Analysis of elastic structures on digital computers

A brief survey of a general method for the analysis of elastic structures is given. The matrices involved are described for certain classes of structures in terms of basic data. Some methods for taking advantage of the general, simplifying pattern of the matrices when programming for an electronic computer are mentioned.     

Vehicle impacts on the environment at different spatial scales: observations in west central Georgia, USA

Roads and vehicles change the environmental conditions in which they occur. One way to categorize these effects is by the spatial scale of the cause and the impacts. Roads may be viewed from the perspective of road segments, the road network, or roads within land ownership or political boundaries such as counties. This paper examines the hypothesis that the observable impacts of roads on the environment depend on spatial resolution. To examine this hypothesis, the environmental impacts of vehicles and roads were considered at four scales in west central Georgia in and around Fort Benning: a second-order catchment, a third-order watershed, the entire military installation, and the five-county region including Fort Benning. Impacts from an experimental path made by a tracked vehicle were examined in the catchment. Land-cover changes discerned through remote sensing data over the past three decades were considered at the watershed and installation scales. A regional simulation model was used to project changes in land cover for the five-county region. Together these analyses provide a picture of the how environmental impacts of roads and vehicles can occur at different spatial scales. Following tracked vehicle impact with a D7 bulldozer, total vegetation cover responded quickly, but the plant species recovered differently. Soils were compacted in the top 10 cm and are likely to remain so for some time. Examining the watershed from 1974 to 1999 revealed that conversion from forest to nonforest was highest near unpaved roads and trails. At the installation scale, major roads as well as unpaved roads and trails were associated with most of the conversion from forest to nonforest. For the five-county region, most of the conversion from forest to nonforest is projected to be due to urban spread rather than direct road impacts. The study illustrates the value of examining the effects of roads at several scales of resolution and shows that road impacts in west central Georgia are most important at local to subregional scales. The insights from these analyses led to several questions about resource management at different spatial scales.     

Simultaneous velocity and concentration field measurements of passive-scalar mixing in a confined rectangular jet

Simultaneous velocity and concentration fields in a confined liquid-phase rectangular jet with a Reynolds number based on the hydraulic diameter of 50,000 (or 10,000 based on the velocity difference between streams and the jet exit dimension) and a Schmidt number of 1,250 were obtained by means of a combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system. Data were collected at the jet exit and six further downstream locations. The velocity and concentration field data were analyzed for flow statistics such as turbulent fluxes, turbulent viscosity and diffusivity, and turbulent Schmidt number (Sc _T ). The streamwise turbulent flux was found to be larger than the transverse turbulent flux, and the mean concentration gradient was not aligned with the turbulent flux vector. The average Sc _T was found to vary both in streamwise and in cross stream directions and had a mean value around 0.8, a value consistent with the literature. Spatial correlation fields of turbulent fluxes and concentration were then determined. The R _u′ϕ′ correlation was elliptical in shape with a major axis tilted downward with respect to the streamwise axis, whereas the R _v′ϕ′ correlation was an ellipse with a major axis aligned with the cross-stream direction. Negative regions of R _u′ϕ′ were observed in the outer streams, and these negatively correlated regions decayed with downstream distance and finally disappeared altogether. The R _ϕ′ϕ′ correlation field was found to be an ellipse with the major axis inclined at about 45° with respect to the streamwise direction. Linear stochastic estimation was used to interpret spatial correlation data and to determine conditional flow structures. It is believed that a vortex street formed near the splitter plate is responsible for the negatively correlated region observed in the R _u′ϕ′ spatial correlations of turbulent fluxes. A positive concentration fluctuation event was observed to correspond to a finger of nearly uniform concentration fluid reaching out into the outer stream, whereas a negative event corresponds to a pocket of nearly uniform fluid being entrained from the outer stream into the center jet region. Large-scale vortical structures were observed in the conditional velocity fields with an elliptical shape and a streamwise major axis. The growth of the structure size increased linearly initially but then grew more slowly as the flow transitioned toward channel flow. Support of this work was provided by the National Science Foundation through grants CTS-9985678 and CTS-0336435 and by the Dow Chemical Company. The author greatly acknowledge Charles Lipp at Dow Chemical and Ken Junk at Emerson Fisher for their valuable assistance in the design and construction of the flow system.     

Population,characteristics and kinematics of vortices in a confined rectangular jet with a co-flow

Vortex behavior and characteristics in a confined rectangular jet with a co-flow were examined using vortex swirling strength as a defining characteristic. On the left side of the jet, the positively (counterclockwise) rotating vortices are dominant, while negatively rotating vortices are dominant on the right side of the jet. The characteristics of vortices, such as population density, average size and strength, and deviation velocity, were calculated and analyzed in both the cross-stream direction and the streamwise direction. In the near-field of the jet, the population density, average size and strength of the dominant direction vortices show high values on both sides of the center stream with a small number of counter-rotating vortices produced in the small wake regions close to jet outlet. As the flow develops, the wake regions disappear, these count-rotating vortices also disappear, and the population of the dominant direction vortices increase and spread in the jet. The mean size and strength of the vortices decrease monotonically with streamwise coordinate. The signs of vortex deviation velocity indicate the vortices transfer low momentum to high-velocity region and high momentum to the low velocity region. The developing trends of these characteristics were also identified by tracing vortices using time-resolved particle image velocimetry data. Both the mean tracked vortex strength and size decrease with increasing downstream distance overall. At the locations of the left peak of turbulent kinetic energy, the two-point spatial cross-correlation of swirling strength with velocity fluctuation and concentration fluctuation were calculated. All the correlation fields contain one positively correlated region and one negatively correlated region although the orientations of the correlation fields varied, due to the flow transitioning from wake, to jet, to channel flow. Finally, linear stochastic estimation was used to calculate conditional structures. The large-scale structures in the velocity field revealed by linear stochastic estimation are spindle-shaped with a titling stream-wise major axis.     

Measurement and imaging of supersonic combustion in a model scramjet engine

Results of tests performed in a free-piston shock tunnel on a model scramjet engine are presented. Two conditions which differed in Mach number were tested. Flow at the lower Mach number condition was achieved using a variable-angle diffuser. Shadowgraph images and floor static pressure measurements were obtained, the latter used as the basis of a finite-difference calculation of flow properties in the scramjet. Received 9 May 1998 / Accepted 30 September 1998