EXERCISE 1
The report is mandatory for the exam
Part 1
Calculate the energy density for these forms of energy.
Natural gas, Hu= 8 570 kcal/Nm³, 𝜌 = 0,8 𝑘𝑔/𝑁𝑚3
𝑘𝑔
Coal, Hu= 6000 kcal/kg, 𝜌 = 1300 𝑚3
Wind, 𝜌 = 1,2 𝑘𝑔/𝑚3 𝑣 = 10 𝑚/𝑠;
𝑘𝑔
𝑘𝐽
Air, thermal energy, 𝜌 = 0,53 𝑚3 , 𝑇 = 400°𝐶, 𝑐𝑝 = 1,09 𝑘𝑔𝐾
Water flow, kinetic energy, 𝜌 = 1000 𝑘𝑔/𝑚3, 𝑣 = 10 𝑚/𝑠;
Water, potential energy, h= 400 m, 𝜌 = 1000 𝑘𝑔/𝑚3
Part 2
Calculate the energy and power density of the energy conversion systems listed below and represent
the points corresponding to the calculated values on a diagram Ev-PA
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Combustion chamber for steam generator
Convection superheater
Steam condenser
Pelton turbine
Kaplan turbine
Centrifugal pump
Steam turbine element with reaction degree 0.5
Axial gas turbine element
4-stroke naturally aspirated petrol engine
2-stroke supercharged slow diesel engine
Wind turbine
Solar collector (PA only)
BWR nuclear reactor
Combustion chamber for steam generator (suppose that 35% of the generated thermal energy is exchanged
by radiation in the combustion chamber, the remaining energy flows through the other heat exchangers): gas
pressure 1.02 * 105 N/m2; temperature 1600 K; air / fuel ratio 17; flue gas velocity 16 m/s; gas density 1.1 *
air density in the same thermodynamic conditions; irradiation constant 4 W/(m2 K4); external temperature of
the evaporator pipes 673 K; Hu = 10000 kcal/kg.
Convection superheater (65% of the thermal energy generated in the combustion chamber passes through
this element): α = 42 W/(m2 K); flue gas temperature 1150°C to 900°C; steam temperature from 470°C to
538°C.
Steam condenser: pressure 0.05 bar; steam density 0.035 kg/m3; α = 4000 W/(m2 K); rx = 500 kcal/kg = 2.1
* 106 J/kg; steam speed 100 m/s.
Turbines and pumps
Pelton turbine
Kaplan turbine
Centrifugal pump
Steam turbine stage
Gas turbine stage
ϕ
2.0
0.4
0.12
0.4
0.7
ψ
2.0
0.1
0.5
1.0
1.0
u[m/s]
80
70
70
300
300
ρ[kg/m3]
103
103
103
0.05
1.1
• 4-stroke naturally aspirated petrol engine: 𝑣𝑚 = 14 𝑚/𝑠; ∆= 14; 𝜂 = 0,27; 𝐻𝑢 = 10000 𝑘𝑐𝑎𝑙/𝑘𝑔.
• 2-stroke supercharged slow diesel engine: 𝑣𝑚 = 6.7 𝑚/𝑠; ∆= 38; 𝜂 = 0,42; 𝜌 = 2,78 𝑘𝑔/𝑚3 ; 𝐻𝑢 =
9500 𝑘𝑐𝑎𝑙/𝑘𝑔.
• Wind turbine: 𝑣 = 10 𝑚/𝑠; 𝜌 = 1,2 𝑘𝑔/𝑚3 .
• Solar collector: 𝑃𝐴 = 1000 𝑊/𝑚2 .
• BWR nuclear reactor: 𝜌 = 104 𝑘𝑔/𝑚3; 𝑃𝐴𝑆 ≤ 1000 𝑘𝑊/𝑚2; 𝐸ℎ = 2,38 ∗ 1012 𝐽/𝑘𝑔.