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CHAPTER 3: Methodology for Developing Radial Inflow Turbine (RIT) 3.5.2. Rotor modelling The choice of non-dimensional parameters for rotor modelling is arbitrary and depends on the availability of performance correlation charts and experience, however, the set of Ns-Ds or set of φ-ψ or solely ν are often used. In this chapter isentropic velocity ratio (ν) is employed as it combines stage expansion ratio and rotational speed. Another advantage of utilizing ν is that plotting the turbine efficiency against ν is almost independent of the rotational speed (Whitfield et al. 1990). Such non-dimensional parameter together with other turbine inputs (Table 3-1) establish the rotor principal geometry and velocity triangles at inlet and exit as shown in Figure 3-6. The velocity ratio shown by Equation 3-10 can be described with ideal-gas laws using Equation 3-11. 𝜈 = 𝑈4 = 𝐶𝑠 𝑈4 𝑃𝛾 √2𝐶𝑇(1−(5) ) 𝑃 𝑡,1 𝑃 𝑡,1 Where Cs (spouting velocity) is the velocity that has an associated kinetic energy equal to the isentropic enthalpy drop from turbine inlet total pressure to the final exhaust pressure (Dixon et al. 2010). With the known turbine input parameters (Table 3-1) spouting velocity (Cs) can be immediately determined leading to determination of the rotor wheel inlet velocity (U4) with the pre-set velocity ratio value. Consequently, the rotor inlet radius (r4), actual specific enthalpy drop (Δhactual) and power will be obtained as below: 𝛥h 𝑎𝑐𝑡𝑢𝑎𝑙 = 0.5𝐶2𝜂 𝑠 𝑠𝑡𝑎𝑔𝑒,𝑡𝑠 𝑟 =𝑈4 Equation3-12 Equation 3-13 Equation 3-14 Where the stage total-to-static efficiency (ηstage,ts) will be iterated based on the loss models as will be discussed in the following sections. 4 𝜔 𝑃𝑜𝑤𝑒𝑟 = 𝑚̇ 𝛥h𝑎𝑐𝑡𝑢𝑎𝑙 𝛾−1 Equation 3-11 64 | P a g ePDF Image | SMALL-SCALE RADIAL INFLOW TURBINE FOR WHR ORC
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