressure pulse and the motion of the particles by generating controlled collisions with an immersed dual pendulum. The experiments were performed for a range of impact velocities, angles of incidence, and distances between the wall and the pairs of particles. The radiated fluid pressure was measured using a high-frequency-response pressure transducer, and the motion of the particles was recorded using a high-speed digital camera. The magnitude of the impulse pressure was found to scale with the particle velocity, the particle diameter and the density of the fluid. Additionally, a model is proposed to predict the impulse field in the fluid based on the impulse pressure theory. The model agrees well with the experimental measurements

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

Linear approximations of nonlinear systems

The development of a method for designing an automatic flight controller for short and vertical take off aircraft is discussed. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system called the modified tangent model was introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this the linear part (about a state space point x sub 0) of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x sub 0 yields the same modified tangent model

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

The thermal and structural performance of a large panel of LI-1542 reusable surface insulation tiles was determined by a series of cyclic heating tests using radiant lamps and aerothemal tests in the Langley 8-foot high-temperature structures tunnel. Aerothermal tests were conducted at a free-stream Mach number of 6.6, a total temperature of 1830 K, Reynolds numbers of 2.0 and 4,900,000 per meter, and dynamic pressures of 29 and 65 kPa. The results suggest that pressure gradients in gaps and flow impingement on the header walls at the end of longitudinal gaps are sources for increased gap heating. Temperatures higher than surface radiation equilibrium temperature were measured deep in gaps and at the header walls. Also, the damage tolerance of the LI-1542 tiles appears to be very high. Tile edge erosion rate was slow; could not be tolerated in a shuttle application. Tiles soaked with water and subjected to rapid depressurization and aerodynamic heating showed no visible evidence of damage

Thermodynamic and transport properties of gaseous tetrafluoromethane in chemical equilibrium

Equations and in computer code are presented for the thermodynamic and transport properties of gaseous, undissociated tetrafluoromethane (CF4) in chemical equilibrium. The computer code calculates the thermodynamic and transport properties of CF4 when given any two of five thermodynamic variables (entropy, temperature, volume, pressure, and enthalpy). Equilibrium thermodynamic and transport property data are tabulated and pressure-enthalpy diagrams are presented

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

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