Tip loss
A characteristic of the actuator disc concept is that the linear theory of lift is maintained right out to the edge of the disc.Physically,recalling Fig.2.1a–2.1c,we suppose the induced velocity,in which the pressure is above that of the surrounding air, to be contained entirely below the disc in a well-defined streamtube surrounded by air at rest relative to it. In reality, because the rotor consists of a finite number of separate blades, some air is able to escape outwards between the tips, drawn out by the tip vortices. Thus the total induced flow is less than the actuator disc theory would prescribe,so that for a given pitch setting of the blades the thrust is somewhat lower than that given by Equation (3.22). The deficiency is known as tip loss and is shown by a rapid falling off of lift over the last few per cent of span near the tip, in a blade loading distribution such as that of Fig. 2.13. Although several workers have suggested approximations [Bramwell (p. 111) quotes Prandtl, Johnson (p. 60) quotes in addition Sissingh and Wheatley] no exact theory of tip loss is available. A common method of arriving at a formula is to assume that outboard of a station r = BR the blade sections produce drag but no lift. Then the thrust integral in Equation (3.21) is replaced by
A characteristic of the actuator disc concept is that the linear theory of lift is maintained right out to the edge of the disc.Physically,recalling Fig.2.1a–2.1c,we suppose the induced velocity,in which the pressure is above that of the surrounding air, to be contained entirely below the disc in a well-defined streamtube surrounded by air at rest relative to it. In reality, because the rotor consists of a finite number of separate blades, some air is able to escape outwards between the tips, drawn out by the tip vortices. Thus the total induced flow is less than the actuator disc theory would prescribe,so that for a given pitch setting of the blades the thrust is somewhat lower than that given by Equation (3.22). The deficiency is known as tip loss and is shown by a rapid falling off of lift over the last few per cent of span near the tip, in a blade loading distribution such as that of Fig. 2.13. Although several workers have suggested approximations [Bramwell (p. 111) quotes Prandtl, Johnson (p. 60) quotes in addition Sissingh and Wheatley] no exact theory of tip loss is available. A common method of arriving at a formula is to assume that outboard of a station r = BR the blade sections produce drag but no lift. Then the thrust integral in Equation (3.21) is replaced by
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