Approximate Solutions of a Class of Similarity Equations for Three-dimensional, Laminar, Incompressible Boundary-layer Flows
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Engineering topics
Publications and source records attributed to Herzig, Howard Z.
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Chapters XI to XIII concern the unsteady compressor operation arising when compressor blade elements stall. The fields of compressor stall and surge are reviewed in Chapters XI and XII, respectively. The part-speed operating problem in high-pressure-ratio multistage axial-flow compressors is analyzed in Chapter XIII. Chapter XIV summarizes design methods and theories that extend beyond the simplified two-dimensional approach used previously in the report. Chapter XV extends this three-dimensional treatment by summarizing the literature on secondary flows and boundary layer effects. Charts for determining the effects of errors in design parameters and experimental measurements on compressor performance are given in Chapters XVI. Chapter XVII reviews existing literature on compressor and turbine matching techniques.
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A survey of unclassified axial-flow-compressor literature is presented in the form of brief reviews of the methods, results, and conclusions of selected reports. The reports are organized into several main categories with subdivisions, and frequent references are made within the individual reviews to pertinent material elsewhere in the survey.
Flow-visualization techniques are employed to ascertain the streamline patterns of the nonpotential secondary flows in the boundary layers of cascades, and thereby to provide a basis for more extended analyses in turbomachines. The three-dimensional deflection of the end-wall boundary layer results in the formation of a vortex within each cascade passage. The size and tightness of the vortex generated depend upon the main-flow turning in the cascade passage. Once formed, a vortex resists turning in subsequent blade rows, with consequent unfavorable angles of attack and possible flow disturbances on the pressure surfaces of subsequent blade rows when the vortices impinge on these surfaces. Two major tip-clearance effects are observed, the formation of a tip-clearance vortex and the scraping effect of a blade with relative motion past the wall boundary layer. The flow patterns indicate methods for improving the blade tip-loading characteristics of compressors and of low- and high-speed turbulence.
An investigation of secondary-flow loss patterns originating in three sets of turbine nozzle blade passages was conducted by means of flow-visualization studies and detailed flow measurements. For all cases, high loss values were measured in the fluid downstream of the corners formed by the suction surfaces of the blades and the shrouds, and these losses were accompanied by discharge-angle deviations from design values. Despite the size of the loss regions and angle gradients, over-all mass-average blade efficiencies were of the order of 0.99 and 0.98 and, therefore, are not a good index of blade performance.
An investigation was made of losses and secondary flows in three different turbine nozzle configurations in annular cascade. Appreciable outer shroud loss cores (passage vortices) were found to exist at the discharge of blades which had thickened suction surface boundary layers near the outer shroud. Blade designs having thinner boundary layers did not show such outer shroud loss cores, but indicated greater inward radial flow of low momentum air, in the wake loss is to this extent an indication of the presence or absence of radial flow. The blade wake was a combination of profile loss and low momentum air from the outer shroud, and the magnitude of the wake loss is to this extent an indication of the presence or absence of radial flow. At a high Mach number, shock-boundary-layer thickening on the blade suction surfaces provided an additional radial flow path for low momentum air, which resulted in large inner shroud loss regions accompanied by large deviations from design values of discharge angle. (author)
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Flow-visualization studies, using smoke, were made of the secondary flows in rectangular bends, tandem cascades, and high-turning configurations. The roll-up of the wall boundary layer of a rectangular bend forms a passage vortex near the suction surface similar to that previously observed for cascades. The vortex so formed then shifts out into the main stream. Because of leading-edge effects, the boundary-layer flows in bends were found to be sufficiently different from the flows in blade rows to make direct application of bend results to blade rows inadvisable. Passage vortices are shown, in the tandem-cascade study, to resist turning with the main stream through which they pass and to disturb the flow in subsequent blade rows. This disturbance may explain in part the appreciable size of the losses sometimes attributed to secondary flows in turbomachines despite the fact that the energy involvement in vortex formation is slight. Tip-flow studies of high-turning blades with relative motion between blades and end wall indicated that if the relative sizes of the passage vortex forces, the tip clearance forces, and the blade-scraping effects are properly controlled, it may be possible to improve the blade-tip loading characteristics in turbomachine.
In order to increase understanding of the origin of losses in a turbine, the secondary-flow components in the boundary layers and the blade wakes of an annular cascade of turbine nozzle blades (vortex design) was investigated. A detailed study was made of the total-pressure contours and, particularly, of the inner-wall loss cores downstream of the blades. The inner-wall loss core associated with a blade of the turbine-nozzle cascade is largely the accumulation of low-momentum fluids originating elsewhere in the cascade. This accumulation is effected by a secondary-flow mechanism which acts to transport the low-momentum fluids across the channels on the walls and radially in the blade wakes and boundary layers. The patterns of secondary flow were determined by use of hydrogen sulfide traces, paint, flow fences, and total pressure surveys. At one flow condition investigated, the radial transport of low-momentum fluid in the blade wake and on the suction surface near the trailing edge accounted for 65 percent of the loss core; 30 percent resulted from flow in the thickened boundary layer on the suction surface and 35 percent from flow in the blade wake.
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