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with the flow of vapor, so condensate temperature cannot be used for control. If the heat transfer coefficients for condensing and subcooling mere equal, this system would have no control over vapor pressure at all, because heat kansfer rate would not depend on liquid level. E ortunately, heat transfer coefficients of condensing vapors are generally much great,er than those of condensate, particularly if the velocity of the condensate is low, as it would be in the shell of the condenser. On the other hand, manipulation of liquid level is a slow process, with 90 phase lag between valve position and heat transfer area. Since vapor pressure is a fast measurement, however, the loop generally performs well dynamically, except perhaps for severe load changes requiring t,he condenser to be filled or emptied. Linearity and rangeabilit y are important factors in its favor.
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When a fuel burns, the products of combustion, along with what ever other vapors may be present, are raised to a flame temperature determined by the energy content of the fuel. Since heat of combustion is rated in Btu/lb or Btu/cu ft, the actual quantity of fuel involved does not affect its flame temperature. To estimate the flame temperature, the sensible heat of either the combustion products or the fuel and air may be used, since the energy balance can be satisfied in either case. The rate of heat generated by the combustion of a given mass flow of fuel l17F, whose heat, of combustion is Hc, is & = WFHC (9.16) This flow of heat must equal what is necessary to raise the flows of fuel and air, WA, to the flame temperature 7 : & = WFCF(T - TF) + WACA(T - TA) (9.17) The terms CF, IF, CA, and A represent the average specific heat and t he inlet temperature of fuel and air, respectively. To ensure complete combustion, a specified ratio of air to fuel, KA, must, be selected, based upon the chemical constituents in the fuel. Substitution of KA for WA/W~ will allow the solution of Eqs. (9.16) and (9.17) for flame temperature:
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T = Hc f CFTF i- KACATA CF + KACA
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(9.18)
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Equation (9.18) must be recognized as being valid only for conditions where there is no excess fuel. Because fuel is more expensive than air, and because incomplete combustion can cause soot and carbon monoxide,
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furnaces are invariably operated with excess air. But it should be apparent that the maximum flame temperature will only be reached with no excess of either. Equation (9.18) also gives an indication of the effect air temperature can have on the flame. The nitrogen, of course, does not participate in combustion and acts as a diluent, reducing the flame temperature. If oxygen is used instead of air, KA can then be reduced fivefold, producing a sizable effect on flame temperature. The flame temperature estimated in Eq. (9.18) will be higher than what would actually be measured, because some of the energy contained in the combustion products partially ionizes them. This ionization increases with temperature, but the energy is recovered when the ions cool sufficiently to recombine into molecules.
Control of Fuel and Air
Since the temperature of the flame falls with either an excess or a deficiency of air, it is not a particularly good controlled variable. The most universally used indication of combustion efficiency is a measurement of oxygen content in the combustion products. The amount of excess air required to ensure complete combustion depends on the nature of the fuel. iSatura1 gas, for example, can be burned efficiently with 8 to 10 percent excess air (1.6 to 2 percent excess oxygen), while oil requires 10 to 15 percent excess air (2 to 3 percent excess oxygen) and coal, 18 to 25 percent excess air (3.5 to 5 percent excess oxygen). The reasons for the differences are the relative state of the fuel and the amount of noncombustibles present. Since the amount of heat transferred by radiation varies with the fourth power of the absolute flame temperature, the greatest efficiency will always be realized with maximum flame temperature. But the distribution of the heat is also important. Increasing the amount of excess air will reduce the flame temperature, thereby reducing the heat transfer rate in the vicinity of the burner. Since the net flow of thermal power into the system has not changed, the rate of heat transfer farther away from the burner tends to increase. Safety dictates certain operating precautions for fuel-air controls. A deficiency of air can allow fuel to accumulate in the furnace, which upon ignition, may explode. Care must be taken, therefore, to ensure that the fuel rate never exceeds what is permissible for given conditions of air flow. Fuel and air flow both can be set from a master firing-rate control, but automatic selection is necessary to achieve this safety feature. A complete control system for control of fuel and air is shown in Fig. 9.8. Notice that the fuel-air ratio is adjust.ed through manipulation of the span of the air measurement by the oxygen controller. Normally the set point would be adjusted, but in order for the selection system to operate,
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