A basic understanding of thermodynamics is needed before learning how to improve plant efficiency. Thermodynamics is the physics that deals with the relationship between heat and other forms of energy. In power generation, thermodynamics is the conversion of chemical energy into other forms of energy.
This article covers thermodynamics associated with steam and fluid systems.
Most thermodynamic considerations start at the laws of thermodynamics, which postulate that energy can be exchanged between physical systems as heat or work and the existence of a quantity named entropy, which can be defined for any system. A system is composed of particles, whose average motions define its properties, which in turn, relate to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes. With these tools, thermodynamics describes how systems respond to changes in their surroundings.
The second law of thermodynamics places restrictions on the conversion of heat to work. Simply put, it is impossible to convert all heat to work. Its significant property is entropy.
Enthalpy (h): Entropy is the sum of the internal energy of the system plus the product of its volume multiplied by the pressure exerted on it by its surroundings. Enthalpy can be thought of as the sum of the heat energy, which depends on temperature, and the work energy that can be produced by the pressure of the substance. Enthalpy is handled on a per pound basis called specific enthalpy. Specific enthalpy, designated by the symbol "h", is a measure of the energy contained in a specific mass of material. Specific enthalpy is expressed in units of energy divided by units of mass; typically, the units are British thermal units/pound mass (Btu/lbm).
British thermal unit (Btu): A Btu is the quantity of heat required to raise one pound-mass of water from 59F to 60F.
Entropy: Entropy is the measure of the unavailability of a systems energy to do work. When a systems energy is defined as the sum of its "useful" energy, (e.g., that used to push a piston), and its "useless energy", i.e., that energy which cannot be used for external work, then entropy may be (most concretely) visualized as the "scrap" or "useless" energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the system.
Density (ρ): Density can be defined as weight per unit volume. Density can be changed by changing either pressure or temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density. It is expressed in units of lbm/ft3.
Volume (V): Volume is the volume per weight, which is the inverse of density. It is expressed in units of ft3/lbm.
Steam tables: The steam tables provide a method to determine the energy in water and steam if pressure and temperature are known. This energy consists of enthalpy and entropy. The steam tables also provide volume and density of steam and water at varying pressures and temperatures. They are used to find energy values at specific plant conditions and calculate plant efficiencies.
Mass and weight: The mass (m) of a body is the measure of the amount of material present in that body. The weight (wt) of a body is the force exerted by that body when its mass is accelerated in a gravitational field.
Specific gravity: Specific gravity is a measure of the relative density of a substance as compared to the density of water at a standard temperature. Physicists use 39.2F as the standard, but engineers ordinarily use 60F. In the International System of Units (SI Units), the density of water is 1.00 g/cm3 at the standard temperature. Specific gravity for a liquid has the same numerical value as its density in g/cm3. Since the density of a fluid varies with temperature, specific gravities must be determined and specified at particular temperatures.
Humidity: Humidity is the amount of moisture (water vapor) in the air. It can be expressed as absolute humidity or relative humidity. Absolute humidity is the mass of water vapor divided by a unit volume of air (grams of water/cm3 of air). Relative humidity is the amount of water vapor present in the air divided by the maximum amount that the air could contain at that temperature. Relative humidity is expressed as a percentage. The relative humidity is 100% if the air is saturated with water vapor and 0% if no water vapor is present in the air at all.
Temperature, pressure, specific volume, and density are examples of intensive properties. Mass and total volume are examples of extensive properties.
Two temperature scales normally employed are the Fahrenheit (F) and Celsius (C) scales. These scales are based on the number of increments between the freezing point and boiling point of water at standard atmospheric pressure. The Celsius scale has 100 units between these points, and the Fahrenheit scale has 180 units. The zero points on the scales are arbitrary.
The freezing point of water was selected as the zero point of the Celsius scale. The coldest temperature achievable with a mixture of ice and salt water was selected as the zero point of the Fahrenheit scale (32F). Water boils at 100 on the Celsius scale and 212 on the Fahrenheit scale (at atmospheric pressure). The relationship between the scales is represented by the following equations:
There is an absolute scale (only positive values) corresponding to both of these scales. The absolute temperature scale that corresponds to the Celsius scale is called the Kelvin (K) scale, and the absolute scale that corresponds to the Fahrenheit scale is called the Rankine (R) scale. The zero points on both absolute scales represent the same physical state, where there is no molecular motion of individual atoms, called absolute zero. The relationships between the absolute and relative temperature scales are shown in Figure 1.
Figure 1: Absolute and Relative Temperature Scales
Figure 2: Absolute, Gauge, Vacuum, and Atmospheric PressuresThe equation below demonstrates how to convert between gauge pressure and absolute pressure:
Pressure can be measured referenced to the force existing in a column of fluid at a certain height. The most common of these are inches of water, inches of mercury, millimeters of mercury, and microns of mercury.
Conversion factors are listed below.
None of these forms of energy can be measured or evaluated directly, but techniques have been developed to evaluate the change in the total sum of all these microscopic forms of energy. These microscopic forms of energy are collectively called internal energy, customarily represented by the symbol U. In engineering applications, the unit of internal energy is the British thermal unit (Btu), which is also the unit of heat. The specific internal energy (u) of a substance is its internal energy per unit mass. It equals the total internal energy (U) divided by the total mass (m).
The specific P-V energy of a substance is the P-V energy per unit mass. It equals the total P-V divided by the total mass m, or the product of the pressure (P) and the specific volume (ν), and is written as p.
Where u is the specific internal energy (Btu/lbm) of the system being studied, P is the pressure of the system (lbf/ft2), and ν is the specific volume (ft3/lbm) of the system. Enthalpy is usually used in connection with an "open" system problem in thermodynamics.
Enthalpy is a property of a substance, like pressure, temperature, and volume, but it cannot be measured directly. However, when working on any steam cycle, a good understanding of enthalpy is essential to maximize efficiency of the plant.
W = Fd
It is important to distinguish between work done by the system and work done on the system by its surroundings. Work is done by the system when it is used to turn a turbine, thereby generating electricity in a turbine-generator. Work is done on the system when a pump moves the working fluid from one location to another. A positive value for work indicates that work is done by the system; a negative value indicates that work is done on the system by its surroundings.
The best way to quantify heats definition is to consider the relationship between the amount of heat added to or removed from a system and the change in the systems temperature. Everyone is familiar with the physical phenomena that heating a system raises its temperature and cooling it lowers the temperature. Heat added to or removed from a substance to produce a change in its temperature is called sensible heat.
Heats units are often defined in terms of the changes it causes or latent heat. Latent heat is "the amount of heat added to or removed from a substance to produce a phase change." Adding latent heat does not change temperature.
There are two types of latent heat:
A substances physical characteristics define its phase. For example, water, used to make steam, has three (3) phases:
Like enthalpy, entropy cannot be measured directly. Also, like enthalpy, a substances entropy is given with respect to some reference value. For example, the reference value for the specific entropy of water or steam is zero at 32F. The fact that the absolute value of specific entropy is unknown is not a problem because it is the change in specific entropy (Δs) and not the absolute value that is important in practical problems.
Although the units of the various forms of energy are different, they are equivalent.
Power is defined as the time rate of doing work. It is equivalent to the rate of the energy transfer. Power is measured in units of energy per unit time. In the English system, the mechanical units of power are foot-pounds-force per second or per hour (ft-lbf/sec or ft-lbf/hr) and horsepower (hp). The thermal units of power are British thermal units per hour (Btu/hr), and the electrical units of power are watts (W) or kilowatts (kW) and, like energy, the units are equivalent.
Our system is the steam plant. Its heat in is from the HRSG. Its heat out is the condenser and losses due to inadequate insulation. Work is done on the system (working fluid) by the condensate and boiler feed pumps. Work is done by the system on the turbine.
Everything external to the system is the thermodynamic surroundings. The system is separated from the surroundings by the system boundaries. In many cases, a thermodynamic analysis must be made of a device, such as a heat exchanger, that involves mass flow into and/or out of the device. The procedure followed by this analysis is to specify a control surface, such as the heat exchanger tube walls. Mass, as well as heat and work (and momentum), may flow across the control surface.
For a pure substance, there is a definite relationship between saturation pressure and saturation temperature: higher pressure means a higher saturation temperature. The graphical representation of this relationship is called the vapor pressure curve.
Thus, if the mass of vapor is 0.2 lbm and the mass of the liquid is 0.8 lbm, the quality is 0.2 or 20%. Quality is an intensive property and only has meaning when the substance is in a saturated state. The area under the bell-shaped curve in Figure 3 shows the region in which quality is important.
Figure 3: Temperature-Volume Curve
Figure 4: Temperature-Volume DiagramLine BC is the constant-temperature process, where the state changes from liquid to vapor and point C is the saturated vapor state. Line CD represents the process where the steam is super-heated at a constant pressure. Temperature and volume are both increasing. If the process takes place at a constant pressure of 100 psia and an initial temperature of 60F; point E represents the initial state, the specific volume being slightly less than 14.7 psia and 60F. Vaporization now begins at point F, where the temperature is 327.8F. Line FG represents the state change (constant temperature) and point G is the saturated-vapor state. GH is the constant-pressure process where the steam is superheated. A constant pressure of 1,000 psia is represented by line IJKL, the saturation temperature being 544.6F.
There are five basic properties of a substance that are usually shown on property diagrams: Pressure (P), temperature (T), specific volume (ν), specific enthalpy (h), and specific entropy (s). When a mixture of two phases, such as water and steam, is involved, a sixth property, quality (x), is also used.
There are six different types of commonly encountered property diagrams. These are:
We will only discuss four: P-ν, P-h, T-s, and h-s.
Figure 5: Pressure-Specific Volume (P-ν) Diagram
Figure 6: Pressure-Enthalpy (P-h) Diagram
Figure 7: Temperature-Entropy (T-s) Diagram
Some tables use v for ÃƒÅ½Ã‚Â½ (specific volume) because there is little possibility of confusing it with velocity. The saturated steam tables cover the energy transfer properties of saturated water and saturated steam at temperatures from 32 to 705.47F (the critical temperature) and for corresponding pressures from 0.08849 to 3208.2 psi. They are normally divided into two parts: temperature tables, listing the properties according to saturation temperature (Tsat), and pressure tables, listing them according to saturation pressure (Psat).
Most practical applications involve steam-water mixtures. The key properties of such mixtures are steam quality (x), defined as "the mass of steam present per unit mass of steam-water mixture," or steam moisture content (m), defined as "the mass of water present per unit mass of steam-water mixture."
To solve problems in thermodynamics, the "state" of the substance and, usually, two properties (v, p, T, h, s) of the substance must be known. The other properties can be found using either the Mollier diagram (if the substance is steam) or the saturated and superheated steam tables.
For any system, energy transfer is when mass and energy cross the control boundary, or external work and/or heat cross the boundary, and the change of stored energy within the control volume. Fluid mass flow described using the kinetic, potential, internal, and "flow" energies affecting the overall energy balance of the system. The exchange of external work and/or heat completes the energy balance. Energies are "balanced" within the system (a region in space (control volume) the fluid passes through). The various energies associated with the fluid are observed as they cross the system boundaries and the balance is made.
In the open system, the most general of the three, mass, heat, and external work, are allowed to cross the control boundary. All energies into the system must equal all energies leaving the system plus any change in stored energies within the system. The energies crossing control volume boundary are those associated with the mass (m) crossing the boundary. Mass in motion has potential (PE), kinetic (KE), and internal energy (U). And, since the flow is normally supplied with some driving power (i.e. a pump), there is another form of energy associated with the fluid caused by its pressure. This form of energy is referred to as flow energy (PÃƒÅ½Ã‚Â½-work). The thermodynamic terms thus representing the various forms of energy crossing the control boundary with the mass are given as m(u + PÃƒÅ½Ã‚Â½+ KE + pe).
In open system analysis, the u and PÃƒÅ½Ã‚Â½ terms occur so frequently that another property, enthalpy, has been defined as h = u + PÃƒÅ½Ã‚Â½. This changes the above expression to m(h +ke + pe). Externally applied work (W), usually designated as shaft work, is another form of energy that may cross the system boundary. To complete and satisfy the conservation of energy relationship, energy that is caused by neither mass nor shaft work is classified as heat energy (Q). The relationship is described by the equation:
m(hin + PEin + KEin) + Q = m(hout + PEout + KEout) + W
When the fluid properties change as a consequence of work, heat, or internal energy exchange, the fluid has gone through a "process." In some processes, the relationships between pressure, temperature, and volume are specified as the fluid goes from one thermodynamic state to another. The most common processes are those where the temperature, pressure, or volume is held constant. These are classified as isothermal or isobaric; Iso means "constant or one." If the fluid passes through a process (or more than one) and returns to its initial state, the system has undergone a cyclic process.
One such cyclic process used is the Rankine cycle. The processes that comprise the cycle are described on the following page (Figure 8).
Figure 8: Rankine CycleFigure 9 shows a typical steam plant cycle. Heat is supplied to the steam generator (boiler) where liquid is converted to steam or vapor. The vapor expands in the turbine producing a work output. Vapor leaving the turbine enters the condenser where heat is removed and the vapor condenses to liquid. The condensation process is the heat-rejection mechanism for the cycle. Saturated liquid is delivered to the condensate pump and then the feed pump where its pressure is raised to the saturation pressure corresponding to the steam generator temperature, and the high-pressure liquid is delivered to the steam generator where the cycle repeats.
Figure 9: Typical Steam Plant Cycle
A typical steam plant system consists of a heat source producing the thermal energy (e.g., nuclear or fossil fuel), a steam generator changing the thermal energy into steam energy, pumps transferring the fluid back to the heat source, a turbine providing useful work (generating electricity via a generator), a condenser, and the necessary piping ensuring the fluid passes through each stage of the process. The steam plant is a large "closed" system. However, each component is thermodynamically analyzed as an open system as the fluid passes through it.
The hot fluid from the heat source (HRSG) passes through the steam generator where its energy passes to the secondary side of the heat exchanger creating steam. This steam is then sent to a turbine where the steam expands across the turbine blading, converting the heat/flow energy of the steam to rotational energy of the turbine which is connected to the generator. The generator then converts rotational energy to electrical energy. The steam exits the turbine at a lower energy level since the turbine has extracted much of it and is sent to the condenser. The condenser changes the steam to liquid so it may be pumped back to the HRSG. The circulating water in the condenser (usually from a river or lake) absorbs the energy from the steam.
The second law of thermodynamics is needed because the first law of thermodynamics does not completely define the energy conversion process. The first law relates and evaluates the various energies in a process. However, no information about the direction of the process can be obtained by applying the first law. Early in thermodynamic science development, investigators noted that while work could be converted completely into heat, the converse was never true for a cyclic process. Certain natural processes always proceed in a certain direction (e.g., heat transfers from hot to cold). The second law was developed to explain these natural phenomena.
The second law of thermodynamics states "The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium." In a simpler definition, the second law states that "energy systems have a tendency to increase entropy" rather than decrease it.
The limitations imposed on any process can be studied, using the second law of thermodynamics, to determine the maximum possible process efficiencies and then compare them to the actual efficiency. One application of the second law is the study of energy-conversion systems. For example, it is not possible to convert all the energy obtained from the HRSG into electrical energy. There must be losses in the conversion process. The second law can be used to derive an expression for the maximum possible energy conversion efficiency taking those losses into account.
The change in entropy is defined as a ratio of heat transferred during a reversible process to the absolute temperature of the system. It is an extensive property that is calculated from specific entropies based on a systems unit mass quantity: S = ms. Specific entropy is used as one of the coordinates when representing a reversible process graphically. The area under a reversible process curve on the T-s diagram represents the quantity of heat transferred during the process.
Thermodynamic processes and cycles are often investigated by substituting reversible processes for the actual irreversible process to aid in analysis. This substitution is especially helpful since only reversible processes can be depicted on the diagrams (h-s and T-s, for example) used for the analysis. Irreversible processes cannot be drawn since they are not a succession of equilibrium conditions. Only the initial and final conditions of irreversible processes are known; however, some thermodynamics texts represent an irreversible process by dotted lines on the diagrams.
The Carnot principle and its resulting cycle demonstrate the maximum theoretical efficiency of a heat engine. And, regardless of engine type, that efficiency is based on two things: temperature of the heat input and temperature of the rejected heat. Knowing this, an equation for Carnot efficiency becomes:
The maximum possible efficiency exists when Th is at its largest possible value or when Tc is at its smallest value. The above efficiency represents an upper limit of efficiency for any given system operating between the same two temperatures. A systems maximum possible efficiency would is Carnot efficiency, but because Carnot efficiencies represent reversible processes, the actual system will not reach it. Thus, the Carnot efficiency serves as an unattainable upper limit for any real systems efficiency.
The following example demonstrates the above principles.
The most important aspect of the second law for our practical purposes is determining maximum possible efficiency of a power system. Actual efficiencies will always be less than this maximum. The losses (friction, for example) in the system and the fact that systems are not truly reversible preclude us from obtaining the maximum possible efficiency.
An open system analysis was performed using the First Law of Thermodynamics in the previous section. The second law problems are treated in much the same manner; that is, isolated, closed, or open systems are used depending on the energy types crossing the boundary. As with the first law, the open system analysis using the second law equations is the more general case, with the closed and isolated systems being "special" cases of the open system.
Figure 10: Power Plant ComponentsA steam turbine is designed to extract energy from the working fluid (steam) and use it to do work (rotate the turbine shaft). The shaft work is converted to electrical energy by the generator. In the application of the first law, the general energy equation to a simple turbine under steady flow conditions, it is found that the decrease in the enthalpy of the working fluid Hin - Hout equals the work done by the working fluid in the turbine.
These relationships apply when the kinetic and potential energy changes and the working fluid heat losses, while in the turbine, are negligible. For most practical applications, these are valid assumptions. However, to apply these relationships, one additional definition is required. The turbines steady flow performance is idealized by assuming that in an ideal case the working fluid does work reversibly by expanding at constant entropy. This defines the so-called ideal turbine. In an ideal turbine, the entropy of the working fluid entering the turbine equals the entropy of the working fluid leaving the turbine.
Defining an ideal turbine provides a basis for analyzing turbine performance. An ideal turbine performs the maximum amount of work theoretically possible. An actual turbine does less work because of blade friction and other losses. Turbine efficiency, sometimes called isentropic turbine efficiency because an ideal turbine is defined as one that operates at constant entropy, is defined as "the ratio of the actual work done by the turbine (Wt, actual) to the work that would be done by the turbine if it were an ideal turbine" (Wt,ideal).
In many cases, turbine efficiency has been independently determined. This permits calculating the actual work directly by multiplying the turbine efficiency by the work done by an ideal turbine under the same conditions. For small turbines, the turbine efficiency is generally 60% to 80%; for large turbines, it is generally about 90%. The actual and idealized performances of a turbine may be compared conveniently using a T-s diagram. The ideal case is constant entropy represented by a vertical line on the T-s diagram. The actual turbine entropy increases. The smaller the increase in entropy, the closer the turbine efficiency is to 1.0 or 100%.
Figure 11: Temperature Entropy CurveA pump is designed to move the working fluid by doing work on it. When applying the first law general energy equation to a simple pump under steady flow conditions, it is found that the enthalpy increase of the working fluid (Hout - Hin) equals the work done by the pump, (Wp), on the fluid.
A heat exchanger is designed to transfer heat between two working fluids. Several heat exchangers are used in power plant steam cycles. In the steam generator or HRSG, the heat source (e.g., CT flue gas) heats and vaporizes the feedwater. In the condenser, the turbine steam exhaust is condensed before being returned to the steam generator. Numerous smaller heat exchangers are used throughout the steam cycle as well.
The Carnot cycle, cycle efficiencies, and component efficiencies have been discussed. In this section, this information will be applied, allowing comparison and evaluation of various ideal and real cycles. This allows determining how a modification affects the cycles energy that is available for work. Since the efficiency of a Carnot cycle is solely dependent on the temperature of the heat source and the heat sink, it follows that to improve a cycles efficiency all we have to do is increase the temperature of the heat source and decrease the temperature of the heat sink. In the real world this ability is limited by the following constraints: for a real cycle, the heat sink is limited because the "earth" is our final heat sink, and therefore, is fixed at about 60F (520R).
The heat source is limited to the combustion temperatures of the fuel being burned or the maximum limits placed on the combustion turbine and its internal components. In the case of fossil fuel cycles, the upper limit is ~3040F (3500R), but is unattainable due to metallurgical restraints of the boilers. It is therefore, limited to about 1,500F (1,960R) for a maximum heat source temperature.
Using these limits to calculate the maximum efficiency attainable by an ideal Carnot cycle gives the following:
This calculation indicates that the Carnot cycle, operating with ideal components under real world constraints, should convert almost 3/4 of the input heat into work. But, as will be shown, this ideal efficiency is well beyond the present capabilities of any real systems.
Figure 12 is a typical power cycle of a fossil fuel plant. The working fluid is water, which places certain restrictions on the cycle. If the pressure limit is at or below 2,000 psia, it is readily apparent that constant heat addition at the maximum temperature of 1,962R is not possible. The nature of water and certain elements in the process require heat to be added in a constant pressure process instead. Therefore, heat is added at an average temperature far below the maximum allowable material temperature.
As can be seen in Figure 12, the actual available energy (area under the 1-2-3-4 curve) is less than half of what is available from the ideal Carnot cycle (area under 1-2-4 curve) operating between the same two temperatures. Typical thermal efficiencies for fossil plants run about 40-60% while nuclear plants have efficiencies closer to 31%. Note that these numbers are far less than the maximum thermal efficiency of the ideal Carnot cycle calculated earlier.
Figure 12: Typical Fossil Fuel Plant Power CycleFigure 13 shows a proposed Carnot steam cycle superimposed on a T-s diagram. As shown, there are several issues making it undesirable as a practical power cycle. First, a great deal of pump work is required to compress a two phase mixture of water and steam from point 1 to the saturated liquid state at point 2. Second, this same isentropic compression will probably result in some pump cavitation in the feed system. Finally, a condenser designed to produce a two-phase mixture at the outlet (point 1) would pose technical problems.
Figure 13: Carnot Steam Cycle and T-s Diagram
Early thermodynamic developments centered on improving the performance of contemporary steam engines. It was desirable to construct a cycle that was as close to being reversible as possible and would better lend itself to the characteristics of steam and process control than the Carnot cycle did.
Toward this end, the Rankine cycle was developed. The main feature of the Rankine cycle, shown in Figure 14, is that it confines the isentropic compression process to the liquid phase only (points 1 to 2). This minimizes the amount of work required to attain operating pressures and avoids the mechanical problems associated with pumping a two-phase mixture.
Figure 14: Rankine CycleThe compression process shown in Figure 15 between points 1 and 2 is greatly exaggerated. In reality, temperature rises only ~1F when compressing water from 14.7 psia to 1,000 psig at a saturation temperature of 212F. In a Rankine cycle, the areas under the curves represent available and unavailable energy on a T-s diagram, the larger the unavailable energy, the less efficient the cycle.
Figure 15: T-s DiagramFrom the T-s diagram in Figure 15, it can also be seen that if an ideal component, in this case, the turbine, is replaced with a nonideal component, the cycle efficiency reduced. This is due to the nonideal turbines increasing entropy increasing the area under the T-s curve. But the increase in the area of available energy (3-2-3) is less than the increase in area for unavailable energy (a-3-3).
Figure 16 is a Rankine Cycle for a power plant with reheat steam capabilities. The first process in the Rankine Cycle is the condensate pressure being pumped from the condenser. Temperature usually increases as pressure increases due to pumping and via heat exchangers called feedwater heaters. The increase in energy resulting from the increase in temperature is represented by line A to B.
Figure 16: Reheat Rankine CycleThe second Rankine cycle process (B to C) is heat added to the water entering the boiler. Within the HRSG, the water changes from a liquid to a gas (steam). This steam generation occurs at a constant pressure. Additional energy is added to the steam as it passes through the superheater (C to D). The steam is then expanded and cooled as it passes through the turbine as represented by line D to E. Here, the steam energy is used to perform work.
Most boilers in the power generation industry are fitted with reheater sections, as represented by line E to F and F to G on the graph. Steam leaving the high-pressure turbine is reheated in the HRSG, raising the energy in the steam to a level even higher than that of main steam allowing the system to do more work.
The last process in the Rankine cycle is condensing the steam exhausting from the turbine, represented by line G to A. During condensation, considerable heat, called the latent heat of vaporization, is lost.
The heat required to make the Rankine cycle work is determined by the area under the lines between points B to F; and the heat lost from the cycle is under the line between points GA. The area between the lines represents the heat converted to useful mechanical energy. The useful mechanical energy is only about 1/3 of the heat required to make the cycle work.
A simplified version of the major components of a typical steam plant cycle is shown in Figure 17. This is a simplified version and does not contain the exact detail that may be found at most power plants. However, for the purpose of understanding the basic operation of a power cycle, further detail is not necessary. The following are the processes that comprise the cycle:
Figure 17: Major Components of a Typical Steam Plant Cycle
Temperature is a measure of the amount of energy possessed by the molecules of a substance. It is a relative measure of how hot or cold a substance is and can be used to predict the direction of heat transfer. The symbol for temperature is T. The common scales for measuring temperature are the Fahrenheit, Rankine, Celsius, and Kelvin temperature scales.
Heat is energy in transit. The transfer of energy as heat occurs at the molecular level due to a temperature difference. Heat can be transmitted through solids and fluids by conduction, through fluids by convection, and through empty space by radiation. The symbol for heat is Q. Common units for measuring heat are the British thermal unit (Btu) in the English system of units, and the calorie in the SI system (International System of Units).
Both represent energy in transition. However, heat is energy transferred due to a temperature difference. While work is the energy transfer due to a force acting through a distance. Neither heat nor work is a thermodynamic property of a system. Heat can be transferred into or out of a system and work can be done on or by a system, but a system cannot contain or store either heat or work. Heat into a system and work out of a system are considered positive quantities. When a temperature difference exists across a boundary, the second law of thermodynamics indicates the natural flow of energy is from the hotter body to the colder one.
The second law of thermodynamics denies the possibility of ever completely converting all heat supplied to a system operating in a cycle into work. For instance, if you draw heat from a reservoir to raise a weight, lowering the weight will not generate enough heat to return the reservoir to its original temperature, and eventually the cycle will stop. If two blocks of metal at different temperatures are thermally insulated from their surroundings and placed in contact with each other, heat will flow from the hotter block to the colder block. Eventually, the two blocks reach the same temperature, and heat transfer will cease. Energy has not been lost; some energy has been transferred from one block to the other.
The convective heat transfer coefficient (h), defines, in part, the heat transfer due to convection. The convective heat transfer coefficient is sometimes referred to as a film coefficient and represents the thermal resistance of a relatively stagnant layer of fluid between a heat transfer surface and the fluid medium.
Convective heat transfer is governed by gas temperature, gas velocity, initial and final steam temperature, operating pressure, and surface area. Gas temperature and velocity are dictated by combustion turbine (CT) operation. Steam temperatures and pressure are set by steam turbine design parameters. Surface area is established during HRSG design to achieve the required final steam conditions.
The forced convection heat transfer mode is best illustrated by the heating felt when a forced air furnace duct blows warm air over your hand. In HRSGs, this is typified as the hot CT exhaust gas flowing over the various steam generating surfaces.
Convective heat transfer is further enhanced by using extended surfaces and a superficial gas velocity approaching 100 feet per second (fps). Gas velocities beyond 100 fps (30.48 meter per second) run the risk of tube wall erosion and excessive CT exhaust gas back-pressure or HRSG pressure drop. The maximum pressure drop for HRSGs is about 15 inches (381 mm) of water column. The extended surfaces used in the HRSG are produced using finned tubes. Fins are steel ribbons wrapped spirally around the outside of the tube. Fins may be serrated or solid and are resistance welded to the tube wall. A finned tube absorbs heat energy from gas stream by convection. Heat energy is not stored in fins, but conducted to the tubes outside wall by conduction. At the tube wall, the energy is transferred across the wall thickness by conduction to the inside tube wall.
The fluid temperature (Tb), referred to as bulk temperature, varies according to fluid flow conditions. For flow adjacent to a hot or cold surface, Tb is the temperature of the fluid that is "far" from the surface, for instance, the center of the flow channel. For boiling or condensation, Tb is equal to the fluids saturation temperature.
Heat transfer by convection is more difficult to analyze than heat transfer by conduction because no single property of the heat transfer medium, such as thermal conductivity, can be defined to describe the mechanism. Heat transfer by convection varies with fluid flow conditions and is frequently coupled with the mode of fluid flow.
Analysis of heat transfer by convection, in practice, is treated empirically, (by direct observation) because of the factors that affect the stagnant film thickness:
Convection involves heat transfer between a surface at a given temperature (Ts) and fluid at a bulk temperature (Tb). For flow in a pipe, Tb is the average temperature measured at a particular cross section of the pipe.
All heat transfer problems involve temperature difference, the geometry, and the physical properties of the object being studied. In conduction heat transfer problems, the object being studied is usually a solid. Convection problems usually involve a fluid medium and radiation heat transfer problems involve either solid or fluid surfaces, separated by a gas, vapor, or vacuum.
This unstable situation continues until the affected surface is covered by a stable blanket of steam, preventing contact between the heat transfer surface and the liquid in the center of the flow channel. The condition after the stable steam blanket has formed is referred to as film boiling. The process of going from nucleate boiling to film boiling is graphically represented below. Figure 18 illustrates the effect of boiling on the relationship between the heat flux and the temperature difference between the heat transfer surface and the fluid passing it.
Figure 18: Nucleate Boiling to Film BoilingFour regions are represented in Figure 18 above. The first and second regions show that as heat flux increases, the temperature difference (surface to fluid) does not change very much. Better heat transfer occurs during nucleate boiling than during natural convection. As the heat flux continues to increase, the bubbles become numerous enough that partial film boiling (part of the surface being blanketed with bubbles) occurs. This region is characterized by an increase in temperature difference and a decrease in heat flux. The increase in temperature difference thus causes total film boiling, in which steam completely blankets the heat transfer surface.
In many applications, CHF is an important parameter. For example, in an HRSG, if the critical heat flux is exceeded and DNB occurs at any location in the evaporator, the temperature difference required to transfer the heat being produced from the surface of the evaporator to the feedwater/steam increases greatly. If the temperature increase causes the evaporator to exceed its design limits, a failure will occur. The amount of heat transfer by convection can only be determined after the local heat transfer coefficient is determined.
Unlike solids, the particles of fluids move through piping and components at different velocities and are often subjected to different accelerations. Even though a detailed analysis of fluid flow can be extremely difficult, the basic concepts involved in fluid flow problems are fairly straightforward. These basic concepts are applied using simplifying assumptions and average values, where appropriate. Even though this type of analysis would not be sufficient in system design engineering, it is very useful in understanding system operation and predicting the approximate response of fluid systems to changes in operating parameters.
Several properties of fluids were discussed in the Thermodynamics section of this text. These included temperature, pressure, mass, specific volume, and density.
Anyone who dives under the surface of the water notices the eardrum pressure change at a depth of even a few feet. Careful measurements show that the pressure of a liquid is directly proportional to the depth, and for a given depth the liquid exerts the same pressure in all directions.
As shown in Figure 19, the pressure at different levels in the tank varies and causes the fluid to leave the tank at different velocities. Pressure was earlier defined to be force per unit area. In the case of this tank, the force is due to the weight of the water above the point where the pressure is being measured. This equation tells us that the pressure exerted by a column of water is directly proportional to the height and density of the water column and is independent of the cross-sectional area of the column.
Figure 19: Pressure at Different LevelsThe pressure 30 feet below the surface of a 1-inch diameter standpipe is the same as the pressure 30 feet below the surface of a large lake.
Frictional loss is that part of the total head loss that occurs as the fluid flows through straight pipes. The head loss for fluid flow is directly proportional to the length of pipe, the square of the fluid velocity, and a term accounting for fluid friction called the friction factor. The head loss is inversely proportional to the diameter of the pipe.
Natural circulation will only occur if the correct conditions exist. Even after natural circulation has begun, removal of any one of these conditions will cause the natural circulation to stop. The conditions for natural circulation are:
There must be two bodies of fluid at different temperatures. This could also be one body of fluid with areas of different temperatures. The difference in temperature is necessary to cause a density difference in the fluid. The density difference is the driving force for natural circulation flow. The difference in temperature must be maintained for the natural circulation to continue. Addition of heat by a heat source must exist at the high-temperature area.
Continuous removal of heat by a heat sink must exist at the low temperature area, otherwise, the temperatures would eventually equalize, and no further circulation would occur. The heat source must be at a lower elevation than the heat sink. As shown by the example of the balloon, a warmer fluid is less dense and will tend to rise, and a cooler fluid is denser and will tend to sink. To take advantage of the natural movement of warm and cool fluids, the heat source and heat sink must be at the proper elevations. The two areas must be in contact so that flow between the areas is possible. If the flow path is obstructed or blocked, then natural circulation cannot occur.
When closing a valve, the kinetic energy of the moving fluid is converted into potential energy. Elasticity of the fluid and pipe wall produces a wave of positive pressure back toward the fluids source. When this wave reaches the source, the mass of fluid is at rest, but under tremendous pressure. The compressed liquid and stretched pipe walls now start to release the liquid in the pipe back to the source and return to the sources static pressure.
This release of energy forms another pressure wave back toward the valve. When this shockwave reaches the valve, due to the momentum of the fluid, the pipe wall begins to contract. This contraction is transmitted back to the source, which places the pressure in the piping below that of the static pressure of the source. These pressure waves will travel back and forth several times until the fluid friction dampens the alternating pressure waves to the static pressure of the source. Normally, the entire hammer process takes place in under one second.
The initial shock of suddenly stopped flow can induce transient pressure changes that exceed the static pressure. If the valve is closed slowly, the loss of kinetic energy is gradual. If it is closed quickly, the loss of kinetic energy is very rapid. A shock wave results because of this rapid loss of kinetic energy. The shock wave caused by water hammer can be sufficient to cause physical damage to piping, equipment, and personnel. Water hammer in pipes has been known to pull pipe supports from their mounts, rupture piping, and cause pipe whip.
Thermal shock and water slugs (i.e., condensation in the steam system) resulting from improper warm up are major concerns.
Water and steam hammer are not uncommon occurrences in industrial plants. Flow changes in piping systems should be done slowly as part of good operator practice. To prevent water and steam hammer, operators should ensure liquid systems are properly vented and ensure gaseous or steam systems are properly drained during startup.
When possible, initiate pump starts against a closed discharge valve, and open the discharge valve slowly to initiate system flow. If possible, startup smaller capacity pumps before larger capacity pumps. Use warm-up valves around main stream stop valves whenever possible. If possible, close pump discharge valves before stopping pumps. Periodically, verify proper function of moisture traps.
Heat exchangers may be divided into several categories or classifications. The heat exchanger described in the previous paragraph is referred to as an "ordinary heat exchanger." The other two types are classified as "regenerators" and "cooling towers." An ordinary heat exchanger can be single-phase or two-phase. In a single-phase heat exchanger, both of the fluids (cooled and heated) remain in their initial gaseous or liquid states. In two-phase exchangers, either of the fluids changes its phase during the heat exchange process. The HRSG and main condenser of combined cycle facilities are of the two-phase, ordinary heat exchanger classification. Single-phase heat exchangers are usually shell-and-tube type; that is, the exchanger consists of a set of tubes in a container called a shell (Figure 20). At the ends of the heat exchanger, the tube-side fluid is separated from the shell-side fluid by a tube sheet. The design of two-phase exchangers is essentially the same as that of single-phase-exchangers.
Figure 20: Shell and Tube Heat ExchangerThe design and construction of ordinary heat exchangers may vary greatly. They may be single- or two-phase; however, their operation and effectiveness are largely determined by the fluid flow direction inside the exchanger. The most common flow paths within a heat exchanger are counter-flow and parallel flow. A counter-flow heat exchanger is one in which the direction of the flow of one of the working fluids is opposite to the direction to the flow of the other fluid. In a parallel flow exchanger, both fluids in the heat exchanger flow in the same direction.
Figure 21 represents the fluid flow directions in the parallel and counter-flow exchangers.
Figure 21: Fluid Flow in Parallel and Counter-Flow Exchangers
Temperature profiles of the two heat exchangers indicate two major disadvantages in the parallel-flow design. First, the large temperature difference at the ends causes large thermal stress. The opposing expansion and contraction of the construction materials due to diverse fluid temperatures can lead to eventual material failure. Second, the temperature of the cold fluid exiting the heat exchanger never exceeds the lowest temperature of the hot fluid. This relationship is a distinct disadvantage if the purpose is to raise the temperature of the cold fluid. A parallel flow heat exchanger is a good choice when bringing two fluids to nearly the same temperature.
The counter-flow heat exchanger has three significant advantages over the parallel flow design. First, the more uniform temperature difference between the two fluids minimizes the thermal stresses throughout the exchanger. Second, the outlet temperature of the cold fluid can approach the highest temperature of the hot fluid (the inlet temperature). Third, the more uniform temperature difference produces a more uniform rate of heat transfer throughout the heat exchanger.
Under comparable conditions, more heat is transferred in a counter-flow arrangement than in a parallel flow heat exchanger.
The water to be cooled is pumped to the top of the tower where it is distributed by spray or wooden troughs. It then falls through the tower, splashing down from deck to deck. A part of it evaporates into the air passing through the tower. The enthalpy needed for evaporation is taken from the water and transferred to the air, which heats as the water cools. The airflow is either horizontal due to wind currents (cross flow) or vertically upward in counter-flow to the falling water due to the chimney effect of the warm humid air in the tower or by fans at the bottom (forced draft) or at the top (induced flow). Mechanical draft towers are smaller and more economical to construct than natural-convection towers of the same cooling capacity.