{"Bibliographic":{"Title":"Cooling tower plume rise and condensation","Authors":"","Publication date":"1971","Publisher":""},"Administrative":{"Date created":"08-17-2023","Language":"English","Rights":"CC 0","Size":"0000021983"},"Pages":["QC\n880\nNOAA Research Laboratories\nA4\nno.53\n.\nAir Resources\nAtmospheric Turbulence and Diffusion Laboratory\nOak Ridge, Tennessee\nCOOLING TOWER PLUME RISE AND CONDENSATION\nSteven R. Hanna\nATMOSPHERIC SCIENCES\nLIBRARY\nJUL 19 1972\nN.O.A.A.\nU. S. Dept. of Commerce\nATDL Contribution No. 53\nU.S. DEPARTMENT OF COMMERCE\nNATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION\n3735\n172","QC\n880\nA4\nno. 53\nCOOLING TOWER PLUME RISE AND CONDENSATION\nSteven R. (Hanna\nAir Resources Atmospheric Turbulence and Diffusion Laboratory\nNational Oceanic and Atmospheric Administration\nOak Ridge, Tennessee\n1. INTRODUCTION\nRecent regulations discourage the use of river or lake water for direct cooling in industrial processes.\nThe trend is towards' the increased use of evaporative cooling towers, in which hot water is cooled by the\nevaporation of part of the water into a passing air stream. The vertical.flow of air through the tower can\nbe driven by natural buoyancy forces or by fans. In order to estimate the effects on the environment of\nheat and moisture discharges from proposed cooling towers, it' necessary to develop theoretical or em-\npirical models of these physical processes and verify them with observations. It is clear from the few\nenvironmental impact statements that we have see (references I and 2 are good examples) that there currently\nare no standard methods for estimating plume rise and cloud formation from cooling towers. Furthermore,\nobservations of cooling tower plumes are very limited. In this paper, methods of estimating cooling tower\nplume rise and the possibility of condensation will be outlined.\nOur ultimate goal is to reduce the environmental impact of plumes from cooling towers as much as possi-\nble. The environmental impact can be described by several criteria, including increases in local and re-\ngional temperature, cloudiness, fog, and rainfall. Local surface effects depend strongly on plume rise.\nRegional temperature and moisture increases depend on the non-linear interaction between the heat and mois- -\nture in the plume and in the environment. As suggested by Hanna and Swisher (3) the regional problem can\nbe analyzed using mesoscale or synoptic-scale computer models of the atmosphere. The Gaussian plume model\n(4)\noutlined by Slade may not be practical for estimating dispersion on regional scales (10 km or greater)\n2. PLUME RISE\nIn this section problems involving total plume rise and the effects of tower configuration are discussed.\nIn order to provide a comprehensive list of useful equations in the space available, lengthy derivations of\nmany of the formulas will be omitted. Complete derivations are given in previous reports by Hanna (5) , (0) and\nBriggs (7)\n2.1 Basic Plume Rise Formulas\nAccording to Briggs (7) , the final rise H of dry plumes dominated by buoyancy in a stable atmosphere can\nbe approximated by the equations:\nH=5.0F 1/4 S -3/8\n(Calm)\n(1)\n2.9 (F /Us) 1/3\n(Windy),\n(2)\nwhere U is the wind speed, S is the stability parameter (g/Tp) (20e/dz), and Fo is the initial sensible heat\nflux\n2\nF o (T po - Teo).\nThe factor TT is omitted from all flux formulations. The parameters g, T, 0, W, and R are the acceleration\n)\nof gravity, the temperature, the potential temperature, the vertical speed of the plume, and the plume\nradius, respectively. The subscripts p,e,o,s represent plume, environment, initial, and saturation variables,\nrespectively. In these equations, plume rise depends only on the initial energy flux from the tower and the\nwind speed and stability of the environment. Equations (1) and (2) have been verified by observations of\nplume rise from conventional smoke stacks over many orders of magnitude of initial heat flux Fo.\nUnlike most conventional smoke stack plumes, the cooling tower plume carries more latent heat than sen-\nsible heat. For the range of typical cooling tower parameters listed in Table 1, about 90% of the energy\nleaving the tower is in the form of latent heat. If this latent heat is not released to the atmosphere\nthrough condensation, then plume rise can be calculated using the sensible heat flux F in equations (1) or\n(2). In order to account for the difference in molecular weight between air and water vapor, the virtual\ntemperature Iv should be used rather than actual temperature T. The resulting plume rise calculations\ndiffer by less than 10%.\nPresented at the Air Pollution Turbulence and Diffusion Symposium, Las Cruces,\nNew Mexico, December 7-10, 1971. Published in meeting proceedings.","TABLE 1\nBuoyancy due to molecular weight differences, and to potential latent heat release, divided\nby buoyancy due to initial temperature differences. Typical cooling tower plumes and en-\nvironment initial temperature and environment relative humidities RH are considered. The\nplume is initially saturated.\n61 (m po -m eo )T po\n(m -m )\npo eo\n(T -T )\nc (T -T )\npo eo\nP po eo\nT\nT\n100%RH\n60%RH\n100%RH\n60%RH\npo\neo\n305°K\n275°K\n.15\n.16\n2.32\n2.48\n315\n285\n.26\n.29\n3.91\n4.24\n305\n285\n.19\n.22\n2.88\n3.37\n315\n295\n.31\n.39\n4.63\n5.68\n305\n295\n.24\n.36\n3.60\n5.43\nIf all the latent heat is released and all the resulting liquid water drops from the plume, then the\ntotal heat flux F is the sum of the sensible heat flux and the latent heat flux:\nR 2 g po - T eo + C P L T po (m po - \"eo' eo\n(3)\nwhere L is the latent heat of condensation, CP is the specific heat of air at constant pressure, and m is the\nwater vapor mixing ratio. The release of latent heat thus can increase the heat flux F several times and\ncan theoretically increase plume rise by 50 to 80% for the cases considered in Table 1. If only a fraction\nof the initial latent heat flux is released, then the second term in equation (3) must be multiplied by this\nfraction in order to more accurately estimate plume rise. Techniques for calculating the fraction of latent\nheat released are suggested in Section 3.\nThe plume rise calculated using a numerical cloud growth model (5) was compared\nwith\nthe\nrise\npredicted\nusing equations (1) and (2) for a variety of initial and environment conditions. For dry plumes, agreement\nwas + 10% and for cases in which condensation occurred, agreement was + 50%. Consequently, it is believed\nthat the simple equations (1) and (2) can be used to estimate plume rise within an error of + 50%, even when\na cloud forms in the plume.\n2.2 Influence of Initial Radius on Plume Rise\n2\nIf the energy flux, Fo, volume flux, VO = wo R'O , and environmental conditions are constant, then the\nquestion arises of whether plume rise can be increased by varying the cooling tower radius. Equations (1)\nand (2) are derived by assuming point sources of heat but are well proven by observations. If the full set\nof governing equations for plume rise are integrated, then factors such as initial source radius can be shown\nto have minor effects.\nSince the relative rate at which environment air is entrained into the plume is inversely proportional\nto plume radius, it can be argued that the plume from a wide source will lose its buoyancy more slowly than\na similar plume from a narrow source. On the basis of laboratory simulations in a calm environment, Brown\nand Sneck (8) state that increases in source radius can increase plume rise by several percent. However, inte-\ngrations of the equations of motion (6) show that Brown and Sneck's conclusion is valid only for values of the\ndimensionless parameters is R less than unity and Wo 2s/2 bo 2 less than two., where bo = Folvo. This usually\noccurs for small, buoyancy dominated energy sources (Fo less than about 10 megawatts) Since Brown and\nSneck's model source is characterized by S R, bo less than .1, their observations validate the theory. However,\nfor the energy fluxes typical of large hyperbolic cooling towers (100 or more megawatts per unit), it is pre-\ndicted that increases in tower radius will decrease plume rise slightly. A good general rule of thumb is that\nwhen the ratio of expected plume rise to source radius drops below about ten, then increases in source radius\n(at constant volume and heat flux) will not increase total plume rise.","2.3 Downwash of Plume\nEven if it were theoretically possible to increase plume rise by increasing the size of the tower\nopening, the resulting low efflux speed, Wo, could result in the downwash of the plume behind the tower\nduring windy conditions. Briggs (7) suggests that downwash of the plume from a narrow, straight-sided\nstack will occur if the ratio Wo/U is less than about 1.5, for initial stack Froude numbers (Fro = 2/2 Robo)\ngreater than about five. Overcamp and Hoult (8) on the basis of laboratory simulations and theoretical work,\nsuggest that the critical value of wo/U decreases to .5 at Fro equal to .25 and decreases further to .2 at\nFro equal to .01. The Froude number Fro ranges from about .5 to 1.5 for the typical data in Table 1, and for\nefflux speed and radius equal to about 5 m/sec and 30 m, respectively. Since the Froude number for most\nlarge cooling towers is on the order of unity, this theory predicts that downwash is likely to occur if the\nwind speed U is greater than the efflux speed wo. However, downwash is not observed, for example, at the\nlarge Keystone hyperbolic cooling towers, where the environment wind speed, U, often exceeds the efflux speed,\n5 m/sec. The inhibition of downwash is probably partly due to the tower's hyperbolic shape, which displaces\nthe low pressure zone downwards from the lip of the tower.\nDownwash has been observed at banks of mechanical draft towers, where the bulky shapes of the towers\npresent more of an obstacle to the airflow. The probability of downwash can be decreased by separating the\nindividual towers, increasing the efflux speed, and encouraging flaired geometrical shapes. If the possi-\nbility of downwash can be eliminated, then problems associated with rain-out and fogging at the ground near\nthe towers can be reduced.\n2.4 Multiple Sources\nThe plume rise theory outlined above applies only to single, isolated, sources. At some large power\nplants, the problem exists of calculating the plume rise from a line of about ten mechanical draft cooling\ntowers. The total rise of all the plumes is probably greater than the rise calculated using the heat flux\nfrom a single tower but less than the rise calculated using the combined flux from all the towers. Based on\nan unpublished analysis of TVA data, Briggs suggests that the total plume rise is influenced by the spacing\nof the towers and the angle between the wind direction and the line of the towers. He defines a \"spacing\nfactor,\" S, as the ratio of the crosswind component of the spacing of the towers to the plume rise expected\nfrom a single tower. The closer the towers, the more the individual plumes will interact. The rough rule\nthat he suggests is that for S less than .1, the plume rise in windy conditions from two, three, and four\ntowers will be 20%, 30%, and 40%, respectively, greater than the rise calculated for a single tower. For S\ngreater than .25, interaction of the plumes can be ignored. Unfortunately, there are currently no published\ndata on plume rise either from more than four multiple sources or from any banks of cooling towers to check\nthese suggestions. There is a need for basic observations of cooling tower plumes.\nOn the basis of the discussions with respect to the problems of downwash and plume risc from multiple\nsources, it is clear that the use of a single hyperbolic tower will result in greater plume rise than the\nuse of banks of mechanical draft towers, for a given heat flux. A single hyperbolic tower is not as suscep-\ntible to downwash as a bank of smaller towers, and its single plume rises higher than their combined plumes.\nAlso, large hyperbolic towers have the added benefit of being taller than mechanical draft towers.\n3. CONDENSATION IN THE PLUME\nQualitatively, condensation occurs in a plume if the flux of water from the cooling tower is sufficient\nto saturate the initial volume flux plus the flux of air entrained into the plume as it rises. It is impor-\ntant to know the characteristics of the entrained air since the flux of entrained air in the plume is usually\nat least an order of magnitude greater than the initial volume flux, by the time the plume nears its level of\nmaximum rise.\nThe initial flux of water (in mass per unit time) is defined by the equation:\n(4)\nao = o Vo O (m po + o po ) ,\nwhere Po and Opo are the initial air density and liquid water mixing ratio (gm water per gm of air). It is\nassumed that vertical speed, concentration of water vapor, and other variables are constant across a given\nplume cross-section. The flux of water Qs at level Z that would saturate the plume is given by the relation:\nQg(2)=p(2) ps (z) + ( V(z) - V. \"ps (2)\n(5)\n,\nwhere m is the average mixing ratio of the air entrained into the plume, defined by\n(6)\n/ Vo","The term (m - me) is sometimes called the \"saturation deficit.\" Saturation is more likely to be achieved\nps\nin an environment where the saturation deficit is small; e.g. a cold environment or a warm humid environ-\nment. Because the water vapor mixing ratio generally decreases with height, the average mixing ratio me in\nthe plume at level Z is generally greater than the mixing ratio me in the local environment. It is then\npossible for Qs to drop below zero at some height as T. approaches Te even if the plume initially contains\nno excess water. In this case, condensation will occur at the level of natural cloud formation.\nThe ratio (Oo - Qg(z) )/Qo is defined as the fraction, A, of the initial water flux Co that is con-\ndensed at any level. If there is an initial liquid water flux, Po po Vo, the fraction, B, of this flux\nremaining as liquid water in the plume at level 2 can be estimated from the equation\n(Q)\n(7)\nWhen B increases to unity, all the initial liquid water has evaporated.\n3.1 Level of First Condensation\nThe fraction A of the initial water flux that is condensed is thus equal to the ratio\n(8)\nIt is seen that A is a function of the initial plume mixing ratio, the vertical variation of plume and en-\nvironment mixing ratio, and the dimensionless ratios p(z)/p. and V(z)/Vo. For heights less than two or three\nkilometers, the ratio p(z)/po can be approximated by the simple expression exp(-gz/RdT), where Rd is the gas\nconstant for dry air. The saturation mixing ratio m is a function of height and temperature and can be\nps\napproximated by the analytical expression:\n\"ps \" \" Eso e\n(9)\nwhere R is the gas constant for water vapor. The temperature difference (Te - Teo) is known from the ver-\ntical distribution of environment temperature and the temperature difference (Ip-Te) is obtained from the\ndefinition\n(10)\nThe ratios F(z)/F and (2)/VC can be calculated using Briggs' (7) theory of plume rise. Detailed deri-\nvations of the following analytical expressions can be found in reference 6:\nWindy\n(11)\nCalm\n(12)\nWindy\n(13)\nP Calm (14)\nThe ratios of volume fluxes V(z)/V are plotted as a function of z/R for various values of U/w and Fr\no\nin Figure 1.","Using the above formulas, it is possible to calculate the fraction A of the initial water flux that is\ncondensed at any level z, based on the initial plume conditions and the vertical variation of environment\ntemperature and wind speed. As Morton (9) concluded from his analysis of moist plume rise during calm con-\nditions, plume rise is highly sensitive to slight variations in environmental mixing ratio. There is a thin\nline between no cloud development and explosive cloud development.\n100\n50\nA\n20\n10\n5\n2\n1\nWINDY CONDITIONS\n0.5\nCALM CONDITIONS\n0.2\n0.1\n200\n500\n1000\n1\n2\n5\n10\n20\n50\n100\nv/vo\nFigure 1. The ratio of the volume flux V to initial volume flux Vo,\nas a function of the ratio of height Z to initial radius P.O.\nfor windy conditions at various values of U/WO, and calm\nconditions at various values of Fro = wo2/2Robo.\nAs an example of the application of these techniques, consider a plume in a well-mixed atmosphere at\ngreat heights, such that potential temperature and mixing ratio are constant with height (0 e = deo and\nme = meo) and plume temperature equals environment temperature. Under these conditions, the plume sat-\nuration mixing ratio m ps can be approximated by meos exp (4.5 gz/Rd T) Furthermore, assume that the\nscale height of the atmosphere, RdT/g, is 8000 m, and the initial liquid water content, is zero.\nThen equation (8) becomes:\n1/2\nA(z) 8000m -2 1 -RH\n(15)\nwhere RHO equals m 'eos' In a specific case, for example, RO = 30 m, U/WO = 4.0, mpo/meos = 3.2, and\neo\nRHO = .8. The first level of condensation (A(z)=0) is at 370 m, and the level at which a quantity of water\nequal to the initial water flux condenses (A(z)=1) is at 410m. This is the height at which an initially dry\nplume would begin to condense.\nAfter working a few examples, one find that the above condensation criterion is sensitive to slight\nvariations in the variables U/WO, RH0, and \"po/meos\" However, we know from many years of experience that\nthe analogous problem of the prediction of the formation of cloud layers is also very difficult.","3.2 Iterative Technique for Estimating Plume Rise\nIt was mentioned in Section 2 that the plume rise equations (1) and (2) are adequate for calculating\ncooling tower plume rise, provided that the initial latent heat flux is accounted for when calculating the\ntotal initial energy flux Fo. Now that we have developed methods for estimating the fraction of the initial\nwater flux that is condensed, it is possible to estimate the latent heat flux at the height, H, of final\nplume rise. The first estimate of plume rise, H1, is calculated assuming that no vapor has condensed.\nThen the fraction A1 of the initial water flux condensed at level H1 is calculated. The value, A1, is\nthen multiplied by the total possible latent heat flux and the new heat flux is used to calculate a new\nestimate of plume rise H2. This procedure is repeated until plume rise, H, and fraction of initial water\ncondensed, A(H), approach constants.\n4. ADDITIONAL REMARKS\nIt is seen that cooling tower plume rise can be easily calculated for either uncondensed or completely\ncondensed plumes. Due to the sensitivity of the condensation processes to slight changes in, for example,\nenvironment mixing ratio, cooling tower plume rise in borderline cases can not be calculated with so much\nconfidence. It is because of this sensitivity that observation programs of cooling tower plumes will re-\nquire much attention to detail.\nIn writing environmental impact statements, it is necessary to determine the diffusion of water vapor\nor drops to the ground from the elevated cooling tower plume. The usual assumption is that water vapor\ndiffuses in the same manner as an inert gas. Consequently the Gaussian dispersion equation (4) may possibly\nbe used, knowing the approximate wind speed and stability class. It is necessary to conduct a comprehensive\nobservation program to determine the limitations of the simple Gaussian equation. If a thin elevated in-\nversion layer is between the plume axis and the ground, dispersion of moisture to the ground may be inhibited.\nNonlinear interactions between plume and environment heat and moisture may also prove to be important.\nThe techniques discussed in this paper provide a starting point for the analysis of the environmental\nimpact of cooling tower plumes. Observations of the rise, condensation, and dispersion of cooling tower\nplumes are practically non-existent. Much more research needs to be done with respect to cooling tower\nbehavior.\nAcknowledgement: The author thanks Dr. Gary A. Briggs for his assistance throughout this project. This\nresearch was performed under an agreement between the National Oceanic and Atmospheric Administration and\nthe Atomic Energy Commission.\nReferences\n(1) Collins, G. F., C. R. Case and C. J. Mule, 1971: Cooling Tower Effects (Fogging) : Vermont Yankee\nGenerating Station, Report prepared for the Vermont Yankee Co. by the Research Corp. of New Eng.\n210 Washington St., Hartford, Conn., 06106, 14 pp.\n(2) McVehil, G. E., 1971: Analysis of Atmospheric Effects of Evaporative Cooling Systems. Quad-Cities\nNucl. Gen. Station, Report TR-0853, prepared for Commonwealth Edison Co., Chicago, by Sierra Res.\nCorp., Boulder, Colo., 49 pp.\n(3) Hanna, S. R., and S. D. Swisher, 1971: Meteorological Considerations of the Heat and Moisture Produced\nby Man. Nuclear Safety, 12, 114-122.\n(4) Slade, D., ed., 1968: Meteorology and Atomic Energy. USAEC Div. of Tech. Inf., TID-24190 (price $6.00)\nfrom Clearinghouse for Fed. Sci. and Tech. Info., U. S. Dept. Commerce, Springfield, Va. 445 pp.\n(5) Hanna, S. R., 1971: Meteorological Effects of Cooling Tower Plumes. Presented at the Cooling Tower Inst.\nAnn. Meet., Houston, Tex., 17 pp.\n(6) Hanna, S. R., 1971, Rise and Condensation of Cooling Tower Plumes. Submitted to J. Appl. Meteorol.\n(7) Briggs, G. A., 1969: Plume Rise, AEC Critical Review Series. TID-25075 (price $6.00) fromClearinghouse\nfor Fed. Sci. and Tech. Info., U. S. Dept. of Comm., Springfield, Va., 82 pp.\n(8) Overcamp, T.J., and D.P. Hoult, 1971: Precipitation in the Wake of cooling towers, Atmos. Envir., 5,\n751-766.\n(9) Brown, D. H., and H. J. Sneck, 1971: Cooling Tower Plume Rise. Presented to the American Power Co.\n33rd Ann. Meet., Chicago, 22 Apr. 1971, 16 pp.\n(10) Morton, B. R., 1957: Buoyant Plumes in a Moist Atmosphere. J. Fluid Mech. 2, 127-144."]}