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ACCEPTED MANUSCRIPT then exit by the flow angle (α2) and absolute velocity (C2). Then the flow comes in the rotor with relative angle (β2) and velocity (W2) where the flow of the working fluid is speeded up to the relative velocity (W3) with the relative angle (β3) at the exit of the turbine’s rotor. In a single-stage axial turbine, 1=0; while, 1=3 in a multi- stage axial turbine. The flow angles at the inlet and outlet of the blade’s passage (stator and rotor) are given by the following equations (Japikse and Baines, 1994; Moustapha et al., 2003): (Ψ ‒ 2𝑅𝑛) tan 𝛽2 = 2𝜙 ‒(Ψ+2𝑅𝑛) tan 𝛽3 = 2𝜙 (Ψ 2+(1‒𝑅𝑛)) 𝜙 The expressions of the degree of reaction, flow and loading coefficient are as follows: ∆h𝑟𝑜𝑡𝑜𝑟 𝑅𝑛 = ∆h𝑠𝑡𝑎𝑔𝑒 𝐶𝑥 (6) tan 𝛼3 = ‒( 2‒(1‒𝑅𝑛)) Ψ} 𝜙 tan 𝛼2 = ∅=𝑈 } (7) 𝑤 ∆h𝑠𝑡𝑎𝑔𝑒 𝛹 = 𝑈2 = (𝑟𝑚Ω)2 The specific speed and specific diameter are dimensionless parameters and defined by equations (8) and (9) as stated in (Balje, 1981; Moustapha et al., 2003; Dixon and Hall, 2010) as follows: m Ω ρexit ns = (∆his)0.75 𝑑𝑟𝑜𝑡𝑜𝑟 (∆his)0.25 ds = m ρexit (8) (9) mean diameter is midway point between the tip and the hub and it can be defined as the diameter that divides the annulus into two equal areas as follows (Dixon and Hall, 2010): 𝑟𝑚2 = (𝑟2𝑡 + 𝑟h2) 2 (10) The PD code of an AFT is developed based on the AMDCKO (Ainley and Mathieson; Dunham and Came; Kacker and Okapuu) losses model, to calculate the losses through the blade’s passage of the AFT. The total losses in terms of profile, secondary flow, tip-leakage and trailing edge losses are used to predict the 9 ThePDF Image | turbine configuration for low-power organic Rankine cycle
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