Ashrae symposium ac 02 9 4 cooling tower model hydeman
An Improved Cooling Tower Algorithm for the CoolToolsDudley J.Benton, Ph.D.Charles F.BowmanMark HydemanPaul MillerDudley J.Benton and Charles F.Bowman are with Chuck Bowman Associates, Inc., Knoxville, Tenn.Mark Hydeman is with Taylor Engi- is with Pacific Gas and Electric Company, San Ramon, Calif.AC-02-9-4AC-02-9-46.The loss of water by evaporation is neglected.7.The force driving heat transfer is the differential enthalpybetween the saturated and bulk air.In 1943, a corporation plotted NTU as a function of thecooling tower liquid to gas () ratio to plot cooling towerdemand curves.Numerous approaches have been devised inan attempt to compensate for several of the above assump-tions.Mickley (1949) introduced temperature and humiditygradients with heat and mass transfer coefficients from thewater to the film of saturated air and from the film to the bulkstream of air.Baker and Mart (1952) developed the concept ofa hot water correction factor.Snyder (1955) developed anempirical equation for an overall enthalpy transfer coefficientper unit of volume of fill material in a crossflow cooling towerbased on tests that he conducted.Zivi and Brand (1956)extended the analysis of Merkel to crossflow cooling towers.Lowe and Christie (1961) performed laboratory studies onseveral types of counterflow fill.Hallett (1975) presented theconcept of a cooling tower characteristic curve where the NTUis expressed as an empirically derived function of the ratio.
Kelly (1976) used the model of Zivi and Brand alongwith laboratory data to produce a volume of crossflow coolingPenney and Spalding (1979) introduced a model for natu-ral draft cooling towers using a finite difference method.Majumdar and Singhal (1981) extended the model to mechan-ical draft cooling towers.Johnson et al.(1983) proposed acomputer model based on the NTU-effectiveness approachused for heat exchangers.Bourillot (1983a, 1983b) developedthe TEFERI computer model based on heat and mass transferequations similar to Zivi and Brand.The TEFERI modelassumes uniform water and air temperatures and flow rates atthe inlet and calculates the loss of water due to evaporation, sothe water flow rate does not remain uniform as it passesthrough the cooling tower.Benton (1983) developed the FACTS model, whichemploys an integral formulation of the equations for conser-vation of the mass of air and water vapor, conservation ofenergy, and the Bernoulli equation to arrive at a numericalsolution apart from the Merkel analogy.FACTS can accom-modate variable inlet water and air temperatures and hybridfills, but it assumes a constant water flow rate through thetower (Benton 1984).Benton and Waldrop (1988) andBowman and Benton (1995) presented the results of compar-isons between FACTS and test data.FACTS is widely used byutilities to model cooling tower performance.
Majumdar et al.(1983) developed the VERA2D model
.VERA2D treats airflow in the cooling tower as two-dimensional and steady andLefevre (1984) revisited the energy balance betweenwater and air that was the original basis for the Merkel equa-tion.The heat loss from the water (i.e., the water flow ratetimes the specific heat of water times the change in the watertemperature plus the heat lost by evaporation) is equal to theheat gained by the air (i.e., the air flow rate times the changein the air enthalpy).Both terms are equal to the mass transfercoefficient times the enthalpy difference times the interfacearea per unit of volume times the incremental cooling volume.Whereas Merkel used a simplified expression for the heat lossfrom the water to arrive at his equation, Lefevre used theexpression for the heat gain of the air.
Lefevre arrived at anexpression for the NTU as a function of the gas to liquid ratio(that he assumed to be constant) and the air enthalpies.Lefevreapplied a dimensionless correction factor to compensate forthe models shortcomings at higher water temperatures.Vance (1984) presented methods for adjusting the perfor-mance of a mechanical draft cooling tower for off-design airand water mass flow rates.Fulkerson (1988) reported heattransfer and pressure drop data for counterflow cooling towersat vendor test facilities.
The ability of several computer codesto predict the results of tests conducted by the Electric PowerResearch Institute (EPRI) on eight crossflow and eight coun-terflow fills was reported by Bell et al.
(1989).Benton (1989)showed that both the Gauss and Lobatto methods of numericalintegration are superior to the four-point Tchebycheff methodfor determining the number of transfer units.Feltzin andBenton (1991) derived a more exact model and compared theresults of this model to the Merkel equation.The Feltzin andBenton model did not include an empirical temperaturecorrection factor.
Desjardins (1992) analyzed the EPRI testdata by employing the concept of an offset hot water temper-ature as proposed by Mickley (1949) and the more exactmethod of Feltzin and Benton.Twelve CTSAs were identifiedThe objective of the improved CTSA was to accuratelyreproduce cooling tower performance and energy consump-development was based on vendor-supplied cooling towerperformance data.A second phase will be based on fieldmeasurements taken on operating towers.The minimalrequired tower specifications are a single design or operatingpoint whether the cooling tower is of the crossflow or coun-terflow design.
Several operating points can be used tocompute an equivalent single design point.Model selectionfor inclusion in DOE2 simulation code was based on the1.Computational speed (as many calculations are required for2.Simplicity of data input (i.e., only data that are commonly3.Ability to simulate response (i.e., variation of all major4.Accuracy5.Algorithm availability (i.e., free of legal encumbrance)6.Compatible source code (viz., FORTRAN)AC-02-9-47.Completeness (i.e., not dependent on excessive auxiliary8.Compactness (i.e., small enough to be in
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