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NASA NTRS2018

Acoustic Radiation Pressure

The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from finite deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in Lagrangian coordinates (not Eulerian coordinates) and that the terms in the BST are not the momentum flux density and mean excess Eulerian stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in Eulerian coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean Eulerian pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the Eulerian pressure. It is shown that the transformation between Lagrangian and Eulerian quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of finite deformation theory, which are defined in terms of the displacement gradients. Finite deformation theory leads to the result that for laterally unconfined, plane waves the Lagrangian and Eulerian radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the Lagrangian radiation pressure in the propagation direction is equal to (2K) and the BST result that the Eulerian radiation pressure in that direction is the momentum flux density.

Finite deformation theory↗

NASA NTRS1972

A theoretical and experimental investigation of the hypersonic turbulent boundary layer subject to normal and longitudinal pressure gradients and cross flow along a windward plane of symmetry.

A theoretical and experimental investigation for the hypersonic turbulent boundary layer undergoing both normal and longitudinal pressure gradients and cross flow along the plane of symmetry on the windward side of a body of revolution is presented. The purpose of this investigation is to provide a method for calculating boundary layers that occur on the centerline of symmetry of an inlet. The three-dimensional compressible integral equations are written along the symmetry plane and integrated numerically, and the effect of the cross flow on the behavior of the boundary layer is also studied. The experiments were performed at Mach number 6 and Reynolds number of 44,000,000/ft for the axisymmetric case and for the case with cross flow. The velocity profiles and the boundary layer parameters agree relatively well with theoretical values with and without cross flow effects. The presence of the cross flow alters significantly the value of the profiles. Total temperature-velocity correlations deviate from the linear Crocco distribution. Heat transfer rates agree with theoretical values and values obtained by the flat plate reference enthalpy method. Cross flow influence on the heat transfer rates is of minor relevance.

Zakkay, V.↗

NASA NTRS1995

Internal and surface phenomena in metal combustion

Combustion of metals has been widely studied in the past, primarily because of their high oxidation enthalpies. A general understanding of metal combustion has been developed based on the recognition of the existence of both vapor-phase and surface reactions and involvement of the reaction products in the ensuing heterogeneous combustion. However, distinct features often observed in metal particle combustion, such as brightness oscillations and jumps (spearpoints), disruptive burning, and non-symmetric flames are not currently understood. Recent metal combustion experiments using uniform high-temperature metal droplets produced by a novel micro-arc technique have indicated that oxygen dissolves in the interior of burning particles of certain metals and that the subsequent transformations of the metal-oxygen solutions into stoichiometric oxides are accompanied with sufficient heat release to cause observed brightness and temperature jumps. Similar oxygen dissolution has been observed in recent experiments on bulk iron combustion but has not been associated with such dramatic effects. This research addresses heterogeneous metal droplet combustion, specifically focusing on oxygen penetration into the burning metal droplets, and its influence on the metal combustion rate, temperature history, and disruptive burning. A unique feature of the experimental approach is the combination of the microgravity environment with a novel micro-arc Generator of Monodispersed Metal Droplets (GEMMED), ensuring repeatable formation and ignition of uniform metal droplets with controllable initial temperature and velocity. The droplet initial temperatures can be adjusted within a wide range from just above the metal melting point, which provides means to ignite droplets instantly upon entering an oxygen containing environment. Initial droplet velocity will be set equal to zero allowing one to organize metal combustion microgravity experiments in a fashion similar to usual microgravity liquid fuel droplet combustion studies. In addition, the internal compositions of rapidly quenched metal particles will be analyzed using SEM technique. Such compositions are similar to those existing during the combustion and provide new insight on metal combustion processes. The results of this experimental work will be used to model the fundamental mechanisms of metal combustion. Preliminary experimental results on Al and Zr particle combustion at normal gravity are discussed here.

Dreizin, Edward L.↗