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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.

Menu
1.2.2 Pressure
1.3.1 Energy
1.3.2 Work
1.3.3 Heat
1.3.3.1 Entropy
1.4.1.3 Steady State
1.5.3 Quality X
1.11.1.1 Conduction
1.11.1.2 Convection
1.11.2.2 Bulk Boiling
1.11.2.3 Film Boiling
1.11.3 Fluid Flow
1.11.4.1 Flow Regimes
1.11.4.1.1 Laminar Flow
1.11.4.1.2 Turbulent Flow
1.11.4.3 Viscosity
1.11.4.4 Head Loss
1.11.6.1 Water Hammer
1.11.6.3 Steam Hammer

Thermodynamics

Thermodynamics studies the relationship between heat, temperature, energy and the transfer of energy from one place to another and from one form to another. The key concept is that heat is a form of energy corresponding to a definite amount of mechanical work.

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.

Definitions

First law of thermodynamics is simply stating the conservation of energy. "The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings." Or simply put, work can be converted to heat and heat can be converted to work. Its significant property is enthalpy.

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.

Intensive and Extensive Properties

Thermodynamic properties can be divided into two general classes: intensive and extensive properties.

  • An intensive property is independent of the amount of mass.
  • The value of an extensive property varies directly with the mass. Thus, if a quantity of matter in a given state is divided into two equal parts, each part will have the same value of the intensive property as the original and half the value of the extensive property.

Temperature, pressure, specific volume, and density are examples of intensive properties. Mass and total volume are examples of extensive properties.

Temperature

Temperature measures the molecular activity of a substance; the greater the movement of molecules, the higher the temperature, or how "hot" or "cold" a substance is. It and can be used to predict the direction of heat transfer.

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

Pressure

Pressure measures the force exerted per unit area on the boundaries of a substance (or system). It is caused by the molecules of the substance colliding with the system boundaries. As molecules hit the boundaries, they exert forces that try to push them outward. The resulting forces cause pressure to be exerted by a system on its surroundings. Pressure is frequently measured in units of lbf/in2 (psi).

  • When pressure is measured relative to a perfect vacuum, it is called absolute pressure (psia).
  • When pressure is measured relative to atmospheric pressure (14.7 psia), it is called gauge pressure (psig).
  • The latter pressure scale was developed because almost all pressure gauges register zero when open to the atmosphere. If the pressure is below atmospheric, it is designated as a vacuum. A perfect vacuum corresponds to absolute zero pressure. All values of absolute pressure are positive, because a negative value would indicate tension, which is considered impossible in fluid. Gauge pressures are positive if they are above atmospheric pressure and negative if they are below atmospheric pressure. Figure 2 shows the relationships between absolute, gauge, vacuum, and atmospheric pressures.


Figure 2: Absolute, Gauge, Vacuum, and Atmospheric Pressures
The 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.

Energy, Work, and Heat

Heat and work are the two ways energy can be transferred across the boundary of a system. One of the most important discoveries in thermodynamics was that work could be converted into an equivalent amount of heat and that heat could be converted into work.

Energy

Energy is defined as the capacity of a system to perform work or produce heat. Two types of energy are potential energy and kinetic energy.

  • Potential energy (PE) is defined as energy of position, normally due to height.
  • Kinetic energy (KE) is the energy of motion.

Specific Internal Energy

Potential energy and kinetic energy are macroscopic forms of energy. They can be visualized in terms of the position and the velocity of objects. Along with these macroscopic forms of energy, a substance possesses several microscopic forms of energy. These include energy due to the rotation, vibration, translation, and interactions among the molecules of a substance.

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).

Specific P-V Energy

Another form of energy is important in understanding energy transfer systems. This form of energy is called P-V energy because it arises from the pressure (P) and the volume (V) of a fluid. It is numerically equal to PV, the product of pressure and volume. Because energy is defined as the capacity of a system to perform work, a system where pressure and volume are permitted to expand performs work on its surroundings. Therefore, a fluid under pressure has the capacity to perform work. In engineering applications, the units of P-V energy, also called flow energy, are the units of pressure times volume (pounds-force per square foot times cubic feet), which equals foot-pounds force (ft-lbf).

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.

Specific Enthalpy

Specific enthalpy (h) is defined as: h = u + 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.

Work

Kinetic energy, potential energy, internal energy, and P-ν energy are properties of a system. Work is not a system property, it is a process done by or on a system, but a system contains no work. Work is a form of energy in transit. This distinction between the forms of energy that are properties of a system and those that are transferred to and from a system is important to understanding energy transfer systems. Work is defined, for mechanical systems, as "the action of a force on an object through a distance." It equals the product of the force (F) times the displacement (d):

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.

Heat

Heat (Q), like work, is energy in transit. This energy transfer occurs at the molecular level as a result of a temperature difference. In engineering applications, British thermal units (Btu) are used. As with work, it is important to distinguish between heat added to and heat removed from a system by its surroundings. A positive value indicates that heat is added to the system. This is in contrast to work that is positive when energy is transferred from the system. The symbol q indicates heat added to or removed from a system per unit mass. It equals the total heat (Q) added or removed divided by the mass (m). The term "specific heat" is not used for q since specific heat is used for another parameter; q is referred to simply as "the heat transferred per unit mass."

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:

  • Latent heat of fusion Latent heat of fusion can be defined as the amount of heat added or removed to change phase between solid and liquid.
  • Latent heat of vaporization - Latent heat of vaporization is the amount of heat added or removed to change phase between liquid and vapor. The latent heat of vaporization is sometimes called the latent heat of condensation.

A substances physical characteristics define its phase. For example, water, used to make steam, has three (3) phases:

  1. Liquid-water
  2. Solid-ice
  3. Vapor-steam

Entropy

Entropy (S) is a property and like pressure, temperature, volume, and enthalpy, its changes are determined by knowing the initial and final conditions of the substance. Entropy is a substances energy that is no longer available to perform useful work. Because entropy tells so much about the usefulness of an amount of heat transferred in performing work, the steam tables include values of specific entropy (s = S/m). Entropy is sometimes referred to as a measure of the inability to do work for a given heat transferred.

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.

Energy and Power Equivalences

The various forms of energy involved in energy transfer systems (potential energy, kinetic energy, internal energy, P-V energy, work, and heat) are measured in many units. Three types are used here to measure energy:

  1. Mechanical units, such as the foot-pound-force (ft-lbf)
  2. Thermal units, such as the British thermal unit (Btu)
  3. Electrical units, such as the watt-second (W-sec)

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.

Thermodynamic Systems and Processes

Defining the appropriate system greatly simplifies a thermodynamic analysis. A thermodynamic system is any three-dimensional region of space bounded by one or more surfaces. The bounding surfaces may be real or imaginary and may be at rest or in motion. The boundary may change its size or shape. The region of physical space that lies outside the selected boundaries is called the surroundings or environment.

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.

Thermodynamic Systems and Surroundings

Thermodynamics is the study of various systems. A thermodynamic system is the collection of matter being studied. It could be the water within one side of a heat exchanger, the fluid inside a length of pipe, or the entire lubricating oil system for a diesel engine. Determining the boundaries to solve a thermodynamic problem for a system depends on the information that is known about the system and the question being asked.

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.

Types of Thermodynamic Systems

Systems in thermodynamics are classified as isolated, closed, or open based on the possible transfer of mass and energy across the boundaries.

  • An isolated system is not influenced in any way by the surroundings. This means that no energy in the form of heat or work may cross the boundary of the system. No mass may cross the system boundary either.
  • A closed system has no transfer of mass with its surroundings, but may transfer energy (either heat or work) to/from its surroundings.
  • An open system is may transfer both mass and energy with its surroundings.

Thermodynamic Equilibrium

When changes occur at the same rate in all directions within a system, the system is in thermodynamic equilibrium. For example, if the gas that comprises a system is in thermal equilibrium, the temperature will be the same throughout the entire system.

Steady State

Steady state implies that no changes are occurring. It is that circumstance where the properties at any point within the system are independent of time.

Thermodynamic Process

When one or more system properties change, the system changes state. The thermodynamic process is the path of the states the system passes through. One example of a thermodynamic process is increasing the temperature of a fluid while maintaining a constant pressure. Another example is increasing the pressure of a confined gas while maintaining a constant temperature.

Saturation

Saturation defines a condition where a mixture of vapor and liquid exist together at a given temperature and pressure. The temperature where vaporization (boiling) starts, at a given pressure, is called the saturation temperature or boiling point. The pressure where vaporization (boiling) begins, for a given temperature, is called the saturation pressure. Water, at 212F, has a saturation pressure of 14.7 psia, and water, at 14.7 psia, has a saturation temperature of 212F.

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.

NOTE:

The process of saturation can be seen anytime water boils. Initially water is at some temperature. When placed on the stove, its temperature goes up -sensible heat is being added because the temperature of the water is changing. When the temperature of the water reaches 212F, the water begins to boil, it is "saturated" with energy. If energy (heat) continues to be added, the temperature does not change. The water changes to steam (phase change), but the steam and water are both at 212'F.

Saturated and Sub-cooled Liquids

If a substance is a liquid at its saturation temperature and pressure, it is called a saturated liquid. If the liquids temperature is lower than its saturation temperature for the existing pressure, it is called sub-cooled.

Quality X

When a substance is part liquid and part vapor at saturation conditions, its quality (x) is defined as "the ratio of the mass of the vapor to the total mass of both vapor and liquid." Mathematically:

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

Moisture Content M

The moisture content of a substance is the opposite of its quality. Moisture (M) is defined as "the ratio of the mass of the liquid to the total mass of both liquid and vapor." The moisture of the mixture in the previous paragraph would be 0.8 or 80%. The following equation shows how to calculate the moisture of a mixture:

Saturated and Superheated Vapors

If a substance exists entirely as vapor at saturation temperature, it is called saturated vapor. The term dry saturated vapor emphasizes 100% X (quality). When the vapors temperature is greater than the saturation temperature, it is said to be superheated. The pressure and temperature of superheated vapors are independent properties, since the temperature may increase while the pressure remains constant.

Constant Pressure Heat Addition

Consider the plot on the temperature-volume diagram (Figure 4), the diagonal lines show constant pressure, representing the states the water of the previous discussion passes through as it is heated from 14.7 psia and 60F. If letter A represents the initial state and letter B represents the start of the saturated liquid line (212F), then, line AB represents the process of heating the liquid from its initial temperature to is saturation temperature.


Figure 4: Temperature-Volume Diagram
Line 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.

Condensation

All the processes discussed on the preceding pages occur during a heat addition to a substance. If heat is removed from a substance, the opposite of the described processes will occur. Adding heat to a saturated liquid, at a constant pressure, causes it to evaporate (change phase from liquid to vapor). Removing heat from a saturated vapor, at a constant pressure, causes it to condense (change phase to liquid). So the processes of vaporization and condensation are the exact opposite of each other. Similarly, freezing is the opposite process of melting.

Property Diagrams

A substances phases and property relationships are most commonly shown on property diagrams. Some standard relationships are: at standard atmospheric pressure and temperature above 212F, water exists as steam and not a liquid; it exists as a liquid at temperatures between 32F and 212F; and, it exists as ice at temperatures below 32F. The properties of ice, water, and steam are related. Saturated steam at 212F and standard atmospheric pressure has a specific volume of 26.8 ft3/lbm. At any other temperature and pressure, saturated steam has a different specific volume. For example, at 544F and 1,000 psia pressure, its specific volume is 0.488 ft3/lbm.

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:

  1. Pressure-Temperature (P-T)
  2. Pressure-Specific Volume (P-ν)
  3. Pressure-Enthalpy (P-h)
  4. Enthalpy-Temperature (h-T)
  5. Temperature-entropy (T-s)
  6. Enthalpy-Entropy (h-s) or Mollier diagrams

We will only discuss four: P-ν, P-h, T-s, and h-s.

Pressure-Specific Volume P-ν Diagram

A P-ν diagram is a common type of property diagram that can be constructed for any pure substance. It is different from a P-T diagram in that there are regions on a P-ν diagram where two phases exist together. For example, in Figure 5 at point A, water with a specific volume given by point B, exists together with steam with a specific volume given by point C. The dotted lines on Figure 5 are constant temperature lines. The mixture quality at any point in the liquid-vapor region can be found if the specific volumes of water, steam, and the mixture are all known.


Figure 5: Pressure-Specific Volume (P-ν) Diagram

Pressure-Enthalpy P-h Diagram

A P-h diagram exhibits the same features as a P-ν diagram and can be constructed for any pure substance. Figure 6 below is the P-h diagram for pure water. Like the P-ν diagram, there are regions on a P-h diagram where two phases exist together. For example, in the liquid-vapor region, water and steam exist together. In Figure 6 at point A, water with an enthalpy (h), given by point B, exists together with steam with an enthalpy (h), given by point C. The quality of the mixture at any point in the liquid-vapor region can be found using diagram.


Figure 6: Pressure-Enthalpy (P-h) Diagram

Temperature-Entropy T-s Diagram

A T-s diagram is the most frequently used diagram for analyzing energy transfer system cycles because the work done by or on the system and the heat added to or removed from the system can be visualized on the T-s diagram. By the definition of entropy, the heat transferred to or from a system equals the area under the T-s curve of the process. A T-s diagram can be constructed for any pure substance and exhibits the same features as P-ν diagrams. Figure 7 below is the T-s diagram for pure water.


Figure 7: Temperature-Entropy (T-s) Diagram

Enthalpy-Entropy h-s or Mollier Diagram

The Mollier diagram, located in the back of steam tables, is a chart on which enthalpy (h) versus entropy (s) is plotted. It is sometimes known as the h-s diagram and has an entirely different shape from the T-s diagrams.

Steam Tables

The steam table manual contains tables showing energy transfer properties of water and steam: saturated and superheated. The tables are tabulations of pressure (P), temperature (T), specific volume (ν), specific enthalpy (h), and specific entropy (s).

Some tables use v for ν (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.

First Law of Thermodynamics

The first law of thermodynamics states: Energy can neither be created nor destroyed; only altered in form and is referred to as the conservation of energy principle.

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 (Pν-work). The thermodynamic terms thus representing the various forms of energy crossing the control boundary with the mass are given as m(u + Pν+ KE + pe).

In open system analysis, the u and Pν terms occur so frequently that another property, enthalpy, has been defined as h = u + Pν. 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).

  • ab: Liquid is compressed with no change in entropy (by ideal pump) pressure increases.
  • bc: Constant pressure transfer of heat in the boiler. Heat is added to the compressed liquid, two-phase, and superheated states.
  • cd: Constant entropy expansion with shaft work output (in ideal turbine).
  • da: Constant pressure transfer of heat in the heat sink. Unavailable heat is rejected to the condenser.


Figure 8: Rankine Cycle
Figure 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.

Second Law of Thermodynamics

It is impossible to construct a device that operates in a cycle and produces no effect other than the removal of heat from a body at one temperature and the absorption of an equal quantity of heat by a body at a higher temperature. In other words, all heat engines must reject heat.

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.

Entropy and the Second Law of Thermodynamics

Entropy was introduced to help explain the second law of thermodynamics. This propertys change is used to determine the direction a given process will go. Entropy can also be explained as a measure of the unavailability of heat to perform work in a cycle. This relates to the second law since the second law predicts that not all heat provided to a cycle can be transformed into an equal amount of work; some must be rejected.

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.

Carnots Principle

In 1824, Sadi Carnot advanced the study of the second law by disclosing a principle consisting of the following propositions:

  • No engine can be more efficient than a reversible engine operating between the same high temperature and low temperature reservoirs. Here, the term heat reservoir is taken to mean either a heat source or a heat sink.
  • The efficiencies of all reversible engines operating between the same constant temperature reservoirs are the same.
  • The efficiency of a reversible engine depends only upon the temperatures of the heat source and heat receiver.

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.

  • Example 1: An inventor claims to have an engine that receives 100 Btu of heat and produces 25 Btu of useful work when operating between a source at 140F and a receiver at 0F. Is the claim a valid claim?The claim is invalid.

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.

  • Example 2: Actual vs. Ideal Efficiency The actual efficiency of a steam cycle is 18.0%. The facility operates from a steam source at 340F and rejects heat to atmosphere at 60F. Compare the Carnot efficiency to the actual 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.

Power Plant Components

To analyze a complete power plant steam power cycle, first analyze the elements that make up the cycle. Although specific designs differ, there are three basic elements in power cycles: (1) turbines, (2) pumps, and (3) heat exchangers. Associated with each of these three elements is a characteristic change in the working fluid properties. Previously, we calculated system efficiency using the temperature of the heat source and the heat sink. It is also possible to calculate each individual components efficiency by comparing the actual work the component produces to that which would have been produced by an ideal component operating isentropically between the same inlet and outlet conditions.


Figure 10: Power Plant Components
A 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 Curve
A 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.

NOTE:

The difference between the turbine equations. A pump increases the energy of the working fluid and a turbine extracts energy from the working fluid, thus the difference.

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.

Heat Rejection

To understand why 73% efficiency is not possible, we must analyze the Carnot cycle, and then compare it using real and ideal components. The energy added to a working fluid during the Carnot isothermal expansion is given by qs. Not all of this energy is available for use by the heat engine since a portion of it must be rejected to the environment.

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 Cycle
Figure 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 Cycle
The 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 Diagram
From 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 Cycle
The 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:

  • 1-2: Saturated steam from the steam generator is expanded in the high-pressure (HP) turbine to provide shaft work output at a constant entropy.
  • 2-3: The moist steam from the exit of the HP turbine is dried and superheated in the moisture separator reheater (MSR).
  • 3-4: Superheated steam from the MSR is expanded in the low-pressure (LP) turbine to provide shaft work output at a constant entropy.
  • 4-5: Steam exhaust from the turbine is condensed in the condenser in which heat is transferred to the cooling water under a constant vacuum condition.
  • 5-6: The feedwater is compressed as a liquid by the condensate and feedwater pump and the feedwater heaters preheat the feedwater.
  • 6-1: Heat is added to the working fluid in the steam generator under a constant pressure condition.


Figure 17: Major Components of a Typical Steam Plant Cycle

Heat and Temperature

A common mistake is interchangeably using the terms heat and temperature. There is a distinct difference between the two.

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).

Heat and Work

There is also a distinction between the energy terms heat and work.

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.

Heat Transfer Modes

Heat always transfers when a temperature difference exists. There are three basic modes of heat transfer:

  1. Conduction is heat transfer by a materials atomic or molecular interactions.
  2. Convection is heat transfer by mixing and the motion of macroscopic portions of a fluid.
  3. Radiation, or radiant heat transfer, is heat transfer by electromagnetic radiation due to the temperature of a body.

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.

Conduction

Conduction is heat transfer by the interaction between a materials adjacent molecules. Heat transfer by conduction depends on the driving "force" of the temperature difference and the materials resistance to heat transfer. The resistance to heat transfer depends on the nature and dimensions of the heat transfer medium.

Convection

Convection is heat transfer by the motion and mixing of "macroscopic" portions of a fluid (that is, fluid flow past a solid boundary). The term natural convection is used if this motion and mixing is caused by density variation due to temperature differences within the fluid. The term forced convection is used if an outside force, such as a pump, causes the motion and mixing. The heat from a hot water radiator into a room is an example of heat transfer by natural convection. Heat transfer from the surface of a heat exchanger to the bulk of a fluid being pumped through it is an example of forced convection. HRSG heat transfer is predominantly forced convection.

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:

  • Fluid velocity
  • Fluid viscosity
  • Heat flux
  • Surface roughness
  • Type of flow (single-phase/two-phase).

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.

Thermal Radiation

Radiant heat transfer moves heat by electromagnetic radiation that arises due to the temperature of a body. Most of this energy type is in the infrared region of the electromagnetic spectrum although some may be in the visible region. The term thermal radiation is used to distinguish this form of electromagnetic radiation from other forms, such as radio waves, x-rays, or gamma rays. The transfer of heat from a fireplace across a room in the line of sight (a straight line) is an example of radiant heat transfer. Radiant heat transfer does not need a medium, such as air or metal, to take place. Any material that has a temperature above absolute zero gives off some radiant energy. When a cloud covers the sun, both its heat and light diminish. This is one of the most familiar examples of heat transfer by thermal radiation.

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.

Boiling Heat Transfer

Convective heat transfer is used to remove heat from a heat transfer surface. The liquid used for cooling is usually in a compressed state, at pressures higher than the normal saturation pressure for the given temperature (sub-cooled). Under certain conditions, some type of boiling (usually nucleate boiling) can take place. A discussion of the boiling processes, specifically local and bulk boiling, will help you understand these processes and provide a clearer picture of why bulk boiling (specifically film boiling) is to be avoided.

Nucleate Boiling

The most common type of local boiling encountered is nucleate boiling. In nucleate boiling, steam bubbles form at the heat transfer surface and then break away and are carried into the main stream of the fluid. This enhances heat transfer because the heat generated at the surface is carried directly into the fluid stream. Once in the main fluid stream, the bubbles collapse because the bulk temperature of the fluid is not as high as the heat transfer surface temperature where the bubbles were created. This heat transfer process is sometimes desirable because the energy created at the heat transfer surface is quickly and efficiently "carried" away.

Bulk Boiling

As system temperature increases or system pressure drops, the bulk fluid can reach saturation conditions. At this point, the bubbles entering the coolant channel do not collapse. The bubbles tend to join together and form bigger steam bubbles. This phenomenon is referred to as bulk boiling. Bulk boiling can provide adequate heat transfer if the steam bubbles are carried away from the heat transfer surface and the surface is continually wetted with liquid water. Film boiling results when this cannot occur.

Film Boiling

When system pressure drops or flow decreases, the bubbles cannot escape as quickly from the heat transfer surface. Likewise, if the temperature of the heat transfer surface is increased, more bubbles are created. As the temperature continues to increase, more bubbles are formed than can be efficiently carried away. The bubbles grow and group together, covering small areas of the heat transfer surface with a film of steam. This is known as partial film boiling. Since steam has a lower convective heat transfer coefficient than water, the steam patches on the heat transfer surface act to insulate the surface, making heat transfer more difficult. As the area of the heat transfer surface covered with steam increases, the temperature of the surface increases dramatically, while the heat flux from the surface decreases.

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 Boiling
Four 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.

Departure from Nucleate Boiling and Critical Heat Flux

In practice, if the heat flux is increased, the transition from nucleate boiling to film boiling occurs suddenly, and the temperature difference increases rapidly, as shown by the dashed line in the figure. The point of transition from nucleate boiling to film boiling is called the point of departure from nucleate boiling, commonly written as DNB. The heat flux associated with DNB is commonly called the critical heat flux (CHF).

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.

Fluid Flow

Fluid flow is an important part of most industrial processes, especially those involving the transfer of heat. Frequently, when it is desired to remove heat from the point where it is generated, some type of fluid is involved. Examples of this are the cooling water circulated through a gasoline or diesel engine, the airflow past the windings of a motor, and the flow of water through the boiling feedwater pumps of a combined cycle facility. Fluid flow systems are also commonly used to provide lubrication.

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.

Fluid Properties

A fluid is any substance that flows because its particles are not rigidly attached to one another. This includes liquids, gases, and even some materials that are normally considered solids, such as glass. Essentially, fluids are materials that have no repeating crystalline structure.

Several properties of fluids were discussed in the Thermodynamics section of this text. These included temperature, pressure, mass, specific volume, and density.

  • Temperature was defined as "the relative measure of how hot or cold a material is." It can be used to predict the direction that heat will be transferred.
  • Pressure was defined as "the force per unit area." Common units for pressure are pounds force per square inch (psi).
  • Mass was defined as "the quantity of matter contained in a body" and is to be distinguished from weight, which is measured by the pull of gravity on a body.
  • The specific volume of a substance is "the volume per unit mass of the substance." Typical units are ft3/lbm.
  • Density, on the other hand, is "the mass of a substance per unit volume." Typical units are lbm/ft3. Density and specific volume are the inverse of one another. Both density and specific volume depend on the fluids temperature and somewhat on the pressure. As the fluid temperature increases, the density decreases and the specific volume increases. Since most liquids are considered incompressible, an increase in pressure results in no change in density or specific. In actuality, liquids can be slightly compressed at high-pressures, resulting in a slight increase in density and a slight decrease in specific volume.

Compressibility

Compressibility is the measure of this volume change of a substance when a pressure is exerted on it. Again, liquids are generally considered to be incompressible. For example, a pressure of 16,400 psig will cause a given volume of water to decrease by only 5% from its volume at atmospheric pressure. Gases on the other hand, are very compressible. Exerting an external pressure on the gas will readily change its volume.

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 Levels
The 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.

Volumetric Flow Rate

The volumetric flow rate of a system is a measure of the volume of fluid passing a point in the system per unit time. The volumetric flow rate can be calculated as the product of the cross sectional area (A) for flow and the average flow velocity (v). If area is measured in square feet and velocity in feet per second, the result is volumetric flow rate measured in cubic feet per second. Other common units for volumetric flow rate include gallons per minute, cubic centimeters per second, liters per minute, and gallons per hour.

  • Example: A pipe with an inner diameter of 4 inches contains water that flows at an average velocity of 14 feet per second. Calculate the volumetric flow rate of water in the pipe.

Mass Flow Rate

The mass flow rate of a system is a measure of the mass of fluid passing a point in the system per unit time. The mass flow rate is related to the volumetric flow rate by the product of density and volumetric flow rate. If the volumetric flow rate is in cubic feet per second and the density is in pounds-mass per cubic foot, the result is mass flow rate measured in pounds-mass per second. Other common units for measurement of mass flow rate include kilograms per second and pounds-mass per hour.

Flow Regimes

All fluid flow is classified into one of two broad categories or regimes: laminar flow and turbulent flow. The flow regime, whether laminar or turbulent, is important in the design and operation of any fluid system. The amount of fluid friction, which determines the amount of energy required to maintain the desired flow, depends upon the mode of flow. This is also an important consideration in certain applications that involve heat transfer.

Laminar Flow

Laminar flow is also referred to as streamline or viscous flow. These terms are descriptive of the flow because, in laminar flow:

  • Layers of water flow over one another at different speeds with virtually no mixing between layers
  • Fluid particles move in definite and observable paths or streamlines
  • Has similar characteristics of viscous (thick) fluid or is one in which viscosity of the fluid plays a significant part

Turbulent Flow

The irregular movement of the fluid particles characterizes turbulent flow. There is no definite frequency as there is in wave motion. The particles travel in irregular paths with no observable pattern and no definitive layers.

Average Bulk Velocity

In many fluid flow problems, instead of determining exact velocities at different locations in the same flow cross-section, it is sufficient to allow a single average velocity to represent the velocity of all fluid at that point in the pipe. This is fairly simple for turbulent flow since the velocity profile is flat over the majority of the pipe cross-section. It is reasonable to assume that the average velocity is the same as the velocity at the center of the pipe. If the flow regime is laminar (the velocity profile is parabolic), the problem still exists of trying to represent the "average" velocity at any given cross-section since an average value is used in the fluid flow equations. Technically, this is done by means of integral calculus. Practically, you should use an average value that is half of the centerline value.

Viscosity

Viscosity is a fluid property measuring the fluids resistance to deforming due to a shear force. Viscosity is the internal friction of a fluid that makes it resist flowing past a solid surface or other layers of the fluid. Viscosity can also be considered to be a measure of the resistance of a fluid to flowing. Thick oil has a high viscosity; water has a low viscosity. The unit of measurement for absolute viscosity is: = absolute viscosity of fluid (lbf-sec/ft2). The viscosity of a fluid is usually significantly dependent on the temperature of the fluid and relatively independent of the pressure. For most fluids, as the temperature of the fluid increases, the viscosity of the fluid decreases. An example of this can be seen in engine lubricating oil. When the engine and its lubricating oil are cold, the oil is very viscous, or thick. After starting the engine, the lubricating oil temperature increases, the viscosity of the oil decreases significantly, and the oil seems much thinner.

Head Loss

Head loss is a measure of the reduction in the total head (sum of elevation head, velocity head and pressure head) of the fluid as it moves through a fluid system. Head loss is unavoidable in real fluids. It is present because of: the friction between the fluid and the walls of the pipe, the friction between adjacent fluid particles as they move relative to one another, and the turbulence caused whenever the flow is redirected or affected in any way by such components as piping entrances and exits, pumps, valves, flow reducers, and fittings. '

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.

Forced and Natural Circulation

Circulation of fluid in systems by pumps is referred to as forced circulation. It is possible to design some fluid systems in a manner that does not require the presence of pumps to provide circulation. The head required to compensate for the head losses is created by density gradients and elevation changes. Flow that occurs under these circumstances is called natural circulation.

Thermal Driving Head

Thermal driving head is the force causing natural circulation to occur. It is caused by the density difference between two bodies or areas of fluid. Consider two equal volumes of the same type of fluid. If the two volumes are at different temperatures, the volume with the higher temperature will have a lower density and, therefore, less mass. Since the volume at the higher temperature will have a lower mass, it will also have less force exerted on it by gravity. This difference in the force of gravity exerted on the fluid will tend to cause the hotter fluid to rise and the colder fluid to sink. One example of this is a hot air balloon. The force causing a hot air balloon to rise is a result of differing density between the hot air inside the balloon and the cooler air surrounding it. Heat added to the air in the balloon adds energy to the air molecules. Their movement increases and takes up more space. The air molecules inside the balloon take up more space than the same number of air molecules outside the balloon. This means the hot air is less dense than the cooler air. Since the air in the balloon is less dense, gravity has less effect on it (it is lighter). The result is that the air in the balloon weighs less than the surrounding air. Gravity pulls cooler air down into the space occupied by the balloon. The downward movement of the cooler air forces the balloon out of the space previously occupied, and the balloon rises.

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:

  1. A temperature difference exists (heat source and heat sink exists).
  2. The heat source is at a lower elevation than the heat sink.
  3. The fluids must be in contact with each other.

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.

Two-Phase Fluid Flow

Previous discussions addressed single-phase flow. At certain important fluid flow system locations, the simultaneous flow of liquid water and steam occurs, known as two-phase flow. The simple relationships used for analyzing single-phase flow are insufficient for analyzing two-phase flow. Two-phase flow friction is greater than single-phase friction for the same conduit dimensions and mass flow rate. The difference appears to be a function of the type of flow and results from increased flow speeds. Two-phase friction losses are experimentally determined by measuring pressure drops across different piping elements. The two-phase losses are generally related to single-phase losses through the same elements. Several techniques are used to predict the head loss due to fluid friction for two-phase flow. One accepted technique for determining the two-phase friction loss based on the single-phase loss involves the two-phase friction multiplier (R), which is defined as the ratio of the two-phase head loss divided by the head loss evaluated using saturated liquid properties.

Water Hammer

Water hammer is a liquid shock wave resulting from suddenly starting or stopping flow. It is affected by the initial system pressure, the density of the fluid, the speed of sound in the fluid, the elasticity of the fluid and pipe, the change in velocity of the fluid, the diameter and thickness of the pipe, and the valve operating time.

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.

Pressure Spike

A pressure spike is the resulting rapid rise in pressure caused by water hammer. The highest pressure spike attained will be at the instant the flow changed.

Steam Hammer

Steam hammer is similar to water hammer except it is for a steam system. Steam hammer is "a gaseous shock wave resulting from the sudden starting or stopping of flow." Steam hammer is not as severe as water hammer for three reasons:

  1. The compressibility of the steam dampens the shock wave.
  2. The speed of sound in steam is approximately one third the speed of sound in water.
  3. The density of steam is about 1,600 times less than that of water.

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

Heat transfer is usually accomplished by means of a device known as a heat exchanger. Common applications of heat exchangers in the power plant include boilers, fan coolers, cooling water heat exchangers, and condensers. The basic design of a heat exchanger is, normally, two fluids of different temperatures separated by some conducting medium. The most common design has one fluid flowing through metal tubes and the other fluid flowing around the tubes. On either side of the tube (within the fluid), heat is transferred by convection. Heat is transferred through the tube wall by conduction. Because this process takes place over the entire length of the exchanger, the fluids temperature, flowing through the exchanger, is not constant, but varies over the entire length. The rate of heat transfer varies along the tube length because its value depends upon the temperature difference between the hot and the cold fluid at any given point.

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 Exchanger
The 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.

Cooling Towers

Typically a cooling tower functions to cool the water of a steam power plant using air brought into direct contact with the water. The water is mixed with vapor diffusing from the condensate into the air. The vapor formation requires a considerable amount of internal energy from the water; the internal energy becomes "latent heat" of the vapor. Heat and mass exchange are coupled in this process, which is a steady-state process like the heat exchange in the ordinary heat exchanger. Wooden cooling towers are sometimes employed at generating facilities and in factories of various industries. They generally consist of large chambers loosely filled with trays or similar wooden/fiberglass elements of construction.

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.