Thermodynamics, Heat Transfer, And Fluid Flow. V.1. Thermodynamics (776129), страница 17
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This additional heat rejected must then be made up for inthe steam generator. Therefore, it can be seen that excessive condenser subcooling will decreasecycle efficiency. By controlling the temperature or flow rate of the cooling water to thecondenser, the operator can directly effect the overall cycle efficiency.Figure 37HT-01Steam Cycle (Real)Page 92Rev.
0SECOND LAW OF THERMODYNAMICSThermodynamicsIt is sometimes useful to plot on the Mollier diagram the processes that occur during the cycle.This is done on Figure 38. The numbered points on Figure 38 correspond to the numbered pointson Figures 35 and 36. Because the Mollier diagram is a plot of the conditions existing for waterin vapor form, the portions of the plot which fall into the region of liquid water do not show upon the Mollier diagram. The following conditions were used in plotting the curves on Figure 38.Point 1:Saturated steam at 540oFPoint 2:82.5% quality at exit of HP turbinePoint 3:Temperature of superheated steam is 440oFPoint 4:Condenser vacuum is 1 psiaThe solid lines on Figure 38 represent the conditions for a cycle which uses ideal turbines asverified by the fact that no entropy change is shown across the turbines.
The dotted lines onFigure 38 represent the path taken if real turbines were considered, in which case an increase inentropy is evident.HT-01Page 94Rev. 0ThermodynamicsSECOND LAW OF THERMODYNAMICSCauses of InefficiencyIn the preceeding sections, cycle and component efficiencies have been discussed, but the actualcauses or reasons for the inefficiencies have not been explained.
In this section we will comparesome of the types and causes for the inefficiencies of real components and cycles to that of their"ideal" counterparts.ComponentsIn real systems, a percentage of the overall cycle inefficiency is due to the losses by theindividual components. Turbines, pumps, and compressors all behave non-ideally due toheat losses, friction and windage losses. All of these losses contribute to the nonisentropic behavior of real equipment.
As explained previously (Figures 24, 25) theselosses can be seen as an increase in the system’s entropy or amount of energy that isunavailable for use by the cycle.CyclesIn real systems, a second source of inefficiencies is from the compromises made due tocost and other factors in the design and operation of the cycle.
Examples of these typesof losses are: In a large power generating station the condensers are designed to subcoolthe liquid by 8-10°F. This subcooling allows the condensate pumps to pump the waterforward without cavitation. But, each degree of subcooling is energy that must be putback by reheating the water, and this heat (energy) does no useful work and thereforeincreases the inefficiency of the cycle. Another example of a loss due to a system’sdesign is heat loss to the environment, i.e.
thin or poor insulation. Again this is energylost to the system and therefore unavailable to do work. Friction is another real worldloss, both resistance to fluid flow and mechanical friction in machines. All of thesecontribute to the system’s inefficiency.Rev. 0Page 95HT-01SECOND LAW OF THERMODYNAMICSThermodynamicsSummaryThe important information from this chapter is summarized below.Second Law of Thermodynamics Summary•Planck’s statement of the Second Law of Thermodynamics is:It is impossible to construct an engine that will work in acomplete cycle and produce no other effect except the raising ofa weight and the cooling of a heat reservoir.•The Second Law of Thermodynamics demonstrates that the maximum possibleefficiency of a system is the Carnot efficiency written as:η = (TH - TC)/TH•The maximum efficiency of a closed cycle can be determined by calculating theefficiency of a Carnot cycle operating between the same value of high and lowtemperatures.•The efficiency of a component can be calculated by comparing the workproduced by the component to the work that would have been produced by anideal component operating isentropically between the same inlet and outletconditions.•An isentropic expansion or compression process will be represented as a verticalline on a T-s or h-s diagram.
A real expansion or compression process will looksimilar, but will be slanted slightly to the right.•Efficiency will be decreased by:Presence of frictionHeat lossesCycle inefficienciesHT-01Page 96Rev. 0ThermodynamicsCOMPRESSION PROCESSESC OMPRESSION PROCESSESCompression and pressurization processes are very common in many types ofindustrial plants. These processes vary from being the primary function of apiece of equipment, such as an air compressor, to an incidental result of anotherprocess, such as filling a tank with water without first opening the valve.EO 1.32Apply the ideal gas laws to SOLVE for the unknownpressure, temperature, or volume.EO 1.33DESCRIB E when a fluid may be considered to beincompressible.EO 1.34CALCULATE the work done in constant pressure andconstant volume processes.EO 1.35DESCRIB E the effects of pressure changes on confinedfluids.EO 1.36DESCRIB E the effects of temperature changes onconfined fluids.Boyle's and Charles' LawsThe results of certain experiments with gases at relatively low pressure led Robert Boyle toformulate a well-known law.
It states that:the pressure of a gas expanding at constant temperature varies inversely to thevolume, or(P1)(V1) = (P2)(V2) = (P3)(V3) = constant.(1-40)Charles, also as the result of experimentation, concluded that:the pressure of a gas varies directly with temperature when the volume is heldconstant, and the volume varies directly with temperature when the pressure isheld constant, orRev. 0V1T1V2T2orP1T1P2T2.(1-41)Page 97HT-01COMPRESSION PROCESSESThermodynamicsIdeal Gas LawBy combining the results of Charles' and Boyle's experiments, the relationshipPvTconstant(1-42)may be obtained.
The constant in the above equation is called the ideal gas constant and isdesignated by R; thus the ideal gas equation becomesPv = RT(1-43)where the pressure and temperature are absolute values. The values of the ideal gas constant(R) for several of the more common gases are given in Figure 39.Figure 39Ideal Gas Constant ValuesThe individual gas constant (R) may be obtained by dividing the universal gas constant (Ro) byRothe molecular weight (MW) of the gas, R. The units of R must always be consistentMWwith the units of pressure, temperature, and volume used in the gas equation. No real gasesfollow the ideal gas law or equation completely.
At temperatures near a gases boiling point,increases in pressure will cause condensation to take place and drastic decreases in volume. Atvery high pressures, the intermolecular forces of a gas are significant. However, most gases arein approximate agreement at pressures and temperatures above their boiling point.HT-01Page 98Rev. 0ThermodynamicsCOMPRESSION PROCESSESThe ideal gas law is utilized by engineers working with gases because it is simple to use andapproximates real gas behavior. Most physical conditions of gases used by man fit the abovedescription. Perhaps the most common use of gas behavior studied by engineers is that of thecompression process using ideal gas approximations.
Such a compression process may occurat constant temperature (pV = constant), constant volume, or adiabatic (no heat transfer).Whatever the process, the amount of work that results from it depends upon the process, asbrought out in the discussion on the First Law of Thermodynamics. The compression processusing ideal gas considerations results in work performed on the system and is essentially the areaunder a P-V curve. As can be seen in Figure 40, different amounts of work result from differentideal gas processes such as constant temperature and constant pressure.Figure 40Pressure-Volume DiagramFluidA fluid is any substance that conforms to the shape of its container. It may be either a liquidor a gas.Compressibility of FluidsUsually a fluid may be considered incompressible when the velocity of the fluid is greater thanone-third of the speed of sound for the fluid, or if the fluid is a liquid.
The treatment of a fluidthat is considered incompressible is easy because the density is assumed to be constant, givinga simple relationship for the state of the substance. The variation of density of the fluid withchanges in pressure is the primary factor considered in deciding whether a fluid isincompressible.Rev. 0Page 99HT-01COMPRESSION PROCESSESThermodynamicsFluids that are compressible have much more complex equations to deal with, due to densitychanges, and have property relationships that vary more rapidly than incompressible fluids.
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