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Ebook Fluid mechanics and thermodynamics of turbomachinery (6th edition): Part 2

(BQ) Part 2 book "Fluid mechanics and thermodynamics of turbomachinery" has contents: Three-Dimensional flows in axial turbomachines; centrifugal pumps, fans, and compressors; radial flow gas turbines; hydraulic turbines; wind turbines. | CHAPTER Three-Dimensional Flows in Axial Turbomachines 6 It cost much labour and many days before all these things were brought to perfection. Defoe, Robinson Crusoe 6.1 INTRODUCTION In Chapters 4 and 5 the fluid motion through the blade rows of axial turbomachines was assumed to be two-dimensional in the sense that radial (i.e., spanwise) velocities did not exist. This assumption is not unreasonable for axial turbomachines of high hub–tip ratio. However, with hub–tip ratios less than about 4/5, radial velocities through a blade row may become appreciable, the consequent redistribution of mass flow (with respect to radius) seriously affecting the outlet velocity profile (and flow angle distribution). The temporary imbalance between the strong centrifugal forces exerted on the fluid and radial pressures restoring equilibrium is responsible for these radial flows. Thus, to an observer travelling with a fluid particle, radial motion will continue until sufficient fluid is transported (radially) to change the pressure distribution to that necessary for equilibrium. The flow in an annular passage in which there is no radial component of velocity, whose streamlines lie in circular, cylindrical surfaces and which is axisymmetric, is commonly known as radial equilibrium flow. An analysis called the radial equilibrium method, widely used for three-dimensional design calculations in axial compressors and turbines, is based upon the assumption that any radial flow that may occur is completed within a blade row, the flow outside the row then being in radial equilibrium. Figure 6.1 illustrates the nature of this assumption. The other assumption, that the flow is axisymmetric, implies that the effect of the discrete blades is not transmitted to the flow. 6.2 THEORY OF RADIAL EQUILIBRIUM Consider a small element of fluid of mass dm, shown in Figure 6.2, of unit depth and subtending an angle dθ at the axis, rotating about the axis with tangential velocity, cθ at radius r. The