Environment & Energy

Environment & Energy Thermal Cycles Conversion of Energy Valentim M B Nunes Unidade Departamental de Engenharias Polytechnic Institute of Tomar, March, 2015

Introduction The development of the steam engine, an invention that secured the first two centuries of the industrial revolution, preceded the discovery of scientific principles involved, in particular the production of mechanical work on a machine that uses combustion with air. The scientific knowledge that explains the “production” of work (energy) from different types of combustion is derived from the laws of thermodynamics. James Watt (1736 – 1819) We will review how the laws of thermodynamics govern the operation of these sources of mechanical work and particularly how those laws limit the amount of mechanical work that can be obtained from the combustion of a given amount of fuel.

Work Thermodynamics studies the interaction between a given material system and its surroundings or exterior. It is through these interactions that we are able to produce mechanical work or other useful effects on the exterior. There are two forms of interaction between a system and its exterior, called work and heat. Each of these is a process in which the system and its exterior suffers chemical or physical modifications related to the type of interaction, heat, work or both simultaneously. There are many examples of interaction for performing work. Consider a gas contained in a cylinder, closed at one end and fitted with a movable piston.

Heat The other form of interaction of the system with the surroundings its by heat transfer. A variation in temperature, ΔT, corresponds to a heat transfer Q given by: where C is the heat capacity. Usually we call this interaction by heat transfer, although the energy is changed in a process of this type.

Zeroth Law of thermodynamics The Zeroth Law of thermodynamics is a law of thermal equilibrium. The thermal energy flows from a region of high temperature to another at lowest temperature, with a diathermic wall between the two regions. T/K = t/°C + 273.15

The 1st Law of Thermodynamics One of the fundamental laws of Nature is the law of conservation of energy. The energy of a system can take several forms (for example, kinetic, potential, heat, light), but cannot be created nor destroyed. For closed systems, macroscopically at rest and without changes in the gravitational field: The internal energy of an isolated system is constant. In a closed system it can only be transferred by heat flux or work performed.

The 2nd Law of Thermodynamics When designing a thermal power station the aim is to create a system that converts the energy of a fuel into work. If we consider the combustion of a fossil fuel, so the aim is to convert all the energy of the fuel in work, such as the first law allows. However, the Second Law of Thermodynamics states that a cyclical process in which heat from a single source is entirely converted to work cannot exist. Instead, only part of the heat can be converted to work; the remainder has to be rejected to a reservoir of heat at lower temperature than the heat source.

The 2nd Law of Thermodynamics The 2nd law of thermodynamics recognizes that there are fundamental asymmetries in Nature. For example, bodies warmer than the environment will cool spontaneously, but objects at room temperature do not become warmer spontaneously. The heat transfers spontaneously from hot bodies to cold bodies. Cold body Hot body Q

The transformation of heat into work must be accompanied by the transfer of part of the heat to a cold source.

Formulations of the 2nd Law The Kelvin formulation of the second Law states that it is impossible to have a process in which the only result is the absorption of heat from a reservoir and its complete conversion to work. The second law says that the transformation of heat into work must be accompanied by the transfer of part of the heat to a cold source. Another asymmetry of Nature: it is impossible to convert heat fully in work, but there is no restriction on conversion of work into heat.

Combustion of fossil fuels The source of energy that is used in the combustion of fossil fuels systems is the chemical energy that is released when the fuel is oxidized by burning with air. The most common fossil fuels are hydrocarbons, mixtures of molecules composed of carbon and hydrogen. After the complete combustion, the fuel is oxidized to carbon dioxide and water vapor, releasing energy. Designating the fuel molecules by CnHm, where n and m are the number of atoms of carbon and hydrogen in the molecule of fuel, the molecular rearrangement that accompanies the complete oxidation can be represented by the reaction:

Fuel Heating Value When a mixture of fuel and air is burned, the temperature of combustion products formed is much higher than the mixture. In many cases, the heat can be transferred from hot combustion products to a colder fluid; for example, a boiler heats water and then bring it to ebullition by converting it into water vapor. The amount of heat available for this process is the calorific value of the fuel (fuel heating value) and is usually expressed in units of energy per unit mass of fuel.

Ideal thermal cycles To understand the implications of the laws of thermodynamics to the conversion of fuel energy into mechanical work, it is necessary to analyze ideal devices, in which a fluid is heated and cooled and produces or consumes work as it completes a cycle. A device of this type can be called a heat engine, since exchanges heat with the exterior while produces work in a cyclic process. The combustion of the fuel is represented in this ideal cycle by the addition of heat from a hot source. Some practical machines, such as gas turbines and car engines, are not heated by an external source. These are called internal combustion engines. However much of its operation can be modeled as ideal thermal machines to understand its operation.

Thermodynamic efficiency Particularly important is the amount of work produced (W) in relation to the amount of heat added (Q), to represent the combustion of fuel. To this reason we call thermodynamic efficiency:

Carnot´s Cycle The Carnot cycle is the prototype of a cycle that has little practical importance but is elegantly illustrative of the limitations of the 2nd Law on conversion of heat into work. This is the simplest cycle of a heat engine. Consists of two thermal reservoirs, a hot reservoir at temperature Th and a cold reservoir at temperature Tc. (we can imagine the hot source held at that temperature for heat transfer from the combustion of a fossil fuel and the cold one as the atmosphere). Consider then the thermal machine as a cylinder equipped with a moveable piston and containing a fluid of unit mass. The cycle consists of four steps: an isothermal expansion, during which a quantity of heat Qh is added to the machine (1 → 2 in the figure); an isentropic adiabatic expansion during which the temperature of the fluid decreases from Th to Tc (2 → 3); an isothermal compression while the system transfers a quantity of heat Qc for the cold sink (3 → 4); and finally an isentropic compression to the initial state (4 → 1). For this cycle the piston work per cycle is:

Combining the two previous relationships we can calculate the thermodynamic efficiency of the Carnot cycle: The most important aspect of this result is that the thermodynamic efficiency depends on the temperature of the two reservoirs and not dependent on any of the properties of the fluid used in the heat engine.

Carnot´s Principles The Second Law imposes limits on the operation of cyclic devices: a cyclic Thermal engine cannot operate by exchanging heat with a single source. We can draw two conclusions (principles of Carnot) 1. The performance of an irreversible heat engine is always lower than that of a reversible heat engine that runs from the same sources (temperatures). 2. The thermal efficiency of all reversiblemachines operating between the same two sources are equal. The maximum efficiency of a thermal power station operating with steam vapor that runs between TH = 750 K and TC = 300 K is 60%. The actual thermal efficiency is around 38-40%.

The Rankine cycle The Carnot´s cycle is a important process to understand how it works a simple thermal machine, but it's not useful in practical terms. Since the beginning of the industrial revolution until the 20th century (and still today), most of the mechanical power generated by burning fossil fuels utilizes a steam cycle, called Rankine cycle. In a thermal power station with steam cycle, the fuel mixed with air is burned to a vaporizer to convert water into steam, which then feeds into a turbine. This is an external combustion system where the working fluid, water-steam, is heated in tubes that are in contact with the hot gases formed in the combustion chamber. In an efficient thermal power station, virtually all the calorific value of the fuel is transferred to the steamer, but only a portion is converted to work on turbine.

Rankine cycle Scheme of a Thermoelectric Power Station

In a thermal power station, room-temperature water is pumped at high pressure and injected into the vaporizer (1 → 2 in the figure) and is heated to its boiling point (3), completely converted into steam (4), and then typically heated to a higher temperature (5). This vaporizer heating occurs at constant pressure, Pb. The steam flows through a turbine (5 → 6) where undergoes a pressure reduction to a much lower value, Pc, while the turbine produces power. The low-pressure steam that leaves the turbine is cooled to a liquid at room temperature in the condenser (6 → 1) and pumped into vaporizer where completes the cycle. In the ideal cycle of Rankine, adiabatic work in continuous flow per unit mass of steam, wt produced in turbine is equal to the change of enthalpy h5 − h6 through the turbine, in virtue of the first law. As this is an isentropic process, the change of enthalpy can be expressed through:

There is a similar expression to calculate the work required to operate the pump. The total work w produced in the cycle can be expressed by: where vs and vw are the specific volume of steam in the turbine and water in the pump and Pb and Pc are the pressures in the vaporizer and condenser. Once the specific volume of liquid water is vastly less than the steam, the pump power is a small fraction of the power produced in the turbine, which is one of the great attributes of the Rankine cycle. Once the steps of heating and cooling of the ideal cycle of Rankine (2 → 5, 6 → 1) occur at constant pressure, while the step in the turbine is isentropic thermal efficiency can be expressed by:

We must highlight some aspects relating to the Rankine cycle. First, unlike the Carnot cycle, the thermal efficiency depends on the properties of the working fluid, water. Second, the efficiency of the cycle increases if the pressure in the boiler (and steam temperature) increases. At the same time, high pressure in the evaporator increases the amount of work produced per unit mass of water flowing in the system, and reducing turbine costs per unit of power produced. The cycle can be further improved with efficiency gains through the use of heat exchangers at the intermediate pressure levels. For Rankine cycles using water as working fluid vaporizer temperatures rarely exceed 550 ◦ C. A cycle of more high pressure and high temperatures is one for which the steam pressure and temperature exceeds the critical point of water. The thermodynamic efficiency of the optimal cycle of Rankine varies in the range from 30 to 45%, depending on the details and complexity of the cycle. The current steam cycle power stations have lower efficiencies for various reasons. Turbines and pumps are not 100% efficient, resulting in less power produced.

Otto cycle The most common fossil fuel powered engine is the automobile engine. Unlike steam plants, automobile engines do not depend on the heat transfer of a working fluid from a combustion source. Instead, the fuel is burned inside the engine, adiabatically, and the combustion products produce more work during the expansion, than that which is used in the compression step. The combustion products that are rejected to the atmosphere are replaced by an air-fuel mixture to give origin to a new cycle. This is referred to as open cycle, unlike steam cycle that is closed.

Otto cycle The Otto cycle is the ideal cycle for gasoline engines. In most gasoline engines the piston performs four complete courses within the cylinder. The crankshaft complete two rotations for each thermodynamic cycle. 1-2: Adiabatic compression; 2-3: Addition of heat at constant volume 3-4: Adiabatic expansion; 4-1: Rejection of heat at constant volume.

Otto cycle efficiency increases depending on the compression ratio, ve/vc, and depends on the thermodynamic properties of the working fluid. Can be expressed by: For a typical gasoline engine the compression ratio is about 9 and Cp/Cv = 1.26, then η = 43.5%. Automobile engines efficiencies are quite smaller than that value. The friction in the piston, power required to operate the valves, cooling pump, fuel supply system, losses of pressure in the intake and exhaust systems and heat loss during the compression and expansion, all contribute to reducing the efficiency. The best thermal efficiencies of automobile engines vary between 28 and 39% for petrol engines and diesel engines.

Brayton cycle Since the mid-20th century, the gas turbine has become the dominant technology for large aircraft engines, because their fitness for high speeds of propulsion, lightness, fuel economy and reliability. Also has application in propulsion of large ships and more recently in thermoelectric power plants. The ideal cycle that models the gas combustion process through a central gas turbine is the Brayton cycle. Consists of an isentropic compression of the air in the compressor inlet pressure Pi for the compressor outlet pressure, Pc (1 → 2 in the figure), followed by a constant pressure heating (2 → 3) that rises the temperature of gas for temperature T3 at the turbine inlet. The gases expand isentropicaly while flow through turbine, being the reduced pressure from Pc to Pi (3 → 4).

Per unit mass of the fluid, the resulting work, w, in gas turbine power station is the difference between the work produced in the turbine and compressor work: The heat added to the fluid coming from the compressor, q, which is due to the temperature rise caused by adiabatic combustion, is equal to the change of enthalpy in the process at constant pressure: Thus, the efficiency η of the Brayton cycle is :

The efficiency of the cycle depends on the ratio between the two pressures P2/P1 = P3/P4 and the thermodynamic properties of air and combustion gases. This efficiency is expressed by: What shows that efficiency increases with compression ratio. As an example, for P2/P1= 10 and Cp/Cv = 1.3 then η = 41.2%. For the Brayton cycle the best efficiencies are around 33%.

Combined cycle The exhaust gases coming out of a gas turbine transport part of the calorific value of fuel that may have been converted to work. This hot gas stream can be used to produce steam in a boiler and produce additional work without burning more fuel. The use of a gas turbine and steam plant to produce more work from a given amount of fuel is called combined cycle.

Thermodynamic efficiency, ηcc of a combined cycle thermal power station can be determined depending on the efficiencies, ηg and ηs, of the gas turbine and steam cycle. For the gas turbine, the wg is equal to ηg × qf, where qf is the heat added per unit mass of combustion products. The amount of heat that can be used in the steam cycle is qf– wg = qf×(1 − ηg). The work produced in the steam cycle ws is so ηs times this heat, or ηs ×qf×(1 − ηg). The efficiency of the combined cycle is always lower than the sum of the efficiencies of the two cycles (Brayton and Rankine). However the combination is always more efficient than any one of its components. For example if ηg = 30% and ηs = 25%, then ηcc = 47.8%.

Combined cycle thermal power plants that burn natural gas or jet fuel are often a good choice, instead of coal-fired power stations, despite the favorable price of coal. The reasons are environmental and financial, including a lower emission of gaseous pollutants, including CO2.

Problem 1 Are required 2.2 million tons of coal per year to feed a 1000-MW power station, which operates with a capacity factor of 70%. If the calorific value of coal is 12000 Btu/lb, calculate the thermal efficiency of the plant.

Problem2 Given a compression reason of P2/P1 = 12 along a gas turbine and a ratio of specific heats of Cp/Cv = 1.35 concerning the working fluid, calculate the thermal efficiency of the Brayton cycle. Explain why the power plants with gas turbines reach thermal efficiencies of just 25 to 35%.

Problem3 A combined cycle power station has a gas turbine efficiency of 30% and a steam cycle efficiency of 30%. Calculate the combined cycle efficiency.

Problem4 A 1000-MW power station, with a thermal efficiency of 35%, during 100 % of the time, uses coal with the formula CH and a calorific value of 30 MJ/kg. How much CO2 emits this unit in ton/year?

Bibliography Fay, J., Golomb, D.S., Energy and the Environment, Oxford University Press and Open University, Oxford, UK, 2004 Azevedo, E.G., Termodinâmica Aplicada, 3ºed., Escolar Editora, Lisboa, 2011

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