# rankine cycle

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Vapor Power Cycles

Prof. Osama A. El Masry Mechanical Engineering Dept. Alexandria University

Overview Review Steam Properties Steam Tables & charts Steam Cycles Steam Cycle Parameters

Prof. O. El Masry

Steam Power CyclesThermodynamic Cycle Work Addition Heat Addition Work Extraction Heat Rejection Basic Cycle = Carnot Cycle Most Efficient Cycle Between Temperature of Heat Addition and Heat Rejection

Prof. O. El Masry

Carnot Cycle within Steam DomeTL TH

L Thermal ! 1

Net Work Area= 1-2-3-4

Heat Rejection =Area 4-3-b-aProf. O. El Masry

To design a Vapor Power Plant Use idealized Carnot cycle as the model; consider limitations and redesign the cycle accordingly Idealized Rankine cycle;

Practical Problems associated with Carnot Cycle Plant Maximum temperature limitation for cycle (a). Isentropic expansion in a turbine from 3-4. What is the quality of the steam inside the turbine? Will high moisture content affect the operation of the turbine? Isentropic compression process in a pump from 1-2. Is it practical to handle two-phase flow (liquid + vapor) using such one system?

The latter two problems can be resolved by the use of cycle (b) from previous slide. However, the (b) cycle requires the compression(1-2)of liquid at a very high pressure (exceeding 22 MPa for a steam, how do I get this number from?) and that is not practical. Also, to maintain a constant temperature above the critical temperature is also difficult since the pressure will have to change continuously.

Prof. O. El Masry

Modified Rankine Cycle To avoid transporting and compressing two-phase fluid, we can try to condense all fluid exiting from the turbine into saturated liquid before compressed it by a pump. When the saturated vapor enters the turbine, its temperature and pressure decrease and liquid droplets will form by condensation. These droplets can produce significant damages to the turbine blades due to corrosion and impact.

One possible solution: superheating the vapor. Also increases the thermal efficiency of the cycle.

Prof. O. El Masry

T-S Diagram for Water/Steam1000 900

Critical Point800

Constant Temperature During Boiling Higher Pressure -> Higher TemperatureSaturated Steam

700

Temperature (deg F)

600

Saturated Water

1000 psia

500

Boiling300 psia

400

300

200

100

Above Critical Point (~220 bar) -> No Phase Change (No Boiling)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

0

Entropy (Btu/lbm/deg R)

Prof. O. El Masry

Rankine Cycle The model cycle for vapor power cycles is the Rankine cycle which is composed of four internally reversible processes: constant-pressure heat addition in a boiler, isentropic expansion in a turbine, constant-pressure heat rejection in a condenser, and isentropic compression in a pump. Steam leaves the condenser as a saturated liquid at the condenser pressure.

Prof. O. El Masry

Rankine Cycle

Steam/Water Properties Constant Pressure Heat Addition1

Concept of Average Temperature of Heat AdditionProf. O. El Masry

The Simple Ideal Rankine Cycle

The McGraw-Hill Companies, Inc.,1998 Prof. O. El Masry

Simple Rankine Cycle Diagram

LEGEND AIR, GAS STEAM WATER

Prof. O. El Masry

Ideal Rankine Cycle Energy analysis: steady flow process, no generation, neglect KE and PE changes for all four devices, 0 = (net heat transfer in) - (net work out) + (net energy flow in) 0 = (qin - qout) - (wout - win) + (hin - hout) 1-2: Pump (q=0) wpump = h2 - h1 = v(P2-P1) 2-3: Boiler (w=0) qin = h3 - h2 3-4: Turbine (q=0) wout = h3 - h4 4-1:Condenser(w=0) qout = h4 - h1 Thermal efficiency = wnet = 1 - qout/q in = 1 - (h4-h1)/(h3-h2) wnet = wout - win/ qin = (h3-h4) - (h2-h1)

ExampleConsider the Rankine power cycle as shown. Steam enters the turbine as 100% saturated vapor at 6 MPa and saturated liquid enters the pump at a pressure of 0.01 MPa. If the net power output of the cycle is 50 MW. Determine (a) the thermal efficiency, (b) the mass flow rate of the system, (c) the rate of heat transfer into the boiler, (d) the mass flow rate of the cooling water from the condenser, in kg/s, if the cooling water enters at 20C and exits at 40C

Solution At the inlet of turbine, P3=6MPa, 100% saturated vapor x3=1, from saturated steam tables, h3=hg=2784.3(kJ/kg), s3=sg=5.89(kJ/kg K) From 3-4, isentropic expansion: s3=s4=5.89 (kJ/kg K) From tables, P4=P1=0.01MPa, T4=T1=45.8C sf4=0.6491, sfg4=7.5019, hf4=191.8, hfg4=2392.8 x4 = (s4-sf4)/sfg4 = (5.89-0.6491)/7.5019 = 0.699 h4 = hf4+x4* hfg4 = 191.8+0.699(2392.8) = 1864.4 (kJ/kg) Or from h-s chart, h4=1865 (kJ/kg), x4=0.699

Solution (cont.) At the inlet of the pump: saturated liquid h1=hf1=191.8 qout = h4-h1=1672.6(kJ/kg) At the outlet of the pump: compressed liquid v2=v1=vf1=0.00101(m3/kg) work input to pump Win = h2-h1 = v1 (P2-P1) = 0.001 (6000-10) = 6.05 h2 = h1 + v1 (P2-P1) =191.8 + 6.05 = 197.85 (kJ/kg) In the boiler, qin=h3-h2=2784.3197.85=2586.5(kJ/kg)

3 P-t r x MPaDry &sat

4

1

2

h(kJ/kg) 2784.3

. 1 MPa 0.01 MPa MPa Sat. liq. X=0. 1864.4 191.8 197.85

Prof. O. El Masry

Solution (cont.) (a)The thermal efficiency =1-qout/qin =1-1672.6/2586.5=0.353=35.% (b) Net power output =50MW=(ms)(Wout-Win)=(ms)((h3-h4)(h2-h1)) mass flow rate (ms)=50000/((2784.3- 1864.4 )-(197.85191.8))=54.7(kg/s) (c) heat transfer into the h2)=54.7(2586.5)=141.5(MW) boiler qin = (ms)(h3-

Solution (cont.) (d) Inside the condenser, the cooling water is being heated from the heat transferred from the condensing steam. q cooling water = qout = (ms)(h4-h1) = 54.7(1672.6) = 91.49 (MW) (mcw)Cp (Tout - Tin) = q cooling water C p (water) = 4.18(kJ/kg K) (mcw) = 91490/(4.177*(40-20)) = 1095.2 (kg/s) Very large amount of cooling water is needed

Rankine Cycle: Actual Vapor Power Deviation and Pump and Turbine Irreversibilities(a) Deviation of actual vapor power cycle from the ideal Rankine cycle. (b) The effect of pump and turbine irreversibilities on the ideal Rankine cycle.(Fig. 9-4)

Prof. O. El Masry

Rankine Cycle Efficiency The thermal efficiency of the Rankine cycle can be increased by increasing the average temperature at which heat is added to the working fluid and/or by decreasing the average temperature at which heat is rejected to the cooling medium. The average temperature during heat rejection can be decreased by lowering the turbine exit pressure. Consequently, the condenser pressure of most vapor power plants is well below the atmospheric pressure.Prof. O. El Masry

9-3

Effect of Lowering Condenser Pressure on the Ideal Rankine cycle(Fig. 9-6)

Prof. O. El Masry

Rankine Cycle Efficiency (cont.) The average temperature during heat addition can be increased by raising the boiler pressure or by superheating the fluid to high temperatures. There is a limit to the degree of superheating, however, since the fluid temperature is not allowed to exceed a metallurgically safe value.

Prof. O. El Masry

Effect of Increasing Boiler Pressure on the Ideal Rankine cycle(Fig. 9-8)

Prof. O. El Masry

Rankine Cycle Enhancements Superheating decreases the moisture content of the steam at the turbine exit. Lowering the exhaust pressure or raising the boiler pressure, however, increases the moisture content. For improved efficiencies at higher boiler pressures and lower condenser pressures, steam is usually reheated after expanding partially in the high-pressure turbine.

Prof. O. El Masry

Rankine Cycle Enhancements Steam is extracted after partial expansion in the high-pressure turbine, it is sent back to the boiler where it is reheated at constant pressure, it is returned to the low-pressure turbine for complete expansion to the condenser pressure.

Prof. O. El Masry

Rankine Cycle Enhancements The average temperature during the reheat process, and thus the thermal efficiency of the cycle, can be increased by increasing the number of expansion and reheat stages. As the number of stages is increased, the expansion and reheat processes approach an isothermal process at maximum temperature. Reheating also decreases the moisture content at the turbine exit.

Prof. O. El Masry

The Ideal Reheat Rankine Cycle

(Fig. 9-11)

Prof. O. El Masry

Rankine Cycle Enhancements Another way of increasing the thermal efficiency of the Rankine cycle is by regeneration. During a regeneration process, liquid water (feedwater) leaving the pump is heated by some steam bled off the turbine at some intermediate pressure in devices called feedwater heaters.

Prof. O. El Masry

Rankine Cycle Enhancements Notes a) The two streams are mixed in open feedwater heaters, and the mixture leaves as a saturated liquid at the heater pressure. b) In closed feedwater heaters, heat is transferred from the steam to the feedwater without mixing.

Prof. O. El Masry

Feedwater Heaters The purpose for feedwater heaters is to increase the temperature of the boiler feedwater to a saturated liquid state prior to entering the boiler Irreversibilities associated with the heat transfer from the flue gas to the steam can be reduced by transferring energy at the highest possible temperature (minimizing the (T)

Prof. O. El Masry

Feedwater Heaters This temperature would be the saturationtemperature for the boiler pressure Minimizing the irreversibilities in the reheaters can be accomplished by increasing the feedwater temperatures in small increments.

Prof. O. El Masry

Feedwater Heaters Introducing several feedwater heaters can reduce the temperature differences and the irreversibilities Counterflow heaters can also reduce temperature differences and irreversibilities Feedwater heaters can have three stages for the extracted steam: a de-superheater (for superheated extraction) a condenser A drain cooler

Prof. O. El Masry

Feedwater Heaters de-superheater condenser drain cooler

Prof. O. El Masry

Open Feedwater Heaters Steam extracted from the turbine is mixed directly with the boiler feedwater. The boiler feedwater must be pumped to a pressure slightly less than the pressure of the extracted steam by a feedwater pump. (If thefeedwater pressure is allowed to exceed the extraction pressure feedwater could flow into the turbine.)

One feedwater pump is required for each open feedwater heater.

Prof. O. El Masry

Open Feedwater Heaters Open feedwater heaters are also used as deaerators because the open feedwater liberates noncondensing gasses that are vented to the atmosphere Each additional feedwater pumps require additional capital expense and are a source of operational problems, service problems and noise problems. As a result, most feedwater heaters are closed feedwater heatersProf. O. El Masry

Ideal Regenerative Rankine Cycle with Open Feedwater Heater(Fig. 9-15)

Prof. O. El Masry

Steam TurbinesTurbines perform the energy conversion in two steps: Step 1: Thermal energy of the steam to kinetic energy of the steam Step 2: Kinetic energy of the steam to mechanical energy of the rotor

Prof. O. El Masry

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Prof. O. El Masry

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