Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POWER PRODUCTION FROM RENEWABLE ENERGY AY 2020-21 19 th July 2021 Prof. Silva Time: 1.5 hours Instructions for the examination: 1) Clearly indicate your name on all the files you will deliver. 2) The score refers to exercises done in a comprehensive manner with exact numerical results. Numerical results correct but not accompanied by explanations will not be taken into account. The final score can be normalized according to the average results. 3) Talking with colleagues and / or cheating will cause the cancellation of the exam. 4) All the needed data for the resolution of exercises lies on this paper. It is NOT ALLOWED to use material other than this (e.g. books, clipboard etc.). Exercise 1 (16 points) A geothermal source has the following characteristics at the outlet of the well: pressure 7 bar, vapor fraction 85%, mass flowrate 15 kg/s. Draw the power plant lay-out in a configuration with a direct mixing of the 2 liquid flows (without atmospheric vessel) (1 point) and determine the net power output (3 points), considering a con- densing pressure of 0.1 bar and assuming a steam turbine isentropic efficiency of 88% and a generator or- ganic-electric efficiency of 97%. Calculate the net electric efficiency considering a minimum reinjection tem- perature of 40°C and an overall auxiliary consumption of 700 kW (2 points). In order to increase the power output, the geothermal fluid is further heated to 440°C (enthalpy 3353.4 kJ/kg, entropy 7.758 kJ/kgK) in a biomass boiler (series configuration and neglecting pressure drops, biomass is oak described in the table below). The boiler has an efficiency of 90% and consists of an evaporator, a super- heater and a regenerative air pre-heater fed by the exhaust gases. Determine the overall net electric efficiency (geothermal+biomass) of the hybrid plant (3 points). Calculate the biomass flowrate on as received basis (con- sider ∆h evaporation,water = 2450 kJ/kg) (3 points). Finally, determine the air pre-heater effectiveness assuming an ambient air temperature of 25°C, cp of exhaust gases 1.1 kJ/kgK, cp of air 1 kJ/kgK, air mass flow rate 7 kg/s, evaporator pinch point 10°C, boiler thermal losses 1%, unburnt carbon and ashes losses equal to 2% of ther- mal power input (4 points). THERMODYNAMIC PROPER TIES OF WATER AT SAT URATION AND SUPER -HE ATED STEAM liquid vapor PRESSURE [BAR] Temperature [°C] h liq.sat. [kJ/kg] s liq.sat. [kJ/kgK] h vap.sat [kJ/kg] s vap.sat. [kJ/kgK] 7 165 697.1 1.992 2762.0 6.705 0.1 45.8 191.8 0.65 2584.8 8.151 oak (harvest conditions) %, weight dry basis C 48,80 H 6,09 O 45,00 ash 0,11 LHV, kJ/kg, dry basis 17769 HHV, kJ/kg, dry basis 19107 Moisture content, % 40 Exercise 2 for Energy Engineering students (14 points) A CSP plant based on parabolic trough collectors adopts molten salts as Heat Trasfer Fluid (T min 290°C - T max 550°C) and a steam cycle for the conversion of thermal power into electricity. The power plant characteristics are reported in the table below: Steam cycle net power 50 MW Piping thermal losses 2 MW Second law efficiency 55% Receiver specific thermal losses (per square meter of mirror aperture) 70 W/m 2 Ambient Temperature 25°C Collector Optical Efficiency 76% Solar Multiple 2.1 Design DNI 800 W/m 2 Aperture of solar collector 5.75 m Distance between parallel rows 2.5 x Aperture Loop lenght 800 m Concentration factor (Aperture colle ctor/ Dglass _envelope ) 70 Calculate (i) the area of the solar collectors (3 points), (ii) the size of the solar field (2 points) and (iii) the solar collector thermal efficiency (2 points). Assuming an average annual DNI of 700 W/m 2, compute (iv) the yearly electricity yield (4 points), (v) the average sun-to-electricity efficiency of the plant (2 points), and (vi) the equivalent hours (1 point) assuming the average values reported in the following table: Average incidence angle 30° Solar field working hours 2800 IAM=IAM(θ) with θ in degrees 1 - 5·10 -4·θ Receiver/piping thermal losses as in the design case Auxiliaries average consumption 1.9 MW Power Block efficiency 90% of the design case Exercise 2 for Management and Mechanical Engineering students (14 points) A three-bladed horizontal axis wind turbine is equipped with a variable speed and variable pitch regulation system. The turbine has a rotor diameter of 130 m, a rated wind speed of 12 m/s and is designed for an optimal λ tip equal to 7.5. Knowing that the machine fluid-dynamic performance is equal to 81% (ratio between the real Cp and the Betz Cp), that the efficiency of the gearbox is equal to 97% and the mechanical-electric generator efficiency is equal to 97.8 %, compute (i) the rated electric power developed in the design condition at sea level, 1 atmosphere and 25°C (the air density in these conditions is equal to 1.225 kg/m 3) (2 points). Calculate (ii) the rotational speed at design conditions (1 point). Assuming the validity of the Betz theorem, calculate (iii) the pitch angle at the blade tip knowing that the optimal incidence angle is equal to 8° (4 points). The electrical power developed by the turbine at the cut-in speed is equal to 235 kW. Assuming that the turbine has no lower limitations for rotational speed and considering the same mechanical and electrical efficiency of the design condition, determine (iv) the wind speed in cut-in conditions (2 points), (v) the machine rotational speed (1 point) and (vi) the variation of the pitch angle with respect to the design conditions (2 points). After that, evaluate the performance of the machine when installed at 4000 m altitude a.s.l. (above sea level) with a reference ambient temperature of 4°C (pressure gradient with altitude equal to 10 Pa/m), in particular calculate (vii) the corrected values respectively of the rated wind speed (1 point) and viii) the cut-in wind speed (1 point). Exercise 1 enthalpy 2452,2 kJ/kg flowrate dry 0,845 kg/s flowrate 12,75 kg/s water 0,5481 vapor fraction (is) 69,1% HHV as received 11464 kJ/kg enthalpy (is) 2123,6 kJ/kg LHV as rec 9678 kJ/kg enthalpy 2200,2 kJ/kg flowrate wet 1,55 kg/s Mechanical power 7163 kW gross electric power output 6948 kW net electric power output 6248 kW 3 punti T in exhaust gas 175,0 °C Q in max 34272 kW m exhaust gases 8,6 kg/s eta el 18,2 % 2 punti T out stack 136,8 °C Q pre -heater 359,2 kW vapor fraction (is) 94,8% T out air 76,3 °C enthalpy (is) 2459,4 kJ/kg h pre -heater 34,2% enthalpy 2566,7 kJ/kg Mechanical power 11802 kW Electrical power 11448 kW Net electric power 10748 kW thermal power input 13518 kW biomass th power input 15020,1 kW overall net plant efficiency 21,8% 3 punti Exercise 2 (Energy Eng. Students) Temp. ML 684,95 K eta lore ntz 56,47% eta first law 31,06% power PB 160,98 MW power PB + storage 338,07 MW solar field power 340,07 MW Solar collectors surface 632093 m^2 Linear lenght of solar collectors 109929 m Number of loops 137,4 Number of loops (integer) 137,0 Solar field width 2749 m Solar field size 2198932 m^2 Thermal losses 44,25 MW Q sun 505,67 MW Eta th 67,25% IAM ( θ) 98,50% cos ( θ) 86,60% K ( θ) = cos ( θ) * IAM ( θ) 85,30% Eta optical 64,83% annual DNI 1960,0 kWh/m^2 Annual radiation over tube 803,19 GWh Net annual Qth solar field 673,70 GWh Annual electricity 183,00 GWh Annual Eta el 14,77% Eta th medio 54,38% h eq 3660 h Exercise 2 (Manag and Mech. Eng. Students) AD 13273 m2 WID nom 14048,4 kW W Betz 8325,0 kW Wpale 6743 kW W el 6397 kW Cp 0,480 omega 1,385 rad/s 13,22 rpm u [m/s] vD [m/s] w [m/s] Teta [rad] Teta [�] Gamma [°] tip 90,00 8,00 90,35 0,088 7 5,1 -2,9 W rotor 247,7 kW W Betz 305,8 kW WID 516,1 kW v cut-in 4,0 m/s omega cut -in 4,40 rpm 0,460 rad/s omega cut -in 0,460 rad/s No pitch variation! P 60000 Pa ro' 0,791 kg/m3 v1' cut -in 4,62 m/s v1' nom 13,89 m/s