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Thermodynamics Professor Lee Carkner Lecture 18

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1 Thermodynamics Professor Lee Carkner Lecture 18
Turbines Thermodynamics Professor Lee Carkner Lecture 18

2 Engine Cheat Sheet Ideal gas law Isentropic (constant specific heats)
Pv = RT Pv/T = Pv/T Isentropic (constant specific heats) (T2/T1) = (v1/v2)k-1 (T2/T1) = (P2/P1)(k-1)/k (P2/P1) = (v1/v2)k q = 0 Isentropic (variable specific heats) (P2/P1) = (Pr2/Pr1) (v2/v1) = (vr2/vr1) Pr and vr are functions of T and you can use to look up u and h Isochoric v = v q = cvDT = Du Isobaric P = P q = cpDT = Dh w = PDv Isothermal T = T q = w

3 PAL # 17 Gas Power Cycles Otto engine: rc = 8, qin = 750 kJ/kg, P1 = 95 kPa and T1 = 300 K, R = 0.287, k =1.4, cv = 0.718 Pv = RT, v1 = RT1/P1 = (0.287)(300)/(95) = m3/kg = vmax = v4 rc = vmax/vmin, vmin = vmax/rc = 0.906/8 = = v2 = v3 T2 = T1(v1/v2)k-1 = (300)(8)0.4 = 689 K

4 PAL # 17 Gas Power Cycles Find heats and work Find efficiency and MEP
DT = q/cv, T3 = (q/cv)+T2 = (750/0.718)+689 =1734 T4 = T3(v3/v4)k-1 = (1734)(1/8)0.4 = 755 P3 = (0.287)(1734)/ = 4404 kPa Find heats and work qout = cv(T4-T1) = (0.718)( ) = 327 kJ/kg Find efficiency and MEP hth = w/qin = 423/750 = = 56.4% MEP = w/(vmax-vmin) = 423/( ) = 533 kPa

5 Brayton Cycle Ideal, air standard, Brayton cycle:
Used for electricity generation and propulsion Ideal, air standard, Brayton cycle: Isentropic compression (compressor) Isentropic expansion (turbine) We replace ignition and exhaust with heat input and output to make a closed cycle

6 Brayton Efficiency The heat in and out take place during constant pressure processes so: We can use this to write the efficiency as: hth,Brayton = 1 – qout/qin = 1 – (T4-T1)/(T3-T2) We can relate the temperatures to the pressures with the isentropic relation: (T2/T1) = (P2/P1)(k-1)/k And thus the efficiency is hth,Brayton = 1 – 1/rp(k-1)/k

7 Brayton Turbines Higher pressure ratio produces more efficiency
Limited by the temperature the turbine blades can withstand Generally have better power to weight ratios than reciprocating engines, but are more expensive and use more fuel

8 Regeneration We can use them to heat the input gases
Such a system called a regenerator Extra efficiency not always worth the expense of the installation and operation costs

9 Effectiveness The gas from the compressor enters the regenerator at T2 and leaves at T5 We can compare the actual energy gain with the best case with the effectiveness, e e = For cold air standard, Dh = cpDT so e = (T5-T2)/(T4-T2)

10 Regeneration Efficiency
Effectiveness generally around 0.85 The efficiency of a turbine with regeneration is: hth,regen = 1 – (T1/T3)rp(k-1)/k Regeneration most effective at low rp and when the difference between the temperatures is high

11 Multistage We do this by using multistage processes where the fluid is heated or cooled between stages Called intercooling or reheating Depending on the number of stages More stages makes the device for complicated and expensive

12 Multistage Properties
The ratio of the input and output pressures of the compressors are equal P2/P1 = P4/P3 P6/P7 = P8/P9 The input temperatures and enthalpies are the same of each compressor T1 = T3, h1 = h3

13 Jet Propulsion If we reduce the work produced by a turbine to just enough to power the compressor, the exit gases will have a lot of energy Used for aircraft propulsion Amount of force (or thrust) is just the difference between the input and output momentum

14 Wp’ = FVaircraft = m’(Vexit-Vinlet)Vaircraft
Jet Efficiency If the wind velocity is small, Vinlet is equal to the aircraft’s speed The propulsive power of a turbojet is just: Wp’ = FVaircraft = m’(Vexit-Vinlet)Vaircraft hp = W’p/Q’in

15 Kinds of Jets Turbofan Afterburner Ramjet Scramjet Rocket
Has a turbine powered fan up front to move more air through Afterburner Ignite exhaust gases for burst of speed Ramjet A engine that is all afterburner Scramjet Supersonic ramjet Rocket A ramjet with its own air supply

16 Next Time Read: Homework: Ch 9, P: 95, 121, Ch 10, P: 15, 34


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