![]() ![]() To maintain the same work output, more heat needs to be transferred to the steam in the boiler.Ĭredit: Olivier Cleynen via Wikimedia Commons Varieties of the Rankine Cycle Heat loss can happen when steam flows through the connecting pipes and the cycle components, which are not perfectly insulated. To compensate for this pressure drop, the water needs to be pumped to a higher pressure. In a non-ideal cycle, fluid friction results in the lower pressure in the line. Some fluid friction losses and dissipation of some heat to the surrounding usually makes this system deviate from the ideality (as for example, shown by the dashed lines). Those processes are shown to proceed isentropically, i.e., without entropy change. The ideal state of this cycle is reflected in the vertical lines 1-2 and 3-4, when the fluid compressed and expanded. The basic Rankine cycle is presented in terms of temperature and entropy change in Figure 10.2. Therefore, the thermal efficiency of this cycle can be presented as follows: The net work done by the system is W turbine-W pump. ( Q in − Q out ) − ( W turbine − W pump ) = 0 The energy balance for the whole cycle is then can be expressed via the following equation: This is important for the Rankine cycle from technological standpoint, since pumps employed in the system require liquid medium to work efficiently and may have problems with water-vapor mixtures. The energy balance on the condenser will be:Īt this stage, the extra heat is withdrawn from the system, and water returns to liquid state. Lastly, the process 4-1 is steam cooling and condensation. So, this expression gives us the positive work value. Note that the enthalpy change is written as "before" minus "after" because the energy of the superheated compressed steam is higher than the expanded steam after it exits the turbine. Here, we again assume that there is no heat exchange with the surrounding, so all the fluid energy change is converted to work. The work done through that process is the useful work, which is the main purpose of the cycle: The next process 3-4 is expansion of the steam in the turbine. There is no pressure change in the boiler, only heat transfer to the fluid therefore, no mechanical work is done here. This heat is supplied to the boiler from the solar concentrator. ![]() Where Q in is the heat used by the boiler. The energy balance in the boiler can be expressed as the change in enthalpy of the fluid from the "before" state (compressed liquid) to "after" state (superheated steam): The next process 2-3 takes place in the boiler. The process, which is not accompanied by any heat exchange with the environment, is termed "adiabatic." So, this step 1-2 is adiabatic compression. In this case, we assume there is no heat exchange with the surroundings, so the energy is not lost (which is an ideal scenario). The work done by the pump to compress water (W pump) can be represented as the change in enthalpy (H) of the water (fluid) before entering the pump and after leaving the pump: The work terms for each component of the cycle can be expressed as follows. In an ideal Rankine cycle, all the units operate with the steady-state flow, and the kinetic and potential energy of the fluid are considered to be negligible compared to the temperature and pressure effects. Credit: Andrew.Ainsworth via Wikimedia Commons
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