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where π and π are the average passage radius from the axis of rotation and the average passage height from hub to shroud, respectively. The clearance mass flow rate is a function of the blade geometry and flow rate. ππΆπΏ =π2ππΆπΏπππππΏπππΆπΏ Eqn.3-14 where bCL is the blade to shroud clearance and UCL is an empirical clearance flow velocity, given by ππΆπΏ = 0.816 π΄π΅π(2βππΆπΏ /π2 ) Eqn. 3-15 Skin Friction is the loss associated with the shear forces of the flow against the surfaces of the impeller and the casing. It is defined as a fractional pressure loss and is given by π =4πΆ ππππ 2 πΏπ Eqn.3-16 π πΉ π π‘ π1 , π π π· π π¦ π where ππππ is the RMS value of relative velocity from impeller inlet to impeller outlet, given by ππππ = 12 π12 + π22 1/2 The turbulent skin friction factor, Cft, is given by πΆππ‘ = πΆππ‘π πΆππ‘π + πΆππ‘π βπΆππ‘π 1β60/π ππ Eqn. 3-17 π ππ < 60 Eqn. 3-18 π ππ β₯60 where π ππ is a Reynolds number which takes into account the roughness of the surface. It is used only to define the friction factors and is defined as π ππ = π ππ β 2,000 π Eqn. 3-19 π·π π¦π where e is the surface roughness, Red is the Reynolds number based on average hydraulic diameter, and Dhyd is the average hydraulic diameter of the impeller passage. The additional subscripts βsβ and βrβ refer to the smooth surface and rough surface friction factors. The roughness effect becomes important when Ree is greater than 60. The friction factors are given 61PDF Image | Supercritical Carbon Dioxide Cycle Analysis
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