MethodsforCalculationofEvaporationfrom Swimming …

1 2014 ASHRAE. THIS PREPRINT MAY NOT BE DISTRIBUTED IN PAPER OR DIGITAL FORM IN WHOLE OR IN PART. IT IS FOR DISCUSSION PURPOSES ONLYAT THE 2014 ASHRAE ANNUAL CONFERENCE. The archival version of this paper along with comments and author responses will be published inASHRAET ransactions, Volume 120, Part 2. ASHRAE must receive written questions or comments regarding this paper byJuly 21, 2014for them to be included calculation of evaporation is required from a varieyof water pools including Swimming pools, water storage tanksand vessels, spent fuel pools in nuclear power plants, etc. Theauthor has previously published formulas for the calculationof evaporation from occupied and unoccupied indoor swim-ming pools, which were shown to agree with all available ,evaporationfrommanytypesofwaterpoolsand vessels is discussed and formulas are provided for calcu-lating evaporation from them.

2 These include indoor andoutdoor Swimming pools (occupied and unoccupied), spentnuclear fuel pools, decorative pools, water tanks, and tables are provided for simplifying manual paper attempts to provide reliable methods for thecalculation of evaporation from many types of water pools,tanks, vessels, and spills. The author has previously publishedformulas for the calculation of evaporation from occupied andunoccupied indoor Swimming pools, which were validatedwith all available test data (Shah 1992, 2008, 2012a, 2013) andare widely used. The calculation of evaporation is alsorequired for many other applications and situations. In thispaper, in addition to the author s published correlations forindoor Swimming pools, formulas and methods are alsoprovided for the calculation of evaporation for the following: Outdoor occupied and unoccupied Swimming pools Pools with hot water, such as spent nuclear fuel pools Decorative pools Pools used for heat rejection from refrigeration systems Vessels/tanks with low water level Water spillsThe calculation methods presented are based on physicalphenomena, theory, and test OF EVAPORATIONC onsider evaporation from an undisturbed water surface,such as that of an unoccupied Swimming pool.

3 A very thinlayer of air, which is in contact with water, quickly gets satu-rated due to molecular movement at the air-water interface. Ifthere is no air movement at all, further evaporation proceedsentirely by molecular diffusion, which is a very slow the other hand, if there is air movement, this thin layer ofsaturated air is carried away and is replaced by the compara-tively dry room air and evaporation proceeds , it is clear that for any significant amount of evapo-ration to occur, air movement is essential. Air movement canoccur due to two mechanisms:1. Air currents caused by the building ventilation system forindoor pools and wind for outdoor pools. This is theforced convection Air currents caused by natural convection (buoyancyeffect). Room air in contact with the water surface getssaturated and thus becomes lighter compared to the roomair, and therefore moves upwards.

4 The heavier and drierroom air moves downwards to replace outdoor Swimming pools, forced convection isusually the prevalent mechanism. For indoor pools, naturalconvection mechanism usually prevails while most publishedformulas have considered only forced for Calculation of Evaporation fromSwimming Pools and Other Water SurfacesMirza Mohammed Shah, PE, PhDFellow/Life Member ASHRAEM irza Mohammed Shahis an independent consultant, Redding, INDOOR Swimming POOLSP resent Author s MethodShah developed formulas for evaporation from undis-turbed water surfaces, which starting with Shah (1981), wentthrough several modifications (Shah 1990, 1992, 2002, 2008).The final version is in Shah (2012), according to which theevaporation rateE0is the larger of those given by the followingtwo equations:(1)(2)withC= 35 in SI units andC= 290 in I-P units,b= SI andb= in I-P 1 is the evaporation due to natural convectioneffect.

5 It was derived using the analogy between heat and masstransfer. The derivation is given in the Appendix. Equation 2shows the evaporation caused by the air currents produced bythe building ventilation system. This was obtained by analyzingthe test data for negative density difference as shown in Figure1. The reasoning was that as natural convection essentiallyceases under such conditions, all the evaporation must be occur-ring due to forced convection. As noted by theASHRAE Hand-book HVAC Applications(ASHRAE 2007), air velocities intypical Swimming pools range between and m/s (10 to30 fpm). The computational fluid dynamics (CFD) simulationsby Li and Heisenberg (2005) of a large Swimming pool showedvery complex airflow patterns along the surface and height ofthe pool, but the velocities within 1 m (3 feet) of the watersurface were also in this range. Equation 2 is therefore consid-ered applicable to velocities up to m/s (30 fpm).

6 This method was validated by comparison with test datafrom 11 sources in Shah (2012b). Table 1 gives the range ofparameters in each of these data sets. In Shah (2008), the samedatabase (except the data of Hyldegard [1990]) was alsocompared to the ten published correlations listed in Table 3 gives the results of these data analyses. It is seen thatthe 113 data points were predicted by the Shah formulas witha mean absolute deviation of giving equal weight toeach data set. All the other correlations gave much inferioragreement with datal; thus, the Shah method is the most reli-able among available methods and therefore may be used forpractical ease of calculation using the Shah method, Equations1 and 2 and Tables 4 and 5 have been prepared. These tablesgive the evaporation rates at discrete values of temperature andhumidity in the range that may occur in Swimming at intermediate values can be obtained by Formulas for Undisturbed Water PoolsMany researchers performed tests in which air was blownor drawn over water surfaces and correlated their own test datain the form:(3)Whereaandbare constants anduis the air 2 lists several such correlations.

7 These are applied toindoor pools by insertingu 0. Such formulas do not take intoaccount natural convection, which depends on air densitydifference, and hence cannot be expected to be generallyapplicable to indoor pools in which natural convection effectsare prevalent. This was pointed out by early researchers. Forexample, Himus and Hinchley (1924) performed tests onevaporation by natural convection as well as with forcedairflow and gave formulas for both cases. They found thattheir forced convection formula extrapolated to zero velocitypredicts three times their formula for natural and Michailoff (1936) stated that forced convectionequations should not be extrapolated to zero velocity as theywill give erroneous results. Nevertheless, such formulas havecontinued to be proposed. The best known among suchformulas is that of Carrier (1918) which is recommended byASHRAE (2011) with correction factors called other researchers performed tests under naturalconvection conditions and correlated their own data by formu-las of the form:(4)E0C w r w 1/3 WwWr =E0bpwpr =Figure 1 Analysis of data at negative density difference toobtain Equation 2 for forced convection evapo-ration in indoor pools.

8 1 Pa= in. Hg, 1kg/m2 h = lb/ft2 + pwpr =Eapwpr n=SE-14-0013 Whereaandnare constants. Such formulas do not take intoaccount density difference, which determines the intensity ofnatural convection, and hence cannot be expected to be gener-ally of the correlations of the type of Equations 3 and 4are listed in Table 2. As is seen in Table 3, these give pooragreement with most INDOOR POOLSE xperience shows that evaporation from occupied poolsis higher than from unoccupied pools. This increase is attrib-uted to an increased area of contact between air and water dueto waves, sprays, wet bodies of occupants, and wetting ofdeck. As deck area is usually comparable to the pool area,wetted deck represents the largest increase in air-water contactarea. The air-water contact area is expected to increase with anincreasing number of occupants. A number of formulas havebeen published according to which the increase in evaporationcompared to unoccupied pools depends only on the number ofoccupants (Hens 2009; Smith et al.)

9 1999; Shah 2003). Thebasic assumption in these formulas is that the rate of evapora-tion from the increased air-water contact area is the same asfrom the pool (2013) pointed out that the rate of evaporation fromthe wetted deck area may not be the same as from the poolsurface. Water spilled on the deck will quickly cool down,approaching the wet-bulb temperature. If the pool watertemperature is higher than the air temperature, the rate of evap-oration from the wetted deck will be much lower than from thepool surface as the density difference between air and waterwill be much lower at the deck, reducing the natural convec-tion intensity. On the other hand, if the water and air temper-atures are about equal, the rate of evaporation from the wetteddeck will be comparable to that from the pool surface. Thus,Table 1. Range ofTest Data for Undisturbed Water Poolswith which Equations 1 and 2 and Other Formulas were ComparedResearcherPool ,%pw prEvaporationRate,Notesm2ft2 C F C FPa in.

10 Hg kg/m3lb/ft3kg/m2 h lb/h ft2 Hyldegard(1990)418 4493 37 1944 (1972)32 344 60 1029 et al.(1946) (1931) andBoelter (1938) &Krumme(1974) ( )200 2150 et al.(1993) 50 2001 (1978)Note 71493 1, 3 Smith et al.(1993)404 4343 (1979)425 4568 28 2142 + + : 1. Field tests on Swimming pool 2. Laboratory tests 3. Private pool, size not given r w 4SE-14-001the increase in evaporation due to occupancy depends not onlyon the number of occupants but also the density differencebetween room air and the air in contact with the pool , Shah presented the following formula for evap-oration from occupied pools:ForN* ,(5)whereN* is the number of occupants per unit pool area.