12.______________________________
Power Cycles for Electricity Generation
Most of our development to this point has been oriented toward obtaining
heated fluid from a solar collector.
Often, the industrial demand to be satisfied by a solar energy system is
for this heat. However, a more valuable
form of energymechanical
or electrical energy (both are equivalent in the thermodynamic sense)
is
sometimes desired either exclusively or in combination with thermal
energy. The device used to produce mechanical
work or electricity from solar generated heat is a power conversion cycle, or
heat engine.
Several considerations peculiar to solar energy systems affect the
choice of the power conversion cycle and how the solar energy system is
designed to incorporate it. These
considerations are discussed in this chapter along with a detailed discussion
of the three power cycles usually considered for solar applications: the
Rankine,
This development will follow the outline below:
o Optimum Operating Temperature
o Heat Transfer Considerations
o Examples of Solar Rankine Cycles
o Free-piston Stirling Engines
· Solar Combined with Fossil Fuel Power Cycles
o Solar Energy for Boosting Combined Cycles
12.1 Solar Considerations
12.1.1 Modularity
For parabolic trough and central receiver applications, a single power cycle large enough to supply the full demand for electricity (or mechanical work) is normally used. In both cases, all of the solar produced heat is brought to a single point where the power cycle can be placed.
In the case of parabolic dish collectors, the system designer has the choice of either transporting heated fluid from a field of dishes to a single power cycle or using small engines at the focus of each collector and transporting electrical power to the point of demand.
The major advantage of using many small engines is that it is often easier to transport electrical energy than thermal energy. Not only is there less energy lost in the transmission process, but it is also easier to bring electrical energy down from the moving receiver to the ground. Other benefits of modularity are that: (l) small engines can be replaced by spares so that a plant comprised of numerous units can deliver close to rated power even while engines are being repaired, and (2) the power system can be easily expanded by adding modules to accommodate growth.
The major disadvantage of this modularity scheme is that many small engines (in the l0-l00-kW output range) must be used; therefore, the economies and increased efficiency of larger sized units are not applicable. In addition, incorporation of significant amounts of thermal storage into these modules is generally considered infeasible. A consideration of less importance is that when located at the focus, engines must be designed to operate at different orientations, an important consideration for engines where phase change takes place and in the design of lubrication systems. Furthermore, maintenance and adjustment of an engine module located off the ground is more difficult.
12.1.2 Thermal Efficiency
Carnot Limitation. A power cycle receives heat energy at a high temperature, converts some of this energy into mechanical work, and rejects the remainder at a lower temperature. The thermal efficiency of any engine is defined as
(12.1)
The ultimate limitation placed on this process by the second law of thermodynamics is that no power cycle can convert more heat into work than the Carnot cycle. A Carnot cycle is a hypothetical engine involving four processes: an adiabatic reversible compression and expansion and a constant temperature heat addition and rejection. The thermal efficiency or the ratio of net work to the heat added, for a Carnot cycle engine is
(12.2)
where TH and TL are the absolute temperatures at which heat is added and rejected, respectively. The major implication here is that the thermal efficiency of an engine is proportional to the spread between the maximum temperature of the cycle and the heat rejection temperature. The wider the spread, the more efficient the conversion from heat to work.
Because it is very difficult to build an engine operating on the Carnot cycle, most real engines operate on other cycles. The best attained efficiencies are a little over one-half of the ideal (Carnot) engine efficiency. However, the effect of temperature spread on efficiency represented by Equation (12.2) is still valid for real engines. The temperature dependence of the efficiency of a real engine can then be represented by
(12.3)
where Ke represents the fraction of Carnot efficiency attained by the real engine.
12.1.3 Optimum Operating Temperature
Equation (12.1) indicated that engine efficiency increases with increase in maximum operating temperature. The efficiency of most combustion-heated engines is limited by the temperature limitations of the metals (and ceramics) used to make the engine. A counteracting factor appears when the engine receives its heat from a solar collector because the efficiency of a solar collector decreases as the operating temperature increases as a result of receiver heat loss.
As discussed in Chapter 5, solar collection efficiency ηcol for a concentrating collector may be defined in terms of a receiver heat balance as
(12.4)
where
Aa = area of collector aperture (m2)
CRg = geometric concentration ratio
Ib,a = beam (direct) aperture irradiance (W/m2)
= rate
of useful heat delivered (W)
Ta = ambient temperature (K)
Tr = receiver operating temperature (K)
Ul = receiver overall heat-loss coefficient (W/m2 K)
= emittance
(effective) of receiver
σB = Stefan-Boltzmann constant (5.6696 × 10-8) (W/m2 K4)
Note: The fourth power temperature term is included for
completeness and may be eliminated by setting = 0 if desired.
The overall efficiency of a solar energy power system is the product of the efficiency of the engine and the efficiency of the solar collector. Since engine operating temperature approximately equals the receiver temperature, an analysis of the product of Equations (12.2) and (12.4) will give an optimum operating temperature where receiver efficiency is maximized. If it is assumed that the engine rejects heat at approximately ambient temperature, it can be shown that
(12.5)
where the following parameters have been defined for simplicity:
where Tr,max is the optimum operating temperature for maximum combined collector/engine efficiency and the temperatures must be in absolute temperature units (Stine, 1984).
Note that the percentage of Carnot efficiency term, Ke in Equation (12.3) does not appear in this expression. This indicates that the optimum operating temperature of a collector/engine combination depends only on the collector design and not on the engine design as long as Ke is considered a constant.
As an example, Figure 12.1 shows the combined engine-collector efficiency for a concentrator having a geometric concentration ratio of 1000 with the loss parameters specified in the figure. The optimum operating temperature for this concentrator when combined with an engine is 780ºC (1436ºF). However, note that this optimum does not represent a sharp peak since a 100ºC change of operating temperature in either direction decreases the system output by less than 2 percent.
Figure 12.1 Combined
collector and engine efficiency variation
with operating temperature. Nominal
collector parameters: CRg = 1000;
Ib,a = 1000 W/m2; Ta = 298 K; Ul
= 60 W/m2 K; ηopt = 0.9; = 0.9.
The optimum operating temperature is a stronger function of the design of the concentrator. Figure 12.2 shows the variation of the optimum operating temperature with geometric concentration ratio. Indicated in this figure are the typical peak operating temperatures of the engine cycles discussed in the following sections. This figure indicates the reason why low-concentration-ratio collectors are normally selected for engines operating at low-temperature and high-concentration-ratio collectors for high-temperature engines.
Figure 12.2 Optimum
operating temperature change with geometric concentration ratio. Nominal collector parameters: Ib,a
= 1000 W/m2; Ta
= 298 K; Ul
= 60 W/m2 K; ηopt = 0.9; = 0.
12.1.4 Heat Transfer Considerations
Engine Cycles. Only those engine cycles that lend themselves to external heat addition are normally considered for solar applications. Unlike internal combustion engines where heat addition occurs within the working fluid, externally heated engines require that heat be transferred to the working fluid through containment walls (i.e., a heat exchanger). Not all engine designs facilitate this heat-transfer process.
Three types of engine will readily accept external heat
exchange and have been used with solar heat sources: the Rankine, the
both have constant-pressure heat-addition processes readily
applicable to external heating. The
Intermediate Heat-Transfer Fluid. Once an engine cycle and appropriate working fluid have been selected, a decision must be made as to whether to pump the engine's working fluid to the receiver of the solar collector and heat the working fluid directly, or to incorporate an intermediate heat-transfer fluid flowing between the receiver and a heat exchanger, and heat the working fluid in the heat exchanger.
Incorporation of an intermediate heat-transfer fluid results in the addition of another pump, a heat exchanger, and a second fluid to the system. The addition of complexity to the system, utilizing an intermediate heat-transfer fluid, will often reduce the size and weight of the receiver because of the lower vapor pressures involved. Also, the expense of high-pressure field piping is eliminated for the same reason. When the working fluid is a gas or in the vapor phase, the use of an intermediate heat-transfer fluid causes reduction in heat loss from the large ducting that would otherwise be required.
Pumping the engine working fluid directly through the receiver can make the system difficult to control during solar irradiation transients. This is especially true for Rankine cycle systems where preheating, evaporation, and superheating all must occur in the receiver; therefore, a specific liquid level must be maintained in the receiver. However, the concept is simple and the engine can operate at a slightly higher temperature since no temperature difference is required by an intermediate heat exchanger.
12.2 Rankine Power Cycles
12.2.1 Cycle Description
The most common power cycle used in solar power systems is the Rankine cycle. This cycle combines constant-pressure heat addition and rejection processes with adiabatic reversible compression and expansion processes. It utilizes a working fluid that changes phase during the heat-transfer processes to provide essentially isothermal heat addition and rejection. The working fluid is usually either water or organic liquids; however, liquid metals have also been used. The following description assumes water/steam as the working fluid. Differences when other working fluids are used are discussed in Section 12.2.3.
Simple Cycle with Superheat. The major components of a simple, ideal Rankine cycle are depicted in Figure 12.3 along with the thermodynamic states of the working fluid plotted on temperature-entropy coordinates. Only ideal processes are depicted. The pressure of saturated liquid leaving the condenser at state 1 is raised in an adiabatic, reversible process by the (ideal) pump to state 2, where it enters the vapor generator (also called a boiler or steam generator). The compressed liquid is heated at constant pressure (often called preheat) until it reaches a saturated liquid state 2' and then at constant temperature (and pressure) until all the liquid has vaporized to become saturated vapor at 3'. More heat is added to superheat the saturated vapor at constant pressure, and its temperature rises to state 3. The superheated vapor now enters an ideal expansion device (often a turbine) and expands in an adiabatic, reversible process to the low pressure maintained by the condenser indicated as state 4. The condenser converts the vapor leaving the turbine to liquid by extracting heat from it.
Figure 12.3 A simple Rankine cycle with superheat.
Often during this expansion process, the vapor reaches saturation conditions and a mixture of saturated liquid and saturated vapor forms in the expander. The requirement to superheat the vapor from state 3' to 3 is defined by the amount of moisture that is permitted in the expander exhaust from state 4 to 4'. If the expander is a high-speed turbine, wet vapor produces destructive erosion of the blades. Some types of expanders such as piston and cylinder expanders permit some condensation during the expansion process. However, the amount of superheat is kept to a minimum so that the boiling temperature and thus the average heat-addition temperature (see Section 12.2.4) can be maximized.
Reheat. In order to reduce the amount of initial superheat required while raising the average heat-addition temperature, vapor reheat is often used. This permits an increase in the temperature at which heat is added to the saturated liquid but still provides for relatively dry vapor leaving the turbine at condenser pressure. As shown in Figure 12.4, partially expanded vapor leaves the expander at state 7, goes back into the vapor generator, where more heat is added to the vapor as it is heated to state 8. State 8 is usually at the same temperature as state 6 but must be at a lower pressure. The reheated vapor is returned to a second, low-pressure expander where it produces more work as it expands to the condenser pressure. The net result is an improvement in thermal efficiency because the average temperature at which heat is added is higher. Large central solar power stations may use two or more stages of reheat to enhance their efficiency.
Figure 12.4 A Rankine cycle incorporating reheat and regeneration feedwater heating; both open and closed feedwater heaters are shown (FWH, feedwater heater; HP, high pressure; LP, low pressure).
Regeneration. Regeneration is the process of using the expanding or expanded vapor to preheat liquid before it enters the vapor generator. Although there is no net heat gain to the cycle in doing this, the efficiency of the cycle is increased because the external heat transfer to the working fluid now occurs at a higher average temperature.
Regeneration is accomplished in two ways for Rankine cycles. In the first, some of the vapor that has partially expanded through the turbine is extracted and used to preheat the compressed liquid before it enters the vapor generator. This is called feedwater heating. In the second, the entire flow of vapor leaving the turbine is passed through a heat exchanger (called a regenerator or recuperator) where heat is transferred to the compressed liquid prior to entering the vapor generator. This second type of regeneration requires that the temperature of the vapor leaving the turbine be higher than the condenser temperature.
Two types of feedwater heaters are in common use, and both are depicted in the cycle shown in Figure 12.4. The open feedwater heater preheats the compressed liquid from state 2 to state 3 by mixing in vapor extracted from the turbine at point b. The extracted vapor must be at the same pressure as the outlet of pump l. A second pump is always required on the outflow side to increase the pressure of the compressed liquid to the vaporizer pressure.
A closed feedwater heater preheats the compressed liquid from state 4 to state 5 by heat exchange across a surface. This heater uses vapor extracted from a port in the turbine that is at state a. The pressure of the extracted vapor does not need to be the same as the compressed liquid it is heating. Once condensed, the extracted liquid (called “drips”) is fed back into the main compressed liquid stream, either at a lower pressure open feedwater heater (as is shown in Figure 12.4) or at the condenser.
A full-flow regenerator is included in a Rankine cycle when the temperature of the vapor leaving the expansion device is higher- than the condensing temperature. This is the case for a class of working fluids used in solar Rankine cycles and other low-temperature applications called drying fluids which are discussed in Section 12.2.3. This class of fluids has the characteristic that the entropy of saturated vapor decreases with decreasing pressure, the opposite of steam. Figure 12.5 shows a cycle using full-flow regeneration with a drying fluid.
Figure 12.5 A Rankine cycle using a drying-type working fluid and incorporating full flow regeneration.
When the high pressure saturated vapor of a drying fluid is expanded in an adiabatic reversible process, the temperature of the vapor when it reaches condenser pressure is above the condenser temperature. Because of this temperature difference, the regenerator can exchange heat from the exhaust vapor (state 5 to state 6) to the compressed liquid, raising its temperature from state 2 to state 3.
12.2.2 Components
Vapor Generators. As discussed previously, the designer must choose whether to generate vapor in the receiver of the solar collector or to use an intermediate heat-transfer fluid between the receiver and the vapor generator.
The choice generally depends on the specific design, but there are several primary considerations.
Receiver vapor generators. Generating vapor in the receiver of the solar collector has the advantage of having fewer components and no loss of temperature required with an intermediate transfer. With both liquid and vapor in a receiver, however, extreme care must be taken in the design of the receiver to ensure that the radiant flux incident on that portion of the receiver containing vapor is less than the flux incident in the regions with liquid and where boiling is taking place. This is because the heat-transfer coefficient into a liquid is significantly higher than into superheated vapor. For similar values of solar flux, burnout of the receiver walls could occur in the regions where vapor exists on the other side of the receiver wall.
Many concentrating collector designs require that the receiver change attitude while the collector tracks the sun. This change of attitude increases the chances of high flux on portions of the receiver containing vapor.
Two examples of solar Rankine power systems where the engine
working fluid vapor is generated directly in the receiver are the Solar One
Pilot Plant at
Heat-exchange vapor generators. Use of an intermediate heat-transfer fluid between the receiver and the engine adds complexity and another fluid to the system. Typically, this requires that three separate heat exchangers be used; a preheater, an evaporator, and a superheater. This type of vapor generator is shown in Figure 12.6. Although the mass flow rate of engine working fluid is the same for all three exchangers, the heat-transfer rates are different, not only because of the different heat-transfer coefficients for liquid, boiling, and vapor heat transfer, but also because of the varying temperature differences between the heat-transfer fluid and the working fluid as depicted in the temperature entropy diagram in Figure 12.6.
Figure 12.6 Vapor generator (boiler) for a Rankine cycle when an intermediate heat-transfer fluid is used.
Process a-b-c-d depicts the temperature change of the heat-transfer fluid (typically an oil) as it transfers heat in counterflow heat exchangers to the cycle working fluid going from states l-2-3-4. If the superheater is sized properly, the temperature at a will be very close to temperature at 4 (the maximum cycle temperature).
A positive temperature difference everywhere along line ab
c-d
line is required for heat exchange to take place. Therefore, the heat-transfer fluid return
temperature at d cannot be as low as the cycle temperature because of the
requirement that temperature c be above the temperature at 2. The condition at state c is called the pinch
point.
A simplified heat balance of the preheater, the vaporizer and the superheater, respectively gives:
(W) (12.6)
where and
are the mass flow rates of engine working
fluid and heat-transfer fluid, respectively, h represents
enthalpies; T represents temperatures; and cp is the heat-transfer fluid specific heat. The overall rate of heat transfer for each
heat exchanger is represented by
and
. The
total rate of energy transferred to the working fluid is the sum of these three
terms.
Condensers. All power cycles must reject a large percentage of the heat added in order to produce mechanical work. For a Rankine cycle, this heat rejection occurs in conjunction with condensation of the working fluid vapor leaving the turbine at low pressure. The lower the heat rejection temperature, the greater the cycle efficiency as indicated in Equation (12.1).
Heat rejection from the condenser to the surroundings can be either direct or through an intermediate heat-transfer fluid loop (usually water). The types of condensers commonly used in solar power systems are shown in Figure 12.7. The most common condenser, a tube-and-shell heat exchanger, requires a supply of cooling water that comes from either a natural source (river, well, or ocean) or water that has been cooled by a cooling tower. The three cooling towers pictured could be designed either to condense the engine working fluid directly or to reject heat from an intermediate cooling water loop that also circulates through a tube-and-shell condenser.
Figure 12.7 Types of condenser and/or heat rejection used in Rankine cycle solar power systems: (a) tube-and-shell condenser; (b) dry cooling tower; (c) wet cooling tower; (d) natural-draft cooling tower.
Each of these heat rejection schemes requires electrical power for operation. This power, considered a parasitic loss from the cycle's output, must be kept to a minimum. Highest parasitic power requirements are usually associated with dry cooling towers since they make use only of the sensible temperature of the air for cooling. This type of cooling is often selected for solar power systems because these systems are often located in hot, arid regions with minimal water resources.
Water evaporation may be utilized to provide additional cooling for the cycle as in examples c and d in Figure 12.7. These units typically provide lower-temperature cooling for less parasitic power than do dry cooling towers. The amount of water resource required may be roughly estimated by assuming that most of the heat rejected by the cycle provides latent heat for evaporation. The rate of water usage by a wet cooling tower may be estimated by
(12.7)
where is the
rate of heat rejection by the cycle and hfg
the enthalpy of vaporization for water (2450 kJ/kg or 1054 Btu/1b).
Expanders. Expanders used most commonly for solar Rankine cycle applications arc turbines and reciprocating piston-cylinder devices. Scroll or screw expanders, rotary-displacement machines (Roots type), and fluid drag disc turbines have also been proposed for small output applications.
The efficiency of an expander is measured relative to an ideal adiabatic, reversible expander. The expansion process of an ideal expander occurs at constant entropy (isentropic). For a real expander, with friction, leakage, and other losses, the entropy of the vapor leaving will be greater than the entropy of the vapor entering. This produces a smaller enthalpy change than would have occurred if the entropy were constant. The isentropic efficiency of an expander, as depicted in Figure 12.8, is written as
(12.8)
where h2 is the actual enthalpy of the vapor leaving the expander and h2s, is the exit enthalpy if the expansion process were isentropic (constant entropy) to the same low pressure. The power output of a real expander is
(12.9)
where is the mass flow rate of vapor through the
turbine.
Figure 12.8 Isentropic efficiency definition for an expander (turbine) and compressor (pump): (a) expander; (b) pump or compressor.
Turbine expanders are most commonly used in solar Rankine cycle systems. Two types of turbine are in common use; the radial-flow turbine and the axial-flow turbine. In radial-flow turbines, the vapor expands from the shaft centerline to the outside periphery of a turbine disc or from outside in. This type of turbine is usually more efficient for small-power-output applications. In axial flow turbines, the vapor flows along the axis of the rotating shaft and passes through blades attached around the periphery of a disc. For large-power-output applications, many axial-flow turbine rotors are stacked together to form a multistage turbine.
Positive-displacement, reciprocating expanders have been proposed for solar power applications. This is the type of expander used in most Rankine cycles a century ago consists of one or more cylinders with pistons driving a rotating crankshaft. In reheat designs, exhaust vapor from a small high-pressure piston and cylinder is reheated in the vapor generator and fed back to a low-pressure piston and cylinder where more expansion work is done.
Pumps. The pump in a Rankine cycle is needed to raise the pressure of the liquid leaving the condenser to the pressure of the vapor generator. A major advantage of the Rankine cycle is that the working fluid is in the liquid phase when it is compressed. Since pump work is inversely proportional to the fluid density, less work is required to pressurize a liquid than a vapor or gas. Since liquids are essentially incompressible, the ideal pump power may be calculated as
(12.10)
where is the mass flow rate through the pump, v
is the fluid specific volume,
p
is the pressure, and h is the enthalpy.
State 2s represents the outlet conditions of an ideal pump, that is, a
constant entropy process. Note that this
expression will give a negative quantity consistent with the sign convention
that work into the cycle is negative.
The ideal pump raises the pressure of a liquid in an adiabatic, reversible process. Real pumps, like turbines, produce an entropy increase in the fluid. Figure 12.8b shows the difference between ideal and real pump performance. As discussed earlier for expanders, the power required to operate a real pump is
(12.11)
Feedwater Heaters. Feedwater heaters use partially expanded hot vapor, extracted from the expander to preheat the working fluid before it enters the boiler thereby increasing overall cycle efficiency. Two types of feedwater heaters are in common use, the open type and the closed type.
An open feedwater heater is simply an insulated mixing chamber where extracted hot vapor is mixed with a flow of compressed liquid. As the vapor condenses, its heat of vaporization is added to the liquid. The chamber must be large enough for this condensation to take place before the liquid reenters the system piping.
A closed feedwater heater is a tube-in-shell heat exchanger in which vapor extracted from the turbine passes on the shell side and condenses, releasing its heat of vaporization to the compressed liquid stream. The condensate is then returned to the compressed liquid stream at a point in the cycle where the pressure is lower.
Figure 12.9 Definition of regenerator effectiveness.
Regenerators. As was shown in Figure 12.5, when a drying fluid is chosen as the working fluid, the vapor leaving the expander still contains heat that can be transferred to the compressed liquid stream since the turbine exit temperature is above the condenser temperature. A vapor-to-liquid heat exchanger, called a regenerator, is typically used for this purpose. The effectiveness of the regenerator is a measure of how well the available temperature difference is utilized. Effectiveness is defined as the ratio of the actual temperature change of the liquid stream to the maximum possible temperature change. Figure 12.9 shows a regenerator and the thermodynamic states of both streams as they flow through the regenerator. The regenerator effectiveness in this case is defined as
(12.12)
where the temperatures are defined on Figure 12.9.
12.2.3 Working Fluid Selection
There are two important aspects to be considered in selecting a working fluid for a Rankine cycle solar power system: (1) to select a working fluid that optimizes cycle efficiency and (2) to match the working fluid states with those of the intermediate heat-transfer fluid if one is used. The effects of different working fluids on these aspects of cycle design are discussed in the following paragraphs.
The Ideal Working Fluid. An ideal working fluid would have the temperature entropy diagram given in Figure 12.10. The following characteristics listed by Abbin and Leuenberger (1974) describe this fluid:
- The
heat capacity of the liquid phase should be small. This makes line 22' in Figure 12.10 almost vertical.
- The critical point should be above the highest operating temperature to allow all heat to be added at that temperature.
- The vapor pressure at the highest operating temperature should be moderate for safety reasons and to reduce the cost of the equipment.
- The vapor pressure at the condensing temperature should be above atmospheric pressure to prevent air leakage into the system.
- The specific volume of the vapor at state 4 should be small to avoid large-diameter turbine wheels, casings, and heat exchangers.
- The saturated vapor line (follows 3-4 in Figure 12.10) should be vertical to avoid expansion into the wet vapor region (negative ds/dT) or expansion into the superheat region (positive ds/dT).
- For low-power turbine applications, the fluid should have a high molecular weight to minimize the rotational speed and/or the number of turbine stages and to allow for reasonable mass flow rates and turbine nozzle areas.
- The fluid should be liquid at atmospheric pressure and temperature for ease of handling and containment.
- The freezing point should be lower than the lowest ambient operating temperature.
- The fluid should have good heat-transfer properties, be inexpensive, thermally stable at the highest operating temperature, nonflammable, noncorrosive, nontoxic, and so on.
Steam. Because it is the most popular Rankine cycle working fluid, more is known about designing Rankine cycle components for steam systems than any other liquid. Because it has a critical temperature and pressure of 374ºC / 22.1 MPa (704ºF / 3206 psia), it can be used for systems operating at fairly high temperatures with most of the heat addition (at constant temperature) and at moderate pressure. The low-temperature characteristics of steam are not quite as ideal since at ambient temperature, steam has a low vapor pressure (0.03 atm) and a very low density. Because of this, it is a major design problem to seal air out of the low-pressure components.
Figure 12.10 An ideal working fluid used with a Rankine cycle.
Steam is a ´wetting fluid´, implying that superheating is required when a turbine is used as the expansion device. As discussed earlier, superheating produces a lower efficiency since most of the heat supplied occurs at a temperature lower than the maximum cycle temperature thereby reducing the average heat-addition temperature.
The major disadvantage of using steam for small Rankine cycles (<1000 kW output) is its low molecular weight (i.e. 18). As is discussed later, in order to attain high turbine efficiencies with low-molecular-weight fluids, very high turbine speeds are called for with small inlet nozzle and blade dimensions.
Because steam is inexpensive to use (although boiler-grade water must be highly distilled and thus costs more than tap water), sealing of the high-pressure portions of a Rankine cycle using steam is not critical. Non-flammability and ready availability of steam are additional advantages. However, its freezing temperature is within the range of ambient conditions. Furthermore, water expands when it freezes, producing large stresses on any structure containing it. Because solar energy systems are located outdoors and are not operational at night, freeze protection or drainage capabilities must be provided for all components in the cycle.
Wetting Versus
Drying Fluids. For some fluids,
the entropy of the saturated vapor increases with increasing temperature. These fluids are called “drying” fluids
because moisture does not form when high-pressure saturated vapor is expanded
reversibly from a high pressure (i.e., in an ideal turbine or nozzle). A notable example used in many solar power
applications is toluene (CH3C6H5). A fluid where
the entropy of the saturated vapor decreases with increasing temperature is
called a “wetting” fluid because moisture forms when high pressure saturated
vapor is expanded reversibly in a turbine or nozzle. The watersteam
combination is a primary example of a wetting fluid. The characteristics of a wetting and a drying
fluid are shown in Figure 12.11, along with real and ideal expansion processes
from saturated vapor.
An ideal fluid, as pointed out in item 6 in the list in the
preceding subsection, would be neither wetting nor drying. Tabor (1962) did an extensive search for
high-molecular-weight fluids that would have an almost vertical saturated vapor
line on temperature-entropy coordinates (ds/dT = 0). A theoretical study showed that the slope of
the entropy-temperature curve was a function of the number of atoms in a
molecule. Molecules with 510
atoms show this tendency. Carbon
tetrachloride, tetrachloroethylene, and monochlorobenzene are all found to have
very small ds/dT
slopes.
As discussed earlier, drying fluids can produce cycle efficiencies almost as great as fluids where ds/dT = 0 if regeneration is used. This is because the higher-temperature heat remaining in the vapor once it has expanded to the pressure of the condenser is not necessarily lost but may be used to preheat the compressed liquid before it enters the vaporizer.
Figure 12.11 Saturation curves for wetting- and drying-type fluid showing ideal and real expansion processes: (a) wetting fluid; (b) drying fluid.
Wetting fluids, on the other hand, will always give less efficient cycles for a given maximum operating temperature because it is necessary to superheat the vapor before it enters the turbine. Superheat is required to ensure that liquid does not form in the vapor as it expands through the turbine. If moisture droplets form, they slow down as they pass through the turbine, finally being hit with great force by the blades. This impact causes erosion of the turbine blades or impeller. Superheat also decreases cycle efficiency because of the lower average heat-addition temperature.
Molecular Weight. The desire for using a heavier molecular weight fluid for small power cycles (item 7 in preceding list) derives from basic turbine design considerations. The most important are the turbine speed, the number of stages, and the size of the flow passages. Proper selection of these is required to design an efficient turbine. A detailed development of turbine design parameters may be found in Baljé (1962).
The data in Table 12.1 show that for turbine power levels of less than 1 to 10 MW, the isentropic efficiency of a steam turbine is considerably lower than that of a turbine designed for heavy-molecular-weight fluids. The reasons why high turbine efficiency cannot be maintained for low-power-level designs using a low-molecular-weight fluid are
1. The first stage nozzle spouting velocity is inversely proportional to the square root of the molecular weight. Since the ratio of blade speed to fluid speed must remain relatively constant, multiple staging and high rotational speeds are called for when low-molecular-weight vapors are used. The added complexity and expense of multi-staging is inappropriate for small turbines because disc friction, leakage, and windage losses become prohibitive in small designs.
2. The volumetric flows in the initial stages of the turbine are proportional to the square root of the molecular weight and therefore low with low-molecular-weight vapors. This requires the use of small nozzles, blades, and flow passages. Partial admission may be used, but this reduces efficiency. Also, blade tip, sealing, and boundary-layer losses become significant in small designs. Even with the use of precision manufacturing techniques, small turbine stages result in a turbine with low efficiency.
Table 12.1. Comparison of Turbine Isentropic
Efficiencies Using Steam (Low Molecular Weight) and
a High Molecular Weight Working Fluid
|
Power Level |
Turbine lsentropic Efficiency (%) |
|
|
|
Steam |
High Molecular Weight |
|
>10MW |
70-80 |
75 |
|
1-5 MW |
50-70 |
75 |