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Energies 2020, 13, 2118 1 5 of 19 πππ‘π‘π‘π‘ = 1 + [πππ π ππ32β2 + (πππππΆπΆ2β2)(h3βh2)]/(h01 β h03) (11) ππ= 1 (12) π‘π‘π‘π‘ 1 + [πππ π ππ32β2 + (πππππΆπΆ2β2)(h3βh2) + πΆπΆ32β2]/(h01 β h03) The definitions of loading coefficient (ππ) and flow coefficient (ππ) for radial outflow turbines are given in Equations (13) and (14) [6,23]. ππ πΆπΆ β ππ πΆπΆ ππ= 2 2ππππ2 3 3ππ (13) ππ = πΆπΆ3ππ (14) ππ2 2.2. Algorithm of preliminary design program Figure 4 shows the flow chart of the preliminary design algorithm presented in this study for ORC radial outflow turbines. This program was developed with MathWorks MATLAB R2016a [24], and the state of the working fluid is based on Nist Refprop V9.1 [25]. The algorithm embedded in the program performs the preliminary design of the turbine based on the following assumptions. β’ The meridian absolute velocity (πΆπΆ ) is constant. β’ Standard stage is applied. ππ β’ The height of the blades (π»π») is constant. β’ The velocity ratio (ππ) is 0.7. In order to satisfy the design conditions, the preliminary design program determines the main specifications of the radial outflow turbine such as the length, angle, and number of blades through iterative calculation. The loss model used in the preliminary design algorithm is Soderberg's correlation [22,26]. It is an equation created from many experimental results, and it is known that the error for a wide range of Reynolds numbers is as low as 3%. The nominal loss coefficient (ππβ) represents the loss when the blade has an aspect ratio (π»π»βππ) of 3 and Reynolds number of 105. The nominal loss coefficient (ππβ) can be expressed as Equation (15). ππβ =0.04+0.06οΏ½ ππ οΏ½2 (15) 100 If the aspect ratio (π»π»βππ) is not 3, the loss coefficients (ππ1) for the nozzle blade and the rotor blade can be expressed by Equations (16) and (17), respectively. For the nozzle blade, 1 + ππ1 = (1 + ππβ)(0.993 + 0.021 ππβπ»π») (16) 1 + ππ1 = (1 + ππβ)(0.975 + 0.075 ππβπ»π») (17) for the rotor blade, If the Reynolds number is not 105, the loss coefficient (ππ2) corrected by the Reynolds number can be obtained through Equations (18)β(20). 105 1β4 where ππ1 (18) π π π π = ππ2πΆπΆ2π·π·h/ππ (19) ππ2 = οΏ½ π π π π οΏ½PDF Image | Analysis of a Radial Outflow Turbine for Organic Rankine Cycles
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