Clausius-Rankine cycle
The Clausius-Rankine cycle is a thermodynamic cycle , named after the German physicist Rudolf Julius Emanuel Clausius and the Scottish engineer William John Macquorn Rankine . It serves as a comparison process for the steam power plant in its simplest constellation with steam turbine T, condenser Ko, feed pump Sp and boiler with superheater Ke. In steam power plants, mechanical work is obtained in that a working medium (usually water, in the Organic Rankine Cycle also others, e.g. ammonia or silicone oils ) evaporates in a closed circuit alternately by supplying heat at high pressure and, after expansion, releasing work by dissipating heat condensed at low pressure. To promote very low compared to the volume of vapor condensate back to the steam pressure in the boiler return, the feed pump must deliver only a fraction of the work involved in the relaxation of by the overheating still increased volume of steam in a turbine or a piston engine released becomes. Like all thermodynamic cycle processes, the Clausius-Rankine cycle can not exceed the efficiency of the corresponding Carnot cycle , which essentially depends on the technically controllable vapor pressure or the attainable temperature.
The four changes of state
- 1 → 2 Adiabatic expansion of the steam in the turbine (since comparison processes are idealized, i.e. internally reversible, the course is isentropic ).
- 2 → 3 Isobaric condensation of the steam in the condenser by cooling by means of a cooling water circuit (the isobaric isothermal in the wet steam area).
- 3 → 4 adiabatic, also isentropic compression by the boiler feed pump , which pumps the condensate into the steam boiler.
- 4 → 1 Isobaric heat supply in the steam boiler , whereby the water is first heated up to the evaporation point , then evaporates (isothermal) and finally experiences further heating, the so-called overheating.
Efficiency
From the Ts diagram it can be seen that most of the heat input is used for evaporation. The advantage of the steam power process over processes with inert gases is the large specific cycle work (the yellow-colored area in the diagrams) due to the low work of the feed pump (small specific volume of the liquid). The ratio of the specific volumes between saturated steam and liquid water cannot be read directly from the pv diagram, as the abscissa is divided logarithmically. At 50 bar it is approx. 31, at 0.03 bar approx. 46000. The efficiency of the comparison process is calculated with:
for the example with a live steam condition of 50 bar at 400 ° C and a condenser pressure of 0.03 bar results:
The numerical values in the equation are the enthalpies in kJ / kg. The units are shortened. The difference in brackets is the work of the boiler feed pump, only about 0.5 percent of the turbine work.
Improvements
The process can be improved by:
- Increase the live steam pressure and the live steam temperature. So that the steam wetness in the last turbine stage is not too high, in addition reheat required, which in turn contributes to the efficiency improvement (comp. Steam power plant ).
- Feed water preheating by extraction steam from the turbine. This increases the mean temperature of the heat supply and the efficiency approaches the thermodynamic maximum of the Carnot efficiency . That is why such and similar efficiency improvements are called Carnotization .
Real process
The usual maximum temperature in fossil-fired steam power plants is now 600 ° C, the pressure is 260 bar. Reheating is absolutely necessary. The pressure in the condenser is - depending on the cooling - around 0.03 bar (i.e. negative pressure) corresponding to a temperature of around 25 ° C. In nuclear power plants only saturated steam with a temperature below 300 ° C is generated. Overheating of the live steam is not possible there, only intermediate overheating by means of live steam.
In the real power plant process, the turbine is largely adiabatic (see adiabatic machine ), but the work is not completely transferred to the shaft due to throttling, shock and friction processes (dissipation), and the entropy increases. For large turbines, the quality grade is around 0.9. The flow pressure losses in the system, in particular in the boiler (no isobaric preheating and no isobaric or isothermal evaporation, in particular no isobaric overheating), also reduce the efficiency. The feed pump does not work isentropically either.
Opposite process to cooling
A corresponding process in the opposite direction (“counterclockwise”) can be used for chillers and heat pumps . In this case, the steps in the circuit schematic and diagram on the right are:
- 4 - 1: Evaporation at a low temperature and pressure level (heat absorption in cooling coils, Q to instead of Q to )
- 1 - 2: compression (e.g. compressor in refrigerator)
- 2 - 3: Cooling, condensation and subcooling at high temperature and pressure levels (heat release Q from instead of Q to )
- 3 - 4: Relaxation of the liquid phase, with partial evaporation taking place. (isenthalpic)
The last step could theoretically be carried out adiabatically with a turbine or piston machine , then this ideal process would correspond to a counter-clockwise Clausius-Rankine process. In practice, however, compression chillers do not use the energy yield of this stage (around 1% of total sales) in order to facilitate the construction. A turbine for evaporating liquid would also hardly be possible. Therefore, the pressure is irreversibly released via a throttle , whereby the enthalpy remains constant. In the TS diagram, point 4 then lies diagonally to the right below point 3, so the energy not released does not have to be taken up again as Q and the coefficient of performance is reduced somewhat.