Lecture 11: Thermodynamic cycles – steam turbines, refrigerators and heat pumps • Steam turbines and refrigerators are examples of what are more generally referred to as vapour cycles. Vapour cycles use a vapour as the working fluid. They cannot be analysed by assuming an ideal gas. Indeed, vapour cycles usually exhibit a change of phase that makes the assumption of ideal gas behaviour completely and utterly wrong! Do not make this mistake. we must therefore use thermodynamic tables and/or charts extensively. Hence the need for an understanding of the properties of steam studied earlier in the semester. • The Carnot cycle with phase change • lecture 10 showed the Carnot cycle to be the most efficient heat engine in theory. • the Carnot cycle can be sketched within the saturation region as follows: • as shown in lecture 10, the thermal efficiency of the Carnot cycle is W T ηth = out = 1 − cold Qin Thot the reason we draw this cycle within the saturation region is simple: heat addition and subtraction can be constant temperature processes when the working fluid is boiling or condensing. Thus, phase change between a liquid and a gas allows us to approximate this ideal Carnot cycle in reality. however, we must note that the Carnot cycle is an idealisation. No real process is truly reversible, and so the Carnot cycle cannot be built in practice. further, compressing ( 1 → 2 ) and expanding ( 3 → 4 ) the working fluid in the saturation region is extremely difficult to realise mechanically, so real cycles avoid this as much as possible. given that no cycle can be more efficient that the Carnot cycle, an important question is then “what cycles can be built that are thermodynamically as close as possible to the Carnot cycle?” two very commonly used cycles answer this question: the Rankine cycle with superheat, and the practical vapour compression refrigeration cycle. • • • • • The Rankine cycle with superheat • the Rankine cycle is the basic cycle used in almost all coal fired, steam turbine power stations. In real power stations, the cycle is actually very complex, but its operation is in principle as follows. • in terms of plant layout, the Rankine cycle can be realised by: • with the following T − s diagram • each process is as follows: 1→ 2 2→3 3→ 4 4 →1 isentropic compression (pumping) constant pressure heat addition (boiling) isentropic expansion (turbine work) constant pressure heat removal (condensation) • note: 1. the term ‘superheat’ is used because the turbine inlet temperature T3 is above the saturation temperature at the same pressure. Rankine cycles without superheat cannot be built because of the above mentioned mechanical issues. 2. the turbine exhaust temperature T4 is not in general at the saturation temperature, but is usually a little within the saturation region. This can be tolerated mechanically provided that the exhaust is not ‘too wet’. • the thermal efficiency of the cycle is w − wFP ηth = t qb = = h 3 − h 4 −( h 2 − h 1 ) h 3 −h 2 h 3 −h 4 if wFP h 3 −h 2 0 • note: 1. the feed pump work is small since the water volume flow rate is (relative to a wet mixture) small and incompressible. The term wFP = h2 − h1 is thus often neglected. 2. there are many variations on the Rankine cycle that can result in increased thermal efficiency. Some of these are detailed in the text, such as the use of reheat and other measures. The fundamental principles of these cycles are no different to that above. The practical vapour compression refrigeration cycle • as discussed in lecture 10, the reversed Carnot cycle is a refrigerator. • in order avoid the practical difficulties with the reversed Carnot cycle, we again avoid use of moving parts within the saturation region. The so-called practical vapour compression cycle is one way to achieve this: • with T − s diagram • note: 1. the use of a throttling valve in process 3 → 4 . A throttle is approximately an isenthalpic device since, from the SFEE (and neglecting the kinetic energy terms): q − w = ∆h =0 =0 2. the fluid is fully evaporated leaving the evaporator, so the compressor handles only a gas. • since throttling creates entropy, the heat transfer in the evaporator is reduced relative to an isentropic expansion through a turbine, for example, i.e. h1 − h4 < h1 − ha Refrigerants • refrigerators use a wide range of working fluids called refrigerants. Examples include chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), carbon dioxide and ammonia. • these fluids are chosen partly because they boil and condense at temperatures that we common require at mechanically reasonable pressures. in principle, they behave no differently to steam, and we will use thermodynamic tables and charts to analyse these fluids in the same way as we work with steam. • The coefficient of performance (COP) of refrigerators and heat pumps • the ‘coefficient of performance’ ( COP ) of a heat pump or refrigerator is analogous to the thermal efficiency ( ηth ) of a heat engine; both quantities define ‘what you get for what you have to put in’ • the useful effect of the refrigerator is the removal of heat from the cold space i.e. what we ‘get’ is Q1 and we ‘put in’ is work W (usually from a compressor). Thus, heat removed Q1 COPrefrig = = work required W conversely, the useful effect of the heat pump is the addition of heat to a hot space i.e. we ‘get’ Q2 for ‘putting in’ work input W . Thus, heat supplied Q2 W + Q1 = = = 1 + COPrefrig COPheat pump = W work required W note: the COP of both a refrigerator and heat pump are bounded by [ 0, ∞ ) , unlike the thermal efficiency of a heat engine • • [0,1) . This is an important thing to remember. Indeed, most actual refrigerators have COP > 1 . • the COP of the practical vapour compression cycle is less than the COP for the equivalent ideal reversed Carnot cycle since: 1. condensation is no longer isothermal 2. throttling is inherently irreversible (i.e. entropy generating).