MD TANVIR ALAM: rankine cycle

refrence from wikipedia

Description

Physical layout of the four main devices used in the Rankine cycle

The Rankine cycle closely describes the process by which steam-operated heat engines commonly found in thermal power generation plants generate power. The heat sources used in these power plants are usually nuclear fission or the combustion of fossil fuels such as coal, natural gas, and oil.
The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid. Also, unless the pressure and temperature reach super critical levels in the steam boiler, the temperature range the cycle can operate over is quite small: steam turbine entry temperatures are typically 565°C (the creep limit of stainless steel) and steam condenser temperatures are around 30°C. This gives a theoretical maximum Carnot efficiency for the steam turbine alone of about 63% compared with an actual overall thermal efficiency of up to 42% for a modern coal-fired power station. This low steam turbine entry temperature (compared to a gas turbine) is why the Rankine (steam) cycle is often used as a bottoming cycle to recover otherwise rejected heat in combined-cycle gas turbine power stations.
The working fluid in a Rankine cycle follows a closed loop and is reused constantly. The water vapor with condensed droplets often seen billowing from power stations is created by the cooling systems (not directly from the closed-loop Rankine power cycle) and represents the means for (low temperature) waste heat to exit the system, allowing for the addition of (higher temperature) heat that can then be converted to useful work (power). This 'exhaust' heat is represented by the "Qout" flowing out of the lower side of the cycle shown in the T/s diagram below. Cooling towers operate as large heat exchangers by absorbing the latent heat of vaporization of the working fluid and simultaneously evaporating cooling water to the atmosphere. While many substances could be used as the working fluid in the Rankine cycle, water is usually the fluid of choice due to its favorable properties, such as its non-toxic and unreactive chemistry, abundance, and low cost, as well as its thermodynamic properties. By condensing the working steam vapor to a liquid the pressure at the turbine outlet is lowered and the energy required by the feed pump consumes only 1% to 3% of the turbine output power and these factors contribute to a higher efficiency for the cycle. The benefit of this is offset by the low temperatures of steam admitted to the turbine(s). Gas turbines, for instance, have turbine entry temperatures approaching 1500°C. However, the thermal efficiencies of actual large steam power stations and large modern gas turbine stations are similar.

The four processes in the Rankine cycle

Ts diagram of a typical Rankine cycle operating between pressures of 0.06bar and 50bar

There are four processes in the Rankine cycle. These states are identified by numbers (in brown) in the above Ts diagram.

Process 1-2: The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage the pump requires little input energy.
Process 2-3: The high pressure liquid enters a boiler where it is heated at constant pressure by an external heat source to become a dry saturated vapour. The input energy required can be easily calculated using mollier diagram or h-s chart or enthalpy-entropy chart also known as steam tables.
Process 3-4: The dry saturated vapor expands through a turbine, generating power. This decreases the temperature and pressure of the vapour, and some condensation may occur. The output in this process can be easily calculated using the Enthalpy-entropy chart or the steam tables.
Process 4-1: The wet vapour then enters a condenser where it is condensed at a constant pressure to become a saturated liquid.

In an ideal Rankine cycle the pump and turbine would be isentropic, i.e., the pump and turbine would generate no entropy and hence maximize the net work output. Processes 1-2 and 3-4 would be represented by vertical lines on the T-S diagram and more closely resemble that of the Carnot cycle. The Rankine cycle shown here prevents the vapor ending up in the superheat region after the expansion in the turbine, ^[1] which reduces the energy removed by the condensers.

Variables

$\dot{Q}$	Heat flow rate to or from the system (energy per unit time)
$\dot{m}$	Mass flow rate (mass per unit time)
$\dot{W}$	Mechanical power consumed by or provided to the system (energy per unit time)
$\eta_{therm}$	Thermodynamic efficiency of the process (net power output per heat input, dimensionless)
$\eta_{pump},\eta_{turb}$	Isentropic efficiency of the compression (feed pump) and expansion (turbine) processes, dimensionless
$h_1, h_2, h_3, h_4$	The "specific enthalpies" at indicated points on the T-S diagram
$h_{4s}$	The final "specific enthalpy" of the fluid if the turbine were isentropic
$p_1, p_2$	The pressures before and after the compression process

Equations

In general, the efficiency of a simple Rankine cycle can be defined as:

$\eta_{therm}=\frac{\dot{W}_{turbine}-\dot{W}_{pump}}{\dot{Q}_{in}} \approx \frac{\dot{W}_{turbine}}{\dot{Q}_{in}}.$

Each of the next four equations^[1] is easily derived from the energy and mass balance for a control volume. $\eta_{therm}$ defines the thermodynamic efficiency of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output, it can be simplified.

$\frac{\dot{Q}_{in}}{\dot{m}}=h_3-h_2$