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3.4 Tip Clearance Loss The tip clearance is modelled as an orifice with shear flow inside the passage (Ghosh et al., 2011). A study by Baines shows that radial clearance has strong influence on the exit flow condition compared to axial clearance (Moustapha et al., 2003). An in-depth examination has showed that the variations of efficiency with axial and radial clearance are not independent as some cross-couplings exist. The cross coupling coefficient was represented with a coefficient, Ka,r and the tip clearance loss is represented by the equation below. U1Zr(KCKCK CC tip 8 aaa rrr a,r arar 3.5 Windage Loss 3. Guess-estimate a value for relative exit flow velocity and entropy drop across the stage 4. Calculate thermodynamic properties at both inlet and outlet 6. Calculate loss coefficient of rotor and entropy drop (back to step 3 if the entropy drop does not converge) 7. Calculate Turbine Efficiency Figure 5: Performance Analysis of Radial Turbine by Implementing Real Fluid Database Windage loss is frictional loss due to leakage of fluid between the back face of the rotor and the back plate. Daily and Nece (Daily & Nece, 1960) considered a simple case of a disk rotating in an enclosed casing. The empirical equations were modified to account for the frictional torque on the back face of turbine rotor. The loss model was then modified and expressed as power loss (Moustapha et al., 2003) and enthalpy loss (Ghosh et al., 2011). Equation (8) shows the windage loss as enthalpy loss. w i n d a g e (8) (7) 1. Supply Geometry Data 2. Construct Velocity Diagram 5. Calculate new relative exit velocity flow based on continuity equation (back to step (3) if the velocity does not converge) k U3r2 11 The performance analysis is conducted by first guess- estimating a value for relative flow velocity at turbine outlet and entropy drop across the turbine wheel. Based on the given turbine dimensions, the blade speed is determined. The velocity diagram is then constructed. The thermodynamic properties at both turbine inlet and outlet are then calculated. The new value of relative flow velocity is then calculated from continuity equation. If the error of the relative flow velocity is less than the tolerance value, the calculation process will be iterated to achieve convergence on the relative flow velocity. The individual loss of radial turbine is then calculated from the loss models discussed in previous sections. A new value of entropy drop across the turbine is then calculated. The calculation process will be iterated until convergence is achieved on the entropy drop. Finally, the stage efficiency is calculated based on the calculated loss coefficient. The design process overview is presented in Figure 5. For rotor with radial blade and no guided nozzle, the relative flow angle β1 is zero and the tangential component of flow velocity Cθ1 is equal to blade tip speed (Serrano et al., 2008). 4. PERFORMANCE ANALYSIS OF TC-1 The simulation result shows that the power output of the radial turbine is increasing with increasing rotational speed and mass flow rate. From Figure 6, at low rotational speed, the power difference is small for different mass flow rate. However, the power difference is significant for different mass flow rate at high rotational speed. The pressure ratio across the turbine wheel is increasing with rotational speed. At high rotational speed and a mass flow rate of 0.1 kg/s. there is a significant increase in pressure ratio when compared to high flow rates of 0.5 kg/s and 1.0 kg/s. f 2 m W 2 2 3.6. Performance Analysis Flow 12 10 8 6 4 2 0 m=0.1 kg/s m=0.5kg/s m=1kg/s 0 10 20 30 40 50 Rotational Speed x1000 (rev/min) Figure 6: Variation of Power with Shaft Speed and Mass Flow Rate Figure 7 shows the performance curve at different mass flow rates and rotational speeds. A clear correlation between the investigated parameters is not found. The figure shows an increase in efficiency at 1 kg/s up to 20,000 rpm before a constant efficiency between 20,000 and 50,000 rpm. The turbine shows a near-to-constant efficiency at 0.5 kg/s and 0.1 kg/s. The smaller mass flow rate of 0.1 kg/s shows a lower efficiency (about 55%) compared to the efficiency at 0.5 kg/s (about 77%). 35th New Zealand Geothermal Workshop: 2013 Proceedings 17 – 20 November 2013 Rotorua, New Zealand Power (kW)PDF Image | TURBOCHARGER AS TURBO-EXPANDER FOR ORGANIC RANKINE CYCLE
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