# Heat Regeneration – Rankine Cycle

## 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 the 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., the 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 network 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 caused to steam turbine blades by low-quality steam.
• Decreasing the turbine exhaust pressure significantly increases the specific volume of exhausted steam, which requires huge blades in the last rows of a low-pressure stage of the steam turbine.

In 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 condensers’ finite size and efficiency.

Boiler Pressure

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

Typically most nuclear power plants operate multi-stage condensing steam 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). Since neither the steam generator is 100% efficient, there is always a temperature difference between the saturation temperature (secondary side) and the temperature of the primary coolant.

The hot primary coolant (330°C; 626°F) is pumped into the steam generator through the primary inlet in a typical pressurized water reactor. This requires maintaining very high pressures to keep the water in a liquid state. To prevent boiling the primary coolant and 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.

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 possible way is to superheat or reheat the working steam. Both processes are very similar in their manner:

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

The pro-superheating process 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.

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 delivering 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., using a multi-stage turbine with a reheater.  It was observed that more than two reheating stages are unnecessary since the next stage increases the cycle efficiency only half as much as the preceding stage.

The turbine’s high pressure and low-pressure ages are usually on the same shaft to drive a common generator, but they have separate cases. The flow is extracted with a reheater 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.

In the superheater, further heating at fixed pressure results in increases in both temperature and specific volume. The process of superheating water vapor in the T-s diagram is provided in the figure between state E and the saturation vapor curve. As can also be seen, wet steam turbines (e.g.,, used in nuclear power plants) use superheated steam, especially at the inlet of low-pressure stages. Typically most nuclear power plants operate 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 exhausts it to a moisture separator-reheater (point D). The steam must be reheated or superheated to avoid damages that could be caused to the blades of the steam turbine by low-quality steam. The high content of water droplets can cause 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 the steam turbine, where it 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%. Still, 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 usually operate a single wet steam turbine.

Heat Regeneration
Significant increases in the thermal efficiency of steam turbine power plants can be achieved by reducing the amount of fuel that must be added to the boiler. This can be done by transferring heat (partially expanded steam) from certain steam turbine sections, 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 economizer that is a heat exchanger intended to reduce energy consumption, especially in preheating 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:

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

• A 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.
• A recuperator is a heat exchanger with separate flow paths for each fluid along its passages, and heat is transferred through the separating walls. Recuperators (e.g.,, economizers) 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

As was discussed, the thermal efficiency can be improved “simply” by increasing 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 fabrication methods 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., 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 of around 43%. Most efficient and complex coal-fired power plants operate at “ultra critical” pressures (i.e., around 30 MPa) and use multiple stage reheat to reach about 48% efficiency.

Supercritical Water Reactor – SCWR

The 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 (TCR = 374 °C;  pCR = 22.1 MPa) and must not be confused with the criticality of the reactor core, which 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 to 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).

## Heat Regeneration

Significant increases in the thermal efficiency of steam turbine power plants can be achieved by reducing the amount of fuel added to the boiler. This can be done by transferring heat (partially expanded steam) from certain steam turbine sections, 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 economizer that is a heat exchanger intended to reduce energy consumption, especially in preheating 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:

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

• A 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.
• A recuperator is a heat exchanger with separate flow paths for each fluid along its passages, and heat is transferred through the separating walls. Recuperators (e.g.,, economizers) 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.

References:
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