Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POWER PRODUCTION FROM RENEWABLE ENERGY AY 2021-22 20 th June 2022 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 15 bar, vapor fraction 85%, mass flowrate 13 kg/s. Draw the power plant lay-out in a configuration without the atmospheric vessel (1 point) and determine the net power output (4 points), considering a condensing pressure of 0.09 bar and assuming a steam turbine isentropic efficiency of 87% and a generator organic-electric efficiency of 97.5%. Calculate the net electric efficiency considering a minimum reinjection temperature of 40°C and an overall auxiliary consumption of 440 kW (2 points). In order to increase the power output, the geothermal fluid is further heated to 410°C in a biomass boiler (series configuration and neglecting pressure drops, biomass is oak described in the table below). The biomass boiler consists of an evaporator, a super-heater and a regenerative air pre-heater fed by the exhaust gases. Deter- mine the biomass flowrate on as received basis (consider ∆h evaporation,water = 2450 kJ/kg) assuming an overall plant efficiency (geothermal+biomass) equal to 24.4% (3 points). Calculate the efficiency of the boiler section (1 point) and the temperature of the exhaust gases at the stack (2 points) and the pre-heater effectiveness (3 points), assuming dry biomass, a reasonable value for ambient air temperature, cp of exhaust gas 1.2 kJ/kgK, cp of air 1 kJ/kgK, air mass flow rate 16.5 kg/s, evaporator pinch point 10°C, unburnt carbon and ashes losses equal to 2% of the thermal power input (molar mass of water 18 kg/kmol). 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] 15 198.3 844.66 2.31 2789.89 6.44 15 410.0 3278.13 7.30 0.09 43.8 183.28 0.62 2581.13 8.19 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, % 45 Density (as received), kg/m 3 850 Exercise 2 for Mechanical and Management 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 122 m, a rated wind speed of 13 m/s and is designed for an optimal λ tip equal to 7.8. Knowing that the machine fluid-dynamic performance is equal to 81% (ratio between the real Cp and the Betz Cp), the efficiency of the gearbox is equal to 97%, the mechanical-electric generator efficiency is equal to 97.5% and the frequency converter efficiency is 98.5%, compute (i) the nominal electric power output at the design condition at sea level: 1013 mbar and 25°C, with a correspondent air density equal to 1.225 kg/m 3 (3 points). Calculate (ii) the rotational speed of the turbine at the same condition (1 point). Given the electrical power output at the cut-in speed, equal to 210 kW, assuming that the turbine has no limitations to the rotational speed and considering constant mechanical and electrical efficiencies, determine (iii) the wind speed at cut-in conditions (2 points), and (iv) the machine rotational speed (1 point). Finally determine (iv) the resulting axial force acting on the nacelle (2 points) and (v) the drag coefficient (5 points) knowing that the lift coefficient is equal to 1.3 and the chord length is equal to 2.5 m (for simplicity perform the calculations assuming an average force applied to the mean diameter of the blade and a constant chord along the radius). Exercise 2 for Energy Engineering students (14 points) A run-of-river hydroelectric plant with a Kaplan turbine, in a diversion-channel configuration, is placed in corre- spondence of a hydraulic head of 15 m and located on a river with flow rates described by the following duration curve: DaysQ [m3/s] 060 1012 12012 3652 Assuming a linear trend of the duration curve between the points described in the table and considering an eco- logical flow requested for the site equal to 0.5 m 3/s, please (i) identify the nominal flow rate of the plant which at a first analysis appears to be suitable for maximizing the plant's profitability, knowing that the plant cost is propor- tional to its power (2 points). Knowing that the minimum operating flow of the turbine is equal to 25% of the nominal value, calculate (ii) the number of days of operation (3 points) and (iii) the annual volume of water derived by the plant (3 points). Moreover, knowing that the penstock has a diameter of 2 m, a length of 44 m, and a dimensionless friction coeffi- cient of 0.03, determine (iv) the net hydraulic head in nominal conditions (2 points) (density of water 1000 kg/m 3). Please note that the distributed friction losses are calculated as: ∆������������= ������������ ∙ ������������ ������������ ∙ ������������ ������������ 2 2 Considering for simplicity that friction losses in all hydraulic conditions are equal to the nominal value, calculate (v) the average annual productivity of the plant (2 points), knowing that the hydraulic efficiency of the turbine is equal to 90% in conditions of nominal flow rate, equal to 80% (simplified hypothesis) in all other conditions and that the organic-electric efficiency is equal to 88%. Finally calculate (vi) the nominal plant power (1 point) and (vii) the equivalent operating hours expected (1 point). RESULTS Exercise 1 Pressure 15 bar Mechanical power 11057 kW enthalpy liq 844,7 kJ/kg Electrical power 10780 kW enthalpy vap 2789,9 kJ/kg Net electric power 10340 kW enthalpy 2498,1 kJ/kg thermal power input 42379 kW steam fraction 0,85 - biomass thermal power in- put 12080 kW entropy 6,441 kJ/kg K flowrate dry 0,680 kg/s flowrate 11,05 kg/s water 0,5481 pressure 0,09 bar HHV as received 10509 kJ/kg isentropic 2027,3 kJ/kg LHV as rec 8668 kJ/kg enthalpy real 2126,4 kJ/kg flowrate wet 1,39 kg/s P mech 7331 kW P el gross 7148 kW T pinch 10 °C P el net 6708 kW 4 punti unburnt 2,0% Q in max 30299 kW m air 16,5 kg/s eta el 22,1 % 2 punti cp exhaust gases 1,2 kJ/kgK T air 20 °C T out 410 °C boiler efficiency 83,9 % p out 15 bar T out stack 102,4 °C moisture 45% T in exhaust gas 208,3 °C LHV dry 17769 kJ/kgdry delta T air 132,4 °C HHV dry 19107 kJ/kgdry effectiveness 68,5 % overall efficiency 24,4 % Q HE 2183,9 kW Enthalpy 3278,13 kJ/kg entropy 7,30 kJ/kg K H 0,0609 p out 0,09 bar isentropic 2301 kJ/kg enthalpy real 2428 kJ/kg Exercise 2 for Mechanical and Management Engineering students AD 11690 m2 WID nom 15730,6 kW W Betz 9281,1 kW Wpale 7518 kW W el 7003 kW Cp 0,478 omega 1,662 rad/s 15,87 rpm Wpale 222,0 kW W Betz 274,1 kW WID 462,6 kW v cut-in 4,01 m/s omega cut -in 0,513 rad/s 4,90 rpm VD 8,6 7 m/s F ax 1075,6 kN average u 50,70 m/s average radius 30,5 m Average Torque 4522, 5 kNm Average tang. Force on one blade 49,43 kN relative speed 51,44 m/s Teta 9,700 ° Lift force 321,3 kN Lift force tang. 54,1 kN Drag force tang. 4,70 kN Drag force 4,77 kN Drag coefficient 0,019 Lift/drag 67,32 Exercise 2 for Energy Engineering students (i) Q nom [m3/s] 11,5 Qmin m3/s 2,875 AQ/gg 0,0408 (ii) working days 331 m3/year part I 1,19E+08 m3/year part II 1,31E+08 (iii) m3/anno tot x 1000 250263 A penstock [m2] 3,14 v penstock [m/s] 3,66 DH 0,451 (iv) net head [m] 14,549 prod I [MWh] 3744 prod II [MWh] 3657 (v) prod tot [MWh] 7401 prod tot [MJ] 2,66E+13 (vi) Pnom [kW] 1300 (vii) heq 5693