What is Thermal Efficiency Improvement – Rankine Cycle

Thermal Efficiency Improvement – Rankine Cycle. There are several methods, how can be the thermal efficiency of the Rankine cycle improved. Thermal Engineering

Thermal Efficiency of Rankine Cycle

In general the thermal efficiency, η_th, of any heat engine is defined as the ratio of the work it does, W, to the heat input at the high temperature, Q_H.

The thermal efficiency, η_th, represents the fraction of heat, Q_H, that is converted to work. Since energy is conserved according to the first law of thermodynamics and energy cannot be be converted to work completely, the heat input, Q_H, must equal the work done, W, plus the heat that must be dissipated as waste heat Q_C into the environment. Therefore we can rewrite the formula for thermal efficiency as:

This is very useful formula, but here we express the thermal efficiency using the first law in terms of enthalpy.

Rankine Cycle - Ts diagram — Rankine cycle – Ts diagram

Typically most of nuclear power plants operates multi-stage condensing steam turbines. In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure; 6 MPa; 275.6°C) from a steam generator and exhaust it to moisture separator-reheater (point D). The steam must be reheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. The reheater heats the steam (point D) and then the steam is directed to the low-pressure stage of steam turbine, where expands (point E to F). The exhausted steam then condenses in the condenser and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa), and is in a partially condensed state (point F), typically of a quality near 90%.

In this case, steam generators, steam turbine, condensers and feedwater pumps constitute a heat engine, that is subject to the efficiency limitations imposed by the second law of thermodynamics. In ideal case (no friction, reversible processes, perfect design), this heat engine would have a Carnot efficiency of

= 1 – T_cold/T_hot = 1 – 315/549 = 42.6%

where the temperature of the hot reservoir is 275.6°C (548.7K), the temperature of the cold reservoir is 41.5°C (314.7K). But the nuclear power plant is the real heat engine, in which thermodynamic processes are somehow irreversible. They are not done infinitely slowly. In real devices (such as turbines, pumps, and compressors) a mechanical friction and heat losses cause further efficiency losses.

To calculate the thermal efficiency of the simplest Rankine cycle (without reheating) engineers use the first law of thermodynamics in terms of enthalpy rather than in terms of internal energy.

The first law in terms of enthalpy is:

dH = dQ + Vdp

In this equation the term Vdp is a flow process work. This work, Vdp, is used for open flow systems like a turbine or a pump in which there is a “dp”, i.e. change in pressure. There are no changes in control volume. As can be seen, this form of the law simplifies the description of energy transfer. At constant pressure, the enthalpy change equals the energy transferred from the environment through heating:

Isobaric process (Vdp = 0):

dH = dQ → Q = H₂ – H₁

At constant entropy, i.e. in isentropic process, the enthalpy change equals the flow process work done on or by the system:

Isentropic process (dQ = 0):

dH = Vdp → W = H₂ – H₁

It is obvious, it will be very useful in analysis of both thermodynamic cycles used in power engineering, i.e. in Brayton cycle and Rankine cycle.

The enthalpy can be made into an intensive, or specific, variable by dividing by the mass. Engineers use the specific enthalpy in thermodynamic analysis more than the enthalpy itself. It is tabulated in the steam tables along with specific volume and specific internal energy. The thermal efficiency of such simple Rankine cycle and in terms of specific enthalpies would be:

It is very simple equation and for determination of the thermal efficiency you can use data from steam tables.

Takaishi, Tatsuo; Numata, Akira; Nakano, Ryouji; Sakaguchi, Katsuhiko (March 2008). “Approach to High Efficiency Diesel and Gas Engines” (PDF). Mitsubishi Heavy Industries Technical Review. 45 (1). Retrieved 2011-02-04.

In modern nuclear power plants the overall thermal efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power. The reason lies in relatively low steam temperature (6 MPa; 275.6°C). Higher efficiencies can be attained by increasing the temperature of the steam. But this requires an increase in pressures inside boilers or steam generators. However, metallurgical considerations place an upper limits on such pressures. In comparison to other energy sources the thermal efficiency of 33% is not much. But it must be noted that nuclear power plants are much more complex than fossil fuel power plants and it is much easier to burn fossil fuel ,than to generate energy from nuclear fuel. Sub-critical fossil fuel power plants, that are operated under critical pressure (i.e. lower than 22.1 MPa), can achieve 36–40% efficiency.

Efficiency of Engines in Power Engineering

Ocean thermal energy conversion (OTEC). OTEC is very sophisticated heat engine that uses the temperature difference between cooler deep and warmer surface seawaters to run a low-pressure turbine. Since the temperature difference is low, about 20°C, its thermal efficiency is also very low, about 3%.
In modern nuclear power plants the overall thermal efficiency is about one-third (33%), so 3000 MWth of thermal power from the fission reaction is needed to generate 1000 MWe of electrical power. Higher efficiencies can be attained by increasing the temperature of the steam. But this requires an increase in pressures inside boilers or steam generators. However, metallurgical considerations place an upper limits on such pressures. In comparison to other energy sources the thermal efficiency of 33% is not much. But it must be noted that nuclear power plants are much more complex than fossil fuel power plants and it is much easier to burn fossil fuel ,than to generate energy from nuclear fuel.
Sub-critical fossil fuel power plants, that are operated under critical pressure (i.e. lower than 22.1 MPa), can achieve 36–40% efficiency.
The supercritical water reactors are considered a promising advancement for nuclear power plants because of its high thermal efficiency (~45 % vs. ~33 % for current LWRs).
Supercritical fossil fuel power plants, that are operated at supercritical pressure (i.e. greater than 22.1 MPa), have efficiencies around 43%. Most efficient and also very complex coal-fired power plants that are operated at “ultra critical” pressures (i.e. around 30 MPa) and use multiple stage reheat reach about 48% efficiency.
Modern Combined Cycle Gas Turbine (CCGT) plants, in which the thermodynamic cycle of consists of two power plant cycles (e.g. the Brayton cycle and the Rankine cycle), can achieve a thermal efficiency of around 55%, in contrast to a single cycle steam power plant which is limited to efficiencies of around 35-45%.

Causes of Inefficiency

As was discussed, an efficiency can range between 0 and 1. Each heat engine is somehow inefficient. This inefficiency can be attributed to three causes.

Irreversibility of Processes. There is an overall theoretical upper limit to the efficiency of conversion of heat to work in any heat engine. This upper limit is called the Carnot efficiency. According to the Carnot principle, no engine can be more efficient than a reversible engine (a Carnot heat engine) operating between the same high temperature and low temperature reservoirs. For example, when the hot reservoir have T_hot of 400°C (673K) and T_cold of about 20°C (293K), the maximum (ideal) efficiency will be: = 1 – T_cold/T_hot = 1 – 293/673 = 56%. But all real thermodynamic processes are somehow irreversible. They are not done infinitely slowly. Therefore, heat engines must have lower efficiencies than limits on their efficiency due to the inherent irreversibility of the heat engine cycle they use.
Presence of Friction and Heat Losses. In real thermodynamic systems or in real heat engines, a part of the overall cycle inefficiency is due to the losses by the individual components. In real devices (such as turbines, pumps, and compressors) a mechanical friction, heat losses and losses in the combustion process cause further efficiency losses.
Design Inefficiency. Finally, last and also important source of inefficiencies is from the compromises made by engineers when designing a heat engine (e.g. power plant). They must consider cost and other factors in the design and operation of the cycle. As an example consider a design of the condenser in the thermal power plants. Ideally the steam exhausted into the condenser would have no subcooling. But real condensers are designed to subcool the liquid by a few degrees of Celsius in order to avoid the suction cavitation in the condensate pumps. But, this subcooling increases the inefficiency of the cycle, because more energy is needed to reheat the water.

Thermal Efficiency Improvement – Rankine Cycle

There are several methods, how can be the thermal efficiency of the Rankine cycle improved. Assuming that the maximum temperature is limited by the pressure inside the reactor pressure vessel, these methods are:

Boiler and Condenser Pressures

As in the Carnot, Otto and Brayton cycle, the thermal efficiency tends to increase as the average temperature at which energy is added by heat transfer increases and/or the average temperature at which energy is rejected decreases. This is the common feature of all thermodynamic cycles.

Condenser Pressure

The case of the decrease in the average temperature at which energy is rejected, requires a decrease in the pressure inside condenser (i.e. the decrease in the saturation temperature). The lowest feasible condenser pressure is the saturation pressure corresponding to the ambient temperature (i.e. absolute pressure of 0.008 MPa, which corresponds to 41.5°C). The goal of maintaining the lowest practical turbine exhaust pressure is a primary reason for including the condenser in a thermal power plant. The condenser provides a vacuum that maximizes the energy extracted from the steam, resulting in a significant increase in net work and thermal efficiency. But also this parameter (condenser pressure) has its engineering limits:

Decreasing the turbine exhaust pressure decreases the vapor quality (or dryness fraction). At some point the expansion must be ended to avoid damages that could be caused to blades of steam turbine by low quality steam.
Decreasing the turbine exhaust pressure significantly increases the specific volume of exhausted steam, which requires huge blades in last rows of low-pressure stage of the steam turbine.

In a typical wet steam turbines, the exhausted steam condenses in the condenser and it is at a pressure well below atmospheric (absolute pressure of 0.008 MPa, which corresponds to 41.5°C). This steam is in a partially condensed state (point F), typically of a quality near 90%. Note that, there is always a temperature difference between (around ΔT = 14°C) the condenser temperature and the ambient temperature, which originates from finite size and efficiency of condensers.

Typical parameters in a condenser of condensing turbines

Boiler Pressure

The case of the increase in the average temperature at which energy is added by heat transfer, requires either a superheating of steam produced or an increase in the pressure in the boiler (steam generator). Superheating is not typical for nuclear power plants.

Steam generator - counterflow heat exchanger — Temperature gradients in typical PWR steam generator.

In a typical pressurized water reactor, the hot primary coolant (water 330°C; 626°F) is pumped into the steam generator through primary inlet. This requires maintaining of very high pressures to keep the water in the liquid state. In order to prevent boiling of the primary coolant and to provide a subcooling margin (the difference between the pressurizer temperature and the highest temperature in the reactor core), pressures around 16 MPa are typical for PWRs. The reactor pressure vessel is the key component, which limits the thermal efficiency of each nuclear power plant, since the reactor vessel must withstand high pressures.

Typical parameters at the inlet of condensing turbines of PWRs.

Superheat and Reheat

As for the Carnot cycle, the thermal efficiency tends to increase as the average temperature at which energy is added by heat transfer increases. This is the common feature of all thermodynamic cycles.

One of possible ways is to superheat or reheat the working steam. Both processes are very similar in its manner:

Superheater – increases the steam temperature above the saturation temperature
Reheater – removes the moisture and increases steam temperature after a partial expansion.

The process of superheating is the only way to increase the peak temperature of the Rankine cycle (and to increase efficiency) without increasing the boiler pressure. This requires the addition of another type of heat exchanger called a superheater, which produces the superheated steam.

Rankine cycle - superheat - superheater — Rankine cycle with superheat of the high-pressure stage. This requires higher temperature in the steam generator.

Superheated vapor or superheated steam is a vapor at a temperature higher than its boiling point at the absolute pressure where the temperature is measured.

Reheat allows to deliver more of the heat at a temperature close to the peak of the cycle. This requires the addition of another type of heat exchanger called a reheater. The use of the reheater involves splitting the turbine, i.e. use of a multistage turbine with a reheater. It was observed that more than two stages of reheating are unnecessary, since the next stage increases the cycle efficiency only half as much as the preceding stage.

High pressure and low pressure stages of the turbine are usually on the same shaft to drive a common generator, but they have separate cases. With a reheater, the flow is extracted after a partial expansion (point D), run back through the heat exchanger to heat it back up to the peak temperature (point E), and then passed to the low-pressure turbine. The expansion is then completed in the low-pressure turbine from point E to point F.

Rankine cycle - reheat - superheat — Rankine cycle with reheat and superheat the low-pressure stage

In the superheater, further heating at fixed pressure results in increases in both temperature and specific volume. The process of superheating of water vapor in the T-s diagram is provided in the figure between state E and saturation vapor curve. As can be seen also wet steam turbines (e.g. used in nuclear power plants) use superheated steam especially at the inlet of low-pressure stages. Typically most of nuclear power plants operates multi-stage condensing wet steam turbines (the high pressure stage runs on saturated steam). In these turbines the high-pressure stage receives steam (this steam is nearly saturated steam – x = 0.995 – point C at the figure) from a steam generator and exhaust it to moisture separator-reheater (point D). The steam must be reheated or superheated in order to avoid damages that could be caused to blades of steam turbine by low quality steam. High content of water droplets can cause the rapid impingement and erosion of the blades which occurs when condensed water is blasted onto the blades. To prevent this, condensate drains are installed in the steam piping leading to the turbine. The reheater heats the steam (point D) and then the steam is directed to the low-pressure stage of steam turbine, where expands (point E to F). The exhausted steam is at a pressure well below atmospheric, and, as can be seen from the picture, the steam is in a partially condensed state (point F), typically of a quality near 90%, but it is much higher vapor quality, than that it would be without reheat. Accordingly, superheating also tends to alleviate the problem of low vapor quality at the turbine exhaust.

Since the temperature of the primary coolant is limited by the pressure inside the reactor, superheaters (except a moisture separator reheater) are not used in nuclear power plants and they operate usually a single wet steam turbine.

Heat Regeneration

Significant increases in the thermal efficiency of steam turbine power plants can be achieved through reducing the amount of fuel that must be added in the boiler. This can be done by transferring heat (partially expanded steam) from certain sections of the steam turbine, which is normally well above the ambient temperature, to the feedwater. This process is known as heat regeneration and a variety of heat regenerators can be used for this purpose. Sometimes engineers use the term economiser that are heat exchangers intended to reduce energy consumption, especially in case of preheating of a fluid.

As can be seen in the article “Steam Generator”, the feedwater (secondary circuit) at the inlet of the steam generator may have about ~230°C (446°F) and then is heated to the boiling point of that fluid (280°C; 536°F; 6,5MPa) and evaporated. But the condensate at the condenser outlet may have about 40°C, so the heat regeneration in typical PWR is significant and very important:

Heat regeneration increases the thermal efficiency, since more of the heat flow into the cycle occurs at higher temperature.
Heat regeneration causes a decrease in the mass flow rate through low-pressure stage of the steam turbine, thus increases LP Isentropic Turbine Efficiency. Note that at the last stage of expansion the steam has very high specific volume.
Heat regeneration causes an increases in working steam quality, since the drains are situated at the periphery of turbine casing, where is higher concentration of water droplets.

Regeneration vs. Recuperation of Heat

In general, the heat exchangers used in regeneration may be classified as either regenerators or recuperators.

Regenerator is a type of heat exchanger where heat from the hot fluid is intermittently stored in a thermal storage medium before it is transferred to the cold fluid. It has a single flow path in which the hot and cold fluids alternately pass through.

Recuperator is a type of heat exchanger has separate flow paths for each fluid along their own passages and heat is transferred through the separating walls. Recuperators (e.g. economisers) are often used in power engineering, to increase the overall efficiency of thermodynamic cycles. For example, in a gas turbine engine. The recuperator transfers some of the waste heat in the exhaust to the compressed air, thus preheating it before entering the combustion chamber. Many recuperators are designed as counterflow heat exchangers.

Supercritical Rankine Cycle

Rankine cycle - supercritical cycle — supercritical Rankine cycle

As was discussed the thermal efficiency can be improved “simply” by an increase in the temperature of the steam entering the turbine. But this temperature is restricted by metallurgical limitations imposed by the materials and design of the reactor pressure vessel and primary piping. The reactor vessel and the primary piping must withstand high pressures and great stresses at elevated temperatures. But currently, improved materials and methods of fabrication have permitted significant increases in the maximum pressures, with corresponding increases in thermal efficiency. The thermal power plants are currently designed to operate on the supercritical Rankine cycle (i.e. with steam pressures exceeding the critical pressure of water 22.1 MPa, and turbine inlet temperatures exceeding 600 °C). Supercritical fossil fuel power plants, that are operated at supercritical pressure, have efficiencies around 43%. Most efficient and also very complex coal-fired power plants that are operated at “ultra critical” pressures (i.e. around 30 MPa) and use multiple stage reheat reach about 48% efficiency.

Supercritical Water Reactor – SCWR

Characteristics of SCWRs — Typical properties of coolant in SCWR.

Supercritical Rankine cycle is also the thermodynamic cycle of supercritical water reactors. The supercritical water reactor (SCWR) is a concept of Generation IV reactor, that is operated at supercritical pressure (i.e. greater than 22.1 MPa). The term supercritical in this context refers to the thermodynamic critical point of water (T_CR = 374 °C; p_CR = 22.1 MPa), and must not be confused with the criticality of the reactor core, that describes changes in the neutron population in the reactor core.

For SCWRs a once through steam cycle has been envisaged, omitting any coolant recirculation inside the reactor. It is similar as in boiling water reactors, steam will be supplied directly to the steam turbine and the feed water from the steam cycle will be supplied back to the core.

As well as the supercritical water reactor may use light water or heavy water as neutron moderator. As can be seen, there are many SCWR designs, but all SCWRs have a key feature, that is the use of water beyond the thermodynamic critical point as primary coolant. Since this feature allows to increase the peak temperature, the supercritical water reactors are considered a promising advancement for nuclear power plants because of its high thermal efficiency (~45 % vs. ~33 % for current LWRs).

Isentropic Efficiency – Turbine, Pump

In previous chapters we assumed that the steam expansion is isentropic and therefore we used T_4,is as the outlet temperature of the gas. These assumptions are only applicable with ideal cycles.

Most steady-flow devices (turbines, compressors, nozzles) operate under adiabatic conditions, but they are not truly isentropic but are rather idealized as isentropic for calculation purposes. We define parameters η_T, η_P, η_N, as a ratio of real work done by device to work by device when operated under isentropic conditions (in case of turbine). This ratio is known as the Isentropic Turbine/Pump/Nozzle Efficiency. These parameters describe how efficiently a turbine, compressor or nozzle approximates a corresponding isentropic device. This parameter reduces the overall efficiency and work output. For turbines, the value of η_T is typically 0.7 to 0.9 (70–90%).