AEDC-TR-71-213 ARCHIVE COPY DO NOT LOAN

PRELIMINARY DESIGN OF A MECHANICAL-DRAFT

COUNTERFLOW COOLING TOWER

01 ] 3 i < : Ü : s x . o

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R. L. Clouse

ARO, Inc.

October 1971

Approved for public release; distribution unlimited.

ENGINE TEST FACILITY

ARNOLD ENGINEERING DEVELOPMENT CENTER

AIR FORCE SYSTEMS COMMAND

ARNOLD AIR FORCE STATION, TENNESSEE

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F4060O-78-C-OO03

mm When U. S. Government drawings specifications, or other data are used for any purpose other than a definitely related Government procurement operation, the Government thereby incurs no responsibility nor any obligation whatsoever, and the fact that the Government may have formulated, furnished, or in any wav supplied the said drawings, specifications, or other data, is not to be regarded by implication or otherwise, or in any manner licensing the holder or any other person or corporation, or conveying any rights or permission to manufacture, use, or sell any patented invention that may in any way be related thereto.

Qualified users may obtain copies of this report from the Defense Documentation Center.

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AEDC-TR-71-213

PRELIMINARY DESIGN OF A MECHANICAL-DRAFT

COUNTERFLOW COOLING TOWER

R. L. Clouse

ARO, Inc.

Approved for public release; distribution unlimited.

AEDC-TR-71-213

FOREWORD

The work reported herein was sponsored by Headquarters, Arnold Engineering Development Center (AEDC), Air Force Systems Command (AFSC) under Program Element 64719F.

The research was conducted by ARO, Inc. (a subsidiary of Sverdrup & Parcel and Associates, Inc.), contract operator of AEDC, AFSC, Arnold Air Force Station, Tennessee, under Contract F40600-72-C-0003. The work was conducted under ARO Project No. BE2151-A11 in the Engine Test Facility (ETF), and the report was submitted for publication on August 23, 1971.

The author wishes to express his appreciation to Mr. J. R. Reeves, Facility Support Branch of the Engine Test Facility, ARO, Inc., for his assistance in the preparation of this report.

This technical report has been reviewed and is approved.

Hans A. Person Ernest F. Moore Facility Development Colonel, USAF

Division Director of Civil Directorate of Civil Engineering

Engineering

li

AEDCTR-71-213

ABSTRACT

The need for a method whereby the preliminary design of a cooling tower can more easily be specified has existed for many years. The numerical techniques commonly used to solve the Merkel cooling tower equation are not adaptable to a direct general solution. This report presents a direct solution to the Merkel equation which, when combined with certain detailed experimental data by others, yields a relatively quick and straightforward method of establishing the preliminary design of a mechanical-draft counterflow cooling tower. Special attention is devoted to cooling tower applications relative to high altitude engine test facilities.

111

AEOC-TR-71-213

CONTENTS

Page

ABSTRACT iii NOMENCLATURE vi

I. COOLING TOWER PRINCIPLES 1 Ii; COOLING TOWER THEORY

2.1. The Merkel .Equation 3 2. 2 Direct Solution of the Merkel Equation for

Counterflow Cooling 4 2. 3 Tower Characteristics: Required and Available ... 7

III. APPLICATIONS OF THEORY TO THE PRELIMINARY DESIGN OF A MECHANICAL-DRAFT COUNTERFLOW COOLING TOWER 8

IV. CONCLUDING REMARKS 11 REFERENCES , 11 BIBLIOGRAPHY 12

APPENDIX ILLUSTRATIONS

Figure

1. Cooling Towers: Basic Cooling Methods a. Counterflow Cooling 15 b. Crossflow Cooling 15

2. Heat and Mass Transfer Relationships between Water, Film, and Air 16

3. Counterflow Cooling 17

4. Tower Characteristic versus Water Temperature Range for twb = 70°F and L/G = 1.0 18

5. Tower Characteristic versus Water Temperature Range for twb = 70°F and L/G = 1.2 19

6. Tower Characteristic versus Water Temperature Range for twb = 70°F and.L/G = 1.4 20

7. Tower Characteristic versus Water Temperature Range for twb = 75°F and L/G = 1.0 . 21

8. Tower Characteristic versus Water Temperature Range for twb = 75°F and L/G = 1.2 22

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Figure Page

9. Tower Characteristic versus Water Temperature Range for twb = 75°F and L/G = 1.4 23

10. Tower Characteristic versus Water Temperature Range for twb ■ 80°F and L/G = 1.0 24

11. Tower Characteristic versus Water Temperature Range for tWD = 80°F and L/G = 1.2 25

12. Tower Characteristic versus Water Temperature Range for twb = 80°F and L/G = 1.4 26

13. Tower Characteristic versus Water Temperature Range for twb = 85°F and L/G = 1.0 . . . 27

14. Tower Characteristic versus Water Temperature Range for twb = 85°F and L/G = 1. 2 28

15. Tower Characteristic versus Water Temperature Range for twb = 85°F and L/G = 1.4 . 29

16. Tower Characteristic versus Effective Height 30

17. Discharge Air Temperature versus Water Temperature Range for twb = 75°F 31

18. Discharge Air Temperature versus Water Temperature Range for twb = 80°F 32

19. Discharge Air Temperature versus Water Temperature Range for twb = 85°F 33

NOMENCLATURE

A, b, d, e, n Constants

a Water surface area per unit tower volume, ft2/ft3

C Constant of integration

c Specific heat, Btu/(lbm)(°F)

D Discriminant of the quadratic expressing the enthalpy potential

G Rate of airflow, lbm/hr

h Enthalpy, Btu/lbm

vi

AEDC-TR-71-213

K .... Overall unit conductance, bulk water to bulk air, lbm air/ft^ (water area) hr, evaluated at bulk water tem- perature

KQ Unit conductance, sensible heat transfer between interface and main air stream, Btu/hr-ft2-°F

Kjyi Unit conductance, mass transfer, interface to main air stream, lbm air/hr-ft2

K\Y Unit conductance, heat transfer, bulk water to interface, Btu/hr-ft2-°F

L Rate of water flow, lbm/hr

m , Mass, lbm

N Number of decks in tower fill

q Rate of heat transfer, Btu/hr

r Latent heat of vaporization for water, Btu/lbm

SH Specific humidity, lbm water vapor /lbm dry air

t Temperature, °F

V Effective cooling tower volume, ft3

Z Effective cooling tower height, ft

A ' Difference

SUBSCRIPTS

a Air

i , Initial

L Latent

m Mixture

p Constant pressure

s Sensible

t Total

w Water

wb Wet bulb

1 Condition No. 1

2 Condition No. 2

vii

AEDC-TR-71-213

SUPERSCRIPTS

Defined in Figs. 2 and 3

Defined in Figs. 2 and 3

Vlll

AEDC-TR-71-213

SECTION I COOLING TOWER PRINCIPLES

A cooling tower is a structure whose function is to cool water through a certain temperature range by exposing the water to ambient air in a combined evaporation and convection heat transfer process. The structure is so designed that the warm water falls from the top to the bottom in thin curtains or droplets while the air enters from the bottom and flows to the top (vertically) for counterflow cooling or from the side (horizontal flow) for crossflow cooling (Fig. 1, Appendix).

Properly designed cooling towers ensure that a relatively large water surface is exposed to the air. This surface is produced by water dropping or splashing through a latticework called "fill" or "packing" usually constructed of decay-resistant wood.

Cooling towers are generally classified in two main groups: natural- draft and mechanical-draft.

Natural-draft towers depend on ambient conditions to produce a cooling airflow and are further subdivided: (1) the atmospheric tower in which prevailing winds provide all the ventilation, (2) the straight- wall chimney type which is rapidly becoming obsolete, and (3) the hyperbolic-wall tower. Both the chimney and hyperbolic type towers have sufficiently large heights such that airflow is established because of the difference in the density of the heated air inside the tower and the ambient air outside.

Mechanical-draft towers create their own air movement by means of a motor-driven fan. There are two primary classifications for these types of towers: (1) forced and (2) induced. The principal difference in the forced and induced towers lies in the location of the fan and auxil- iaries. The forced-draft tower has the fan mounted on the lower side of the tower, where the air is blown in, allowing a more firm fan equipment support, thus reducing vibration. The induced-draft tower has the fan mounted on top of the tower to draw the air out. Since some of the fan velocity pressure is converted to static pressure in the forced-draft system, the exit velocity of the air is less than that of the induced type, thus allowing a greater degree of recirculation of the hot humid exhaust air. Exhaust vapors usually leave the forced-draft tower at such a low velocity that a cross wind causes them to be drawn back in the fan suction, thus artificially raising the wet-bulb temperature of the enter- ing air which results in a higher cold water temperature. It is primarily for this reason that the forced-draft tower is rapidly losing favor in

AEDC-TR-71-213

industrial applications. In induced-draft towers, the exhaust air leaves at a much higher velocity and usually at a higher elevation (through the use of exhaust stacks) and the tendency to recirculate is reduced. Therefore, induced-draft towers are always used when it is desirable to maintain the lowest possible cold water temperature.

Mechanical-draft towers in general and induced mechanical-draft towers in particular have many advantages over other types of cooling equipment: (1) the area required is significantly less than that for an atmospheric tower, (2) cold water temperatures are more stable and predictable, (3) independence of wind which in turn allows (4) freedom of choice in location, and (5) minimum of drift nuisance when compared to the atmospheric tower which in turn leads to (6) smaller make-up water requirements. Disadvantages include higher first cost (except the hyperbolic type) and higher operating and maintenance cost.

In cases where a stable water exit temperature is needed, natural draft towers are almost never used because changes in wind velocity and direction cause the cold water temperature to fluctuate. Under certain extreme ambient conditions, this becomes especially important in high altitude engine test facilities where fluctuations in cold water temperature can lead to undesirable changes in simulated altitudes. A change in the cold water temperature of the exhaust gas surface cooler serviced by the cooling tower in such installations leads to a change in temperature of the exhaust gases being cooled. This, in turn, will change the performance of the exhaust compressor system which leads directly to a change in exhaust pressure (altitude).

In applications where large heat loads must be dissipated, natural draft towers (except hyperbolic) are almost never found. Again in rela- tion to high altitude test facilities where large heat loads are commonly encountered, the required physical size and associated cost of a natural - draft tower would be prohibitive.

The hyperbolic tower, whose European popularity has been high for many years, is now increasing in favor in the United States. Enormous in size and heat load capability, these towers have the advantage of no moving parts and hence low operating and maintenance cost. The high initial installation cost is usually justified in industrial applications such as electric power plants where continuous operation is a necessity and shutdown due to mechanical failures must be avoided.

Hyperbolic towers and their associated higher initial cost cannot be justified at high altitude engine test facilities because continuous opera- tion is unnecessary and occasional failures connected with mechanical- draft towers can be tolerated.

AEDC-TR-71-213

SECTION II COOLING TOWER THEORY

2.1 THE MERKEL EQUATION

The generally accepted concept of cooling, tower performance was developed by Merkel in 1925. The Merkel equation results from an analysis which combines the sensible and latent heat transfer into an overall process based on enthalpy potential as the driving force. Figure 2 shows the process schematically where each particle of the bulk water in the tower is assumed to be surrounded by an interface to which heat is transferred from the water.

The process will reach equilibrium when ta = tw and the air be- comes saturated with moisture at that temperature. Under adiabatic conditions, equilibrium is reached at the temperature of adiabatic saturation, or at the thermodynamic wet-bulb temperature of the air.

The total heat transfer from the water is the sum of the sensible and latent portions:

dqt = dqs 4 dqL = KG (a dV) (f - ta)

+ r-KM (a dV) <SH" - SHa) = G dha

Merkel utilized the Lewis relationship,

s 1 *G KMcpm

in the development of the final equation:

dqt = dqs 4 dqL = KMcpm- (a-dV) (f - ta)'

4 rKM (a dV) (SH" -SHa) = G dha

= KM (a dV)'[cpm t' + rSH") - (cpm ta +■ rSHa)] = G dha

but, since enthalpy for an ideal gas mixture of air and water vapor is defined as

h = cp t 4 rSH

then

dqj. = dqg 4 dqL = KM (a dV) (h" - ha) = G dha (1)

KaV *W1

*W2

dtw L (h' - ha)

KaV G

hai

-I (h'- ha)

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The enthalpy potential in Eq. (1) is from the interface to the airstream which is indeterminate. This difficulty is overcome by ignoring the resistance of the film and considering an overall coefficient, K, which relates the driving force for the process to the enthalpy, h', at the bulk water temperature, tw.

The total heat transfer must also equal the total heat removed from the water. By neglecting the water loss by evaporation and assuming Cpw equals unity, the equation now becomes

L dtw = G dha = K (a dV) (h' - ha)

which upon integration yields

,twl rft f dtw (2)

(3)

Figure 3 illustrates the cooling process in a counterflow cooling tower. As the water is cooled from temperatures corresponding to A to B, respectively (cooling range), the film enthalpy follows the saturation curve from C to D. The entering air at twb has as enthalpy correspond- ing to B' which has the same value of enthalpy as point B. The differ- ence between tw„ and tw^ is called the approach temperature. Since,

L dtw = G dha (4)

the slope of line BA, dha/dtw, is equal to L/G.

2.2 DIRECT SOLUTION OF THE MERKEL EQUATION FOR COUNTERFLOW COOLING

In the past, investigators have resorted to time-consuming numerical integration techniques in solving Eq. (2) for the design of a counterflow cooling tower. In addition, this indirect method of solu- tion is very cumbersome and sometimes impossible to apply to the analysis of an existing tower to solve for certain critical parameters. Therefore, some direct method of solution is needed.

Close inspection of Eq. (2) and Fig. 3 will reveal that, if the en- thalpy potential, h' - ha, could be expressed as a function of water

AEDC-TR-71-213

temperature, tw, then Eq. (2) could be integrated to obtain a direct solution. The difficulty of the integration process and the application of the resulting solution would, of course, depend on the mathematical complexity of the enthalpy potential.

Since, from Eq. (4);

dha_ _L_ dtw G

integration yields ha = C + L/G tw (5)

At a water temperature of tw„, ha must equal haj. Therefore, C must

equal haj - L/G tw_ and the resulting equation for ha is

ha = <hai " WG *w2) + L/G tw or

ha = hai 4 L/G (tw - tW2) (6)

where ha^ is a function of ambient wet-bulb temperature, twjj, only.

Obtaining a relationship for h' as a function of water temperature is much more difficult and time consuming. The final relationship results from the method of "curve-fitting" which involves the assump- tion of general equation form and then fitting the arbitrary constants to form the particular solution.

After many assumptions, the resulting equation for h' is a quadratic in tw:

t 2

h' = -~^ - 2.366 tw + 96.91 (7)

The equation is within 1. 5-percent accuracy in the cooling range of 75 < tw < 120°F. By combining Eqs. (6) and (7), the enthalpy potential can now be expressed in terms of tw:

t 2

h' - ha = ^y-g - (2. 366 + L/G) tw 4 (96. 91 4 L/G tWg - hai)

Substitution into Eq. (2) gives

ABDC-TR-71-213

t KaV r

w. dt w

<h' - ha) w

t\Vi

tw»

47. 2 dt w

tw2 - 47. 2(2. 366 + e) tw + 47. 2 (96. 91 - d)

(8)

where d = hai - L/G tW2

e = L/G

Integration yields

KaV _ 47.2

L = V5" in

2tWj + b - -/DT

2tWl + b +TfD

2tW2 + b -yJ~D

2tW9 + b +ypD

when D > 0, or

KaV 47.2(2) V=D" tan

x (2twl + b)

V^ tan

(2tWg + b)

when D < 0, or

KaV = -47.2(2) [(2tWl + b) " (2tW2 + b)J

when D = 0, where,

D = b2 - 4c

b = -47.2 (2.366 + e)

c = 47.2 (96.91 - d)

(9)

(10)

(11)

In order to obtain the correct solution from the three possibilities, reference is made to Fig. 3. Point A is always less than the correspond- ing point C for any operating condition because it is impossible for the wet-bulb temperature of the exhaust air to be equal that of the hot water. Point B is always less than point D because a zero approach temperature

AEDC-TR-71-213

can never be achieved in practice. Furthermore, for a good design, all the intermediate points on line BA will be less than those on DC. In relation to Eq. (8), this means that the discriminant, D, of the denominator must always be negative, and the proper solution is

KaV _ 47.2(2) L = v^ (2tWl + b) (2tw2+b)

tan-1 z= - tan-1 ——— D ^-D

The cumbersome numerical integration technique has thus been avoided, and a direct general solution is available. Figures 4 through 15 present the solution of Eq. 10 for some typical design conditions.

2.3 TOWER CHARACTERISTICS: REQUIRED AND AVAILABLE

When Eq. {10) is solved for a set of design conditions, the result- ing value for KaV/L is referred to as the Number of Tower Character- istics (NTC)l -required for the conditions selected. The required NTC represents a ''degree of difficulty" for the conditions selected. When the same calculation is applied to a set of test data, the result is the available coefficient for the tower operating at those conditions under which the data were taken. Because of the idiosyncrasies in the be- havior of the atmosphere in the vicinity of the cooling tower, the avail- able coefficient at design conditions is extremely difficult to obtain. Methods have been proposed, however, which allow the "off-design" available coefficient to be corrected to obtain predicted cooling tower performance at design conditions.

A very detailed set of test data {Ref. 1) for ten different repre- sentative industrial fill geometries has shown that for any given geom- etry the available coefficient can be expressed in terms of the height of the filled section (effective height) and the water-to-air ratio, L./G:

KaV/L = 0. 07 + AN (L/G)"n

where A and n are constants and N is the number of decks in the fill. When information relative to the vertical deck spacing for the ten geom- etries are included and the two geometries with the highest and lowest

^Some authors prefer to call this the Number of Transfer Units (NTU). However, NTU is the value for KaV/G (named after Colburn) and NTC is KaV/L (named after Lichtenstein). Obviously, the numberical value differs only by the L/G ratio.

= 0.07 + 0.0628 Z (L/G = 1.0) (12)

= 0.07 + 0. 0565 Z (L/G = 1.2) (13)

= 0.07 + 0.0515 Z (L/G = 1.4) (14)

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performance are omitted, the available coefficient for the eight remain- ing geometries can be expressed as

KaV L

KaV L

KaV

within 17-percent maximum variation from the average. The maximum variation occurs, of course, for the two extreme geometries, and the variation for the remaining six is less. Figure 16 presents KaV/L versus height for the L/G ratios of 1. 0, V.-2, and 1. 4.

Equations (12), (13), and (14) along with Eq. (10) can be of particular value to the design engineer during initial preliminary in- vestigation. Once the design conditions have been selected, Eq. (10) will predict the required coefficient. The substitution of the required coefficient for the available coefficient into the appropriate Eq. (12), (13), or (14) will yield an approximation of the necessary effective tower height.

SECTION III APPLICATIONS OF THEORY TO THE PRELIMINARY DESIGN

OF A MECHANICAL-DRAFT COUNTERFLOW COOLING TOWER

With the exception of the Merkel equation, the equations developed in Section II are valid only for counterflow cooling. The crossflow process, with its associated complexity of analysis, has thus far re- sisted a direct theoretical solution. In such cases, numerical or graphical techniques are employed. However, when the flow of air through a crossflow cooler approximates the counterflow path, the re- sults presented herein can be used to obtain a rough preliminary esti- mate of crossflow cooling performance.

Normal design parameters for a cooling tower are: (1) wet-bulb temperature, (2) total heat load, (3) cooling range, and (4) approach. The equipment to be serviced by the tower and the ambient weather con- ditions will dictate the magnitude of each of the four parameters.

The selection of the design wet-bulb temperature is certainly critical and is almost always compromised by economic considerations.

AEDC-TR-71-213

For a constant approach, range, and L/G ratio, the higher the design wet-bulb temperature is, the lower the required tower characteristic, KaV/L, required to accomplish the cooling. This is primarily because for increased temperature the air has an increased capability for evaporative cooling. Even though the required tower characteristic will decrease with increasing wet-bulb temperature, the parameter sacrificed will be the cold water temperature which for the same approach will increase with increased design wet-bulb temperature. Therefore, from a performance standpoint a LOW design wet-bulb temperature is desirable because it produces a higher required tower characteristic and thus increases the number of hours per year that the tower will operate within the guarantee zone. A common practice is to select a wet-bulb temperature that will prevail or be exceeded 5 percent of the time during the four summer months. Information relative to design wet-bulb temperature for specific locations in the United States may be found in Ref. 2.

By neglecting the usually small heat losses to the ambient air, the total heat load is identically equal to the heat produced by the equipment being serviced by the cooling tower.

Because the specific heat of liquid water is approximately unity, the cooling range is related directly to the total heat load through the total water flow rate:

or

qt = L Atw = L (range)

range = qt/L

The total water flow rate, L, must be selected sufficiently large to maintain the range within reasonable limits. Consideration of other components of the entire cooling system must also be made in deter- mining L. Mechanical-draft cooling towers are most commonly de- signed for a range, Atw, of between 20 and 40°F. As the range is increased, the required tower characteristic is increased, other parameters remaining constant.

Cooling tower design is very sensitive to approach temperature. As the approach temperature is decreased, the required tower character- istic increases sharply. It is only when the particular application dic- tates that the lowest possible cold water temperature be maintained that a small approach temperature is selected. Common cooling tower designs limit the minimum approach temperature to approximately 5°F. In cool- ing tower application to high altitude engine test facilities, the stability of

AEDC-TR-71-213

the cold water temperature is more important, within reasonable limits, than the magnitude, and hence, a higher approach temperature of 10 to 15°F should be selected.

Figures 4 through 15 present the required tower characteristic in terms of the parameters previously discussed and the water-to-air ratio, L/C It should be noted that the required NTC is independent of the absolute magnitudes of L and G and dependent only on the ratio L/G. In actual practice, however, both L and G are limited. Economic con- siderations involving capital charges and fan power costs limit the fan power and the resulting airflow rate to about 1800 lbm/hr-ft^ of effective tower area. If the water flow is increased beyond around 3000 lbm/hr-ft2, the water tends to cascade in streams so that the effective surface area is reduced. Furthermore, if the water flow drops to about 600 lbm/hr-ft2, surface tension causes the water flow to channel. For preliminary design, it is suggested that a water load- ing of about 2160 lbm/hr-ft^ in conjunction with an air loading of 1800 lbm/hr-ft2 t,e used, resulting in an L/G ratio of 1. 2. As the state- of-the-art progresses and refinements are made in tower fill material and geometry, higher loadings can be expected.

After the design parameters have been selected, the preliminary cooling tower design can be established as follows:

1. Equation (10) or the appropriate Fig. 4 through 15 yields the required tower characteristic.

2. With the required tower characteristic, enter Fig. 16 and obtain the required effective cooling tower height (height of the filled section).

3. The quotient resulting from the total water flow, L, and the water loading of 2160 lbm/hr-ft^ gives the necessary effective plan area.

4. The plan area in conjunction with an air loading of 1800 lbm/hr-ft2 results in the total airflow, G, which gives an indication of fan size and quantity.

5. The appropriate Fig. 17 through 19 yields the dis- charge air temperature.

It should be emphasized that, even though the design parameters establish a design point, the cooler will operate at any point along the constant NTC line predicted in step No. 1 above. As the warm water temperature is changed, the cooling tower will simply readjust to a different approach temperature and range at the same value of NTC.

10

AEDC-TR-71-213

Because the NTC is essentially constant for the same L/G ratio, the selection of a design point results automatically in the selection of a design line.

SECTION IV CONCLUDING REMARKS

The information contained in this report should prove to be very useful to the design engineer in obtaining the preliminary design of a mechanical-draft counterflow cooling tower. By using this method, an estimate of the required physical size of a cooling tower can be obtained rather quickly, thus allowing important conclusions to be made concern- ing the feasibility of a cooling tower installation to the particular applica- tion.

In addition to being straightforward and much less time-consuming, the development of this design method, with the exception of Eqs. (12) through (14), is more accurate than the commonly used numerical tech- nique. Even the 17-percent maximum variation contained in Eqs. (12) through (14) is usually within the range of engineering accuracy for pre- liminary calculations. When establishing a more detailed design, the design engineer could eliminate this approximation by selecting a specific fill geometry and then utilizing Ref. 1 to determine the exact fill performance.

REFERENCES

1. "Comparative Performance of Cooling Tower Packing. " Arrange- ments by Neil W. Kelly and Leonard K. Swenson, Chemical Engineering Progress, Vol. 52, No. 7(1956), pp. 263-268.

2. DeFlon, James G. "Cooling Equipment. " Kent's Mechanical Engineers' Handbook, Power, Twelfth Edition. New York: John Wiley & Sons, Inc., 1950.

11

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BIBLIOGRAPHY

1. Baker, D. R. "Use Charts to Evaluate Cooling Towers. " Hydro- carbon Processing Petroleum Refiner. Vol. 41, No. 1, January 1962, pp. 233-236.

2. Baker, Donald R. "Cooling Tower Performance. " Chemical Engineering, Vol. 59, No. 10, October 1952, pp. 196-199.

3. Baker, Donald R. and Shryock, Howard A. "A Comprehensive Approach to the Analysis of Cooling Tower Performance. " Journal of Heat Transfer, Transactions of the ASME, Vol. 83, Series C, No. 1, August 1961, pp. 339-350.

4. Berman, L. D. Evaporative Cooling of Circulating Water. Trans- lated from the Russian by Raymond Hardbottle, New York, Pergamon Press, 1961.

5. Chilton, H. "Performance of Natural-Draught Water-Cooling Towers. " Institution of Electrical Engineers Proceedings, Part II, Power Engineering, Vol. 99, No. 67, February 1952, pp. 440-456.

6. "Cooling Towers and Spray Ponds. " ASHRAE Guide and Data Book, Systems and Equipment for 1967. New York, ASHRAE, Inc.

7. Crawshaw, C. J. "Investigation into Variations of Performance of a Natural-Draught Cooling Tower. " The Institution of Mechanical Engineers Proceedings 1963-64, Vol. 178, Part I, pp, 927-948.

8. Fraas, Arthur P. and Ozisik, Necati M. "Cooling Towers. " Heat Exchanger Design. London, John Wiley & Sons, June 1965.

9. Mechanical Engineers' Handbook. Edited by Lionel S. Marks, New York: Hill Book Company, Inc., 1951.

10. Stoecker, W. F. "Cooling Towers and Evaporative Condensers. " Refrigeration and Air Conditioning. Toronto, McGraw-Hill Book Company, 1958.

11. Threlkeld, J. L. "Direct Contact Transfer Processes between Moist Air and Water. " Thermal Environmental Engineering. New Jersey, Prentice-Hall, Inc., 1962.

12. Woodson, Riley D. "Cooling Towers. " Scientific American, Vol. 224, No.; 5, May 1971.

12

AEDCTR-71-213

APPENDIX ILLUSTRATIONS

13

Ol

Air

Air

t r ///////////

l-^-Z-T'

v. J c

Drift Eliminators

Warm Water Distribution-

System ^ Ä Ä W ^

'; ft '/!»» /»?.» «it' /ilV ■;!•■•'•■ i•■•• •* iii i

/" Fill or Packings. >s

Air

Louvers

Air >s_

S X" - — — x* y - — — X* — x!

^

Water Basin c Water Basin

Cooled Water

c.

Air

Cooled Water

a. Counterflow Cooling b. Crossflow Cooling

Fig. 1 Cooling Towers: Basic Cooling Methods

> m D O H

iv]

w

Bulk Air at t.

*. < ha <

SH < I SH" <l SH' a '

Sensible

dqs = KG (a dV)(f - tft)

> m o o H 3D

U

c dt /= Kw (a dV)(t - t')

Latent

dm = KM (a dV)(SHM - SHa) dqL = r dm = rKM (a dV) (SHM - SHa)

Fig. 2 Heat and Mass Transfer Relationships between Water, Film, and Air

AEDC-TR-71-213

Temperature, °F

Fig. 3 Counterflow Cooling

17

AEDC-TR-71-213

> re

u

■G 2

——^ i

5.0 *wb ■70°F L/G - 1. )

i-% i ,mmt

4.0 A| iproach ■ 5°P\ 1 «nJ

f-Hi

1 ""Hi

l «^ r Si 1 *"*!

(

1

1 1

' / /

1/ —■—1

3.0 / [^ -^1 1

I

/ y St

S^L— / r i

S* 1 1 /

/ / /

i i

^_-i 4. 1

r / /

/ i

2.0 / ft/

1 1

—r /

/f / # / 1

t

/ 1 / i

\\/ I i

/ /

/ / /

1 I f

i

/ y /i / t /

&^~3 /

/i --,4-

/1 /L. *\

1.0 Si

(/A Vl5 °F / A /O 1/ (S\ ^-K l°F

^-7.5° ;

( r( ) i 1 3 1 5 20 25 30 5 40 45

Water Temperature Range (t^ - t^), °F

Fig. 4 Tower Characteristic versus Water Temperature Range for t„b = 70°F and L/G = 1.0

18

AEDCTR-71-213

B.tf .HI L/G • 1.2

•^ i i 1 Ll_

«—i

: 1 7 n ~7^~\ — f-Hl

•

— J

■HI

k n / i

-| I;" ii . / <* 3.U

> i

f

» / i / /

-/ / f

m LI « / 1 « 4.0 E f!

/

ID

u

/i

;

f i t /

L. u 1

9 n i. u i j I

—i-ytr-

i,. / 1

-/- I

^ VÜ

/ /

-/- / f— ? n

A i 1

1 1

-linnüs _ V

1 1 ^-15°F

l n / i v' 1^ *\ ^10°F

fy/6 s\ ^-ft

|

"Ay

// S* p— Approac h ■ 7.5°F

0

^r

0 5 10 15 20 25 30 35 40 45

Water Temperature Range (t^ - t^), °F

Fig. 5 Tower Characteristic versus Water Temperature Range for t„b = 70°F and L/G = 1.2

19

AEDC-TR-71-213

5 o

| i f VA " 7OPF

L/G - 1.4

i

i i i

A n i

0. U

-^ 1 1

y —A a <- 1

*

5.0

-{—

Si I i i

^ ■» 3| ■1 J ■ i i i

-/i L . 4 -

i

4.0

I Ä 1 / u 1 /

i

1 i

1 i i ^^l

i LI

S\

i 1

3.0 / /

/ i U- 1 / / /

/

A ' / \ /

r l 1 .1

/ / » /

/ /

■"I /

-■/--

/

1 1

/ / /

2.0 ~l

1 / i

i /

f

7 / / /

1 1 1 I

t /

1// y

l~ 1 i >

(7* 1 ^15° F § 1

J*^x \- inOc

1.0 II

lu^r

/XäZIZX- 1 -7 5°F

/Z/% 1 1 UJbS

u^ ^-Approach -5°F

n IM A

L- 10 15 20 25 30 35

Water Temperature Range (t^ - ty^), °F

40 45

Fig. 6 Tower Characteristic versus Water Temperature Range for t«,,, = 70°F and L/G = 1.4

20

AEDC^TR-71-213

4.0

3.0

> cd

• 2.0 o a

» O

1.0

-^wb

1 «= 75°F

L/G ■= 1 .0 1

Vppr oacb - S °F— « i f

1 1

tk. i

/

/ I

/_ SI 1 / xl /

/ /

"7

/ i

/ /" / i

0

•7 -if

A/ -/-

/

/ / 1

0

O

c / •^7

-^ 1 1

< c

— c 1^ /

/ /

1 I

1 5 1

/ /

/ / /

/ /

J

1

f 1 B

(f 0!

I7r~ M- /

/ ^*

/ / i /

/ c y^ «""^A n/ 1/

/ f

A A

X >

/i • /

y* IS /

\ ^L^0"^ i -15°F

/Ä A^ ^—] 0°F

/s — 7. j'F

5 10 15 20 25

Water Temperature Range (t

30

V- *r

Fig. 7 Tower Characteristic versus Water Temperature Range for twt =75°Fand L/G -1.0

21

AEDC-TR-71-213

5.6

4.0

> cd

is +» ü et u « ü

o » o H

3.0

2.0

1.0

1 1 ■= 75°F

L/G = 1.2 1 1

1 l 1

* 1 ° 1

Ap pros ch - 5 *—1 l i

' o 1

H 1 1H|

w 1'

°F-v

.-/

y c °J ff

/

/ / / /

O ■

1^

/

^ o. / /

0 , «ol-

1 '

/ M ■ 0 1 / °/— 1 °l ' 7/

/ ^/ /

/ /

/ y1 / /

/ /

// f i

1 y / /

/ /

/ /

/

/

/

/ /

/ /

/

i

/ '/-

/

/ /

/ it 7 1 ^ f

/ /

/

OS ' \ S '•

yf Ö '^

/ \ / /u ̂1

/l JLi ^ 1/ A 1 1

\ 1 >—15° F

//> / \A*^\ 1 1

10°F

1/ / > x—7 .5aF

r 10 15 20 25 30 35 40

Water Temperature Range (t - t ), °F "i «2

Fig. 8 Tower- characteristic versus Water Temperature Range for ^b = 75°F and L/G = 1.2

22

AEDC-TR-71-2131

1 7.0 twb ■ 75°F

UG - 1.4 /f

Approach ■ 5°F-^

_! *■[ s\ 6.0 -! J

1 1—

1 i-H 1

X . L

-1 •

/ O r L 31

Ha

5.0 A jj

7HS ■

> 2

ts 4.0 a> 1

1 I

"G ca

/ e •

^i i 1^. ̂ 1 I

o I

1 1

. .i a>

1 3.0 i

. S 1 l 1

y\ / /

r /

I I

A

i i

/" /

7 /

"7 / I ^0» l

l

2.0 l I 1

I 1

/fe /'I

ft

t 1

/ (5>l l vT

i-—'/-

\/1 ? /

1 1

/ / 1

i n bt> JM/ 1. u VI / AT

VJ P—

L/vv T ii J°F /^

^T7-5?"1

n lr\ 1 u

( ) E 10 15 20 25 30 35 40 Water Temperature Range {t^ - 1^), °F

Fig. 9 Tower Characteristic versus Water Temperature Range for twh =75°Fand L/G = 1.4

23

AEOC-TR-71-213

> es

o ■H ■P I» •H h © +• 0 es

es J3 U

h ©

O EH

a.a 1 80°F

L/G =1.0 j ippr oach = 5 °F —

/ "" * /

^/

9 ft ' I

/

\7

//

-**

/

7.5 °F-^ 0 / «0/

r 7/

/

/( /A / / /

/ /

/I xw / /

/ 7 /

1 ft J w vvi /

'</

1 /

V^'Jrt t^ • .... Y/

•

/ SiW,' ̂ •

■ \—10DI ■

/ X ^>

15°] '

0 ^

^x-

5 10 15 20

Water Temperature Range (t

25

- t

30

), °F

Fig. 10 Tower Characteristic versus Water Temperature Range for ^b = 80°F and L/G = 1.0

35

24

AEDC-TR-71-213

ü •H

u <o

■p u

X! O

O

1 1 1

*wb

1 = 80 °F

i 3.0

L/G = 1. 2

I ft,

App roac b - 5°F- •

/ ft,/

/ /

/

>/■

2/ <-Y#

"'/ /

•/ 1

«o/

/ /" / a *

/ / / /

2 0 7.5° F-v //

/

/ -""V

V / if/ /

/

/ i

//

Ui-

< k\ / /

/ /

i /

IS 1 /

/ / ^X

1 0 / /l

[7 /

\ / VI

' VW V ^ ■io°: ?

M/j vZ*** k L5°F

0 10 15 20 25

Water Temperature Range (t - t" ) ,

30

°F

Fig. 11 Tower Characteristic versus Water Temperature Range for twb = 80°F and L/G = 1.2

35

25

AEDC-TR-71-213

4.0

£ 3.0 «

■p CD •H U CO -P CJ

U 03

u 2.0

1.0

t . 1

■= 80 °F

L/G = 1. 4 X 1 |

i

/ 1

f / i

/ /

A pprc ach = 5° F7 i

/ /_ &

/ 1

i

/ -/-

/

0 O

i~l

II

— «i

/

/ /

'J-1

/ i 1 / /

o /

/

< /

1—'■ /

/ A.' \^y>

/

t 0

«0 ©

/ *Y ly* / /

/ /

/ /

' 1 /

/ /

/

0 Q

S l

i

/ /

L /

/.

1

^7 i**

S/ /

/ » Si

Al / /

/

^N/ / / -K • is9: P

'yn7 z ̂ \ in0 P

r/ÄJ^ >-7.5°F 1 1

10 15 20 25 30 35

Water Temperature Range (t - t ), °

Fig. 12 Tower Characteristic versus Water Temperature Range fortwb =80°Fand L/G = 1.4

26

AEDC-TR-71-213

2.0 -

ü •H

■H U at

+J u oj

SS Ä u u

o

1.0

1 1 i5°F

ippr ^

0

L/( ■i i B ■ L.O oach = 5 wj?'—>

#

'

7.5°

/, /

F~\ <:

^"7 / /

\Jt

S? "V~ ^

/ XJtv » \

■

/ ><fe Z^\ ̂15

\ -10' *F

i^ F

10 15 20 25 30

Water Temperature Range (t - t ), °F

Fig. 13 Tower Characteristic versus Water Temperature Range for tvvt = 85°F and L/G = 1.0

27

AEDC-TR-71-213

> a

•H ■p to •H U i>

Ü a u a .c v u Q)

O

*wb = 8f

| |

Approach - 5 °F\ A.

9 o

L/G »= 1. 2

/

/• P /ey

M /

/ „ Si

f 7/

/ /

7. 5°F- /

>

V ^7 A**^^

i n r^- /

""V /

<? * i

/

^-10° F

/ \S^

o' c ̂

n 1 1 > I 5 i 0 1 5 2 0 2 '5 30

Water Temperature Range (t Wi *W2

) '

Fig. 14 Tower Characteristic versus Water Temperature Range for twb = 85°F and L/G = 1.2

28

AEDCTR-71-213

3.0

> es

CJ •H

m •H h <D

U cd

OS

O

<D i* O

2.0

1.0

0

t wb 85° F J L /G = 1.4

Approach = 5°F

/

a/ —

/-

/

-7 s »IT—i

7/ 1

I

"/ t

1^ /

^ .1 / ^ ̂ 7 ^"7 V /

/

/ X22J /

/x/ >T -ioe F

^^ ̂ ^15°F

1 1 5 10 15 20

Water Temperature Range (t Wi

25

- t ), w2

Fig. 15 Tower Characteristic versus Water Temperature Range for t«,, = 85°F and L/G = 1.4

30

29

AEDC-TR-71-213

4.0

3.0

>

o •H

to •H *H (1)

+J Ü a u a

■cj u

o

2.0

1.0

/ 1/ /

L/G - 1.0 -\ /I/ /

^7 /

/

/

- / / \— L/G =1.4

1 1

A z 1 ' ^— L/G =1.2

y //

y A/

10 20 30 40 50 60

Effective Height (Z) , ft

Fig. 16 Tower Characteristic versus Effective Height

30

AEDC-TR-71-213

110

h 105

H et S loo O h s

■p et 0

(D

es si ü

90

85

80

75

*wb = 75 °F

y[}/ L/G -1.4-

y /\A\

/ A AX. /x \ ' ]

L/G = 1. 0

y £-A /

- u/u — X.

y y s f ̂ r J

/? f

—2©

10 15 20 25 30 35 40

Water Temperature Range (t - t ), °F

Fig. 17 Discharge Air Temperature versus Water Temperature Range for twb = 75° F

31

AEDC-TR-71-213

a h 3

h 0» P.

0 he u et JS ej m

115

110

105

100

95

90

85

80

twb - 80-F

• y^\J^ . » - - - - - - ■ - .•- ^T-J<T. Lx

S^ 'T.

L/G =1.4 —. \y

" /

/^x — L/G ' ' 1.0

/ / Z' \

\_ 1 1

L/G =1.2

/* 71/

yy^*

—A rf 1 10 15 20 25

Water Temperature Range (t Wl

30

- V- 35 40

Fig. 18 Discharge Air Temperature versus Water Temperature Range for t^ = 80°F

32

AEDC-TR-71-213

115

110

e g 105 +> tt u «

§ 100

IS

u m

■H Q

95

90

85

*wb - 8£ >'F yr V

i -

» - i -

"**

L /G = • i.< \ —y 'Ccf \>

/ > y S\ . >^ S

1

/

\/T

v— T ,/G • = 1.1 1

/ y y \/r — i ,/G = 1.2

jy/ /^

5 10 15 20 25 30 35

Water Temperature Range (t - t ), CF

Fig. 19 Discharge Air Temperature versus Water Temperature Range for tWb s 85° F

40

33

UNCLASSIFIED Security Classification

DOCUMENT CONTROL DATA -R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report la ctassllled)

1. ORIGIN* TINO ACTIVITY (Corporate author)

Arnold Engineering Development Center, Arnold Air Force Station, Tennessee 37389

2a. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED 2b. CROUP

N/A 3. REPORT TITLE

PRELIMINARY DESIGN OF A MECHANICAL-DRAFT COUNTERFLOW COOLING TOWER

4 DESCRIPTIVE NOTES (Type ol report and Inclusive datee)

Final Report 8. AUTHORIS) (First name, middle Initial, laat name)

R. L. Clouse, ARO, Inc.

6- REPORT DATE

October 1971 7a. TOTAL NO. OF PAGES

41 7b. NO. OF REF3

Sa. CONTRACT OR GRANT NO F40600-72-C-0003

b. PROJECT NO.

Program Element 64719F

«a. ORIGINATOR'S REPORT NUMBERISJ

AEDC-TR-71-213

9b. OTHER REPORT NOIS) (Any other numbers that may be a»signed this report)

ARO-ETF-TR-71-162 10 DISTRIBUTION STATEMENT

Approved for public release; distribution unlimited.

II. SUPPLEMENTARY NOTES

Available in DDC

12. SPONSORING MILITARY ACTIVITY

Arnold Engineering Development Center, Air Force Systems Command, Arnold Air Force Station, Tennessee

13. ABSTRACT

The need for a method whereby the preliminary design of a cooling tower can more easily be specified has existed for many years. The numerical techniques commonly used to solve the Merkel cooling tower equation are not adaptable to a direct general solution. This report presents a direct solution to the Merkel equation which, when combined with certain detailed experimental data by others, yields a relatively quick and straightforward method of estabilishing the preliminary design of a mechanical-draft counterflow cooling tower. Special attention is devoted to cooling tower application relative to high altitude engine test facilities.

DD ,FN°ORV\.1473 UNCLASSIFIED Security Classification

UNCLASSIFIED Security Classification

KEY WORDS ROLE WT

LINK C

HOLE ROLE

test facilities

t, cooling towers design

mathematical analysis

experimental data

£ c^u^iy^^^ J

£-£<4t^o

UNCLASSIFIED Security Classification