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The stator outlet flow enters the rotor with an absolute velocity inclined of the α angle with respect to the tangential direction of the reference system. The rotor rotational velocity generates a dragging speed of the inlet blades which has the same direction as the tangential component of the inlet flow absolute velocity. The inlet rotor flow relative velocity is a function of the rotor rotation velocity as well as the absolute flow velocity: 𝑐= 𝑢 (3) 𝑠𝑖𝑛 𝛼 In the ideal case the rotor inlet flow has zero incidence, therefore the relative velocity is exclusively radial, so the rotor blades have a radial inlet shape. The zero incidence does not allow the minimum value of losses due to the fluid-dynamic nature of the relative flow that enters radially into the blades, since a counter-rotating vortex must be generated which will restore the irrotational conditions of the absolute flow velocity. Radial blades will be assumed in the implemented model because they have the following advantages, better response to high centrifugal loads, due to the rotational velocity, and mechanical stresses. Furthermore, radial blades are very versatile in off-design conditions because they react well to directions of the relative flow different from the design one. In the radial blades hypothesis, the incidence will not be null, therefore an unguided component of the flow is generated, therefore the inlet relative flow will have a radial and tangential component. The model developed RTGD estimates the optimal incidence necessary to minimize losses. The tangential velocity component generated by the non-zero incidence is a function of the rotor number of revolutions and blade numbers, therefore, it is of fundamental calculating the correct number of blades. Generally, in real applications, many vanes are not used for several reasons, e.g. excessive flow blockage at rotor exit, a disproportionally large wetted surface causing high friction losses, and because the weight and inertia of the rotor may become too high. The optimum number of blades [5] in the RTGD is determined by a relationship that is a function of the rotor inlet flow angle α1. The incidence losses refer to the losses that occur at the inlet of the radial inflow turbine rotor blade passages when the turbine is operating at a non-zero incidence and, therefore, the flow does not enter the passage in the optimum direction. Losses in the rotor blade passage are mainly due to the occurrence of secondary flows, and these are considerably affected by the flow deviation from optimum incidence. The incidence angle is obtained from the difference between the inlet blade angle and inlet optimum blade angle β1_opt [4]. The experimentally optimum incidence should lie within the range of about -20° to -40° [12]. The term passage losses include a wide spectrum of different phenomena occurring to the fluid crossing the rotor. In fact, after a rapid acceleration in the flow direction, the fluid is turned in the meridional plane along the camber line: this creates a complex pattern of secondary and cross-stream flows, which still today are not completely understood. Moreover, this causes the growth of boundary layers with loss of kinetic energy and blockage. A fully detailed model that considers separately all these loss sources, as the ones existing for the axial turbines, has not yet been developed. In fact, in axial turbine cascades, this can be done by a careful set up and measures, but this is not actually possible for radial turbines, due to the three-dimensionality of the flow pattern, which does not permit to differentiate the losses. A passage loss model, namely the CETI model [12], was developed to estimate more realistically the losses due to the secondary flow and friction in the rotor passages. This loss type is estimated between the inlet and the throat of the rotor section: 4𝑡h𝑡𝑡 𝛥h =0.11𝑤2+𝑤2(𝐿 +0.68(1−(𝑟)2)𝑐𝑜𝑠𝛽 ) (4) 𝑝2𝐷h 𝑟4b𝑡 𝑐 The impeller blades mate up against the turbine housing with a small clearance to avoid mutual contact. In addition, the fluid pushes on the suction surface of each blade essentially creating a pressure difference between the suction and pressure blade surfaces i.e. across the blade. This pressure difference gives rise to a flow through the blade-housing clearance gap. This flow results in pressure dissipation and a consequent loss. In the radial and axial turbines, the tip clearance is defined as the gap between the rotor blade and the shroud. The radial clearance contributes to generate training the secondary flow and deviation of exit flow angle. The third 020097-5PDF Image | Radial turbine preliminary design and performance prediction
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