The new method described in this paper employs an incomplete set of free-boundary normal modes of vibration, augmented with a low-frequency account for the contribution of neglected (residual) modes. The "residual effects" improve the accuracy of forced dynamic response in a manner which is related to the benefit of the mode-acceleration method. The new method adds residual inertial and dissipative effects to the residual flexibility introduced by MacNeal. All effects are derived from the solution of a special statics problem, followed by removal of the contributions of the retained modes. A structural component can then be represented in a stiffness-matrix form for various applications, one of which is modal synthesis. Numerical results of modal analysis for a cantilevered rod show the new method to yield superior accuracy to several other methods (including those of Hurty, Bamford, and MacNeal). All parameters for the new representation can be derived from test; this is not true for most other methods. Required are the free-boundary normal modes and the dynamic flexibility matrix vs frequency for the boundary points. Consequently, any desired mix of analytically derived and experimentally derived parameters can be employed.

Improved Component-Mode Representation for Structural Dynamic Analysis

Breakup of a liquid drop suddenly exposed to a high-speed airstream

Laser diagnostic techniques play a large and growing role in combustion research and development. Here we highlight three areas where quantitative sensing based on laser absorption has had strong influence: chemical kinetics, propulsion, and practical energy systems. In the area of chemical kinetics, measurements in shock tubes of high-temperature reaction rate coefficients using species-specific laser absorption techniques have provided new and accurate answers to questions about combustion chemical processes. In the area of propulsion, wide-bandwidth measurements of flow temperatures, species concentrations, and velocity have provided engine designers with the necessary information to improve operation and performance. In the area of practical energy systems, real-time measurements of combustor operating conditions and emissions have enabled needed incremental improvements in large power plants and improved safety of operation. Yet, there is still more to be done, and opportunities for new applications will grow as laser sensors evolve. This review seeks to provide an overview of the current power and future potential of these modern diagnostic tools.

Applications of quantitative laser sensors to kinetics, propulsion and practical energy systems

Drop deformation and breakup due to shock wave and steady disturbances

Droplet breakup phenomena in flows with velocity lag

An analysis is made of the motion of small, spherical, noninteracting solid or liquid particles through hypersonic flowfields over spheres and cones. It is shown that the motion of the particles depends only on the density ratio across the shock and a dimensionless ballistic parameter. Approximate solutions to the particle equations of motion are obtained in closed form in terms of these parameters for two flow configurations, a sharpcone and the stagnation region of a sphere. A technique is derived for the determination of the aerodynamic heating and melting (or vaporization) of the particles as they traverse the shock layer. Results for the particle mass loss as a result of heating are presented for the stagnation region, the more severe heating environment. Existing correlations of experimental data on the breakup of drops due to aerodynamic forces are used to predict the extent of raindrop breakup in the shock layer.

Particle trajectories, heating, and breakup in hypersonic shock layers

Recent results are presented from an experimental study to develop Planar Laser-Induced Fluorescence (PLIF) diagnostics for application to scramjet combustor development. The measurements are made in a reacting flow shock-tunnel facility which generates Mach 3 air at static conditions of 1500 K and 0.3 atm. Hydrogen or other gases may be injected into the rectangular test section downstream of a rear-facing step. PLIF measurements of NO, naturally present in the reflected shock-heated, freestream air, are used to determine basic flow features, and a technique is demonstrated for determining static temperature variations in nonreacting, non-mixing portions of the flow. pLIF measurements of OH are used to reveal the instantaneous reaction zone interface from a dual round jet injector configuration

Fluorescence imaging of OH and NO in a model supersonic combustor

The problem of predicting raindrop breakup effects in the shock layer of a high-speed vehicle is discussed. Relevant experimental data, obtained in a shock tube with shadowgraph and x-ray photography, are presented in the form of correlations of the nondimensional time to breakup with the Weber number, together with the drop mass variation and trajectory as a function of nondimensional time. The relationship between the experimental situation and the flight case is delineated for the stagnation and downstream conical-flow regions of a high-speed shock layer. Based on the experimental correlations, calculations are made of the impacting drop mass fractions, velocities, and impact angles for a vehicle traversing a rainstorm.

W. G. Reinecke

Papers

Particle trajectories, heating, and breakup in hypersonic shock layers

Fluorescence imaging of OH and NO in a model supersonic combustor

Raindrop Breakup in the Shock Layer of a High-speed Vehicle

Experiments on water drop breakup behind mach 3 to 12 shocks.

Debris Shielding during High-speed Erosion