NOMENCLATURE H L N Q R DISCUSSION OF PHYSICAL FACTORS INFLUENCING TOWER PERFORMANCE. A. Whillier H.Se. (Eng.) (Rand) Se.D. (M.I.T.

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1 The design of underground A. Whillier H.Se. (Eng.) (Rand) Se.D. (M..T.) (Fellow),* cooling towers t SYNOPSS Recoendations are given for the design of vertical cooling towers for use underground in ines and a ethod is given for predicting the entering and leaving water teperatures when a given aount of heat has to be dissipated. A B BPF Gp Fo Fv Fwb Fs G H L N Q R S tw ta v V w LG WARo 1Ja 1Jw 6P 6tw Subscripts: w a NOMENCLATURE cross-section area of cooling tower constant in equation 11 Barenbrug perforance factor=1ja+1j w specific heat capacity of liquid water basic efficiency factor (figure 3) factor correcting for air velocity factor correcting for wet-bulb teperature factor correcting for the nuber of screens in the tower ass flow rate of air in tower per unit area, dry basis height of spray-filled portion of tower, ass flow rate of water entering the tower, per unit area nuber of screens rate of heat reoval fro circulating water capacity factor, equal to ratio of actual waterair ratio to reference water-air ratio siga heat of air, per unit ass water teperature wet- bulb teperature of air specific volue of air, dry basis velocity of air up tower V =G xv density of air, kg/3 water air ratio (equation 2) reference water-air ratio (equation 3) air efficiency (equation 6) water efficiency (equations 5 and 1) pressure drop across tower, bar drop in teperature of the water passing through the tower 6t w=t wi-t wo= 'range' in coputer progra. water air in out NTRODUCTON The capacity of underground refrigeration plant installed in South African gold ines during the past few years has grown by about 1 per cent per year, and Chief, Applied Mechanics Division, Mining Research Laboratory, Chaber of Mines of Routh * Africa. tcontribution to joint R.A..M.M.jMVS colloquiu on Ventilation 17 Noveber, there is every indication that with ines going deeper this rate will be aintained in the future. An iportant coponent of any underground refrigeration plant is the cooling tower which is used to transfer heat rejected by the condenser cooling water into the up cast air. The efficient operation of the cooling tower plays a vital role in the econoic operation of the whole plant. Under typical conditions encountered in underground refrigeration plant, a reduction in the teperature of the condenser by 1 QC results in a reduction in refrigerator power costs of between 21 and 3 per cent. t is therefore highly desirable that the cooling tower should be designed to cool the condenser cooling water to the lowest teperature possible. The efficiency of any particular tower depends to a large extent on the degree to which certain rather obvious practical conditions are satisfied. These are siply that the air distribution and the water distribution over the cross sectional area of the tower ust be unifor, and that the water droplets should be sall, should reain sall and should be kept in contact with the air for as long as possible. Most cooling towers used in ines are of the forced draught vertical counterflow type in which the water droplets fall down through an upward-rising air strea. nternal packing is not used, although several horizontal wire esh screens are often placed across the tower in order to obtain ore unifor air flow. Only this type of tower is considered here. Generally speaking in cooling tower design a known aount of heat has to be dissipated into a known aount of air entering the tower at a known teperature and huidity. The proble is to predict the entering and leaving water teperatures for a range of assued water flow rates and assued tower cross-sectional areas. A ethod for doing these calculations is given later in the paper but first it is necessary to discuss the any factors that have to be taken into account, and to ake specific recoendations for the construction of cooling towers. DSCUSSON OF PHYSCAL FACTORS NFLUENCNG TOWER PERFORMANCE A unifor distribution of the water in a tower can be assured by arranging the water inlet sprays uniforly across the tower, and by ensuring good air distribution. JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY OCTOBER

2 Experience indicates that the water tends to channel if the water loading of the tower exceeds about 1 litre/ sec per 2 of tower cross-section (12 gal/in per ft2). Hence, towers should not be operated at water loadings exceeding this value. The ost difficult proble in tower design is to ensure that the air flow up the tower is unifor and without excessive turbulence. This can be achieved by ensuring unifor entry of the air into the tower around its entire periphery with as little eddy foration (turbulence) as possible, and by providing wire screens across the tower to assist in aintaining a unifor air distribution and in suppressing eddies or turbulence. A sall conical skirt at the botto of the tower will prevent the foration of a vena contracta, and will hence ensure ore unifor flow of air up the tower. The retention tie of the water droplets in the tower can be increased by ensuring that the size of the water droplets leaving the sprays is reasonably sall, usually about 2 in diaeter. An additional benefit of having screens in the tower is that the free-fall of the droplets is interrupted and, hence, the retention tie is increased further. The screens also help to break up the water into saller droplets when localized cascading occurs. A sall but iportant increase in the retention tie of one to two seconds can be achieved by arranging the nozzles to spray upwards rather than downwards. t is desirable that proven non-clogging spray nozzles be used. A pressure at the sprays of.3 to.5 bar is usually adequate (depending on the type of spray nozzle used), this pressure being independent of whether the sprays point upwards or downwards since the pressure serves priarily to break the water strea into sall droplets. Spray nozzles having holes less than 1 in diaeter have been found to be easily blocked. Since the terinal speed, relative to the rising air, of falling droplets of given size is independent of the air speed it follows that increasing the air velocity will keep the drops in suspension in the tower for a longer tie. Experience suggests an upper liit of 8 to 9 /sec above which carry-over of the droplets becoes large(l). Pressure losses at such high air speeds would also be high, so that in practice a soewhat lower air speed, perhaps 6 /s, is desirable. t is usual to ake towers larger than initially required so that should it subsequently becoe necessary to increase its duty and to increase the air quantity the air speed will still not be uch greater than 6 /so The carry-over of water in towers operating at relatively high air speeds can be prevented by providing a soewhat enlarged tower cross-section above the level of the water sprays. The enlarged zone should be sufficient to reduce the air velocity to about one half its value below the sprays. This is to ensure that carry-over will not becoe a proble at a later stage if it should be decided to increase the quantity of air passing through the tower. DESGN RECOMMENDATONS The following specific recoendations for the construction of cooling towers are based upon the considerations discussed earlier, and should be followed as closely as possible. Nuerical calculations that are needed in the selection of sizes and in the prediction of perforance are considered in the next section: Water loading.. The water loading should be as low as possible, and preferably not ore than 1 litre/sec per 2 of tower area (12 gp/ft2). Loadings down to one-third of this value are coonly used. Air velocity The air velocity ust never exceed 9 /sec, and should be of the order of 6 /sec ( 2 ft/in). Speeds between.5 and 1.4 of the latter value are coonly used. Water-air ratio Generally speaking, as uch air as possible should be sent through the tower. For a given air quantity the lowest condenser teperature will be obtained if the actual water-air ratio is about equal to the reference water-air ratio, ie, if the capacity factor R is about equal to 1. Actual water-air ratios, L/G, found in existing underground towers vary fro.5 to 2.5. Diaeter of tower The diaeter of the tower should be chosen so as to keep the water loading and air velocity less than the axiu values given above. Figure has been prepared to assist in the selection of the tower size. New N E{!5 1 N E? 5..J.. i!..,7 11,8 r; Ē. ' 9 1. :;: or 1.1 Air flowrul' G b/in.ft Air flow rul, G kg/so 2 l>tw.6'c 1 1,. 'e..j.. i! 5 ;: :;; ;,=:- " D "6' OS 15 j 16 ".!! 'ij 17 J; Fig 1-Water and air flow relationships in cooling towers 86 OCTOBER 1971 JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY

3 towers are usually oversized in order to allow for possible later increases in duty. Height of tower fro sup water level to spray level Usually 4 to 6 diaeters. Miniu 12, axiu 25. Sprays Non-clogging spray nozzles of proven design should be used, and should not have holes saller than 1 diaeter. The sprays should face upwards, and should be positioned so as to ensure unifor distribution of the water. The pressure at the sprays will depend on the type of spray used. For exaple, one type of spray nozzle requires a pressure of.3 to.5 bar. Tower above spray level The tower should extend above the sprays for at least 2 tower diaeters. The diaeter of this portion of the tower should be at least 4 per cent greater than that of the ain part of the tower. Air entry to the tower The air should enter the tower at sup water level, uniforly around the full perieter of the tower. The radial entry velocity should be about 4 /so A short conical skirt will prevent foration of the unwanted vena contracta. Screens across the tower Two or three wire screens are needed across the tower. The lower screen should be 3 to 5 etres above the sup water level, while the top screen should be about 2 etres below the water sprays (to serve as a working platfor, if needed). nterediate screens should be equi-spaced between the top and botto screens. The screens should be of stainless steel with 3 diaeter wires spaced about 2 apart. There should be no internal stairways, although a siple ladderway is desirable to facilitate periodic inspection, and occasional reoval of debris fro the screens. Water teperature range, LJ w Towers are usually designed so as to cool the condenser water by 7 to 9 QC. The water flow rate then depends on the aount of heat to be transferred. THERMODYNAMC FACTORS N COOLNG TOWER PERFORMANCE n vertical counterflow cooling towers the hot water is introduced near the top of the tower through suitable spray nozzles, and falls through the rising air strea. Between 8 and 9 per cent of the cooling of the water droplets is the result of evaporation, with convective cooling being relatively uniportant. The laws of therodynaics ipose the following liitations on this cooling process: First law of therodynaics Conservation of energy requires that the energy lost by the water ust equal the energy gained by the air. with due allowance for the evaporation which takes place. This can be expressed algebraically as follows: Q - LAGpL.tw=GALSa where A Gp - cross-sectional area of the tower - specific heat capacity of the water (1) G - air ass flow rate, on a dry basis, per unit area of tower L - water ass flow rate entering the tower per unit area of tower LSa = increase in siga heat per unit ass of the air passing through the tower Lt w = decrease in teperature of the water Q - rate of heat rejection by the water. n equation () only partial allowance is ade for evaporation, a sall additive correction ter on the right-hand side, the agnitude of which is 3 to 4 per cent, being oitted. The considerable coplication in the calculations that results fro its inclusion is not warranted. Enthalpy rather than siga heat ay be used in equation (), but the corrective ter is then negative and has a agnitude of between 7 and 8 per cent. Rearranging equation () leads to an expression for the water-air ratio, L/G: L/G = LSa/Gp Ltw Second law of therodynaics (2) The liitations iposed by the second law are that the water cannot leave the tower at a teperature lower than the wet-bulb teperature of the entering air, and the wet-bulb teperature of the air leaving the tower cannot exceed the teperature at which the water enters the tower. Reference water-air ratio The cobination of the liitations iposed by the first and second laws leads to the concept of the reference water-air ratio, (W AR)o, a nuber which has an iportant role in deterining the perforance of cooling towers. This is defined as that water-air ratio at which, heat and ass transfer peritting, the water would be cooled to the entering wet-bulb teperature of the air, while the air would be heated to a wet-bulb teperature equal to that of the entering water. Thus: (W AR)o= (Swi-Sad/Gp (twi-tad (3) where ( WAR) = reference water-air ratio tat - wet-bulb teperature of the inlet air t wi - water inlet teperature 1.9wi - siga heat of air at a wet- bulb teperature equal to t wi Sai - siga heat of the entering air. t is iportant to note that the reference water-air ratio depends only on the teperatures of the air and water entering the tower, tat and twi, and on the baroetric pressure. t is independent of the type of tower, the efficiency of the tower, or the actual water and air flow rates. Since the prediction of the perforance of any cooling tower requires that its value be known, curves of reference water-air ratios at various inlet air wet-bulb teperatures are shown in Figure 2 for six typical baroetric pressures that are encountered underground, and for various values of (t wi- tad. Experience has shown that ost ine cooling towers operate at teperatures such that the reference water-air ratio, (W AR)o, is between 1.45 and JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY OCTOBER

4 of of BP = 95 b (28.5 "Hg) BP= 1b (29.53 "Hg) '\)\'\ _'t-rle\, \ \'t-rl'tet W E' BP=15b(31.1"Hg)...E' BP=OOb (3248 "Hg) a a 't '\)\'\ e 't '\)\'\ \t\ -'t-rle. 'a \'t-rl'tet 'a \ 't-rl'tet \t\ 1.2 \t\ t 1.2 \t\ t' ' u u c c.... :t; :t; '1ii 't a 1.8 a 1.8 BP=115b (33.96 "Hg) BP= 12b (35.44 "Hg) 't '\)\'\ 1.4 't-rle\t\ '\)\'\ 1.2 \'t-rl'tet 't-rle. \t\ \t\ \'t-rl'tet \t\ Entering wet bulb C.6 Entering wet bulb C Fig 2-Reference water-airjatio, WARo Effect of deviations fro the reference water-air ratio At a water-air ratio, LG, less than the reference value, (W AR)o, the air will not be fully utilized in that it will leave the tower at a teperature considerably lower than its axiu possible wet-bulb teperature. Siilarly, at a water-air ratio, LG, greater than (W AR)o the air will approach its axiu possible teperature rapidly while the water will leave the tower uch hotter than its iniu possible teperature. Thus, in either case, one or other of the fluid streas will not be utilized to its axiu effectiveness. For ost econoical refrigeration perforance it is desirable that the condenser water be as cold as possible, so that water-air ratios less than (W AR)o are to be preferred. A very iportant paraeter in cooling towers is the capacity factor, R, being the ratio of the actual waterair ratio, LG, to the reference water-air ratio, (W AR)o. Thus: R = (LG)/(W AR)o..... (4) Water and air efficiencies of the cooling tower The perforance of a cooling tower is usually defined in ters of its water efficiency and its air efficiency. The water efficiency, 'Y)w, is defined as the ratio of the actual drop in teperature of the water passing through the tower, to the axiu possible drop in teperature as iposed by the second law. Thus: 'Y}w = (twi-two)/(twi-tai)=lcjwl(twi-tai). (5) The axiu possible value of the water efficiency is 1. However, when the ratio R is greater than 1, the axiu possible water efficiency is always less than 1, being equal to l/r. The air efficiency, 'Y}a,is defined in ters of siga heats, being the ratio of the actual increase in heat content of the air to the axiu possible increase in heat content as iposed by the second law. Thus: 'Y}a = (Sao-Sai)/(S wi-sai) The axiu possible value of the air efficiency is equal to R when R is less than 1, and is equal to 1 if R is greater than 1. With the aid of equations (2) and (3) the relationship between the air and water efficiencies is easily shown to be: 'Y}a = R 'Y}w (7) An iplied liitation on equation (7) is that neither 'Y}anor 'Y}w can be greater than 1.. """ (6) 88 OCTOBER 1971 JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY

5 Other tower perforance factors Barenbrug(2) has suggested that a ore eaningful easure of the perforance of a cooling tower is to take the su of the air and water efficiencies to yield a perforance factor, BPF. Thus: BPF = 7)w+7)a (8) With the aid of equation (7) this can also be written as: BPF =7)w(l+R) (9) The axiu possible value of the Barenbrug perforance factor is equal to 2, although this can occur only when R= 1. Griesel(3) has proposed a soewhat different perforance factor, the nuerical value of which is always 4 to 8 per cent larger than Barenbrug's perforance factor. t is interesting to note that the Griesel and Barenbrug factors would be identical if the relationship between siga heat and wet-bulb teperature were linear. The use of Griesel's factor involves additional calculations and offers no particular advantages so it will not be referred to again. A odified for of the water efficiency, called the 'tower' efficiency is soeties used, its erit being that its axiu possible value is 1 at all values of R. At values of R less than 1, the tower efficiency is equal to the water efficiency. At values of R greater than 1, the tower efficiency is equal to R ties the water efficiency, that is, it is equal to the air efficiency. Because it is seldo used in practice, the tower efficiency will not be referred to again; it is entioned only for the sake of copleteness. PREDCTNG THE PERFORMANCE OF COOLNG TOWERS Fro the above equations it will be appreciated that for a known aount of heat to be dissipated (with known air flow rate, assued water teperature range t w, and known inlet air conditions), the prediction of the entering and leaving water teperatures requires that the water efficiency of the tower be known. The proble therefore is to be able to predict the water efficiency in advance, once the physical shape of the cooling tower has been chosen. The ethod given below has been derived fro a study of the perforance of a large nuber of existing ine cooling towers, and represents a prediction ofthe efficiency that would be attained (and even exceeded in soe instances) provided that the cooling tower is constructed according to the recoendations given earlier. The water efficiency, 7)w, depends priarily on the capacity factor R, and to a lesser extent on the air velocity, the entering air wet-bulb teperature, and the nuber of screens. ts value can be predicted fro equation (1): 7)w = F o. F v. F wb. Fs (1) where Fo = basic factor corresponding to the actual water-air ratio F v - factor correcting for the air velocity F wb - factor allowing for the wet-bulb teperature of the entering air Fs = factor ailowing for the nuber of screens in the tower. Nuerical values of these factors ay be read fro the graphs in Figure 3. The basic factor, F, is by far the ost significant. n order to deterine F it is necessary to use Figure 2 to ake a preliinary estiate of (WAR)o in order to calculate R. Having calculated the water efficiency fro equation (1), the teperature of the water entering the tower can then be deterined fro equation (5), since tw has been fixed in advance, by assuption. With all teperatures known it is now possible to deterine ore exactly the reference water-air ratio, (W AR)o, using Figure 2 or equation (3), and to repeat the calculation in order to deterine ore precise values of the water teperatures. Usually it will be desirable to repeat the entire calculation for a range of assued values of air speed and of t w, in order to provide a basis for the selection of the area of the cooling tower and of the value of t w and, hence, of the total water flow rate through the condenser. n the Appendix a listing is given of a coputer progra which enables these calculations to be done rapidly for a range of conditions. An exaple of the coputer print-out is also given. t is desirable to design the cooling syste so as to yield the lowest possible average water teperature, (twi+two)j2, since this will yield the lowest possible condenser teperature for the refrigeration plant. Other constraints, such as the power costs for water circulation and for overcoing the pressure drop of the air flowing through the tower ust of course also be taken into account in choosing the optiu operating condition. Pressure drop across cooling towers The air pressure drop across the cooling tower is partly due to friction, partly to the losses that occur whenever air changes direction or speed, and partly to the falling water droplets. The following equation ay be used for estiating this pressure loss: p - [B+(2 xn)] (wj1.2) (Vj2.9)2 +.1 (LxH)j(12-V). (11) where p - pressure drop, bar V - air speed in tower, js H - height of spray-filled portion of tower, L = water loading, kg/s, 2 w - density of air, kg/3 N - nuber of screens or obstructions in tower B - constant depending on the tower layout. The constant B varies considerably fro one tower to another, a typical value being 1. t can be as low as 5 or as high as 2. ts nuerical value is best deterined by easureent on actual towers. Equation 11 ay be used when it is necessary to deterine the fan pressure and fan power needed to drive the air through the cooling tower. n the coputer progra given in the Appendix the pressure drop across the tower is coputed on the assuption that B=lO andh=25, these being typical JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY OCTOBER

6 LE u Cl -Q 1. Cl u:.6 ū \.E \.8 u.9 -v-- Maxiu Gi possible "'w > > 5 1 u.. 1. ft/in.9 \ Air velocity /sec u \ \ 1. \ \ U.95 \.E c \ C C u Cl) of C nlet air wet - bulb teperature Ratio R - (L/G).8 - (WAR)o Water efficiency "'w = Fo x Fy x Fwb x Fs Fig 3-Curves for predicting water efficiency Nuber of screens values for underground cooling towers in South African gold ines. EXAMPLE n order to illustrate the ethod of calculation, the case will be considered of a noinal 3 5 kw (1 ice ton) capacity refrigeration plant, the condenser of which ust reject Q=422 kw of heat. Three screens are to be installed in the tower. Air is available at 31 C wet-bulb and 33 C dry-bulb. The baroetric pressure is 15 b and the axiu quantity of air available is 8 3/sec at a specific volue of.872 3/kg. There is soe latitude in the choice of the crosssectional area of the tower, although to allow for possible future expansion of the refrigeration plant it is usual to choose a tower soewhat larger than the iniu that is required initially. n this instance the area will be chosen so as to give an air velocity in the tower of 4 /s, necessitating a tower of cross-sectional area 2 2. Since the water flow rate is not specified it is usual to repeat the calculations for several assued values so chosen as to give a drop in teperature of the water in the range 6 C to looe. The reference water-air ratio, (W AR)o, can be estiated fro Figure 2, since the baroetric pressure and entering wet-bulb teperature of the air are known. At an assued difference of looe between the entering water teperature and entering wet-bulb teperature of the air, ie, twi-ta!=lo the value of (W AR)o will be about 1.5. (A trial and error solution is needed in order to deterine a ore accurate value of (W AR)o. Usually one iteration is sufficient.) The steps in the calculation leading to the water entering and leaving teperatures are shown in Table 1. The calculations are straight forward and require no explanation. This sae exaple has been calculated using the coputer listed in the appendix, the print-out also being given in the appendix. 9 OCTOBER 1971 JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY

7 ACKNOWLEDGEMENT The work reported in this paper was undertaken as part of the research progra of the Applied Mechanics Division of the Mining Research Laboratory of the Chaber of Mines of South Africa. The author is grateful to Mr A. W. T. Barenbrug for any stiulating discussions, and to Mrs L. Kuhn, Miss S. Thorpe, Miss C. Ellis and Mr M. W. Harrison who assisted with the preparation of the figures and the coputer progra. REFERENCES 1. LAMBRECHTS,J. DE V. 'Experiental studies in high velocity cooling towers'. J. Mine Vent. Soc. of S. Afr., Vol. ll, p. 66, March, BARENBRUG,A. W. T. 'Contribution to discussion of Reference 3. J. Mine Vent. Soc. of S. Afr., Vol. 22, No. 7, p. 133, July, GRESEL, G. D. 'Cooling Tower Geoetry' J. Mine Vent. Soc. ofs. Afr., Vol. 22, No. 6, p , June, CONVERSON FACTORS FOR S UNTS Energy Volue flow Velocity Pressure Siga heat Specific heat Mass flow Density Refrigeration 1 kj=.9478 Btu=1 kw/sec 1 3/s=2 118 cf 1 /s= ft/in 1 bar=.2953 inch Hg 1 bar=.4l5 inch wg bar=1 inch Hg lkj /kg=.4299 Btu/lb kj /kg C=.2388 Btu/lb F 1 kg/s 2=12.3 lb/in ft2 1 kg/3=.6243 b/ft3 1 ice ton= W cooling evaporator. rate at 'fable 1 EXAMPLE OF PREDCTON OF WATER TEMPERATURES Heat 422 kw, nlet air 31 Cf33 Cfl5 bar Air quantity 8 "fs, Tower area 22 Assued Equation 1 8/.872 x 2 Assued Equation 4 Figure 3 Figure 3 Figure 3 Figure Dtw c Water rate L kg/s, Air rate G kg/s, L/G (WAR)o R Fo Fv Fwb Fs Equation 1 7] Equation 5 (twi-tai) c Repeat using better value of (W AR)o fro Fig 2 or equation 3 Figure 2 (WARo) Equation 4 R Figure 3 Fo Equation 1 7] Equation 5 twi-tai c twi c two c JOURNAL OF THE SOUTH AFRCAN NSTTUTE OF MNNG AND METALLURGY OCTOBER

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