Energy Engineering - Wind, Hydro and Geothermal Power Generation

Full exam

POWER PRODUCTION FROM RENEWABLE ENERGY AY 2021-22 16 th January 2023 Prof. Silva Time: 1.5 hours Instructions for the examination: 1) Clearly indicate your name on all the sheets 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) Answer briefly and clearly only to the asked questions. Calculations and explanations which do not respond to the questions will not be considered for evaluation even if correct. 4) Talking with colleagues and / or cheating will cause the cancellation of the exam. 5) 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 12 bar, vapor fraction 80%, mass flowrate 15 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 0.08 bar and assuming a steam turbine isentropic efficiency of 87% and a generator organic-electric efficiency of 97%. Calculate the net electric efficiency considering a minimum reinjection temperature equal to the condensing temperature and an overall auxiliary consumption of 550 kW (2 points). In order to increase the power output, the geothermal fluid is further heated to 410°C in a biomass boiler, corresponding to an enthalpy of 3278,13 kJ/kg and an entropy of 7,303 kJ/kgK (series configuration, eliminat- ing the demister and neglecting pressure drops, biomass is oak described in the table below). The biomass boiler consists of an evaporator, a super-heater and a recuperative air pre-heater fed by the exhaust gases. Determine the biomass flowrate on as received basis (consider ∆h evaporation,water = 2450 kJ/kg), assuming an overall plant efficiency (geothermal+biomass) equal to 24.8% (3 points). Calculate the efficiency of the boiler section and the temperature of the exhaust gases at the outlet of the boiler (2 points). Determine the air pre- heater effectiveness, assuming a reasonable value for ambient air temperature, and knowing that: cp of ex- haust gases is 1.15 kJ/kgK, cp of air 1 kJ/kgK, air mass flow rate 13 kg/s, evaporator pinch point 15°C, unburnt carbon and ashes losses equal to 1.5% of thermal power input (4 points). THERMODYNAMIC PROPER TIES OF WATER AT SAT URATION 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] 12 188,0 798,4 2,22 2782,73 6,52 0,08 41,5 173,86 0,59 2577,11 8,23 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, % 50 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 130 m, a rated wind speed of 12.5 m/s and is designed for an optimal λ tip equal to 7.85. Knowing that the machine fluid-dynamic performance is equal to 80% (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 98.8%, 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 235 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 25 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 74 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). Exercise 1 enthalpy 2385,9 kJ/kg Mechanical power 12955 kW entropy 5,7 kJ/kgK Electrical power 12566 kW Vapour fraction 0,78 Net electric power 12016 kW h isentropica 2038,9 kJ/kg thermal power input 48451 kW entalpiaout 2135,6 kJ/kg biomass thermal power in- put 15269 kW potenza meccanica 7765 kW flowrate dry 0,859 kg/s potenza elettrica lorda 7532 water 0,5481 potenza elettrica netta 6982 kW HHV as received 9554 kJ/kg Q in max 33182 kW LHV as rec 7661 kJ/kg eta el 21,0 % flowrate wet 1,99 kg/s T out 410 °C p out 15 bar m air 13 kg/s moisture 50% cp exhaust gases 1,15 kJ/kgK LHV dry 17769 kJ/kgdry T air 15 °C HHV dry 19107 kJ/kgdry boiler efficiency 87,7 % overall efficiency 24,8 % T in exhaust gas 203,0 °C Enthalpy 3278,1 kJ/kg T out stack 111,1 °C entropia 7,30 delta T air 121,9 °C H 0,0609 effectiveness 64,8 % p out 0,08 bar Q HE 1584,5 kW isentropica 2285 kJ/kg entalpia out 2414 kJ/kg Exercise 2 (Mechanical and Management Engineering students) AD 13273 m2 WID nom 15878,6 kW W Betz 9409,6 kW Wpale 7528 kW W el 7034 kW Cp 0,474 omega 1,510 rad/s 14,42 rpm Wpale 248,5 kW W Betz 310,6 kW WID 524,1 kW v cut-in 4,01 m/s omega cut -in 0,484 rad/s 4,62 rpm VD 8,33 m/s F ax 1129,1 kN average u 49,06 m/s average radius 32,5 m Average Torque 4986, 5 kNm Average tang. Force on one blade 51,14 kN relative speed 49,77 m/s Teta 9,640 ° Lift force 320,4 kN Lift force tang. 53,7 kN Drag force tang. 2,52 kN Drag force 2,55 kN Drag coefficient 0,010 Lift/drag 125,55 Exercise 2 (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/ year tot x 1000 250263 A penstock [m2] 3,14 v penstock [m/s] 3,66 DH 0,758 (iv) net head [m] 24,24 prod I [MWh] 6238 prod II [MWh] 6094 (v) prod tot [MWh] 12332 prod tot [MJ] 4,44E+13 (vi) Pnom [kW] 2166 (vii) heq 5693