Three dimensional laminar boundary layer with small cross-flow

Important problems involving three-dimensional boundary layer occur in almost all internal and external aerodynamic configurations. For many of these, the flow outside the boundary layer may be resolved into a large principal component and a small crosswise velocity. In this paper, three-dimensional laminar boundary-layer flows over flat and curved surfaces are treated under such a simplification. For flat surfaces, the solutions demonstrate the effect of the free stream turning on the velocity profiles in the crosswise and primary flow directions. When the surface curvature is large and varies so as to resemble a corner, the computed examples show the manner in which the asymmetric behavior of the boundary layer results from the cross-flow. The detailed examples are chosen to illustrate flows occurring on the casing and in the blade fillets of turbomachinery

The interaction of multiple stellar winds in stellar clusters: potential flow

While several studies have investigated large-scale cluster winds resulting from an intra-cluster interaction of multiple stellar winds, as yet they have not provided details of the bordering flows inside a given cluster. The present work explores the principal structure of the combined flow resulting from the interaction of multiple stellar winds inside stellar clusters. The theory of complex potentials is applied to analytically investigate stagnation points, boundaries between individual outflows, and the hydrodynamic structure of the asymptotic large-scale cluster wind. In a second part, these planar considerations are extended to fully three-dimensional, asymmetric configurations of wind-driving stars. We find (i) that one can distinguish regions in the large-scale cluster wind that are determined by the individual stellar winds, (ii) that there are comparatively narrow outflow channels, and (iii) that the large-scale cluster wind asymptotically approaches spherical symmetry at large distances. The combined flow inside a stellar cluster resulting from the interaction of multiple stellar winds is highly structured.Comment: 8 pages, 8 Figure

Chronology of fans and terraces in the Galatea Basin

Air-borne volcanic ash beds are used to date fans and terraces in the Galatea Basin and to outline the depositional history of this part of the Rangitaiki Valley. The basin is interpreted as a fault-angle depression formed by a downwarped sheet of ignimbrite and an upthrusted block of greywacke which forms the Ikawhenua Range. It is from this range that much of the detritus has been derived to fill the basin, deposited mainly in the form of fans and terraces. The larger fans cover a wide area and their surfaces are older than the Rotoma eruption of c. 8000 years B.P. The widespread occurrence of these fans indicates a major erosion interval between c. 11,000 and c. 8,000 years ago. The younger fans are distributed in a particular order with fans of the Pre-Taupo surface north of the Horomanga Stream and those of the Pre- and Post-Kaharoa surfaces south of the same stream. This ordered distribution of the younger fans suggests a climatic control of fan building. Aggradation and degradation phases in the Rangitaiki and Whirinaki Rivers have formed a pronounced meander trough containing terraces of the Pre-Taupo, Pre-Kaharoa, and Post-Kaharoa surfaces. The terrace of the Pre-Kaharoa surface, largely of Taupo Pumice alluvium, is the most common. Degradation, however, is controlled by a local base level at the ignimbrite rapids on the Rangitaiki River just north of the Galatea Basin

Simulation of the spatio-temporal extent of groundwater flooding using statistical methods of hydrograph classification and lumped parameter models

This article presents the development of a relatively low cost and rapidly applicable methodology to simulate the spatio-temporal occurrence of groundwater flooding in chalk catchments. In winter 2000/2001 extreme rainfall resulted in anomalously high groundwater levels and groundwater flooding in many chalk catchments of northern Europe and the southern United Kingdom. Groundwater flooding was extensive and prolonged, occurring in areas where it had not been recently observed and, in places, lasting for 6 months. In many of these catchments, the prediction of groundwater flooding is hindered by the lack of an appropriate tool, such as a distributed groundwater model, or the inability of models to simulate extremes adequately. A set of groundwater hydrographs is simulated using a simple lumped parameter groundwater model. The number of models required is minimized through the classification and grouping of groundwater level time-series using principal component analysis and cluster analysis. One representative hydrograph is modelled then transposed to other observed hydrographs in the same group by the process of quantile mapping. Time-variant groundwater level surfaces, generated using the discrete set of modelled hydrographs and river elevation data, are overlain on a digital terrain model to predict the spatial extent of groundwater flooding. The methodology is applied to the Pang and Lambourn catchments in southern England for which monthly groundwater level time-series exist for 52 observation boreholes covering the period 1975–2004. The results are validated against observed groundwater flood extent data obtained from aerial surveys and field mapping. The method is shown to simulate the spatial and temporal occurrence of flooding during the 2000/2001 flood event accurately

Changing Course: Recommendations for Balancing Regional Growth and Water Resources in Northeastern Illinois

In this new era of global environmental concerns and economic competition between the world's metropolitan areas, basic questions about the sustainability of the greater Chicago region must be considered. Foremost among these concerns are the increasing pressures on the supplies of two of our most vital and interrelated resources -- land and water. Factors like the amount of open space, density of new development and intensity of farming practices greatly affect the quantity and quality of the region's water resources. Conversely, the quality and quantity of the region's lakes, streams and underground aquifers have a major influence on local land use decisions. Sustainable land use practices are essential to meet increasing demands for clean water. Although the quality of surface water in northeastern Illinois has improved in the past three decades, the supply remains limited by pollution from stormwater runoff, U.S. Supreme Court decisions capping the amount that can be drawn from Lake Michigan, steadily increasing urbanization of the region, inefficient water supply systems and unregulated groundwater withdrawals. To determine how to address these problems across a 12-county region in northeastern Illinois, the Joyce Foundation provided support to the Metropolitan Planning Council and Openlands, in partnership with the Campaign for Sensible Growth, to undertake a study to examine the relationship between development practices, land use, and water quality and quantity. This study addresses five areas: the state of the region's water resources; the state and federal policies that impact water; regional watershed planning efforts; local development practices and model ordinances; and techniques for reducing the impacts of urbanization on regional water resources

Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are encountered: a Stokes flow near a rough wall and the stress distribution on the rough interface of a material in uni-axial tension. We perform a complete numerical solution of these two-dimensional problems for any univalued rough surfaces. We present results for sinusoidal and self-affine surface whose slope can locally reach 2.5. Beyond the numerical solution we present perturbative solutions of these problems. We show in particular that at first order in roughness amplitude, the surface stress of a material in uni-axial tension can be directly obtained from the Hilbert transform of the local slope. In case of self-affine surfaces, we show that the stress distribution presents, for large stresses, a power law tail whose exponent continuously depends on the roughness amplitude

Theoretical Prediction of Pressure Distributions on Nonlifting Airfoils at High Subsonic Speeds

Theoretical pressure distributions on nonlifting circular-arc airfoils in two-dimensional flows with high subsonic free-stream velocity are found by determining approximate solutions, through an iteration process, of an integral equation for transonic flow proposed by Oswatitsch. The integral equation stems directly from the small-disturbance theory for transonic flow. This method of analysis possesses the advantage of remaining in the physical, rather than the hodograph, variable and can be applied in airfoils having curved surfaces. After discussion of the derivation of the integral equation and qualitative aspects of the solution, results of calculations carried out for circular-arc airfoils in flows with free-stream Mach numbers up to unity are described. These results indicate most of the principal phenomena observed in experimental studies

Condensate removal device for heat exchanger

A set of perforated tubes disposed at the gas output side of a heat exchanger, in a position not to affect the rate of flow of the air or other gas is described. The tubes are connected to a common manifold which is connected to a sucking device. Where it is necessary to conserve and recirculate the air sucked through the tubes, the output of the manifold is run through a separator to remove the condensate from the gas. The perforations in the slurper tubes are small, lying in the range of 0.010 inch to 0.100 inch. The tubes are disposed in contact with the surfaces of the heat exchanger on which the condensate is precipitated, whether fins or plates, so that the water may be directed to the tube openings by means of surface effects, together with the assistance of the air flow. Only about 5 percent of the air output need be thus diverted, and it effectively removes virtually all of the condensate

Analytical Investigation of Some Three-Dimensional Flow Problems in Turbomachines

One problem encountered in the theory of turbomachines is that of calculating the fluid velocity components when the inner and outer boundaries of the machine as well as the shape of or forces imparted by the blade row are given. The present paper discusses this problem under the restrictions that the fluid is inviscid and incompressible and that the blade rows consist of an infinite number of infinitely thin blades so that axially symmetric flow is assumed. It is shown, in general, that the velocity components in a plane through the turbomachine axis may be expressed in terms of the angular momentum and the leading-edge blade force normal to the stream surfaces. The relation is a nonlinear differential equation to which analytic solutions may be obtained conveniently only after the introduction of linearizing assumptions. A quite accurate linearization is effected through assuming an approximate shape of the stream surfaces in certain nonlinear terms. The complete linearized solution for the axial turbomachine is given in such form that blade loading, blade shape, distribution of angular momentum, or distribution of total head may be prescribed. Calculations for single blade rows of aspect ratio 2 and 2/3 are given for a radius ratio of 0.6. They indicate that the process of formation of the axial velocity profile may extend both upstream and downstream of a high-aspect-ratio blade row, while for low aspect ratios the major portion of the three-dimensional flow occurs within the blade row itself. When the through-flow velocity varies greatly from its mean value, the simple linearized solution does not describe the flow process adequately and a more accurate solution applicable to such conditions is suggested. The structure of the first-order linearized solution for the axial turbomachine suggested a further approximation employing a minimizing operation. The simplicity of this solution permits the discussion of three interesting problems: Mutual interference of neighboring blade rows in a multistage axial turbomachine, solution for a single blade row of given blade shape, and the solution for this blade row operating at a condition different from the design condition. It is found that the interference of adjacent blade rows in the multistage turbomachine may be neglected when the ratio of blade length to the distance between centers of successive blade rows is 1.0 or less. For values of this ratio in excess of 3.0, the interference may be an important influence. The solution for the single blade row indicated that, for the blade shape considered, the distortion of the axial velocity profile caused by off-design operation is appreciably less for low- than for high-aspect-ratio blades. To obtain some results for a mixed-flow turbomachine comparable with those for the axial turbomachine as well as to indicate the essential versatility of the method of linearizing the general equations, completely analogous theoretical treatment is given for a turbomachine whose inner and outer walls are concentric cones with common apex and whose flow is that of a three-dimensional source or sink. A particular example for a single rotating blade row is discussed where the angular momentum is prescribed similarly to that used in the examples for the axial turbomachine