The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 62
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The various pressure drops are conveniently expressed asDPi = Ni© 1999 by CRC Press LLCrGi Vi 22(4.8.21)4-256Section 4TABLE 4.8.2b Mass Transfer and Pressure Drop Correlations for Cooling TowersPackingNumberC1, m–1n1n2n3C2, m–1n4n50.000.000.000.00–0.34–0.40–0.35–0.54–0.45–0.60–0.52–0.382.723.133.383.8719.229.5510.104.332.368.331.516.270.350.420.360.520.340.310.230.851.100.270.990.31–0.35–0.42–0.36–0.360.190.05–0.04–0.60–0.64–0.140.040.101.441.971.381.253.184.493.444.890.660.721.300.890.760.710.710.59–0.73–0.820.220.07–0.80–0.59–0.850.16Counterflow Packings: L0 = G0 = 3.391 kg/m2 sec1234567891011120.2890.3610.3940.4592.7231.5751.3780.5580.5251.3120.7551.476–0.70–0.72–0.76–0.73–0.61–0.50–0.49–0.38–0.26–0.60–0.51–0.560.700.720.760.730.500.580.560.480.580.620.930.60Cross-Flow Packings: L0 = 8.135 kg/m2 sec, G0 = 2.715 kg/m2 sec123456780.1610.1710.1840.1670.1710.2170.2130.233–0.58–0.34–0.51–0.48–0.58–0.51–0.41–0.450.520.320.280.200.280.470.500.45–0.44–0.43–0.31–0.29–0.29–0.34–0.42–0.48Correlations (SI units)Mass transfer:where L+ =g ma[L kg m 2 secL,L0G+ =]G,G0n1+ n2n3+HW( ) ( G ) (T )= C1 L++=THW; Pressure drop:N= C2 L+H or Xn+ ns( ) + (G )1.8TL,in [°C] + 32110Sources: Lowe, H.J.
and Christie, D.G. 1961. “Heat transfer and pressure drop data on cooling tower packings,and model studies of the resistance of natural draft towers to airflow” Paper 113, International Developments inHeat Transfer, Proc. of the International Heat Transfer Conference, Boulder, CO, ASME, New York; Johnson,B.M., Ed. 1990. Cooling Tower Performance Prediction and Improvement, Vols. 1 and 2, EPRI GS-6370, ElectricPower Research Institute, Palo Alto, CA. With permission.Where Ni is the loss coefficient and Vi is the air velocity at the corresponding location.
The pressuredrops are associated with the shell, the packing, the mist eliminators, supports and pipes, and the waterspray below the packing. Some sample correlations are given in Table 4.8.3.Water loadings in counterflow natural-draft towers typically range from 0.8 to 2.4 kg/m2 sec, andsuperficial air velocities range from 1 to 2 m/sec.
The ratio of base diameter to height may be 0.75 to0.85, and the ratio of throat to base diameter 0.55 to 0.65. The height of the air inlet is usually 0.10 to0.12 times the base diameter to facilitate air flow into the tower.
In practice the air flow distribution innatural-draft towers is not very uniform. However, the assumption of uniform air and water flows in ourmodel of counterflow packing is adequate for most design purposes.Cost-optimal design of cooling towers requires consideration of the complete power or refrigerationsystem. For refrigeration, the economics are determined mainly by the operating cost of the chiller(Kintner-Meyer and Emery, 1955).© 1999 by CRC Press LLCHeat and Mass TransferTABLE 4.8.3Eliminators4-257Pressure Drop Correlations for Cooling Tower Shells, Sprays, Supports, and Mist1.Shell (natural draft counterflow):2.æD öN = 0.167ç B ÷è b øwhere DB is the diameter of the shell base and b is the height of the air inlet.Spray (natural-draft counterflow):23.4.5.N = 0.526(Zp[m] + 1.22) ( m˙ L / m˙ G )1.32Mist eliminators:N = 2–4Support columns, pipes, etc.
(natural-draft counterflow):N = 2–6Fan exit losses for mechanical-draft towers (velocity based on fan exit area):N = 1.0, forced draft6.. 0.5, induced draft, depending on diffuser designMiscellaneous losses for mechanical-draft towers (velocity based on packing crosssectional area):N.3Note: N is the loss coefficient defined by Equation 4.8.21, with velocity based on cross-sectional area for air flowunderneath the packing in items 1 through 4.Sources: Lowe, H.J. and Christie, D.G. 1961. Heat transfer and pressure drop data on cooling tower packings, andmodel studies of the resistance of natural draft towers to airflow.
Paper 113, International Developments in HeatTransfer Proc. of the International Heat Transfer Conference, Boulder, CO, ASME, New York; Singham, J.R. 1990.Natural draft towers, in Hemisphere Handbook of Heat Exchanger Design, Sec. 3.12.3, Hewitt, G.E., Coord. Ed.,Hemisphere, New York. With permission.Cooling Tower BehaviorThere are a number of computer programs available that use variations of Merkel’s method to calculatethe cooling tower performance, for example, TEFRI (Bourillot, 1983), VERA2D-84 (Mujamdar et al.,1985), CTOWER (Mills, 1995). These programs can be used to perform parametric studies to obtainthe response of cooling towers to environmental, duty, and design changes.
However, before using suchprograms, some thought should be given to the important characteristics of cooling tower behavior. Forthis purpose, it is useful to consider a graphical representation of Merkel’s theory for a counterflowtower. Figure 4.8.10 shows a chart with moist air enthalpy plotted vs. water enthalpy (or, equivalently,water temperature) at 1 atm pressure. The saturation curve hs(Ts) is the enthalpy of saturated air. Theoperating lines hG(hL) are given by Equation (4.8.13) and relate the air enthalpy to the water enthalpyat each location in the packing.
The slope of an operating line is L/G. Since the assumption Ts = TL ismade in Merkel’s method, vertical lines on the chart connect hs and hG at each location in the packing.The driving force for enthalpy transfer, (hs – hG), is the vertical distance between the saturation curveand the operating line. The integral in Equation (4.8.12) averages the reciprocal of this distance. Byusing this chart, a number of observations about cooling tower behavior can be made.1. Figure 4.8.10 shows the effect of L/G for fixed water inlet and outlet temperatures, and fixed inletair temperature and humidity. If we imagine L to be fixed as well, we see that as G decreases,the driving forces decrease, and so a larger NTU is required.2. The minimum NTU required corresponds to L/G = 0, that is, an infinite air flow rate, for whichthe operating line is horizontal.3.
Due to the curvature of the operating line, it is possible for the operating line to be tangent tothe saturation curve. The indicated NTU is then infinite, which tells us that the air flow rate mustbe increased in order to achieve the desired water cooling range.© 1999 by CRC Press LLC4-258Section 4FIGURE 4.8.10 Counterflow cooling tower operating lines for various water-to-air flow-rate ratios shown on anenthalpy chart.4. For a mechanical-draft tower, the optimal value of L/G lies between the two limits described initems 2 and 3 above.
If L/G is large, the required height of packing is large, and the capital costwill be excessive. If L/G is small, the fan power will be excessive (since fan power is proportionalto air volume flow rate times pressure drop).Range and ApproachCooling tower designers and utility engineers have traditionally used two temperature differences tocharacterize cooling tower operation. The range is the difference between the water inlet and outlettemperatures (also called simply the hot and cold water temperatures).
The approach is the differencebetween the outlet water temperature and the wet-bulb temperature of the entering (ambient) air. Theapproach characterizes cooling tower performance; for a given inlet condition, a larger packing willproduce a smaller approach to the ambient wet-bulb temperature, and hence a lower water outlettemperature. (The water cannot be cooled below the ambient wet-bulb temperature.) The approachconcept is useful because the ambient dry-bulb temperature has little effect on performance at usualoperating conditions (for a specified wet-bulb temperature).Cooling Demand CurvesElectrical utility engineers have found it convenient to use charts of cooling demand curves to evaluatepacking specifications. Figure 4.8.11 is an example of such a chart, on which the required NTU, for agiven inlet air wet-bulb temperature and range, is plotted vs.
L/G with the approach as a parameter. Sucha plot is possible since the inlet air dry-bulb temperature has only a small effect under usual operatingconditions. Now, if it is possible to correlate the mass transfer conductance as-ng maL= Cæ öè GøL(4.8.22)-ng m S g m aHL== Cæ ö Hè Gøm˙ LL(4.8.23)the NTU of a packing of height H is© 1999 by CRC Press LLCHeat and Mass Transfer4-259FIGURE 4.8.11 Example of cooling demand curves for a specified wet-bulb temperature and range: NTU vs. flowrate ratio for a fixed approach.Equation (4.8.23) can also be plotted on the chart to give the packing capability line.
For a requiredapproach, the operating point of the tower is the intersection of the cooling demand curve and packingcapability line. Charts of cooling demand curves are available (Cooling Tower Institute, 1967; Kelly,1976). Correlations of the form of Equation (4.8.22) do not necessarily fit experimental data well. Adependence gma aL 1–nGn is implied and, in the past, experimental data were often forced to fit such arelation. If the gma correlation does not have the form of Equation (4.8.22), the NTU cannot be plottedas a line on a cooling demand chart.With the almost universal use of computers and the availability of suitable computer programs, onecan expect less use of cooling demand charts in the future. The major sources of error in the predictionsmade by these programs are related to nonuniform air and water flow, and the correlations of packingmass transfer and pressure drop experimental data.
The experimental data are obtained in small-scaletest rigs, in which it is impossible to simulate many features of full-size towers — for example,nonuniform flow due to entrance configuration, nonuniform wetting of the packing, and, in the case ofcounterflow towers, the effect of spray above the packing and rain below the packing. Furthermore, sincetesting of packings in small-scale test rigs is itself not easy, considerable scatter is seen in such test data.Correlations of the data typically have root mean square errors of 10 to 20%.Legionnaires’ DiseaseLegionnaires’ disease is a form of pneumonia caused by a strain of legionnella bacteria (sero group I).Smokers and sick people are particularly vulnerable to the disease.
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