33
The Basics of AIR-COOLED HEAT EXCHANGERS HUDSON Products Corporation A Subsidiary of Hudson Products Holdings, Inc. www.hudsonproducts.com
The Basics ofAIR-COOLED HEAT EXCHANGERS
HUDSONProducts Corporation
A Subsidiary of Hudson Products Holdings, Inc.
www.hudsonproducts.com
CONTENTS
Page
FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii
I. DESCRIPTION OF AIR-COOLED HEAT EXCHANGERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Tube Bundle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
Axial Flow Fans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Plenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Mechanical Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Comparison of Induced and Forced Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Induced Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
Forced Draft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
II. THERMAL DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
Typical Heat Transfer – Case I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13
Application of Design Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Sample Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
Fan Selection – Horsepower Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
III. PERFORMANCE CONTROL OF ACHEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .21
Varying Air Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Extreme Case Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Internal Recirculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
External Recirculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Co-current Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
Auxiliary Heating Coils – Steam or Glycol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
IV. NOISE CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
V. DESIGN OF ACHEs FOR VISCOUS LIQUIDS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
VI. COST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
TABLESPage
1. Guide to First Estimates of Bundle Rows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
2. Typical Heat Transfer Coefficients for Air-Cooled Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . .19
FIGURESPage
1. Typical Components of an Air-Cooled Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
2. Typical Construction of Tube Bundles with Plug and Cover Plate Headers . . . . . . . . . . . . . . . . . . . . . .3
3. Fin Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
4. Header Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
5. Axial Flow Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
6. Mechanical Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
7. Comparison of Induced and Forced Draft Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
8. Thermal Optimization Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
9. MTD Correction Factors, One Pass – Cross Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
10. MTD Correction Factors, Two Pass – Cross Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
11. MTD Correction Factors, Three Pass – Cross Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
12. Air Cooler Sizing Chart – One Pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
13. Air Cooler Sizing Chart – Two Pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
14. Air Cooler Sizing Chart – Three Pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
15. Air Cooler Sizing Chart – Four Pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .18
16. Unit Weight and Surface per Unit Fan HP as a Function of Bundle Depth . . . . . . . . . . . . . . . . . . . . .22
17. Air Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
18. Unit Price as a Function of Total Surface and Bundle Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
i
FOREWARDThis brochure is designed to familiarize user with the types, components, and featuresof Air-Cooled Heat Exchangers (ACHEs) by means of simplified explanations andprocedures. It discusses the advantages and disadvantages of each type of helpdesigners become more discriminating, competent, and confident as users of thisequipment.
The brochure also provides a method of estimating ACHE size, weight, price andpower consumption in the planning stage, but is not intended to provide informationsufficient for detailed and final design. If specific assistance is needed, please contactHudson Products Corporation at (281) 275-8100.
NOMENCLATUREEnglish Letter Symbols
a = heat transfer surface area per unit length of tube ft2/ftA = total exchanger bare tube heat transfer surface ft2
Aw = average wall thickness inBWG = Birmingham wire gaugecp = specific heat Btu/(lb•°F)Cair = Ccold = Q / ∆t = Q / (t2-t1) = air-side heat capacity rate Btu/(hr•°F)
= 1.08 • FV • L • WCtube = Chot = Q / ∆T = Q / (T1-T2) = tube-side heat capacity rate Btu/( hr•°F)
= McpCmin = minimum heat capacity rate Btu/( hr•°F)Cmax = maximum heat capacity rate Btu/( hr•°F)CMTD = corrected mean temperature difference °F
= F • LMTDE = exchanger thermal effectives Dimensionless
= Chot • (T1-T2)Cmin • (T1-t1)
= Ccold • (t2-t1)Cmin • (T1-t1)
F = MTD correction factor Dimensionlessf = Fanning friction factor Dimensionless
ii
FA = face area ft2
FV = standard air face velocity std ft/minG = mass velocity lb/(sec•ft2)h = individual heat transfer coefficient Btu/( hr•ft2•°F)ID = inside diameter of tube ftK = thermal conductivity Btu/( hr•ft•°F)k = parameter, NTU or NTU • R Dimensionless
= n • N • a1.08 • FV • (I / U)
L = tube length ftLE = calmed length ftLMTD = log mean temperature difference °FM = mass flow rate lb/hrmw = minimum wall thickness inn = tubes per row, per foot of exchanger width l/ft
N = rows of tubes in direction of air flow DimensionlessNRe = Reynolds Number DimensionlessNtu = number of heat transfer units DimensionlessOD = outside diameter of tube ftP = number of tube-side passes DimensionlessQ = total exchanger heat load (duty) Btu/hrr = individual heat transfer resistance (hr•ft2•°F)/BtuR = Cmin / Cmax = heat capacity rate ratio DimensionlessS = specific gravity Dimensionlesst = air temperature °FT = hot fluid temperature °FTavg = bulk average temperature °FU = overall heat transfer coefficient (rate) Btu/( hr•ft2•°F)
= 1(ri + rair + rf + rm)
W = width of exchanger ftZ = parameter, E or E • R Dimensionless
= T1 – T2T1 – t1
iii
Greek Letter Symbols
µ = viscosity centipoiseρ = density lb/ft3
Subscripts
air = air side max = maximumcold = cold fluid = air min = minimumf = tube-side fouling t = totalhot = hot fluid = tube-side fluid 1 = inleti = tube side 2 = outletm = tube metal
1
AIR COOLED HEAT EXCHANGERS
A proven means for cooling in the processand power industries
I. DESCRIPTION OF AIR-COOLEDHEAT EXCHANGERS
An ACHE is a device for rejecting heat from a fluiddirectly to ambient air. This is in contrast to rejectingheat to water and then rejecting it to air, as with ashell and tube heat exchanger and a wet coolingtower system.
The obvious advantage of an ACHE is that it does notrequire water, which means that plants requiring largecooling capacities need not be located near a supplyof cooling water.
An ACHE may be as small as an automobile radiatoror large enough to reject the heat of turbine exhauststeam condensation from a 1,200 MW power plant –which would require 42 modules, each 90 feet wideby 180 feet long and served by two 60-foot diameterfans driven by 500-horsepower motors.
Components
An ACHE consists of the following components:
(See Figure 1):
· One or more bundles of heat transfer surface.
· An air-moving device, such as a fan, blower,or stack.
· Unless it is natural draft, a driver and powertransmission to mechanically rotate the fan orblower.
· A plenum between the bundle or bundles and theair-moving device.
· A support structure high enough to allow air toenter beneath the ACHE at a reasonable rate.
· Optional header and fan maintenance walkwayswith ladders to grade.
· Optional louvers for process outlet temperaturecontrol.
· Optional recirculation ducts and chambers forprotection against freezing or solidification of highpour point fluids in cold weather.
· Optional variable pitch fan hub for temperaturecontrol and power savings.
Tube Bundle
A tube bundle is an assembly of tubes, headers, sideframes, and tube supports as shown in Figure 2.Usually the tube surface exposed to the passage of airhas extended surface in the form of fins tocompensate for the low heat transfer rate of air atatmospheric pressure and at a low enough velocity forreasonable fan power consumption.
The prime tube is usually round and of any metalsuitable for the process, due consideration being givento corrosion, pressure, and temperature limitations.Fins are helical or plate type, and are usually ofaluminum for reasons of good thermal conductivityand economy of fabrication. Steel fins are used forvery high temperature applications.
2
1. Fan2. Fan Ring3. Plenum
4. Nozzle5. Header6. Tube Bundle
INDUCED DRAFT
FORCED DRAFT
7. Drive Assembly8. Column Support9. Inlet Bell
1
2
9
3
4
5
4
6
7
8
6
4
5
4
3
1
2
9
7
8
Typical Components of an Air-Cooled Heat ExchangerHudson Products Corporation
Sugar Land, Texas, USAFigure 1
3
16
16
3
9
3
1
2
8
6
4
10
5 13 14
15
711
12
16
3
9
3
1
18
17
64
10
13 14
15
18
17
11
12
1. Tube Sheet2. Plug Sheet3. Top and Bottom Plates4. End Plate5. Tube6. Pass Partition7. Stiffener8. Plug9. Nozzle
10. Side Frame11. Tube Spacer12. Tube Support Cross-member13. Tube Keeper14. Vent15. Drain16. Instrument Connection17. Cover Plate18. Gasket
PLUG HEADER
COVER PLATE HEADER
Typical Construction of Tube Bundles with Plug and Cover Plate HeadersHudson Products Corporation
Sugar Land, Texas, USAFigure 2
4
Fins are attached to the tubes in a number of ways:
1) by an extrusion process in which the fins areextruded from the wall of an aluminum tubethat is integrally bonded to the base tube forthe full length.
2) by helically wrapping a strip of aluminum toembed it in a pre-cut helical groove and thenpeening back the edges of the groove againstthe base of the fin to tightly secure it, or
3) by wrapping on an aluminum strip that is footedat the base as it is wrapped on the tube. Figure3 shows a cutaway view of these finned tubes.
Figure 3
Sometimes serrations are cut in the fins. This causes aninterruption of the air boundary layer, which increasesturbulence which in turn increases the air-side heattransfer coefficient with a modest increase in the air-side pressure drop and the fan horsepower.
The choice of fin types is critical. This choice isinfluenced by cost, operating temperatures, and theatmospheric conditions. Each type has different heattransfer and pressure drop characteristics. The extrudedfinned tube affords the best protection of the liner tubefrom atmospheric corrosion as well as consistent heattransfer from the initial installation and throughout thelife of the cooler. This is the preferred tube foroperating temperatures up to 600°F. The embedded fin
also affords a continued predictable heat transfer andshould be used for all coolers operating above 600°Fand below 750°F. The wrap-on footed fin tube can beused below 250°F; however, the bond between the finand the tube will loosen in time and the heat transfer isnot predictable with certainty over the life of thecooler. It is advisable to derate the effectiveness of thewrap-on tube to allow for this probability.
There are many configurations of finned tubes, butmanufacturers find it economically practical to limitproduction to a few standard designs. Tubes aremanufactured in lengths from 6 to 60 feet and indiameters ranging from 5/8 inch to 6 inches, the mostcommon being 1 inch. Fins are commonly helical,7 to 11 fins per inch, 5/16 to 1 inch high, and 0.010to 0.035 inch thick. The ratio of extended to primesurface varies from 7:1 to 25:1. Bundles arerectangular and typically consist of 2 to 10 rows offinned tubes arranged on triangular pitch. Bundles maybe stacked in depths of up to 30 rows to suit unusualservices. The tube pitch is usually between 2 and 2.5tube diameters. Net free area for air flow throughbundles is about 50% of face area. Tubes are rolled orwelded into the tube sheets of a pair of box headers.
The box header consist of tube sheet, top, bottom, andend plates, and a cover plate that may be welded orbolted on. If the cover is welded on, holes must bedrilled and threaded opposite each tube formaintenance of the tubes. A plug is screwed into eachhole, and the cover is called the plug sheet. Boltedremovable cover plates are used for improved accessto headers in severe fouling services. Partitions arewelded in the headers to establish the tube-side flowpattern, which generates suitable velocities in as nearcountercurrent flow as possible for maximum meantemperature difference. Partitions and stiffeners(partitions with flow openings) also act as structuralstays. Horizontally split headers may be required toaccommodate differential tube expansion in serviceshaving high fluid temperature differences per pass.Figure 4 illustrates common heat types.
5
Figure 4
Bundles are usually arranged horizontally with the airentering below and discharging vertically.Occasionally bundles are arranged vertically with theair passing across horizontally, such as in a naturaldraft tower where the bundles are arranged verticallyat the periphery of the tower base. Bundles can also bearranged in an “A” or “V” configuration, the principleadvantage of this being a saving of plot area. Thedisadvantages are higher horsepower requirements fora given capacity and decreased performance whenwinds on exposed sides inhibit air flow.
With practical limits, the longer the tubes and thegreater the number of rows, the less the heat transfersurface costs per square foot. One or more bundles ofthe same or differing service may be combined in oneunit (bay) with one set of fans. All bundles combinedin a single unit will have the same air-side staticpressure loss. Consequently, combined bundleshaving different numbers of rows must be designed fordifferent velocities.
Figure 5
Axial Flow Fans
Figure 5 displays the air moving device for an ACHEwhich is commonly an axial flow, propeller type fanthat either forces the air across the bundles (forceddraft) or pulls it across (induced draft). To provideredundancy in case a mechanical unit fails and toprovide the basic control achievable by running onefan or two, a bundle or set of bundles is usuallyprovided with two fans.
Even distribution of the air across the tube bundle iscritical for predictable, uniform heat transfer. This isachieved by adequate fan coverage and static pressureloss across the bundle. Good practice is to keep thefan projected area to a minimum of 40% of theprojected face area of the tube bundle and the bundlestatic pressure loss at least 3.5 times the velocitypressure loss through the fan ring. For a two fan unitthis is generally assured if the ratio of tube length tobundle width is in the range of 3 to 3.5 and thenumber of tube rows is held to 4 rows minimum withthe net free area for air flow at about 50% of the facearea of the bundle.
Fans can very in size from 3 to 60 feet in diameter andcan have from 2 to 20 blades. Blades can be made ofwood, steel, aluminum, or fiberglass-reinforcedplastic, and can be solid or hollow. Blades can have
6
straight sides or be contoured. The more efficient typehas a wide chord near the center and tapers to anarrow chord at the tip, with a slight twist. The twistand taper compensate for the slower velocity of theblade nearer the center to produce a uniform, efficientair velocity profile.
Fans may have fixed or adjustable pitch blades. Exceptfor small diameters (less than 5 feet), most ACHEshave adjustable pitch blades. Adjustable pitch fans aremanufactured in two types. One is manuallyadjustable (with the fans off) and the other isautomatically adjustable (while running). Mostautomatically adjustable pitch fans change their pitchby means of pneumatically actuated diaphragmworking against large springs inside the hub.
Plenum
The air plenum is an enclosure that provides for thesmooth flow of air between the fan and bundle.Plenums can be box type or slopesided type. Theslopesided type gives the best distribution of air overthe bundles, but is almost exclusively used withinduced draft because hanging a machinery mountfrom a slopesided forced draft plenum presentsstructural difficulties.
Mechanical Equipment
Fans may be driven by electric motors, steam turbines,gas or gasoline engines, or hydraulic motors. Theoverwhelming choice is the electric motor. Hydraulicmotors are sometimes used when power from anelectric utility is unavailable. Hydraulic motors alsoprovide variable speed control, but have lowefficiencies.
The most popular speed reducer is the high-torquepositive type belt drive, which uses sprockets thatmesh with the timing belt cogs. They are used withmotors up to 50 or 60 horsepower, and with fans upto about 18 feet in diameter. Banded V-belts are stilloften used in small to medium sized fans, and gear
drives are used with very large motors and fandiameters. Fan speed is set by using a propercombination of sprocket or sheave sizes with timingbelts or V-belts, and by selecting a proper reductionratio with gears. Fan tip speed should not be above12,000 feet per minute for mechanical reasons, andmay be reduced to obtain lower noise levels. Motorand fan speed is sometimes controlled with variablefrequency drives. Figure 6 provides a breakdown ofthe mechanical equipment.
Figure 6
Structure
The structure consists of columns, braces, and crossbeams that support the exchanger at a sufficientelevation above grade to allow the necessary volumeof air to enter below at an approach velocity lowenough to allow unimpeded fan performance and toprevent unwanted recirculation of hot air. To conserveground space in oil refineries and chemical plants,ACHEs are usually mounted above, and supported by,pipe racks with other equipment occupying the spaceunderneath the pipe rack. ACHE structures aredesigned for appropriate wind, snow, seismic, piping,dead and live loads.
7
Comparison of Induced and Forced Draft Units
Figure 7
Induced Draft
Advantages:
1) Better distribution of air across the bundle.
2) Less possibility of hot effluent air recirculatinginto the intake. The hot air is discharged upwardat approximately 2.5 times the intake velocity,or about 1,500 feet per minute.
3) Better process control and stability because theplenum covers 60% of the bundle face area,reducing the effects of sun, rain, and hail.
4) Increased capacity in the fan-off or fan failurecondition, since the natural draft stack effect ismuch greater.
Disadvantages and Limitations:
1) Possibly higher horsepower requirements if theeffluent air is very hot.
2) Effluent air temperature should be limited to220°F to prevent damage to fan blades,bearings, or other mechanical equipment in thehot air stream. When the process inlettemperature exceeds 350°F, forced draft designshould be considered because high effluent air
temperatures may occur during fan-off or lowair flow operation.
3) Fans are less accessible for maintenance, andmaintenance may have to be done in the hot airgenerated by natural convection.
4) Plenums must be removed to replace bundles.
Forced Draft
Advantages:
1) Possibly lower horsepower requirements ifthe effluent air is very hot. (Horsepower variesinversely with the absolute temperature.)
2) Better accessibility of fans and upper bearingsfor maintenance.
3) Better accessibility of bundles for replacement.
Accommodates higher process inlet temperatures.
Disadvantages:
Less uniform distribution of air over the bundle.
Increased possibility of hot air recirculation, resultingfrom low discharge velocity from the bundles, highintake velocity to the fan ring, and no stack.
Low natural draft capability of fan failure.
Complete exposure of the finned tubes to sun, rain,and hail, which results in poor process control andstability.
In most cases, the advantages of induced draft designoutweigh the disadvantages.
8
II. THERMAL DESIGN
Figure 8
There are more parameters to be considered in thethermal design of ACHEs than for shell and tubeexchangers (see Figure 8). ACHEs are subject to widevariety of constantly changing climatic conditionswhich pose problems of control not encountered withshell and tube exchangers. Designers must achievean economic balance between the cost of electricalpower for the fans and the initial capital expenditurefor the equipment. A decision must be made as towhat ambient air temperature should be used fordesign. Air flow rate and exhaust temperature isinitially unknown and can be varied in the designstage by varying the number of tube rows and thusvarying the face area.
Because the number of tube rows, the face area, theair face velocity, and the geometry of the surface canall be varied, it is possible to generate many solutionsto a given thermal problem. However, there isobviously an optimum solution in terms of capital andoperating costs.
The basic heat transfer relationships that apply toshell and tube exchangers also apply to ACHEs.The fundamental relation is the Fourier equation:
Q = U • A • (T – t)mean
Where
(T – t)mean = CMTD = LMTD • F
F is a factor that corrects the log mean temperaturedifference for any deviation from true counter-currentflow. In ACHEs, the air flows substantially unmixedupward across the bundles and the process fluid canflow back and forth and downward as directed by thepass arrangement. With four or more downwardpasses, the flow is considered counter-current; and, sothe factor “F” is 1.0. The correction factors for one,two, and three passes, given by Figures 9 – 11, werecalculated from the effectiveness values developed byStevens, Fernandez, and Wolf1 for the appropriatecounter-cross flow arrays.
As is apparent, initially neither the area nor the overallheat transfer rate nor the effluent air temperatures areknown. The traditional approach in the design ofACHEs entailed an iterative trial and error procedureboth on the CMTD and the transfer rate until the areasatisfied both. Specifically, an air rise was assumed,the CMTD was calculated, an overall heat transfercoefficient was assumed, and an exchanger size wasselected with the expected necessary area. Anappropriate face velocity was then used to calculatean effluent air temperature, and the process wasrepeated until the assumed effluent air temperaturematched the calculated value. The individualcoefficients and the overall coefficient were thencalculated, and the whole process was repeated untilthe calculated “U” and CMTD were sufficiently closeto the assumed values.
• F(T1 – t2) –(T2 – t1)
1n[ ](T1 – t2)
(T2 – t1)
9
However, there is another method that eliminates trialand error on the CMTD and leaves only the trial anderror on the tube-side film coefficient. The followingdiscussion presents the Ntu Method described by Kaysand London in Compact Heat Exchangers2, as appliedto ACHES.
The following are definitions based on Compact HeatExchangers:
1.Hot fluid heat capacity rate = Ch = Ctube
= (Mcp)tube =
2. Cold fluid heat capacity rate = Cc = Cair
= (Mcp)air =
3. Number of heat transfer units = Ntu =
4. Heat capacity rate ratio = R =
5. ACHE heat transfer effectiveness = E
E = =
See pages i – iii for additional definitions andnomenclature.
We define air flow in terms of standard cubic feet perminute (scfm) as the product of the effective width andlength of the exchanger in feet, and the face velocity(FV) in standard feet per minute (sfm). For any ACHEservice, it will not necessarily be apparent at thedesign stage whether the air or the hot tube-side fluidwill have the minimum heat capacity rate, since themass flow rate of the air is unknown. The two casespresented below will cover both design situations.
Cc (t2 – t1)
Cmin (T1 – t1)
Ch (T1 – T2)
Cmin (T1 – t1)
Cmin
Cmax
A•U
Cmin
Q
t2 – t1
Q
T1 – T2
10
INLE
T
0.1
.2.3
.4.5
.6.7
.8.9
1.0
TYPI
CAL
TUBE
LAYO
UTS
NO
MEN
CLAT
URE
:
T 1=
INLE
TTE
MPE
RATU
RETU
BESI
DE
T 2=
OU
TLET
TEM
PERA
TURE
TUBE
SID
E
t 1=
INLE
TTE
MPE
RATU
REA
IRSI
DE
t 2=
OU
TLET
TEM
PERA
TURE
AIR
SID
E
MTD
CORR
ECTI
ON
FACT
ORS
1PA
SS-C
ROSS
FLO
WBO
THFL
UID
SU
NM
IXED
T 1–
T 2
t 2–
t 1
R=
CORRECTIONFACTORF
CORRECTIONFACTORF
OU
TLET
INLE
T
OU
TLET
1.0 .9 .8 .7 .6 .5
1.0
.9 .8 .7 .6
t 2–
t 1
T 1–
t 1
r=r
R8.
06.
05.
04.
03.
02.
5
1.2
1.0
0.8
0.6
0.4
0.2
2.0
1.5
1.75
MTD
CorrectionFactors/1Pass-Cross
Flow
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure9
11
INLE
T
0.1
.2.3
.4.5
.6.7
.8.9
1.0
TYPI
CAL
TUBE
LAYO
UTS
NO
MEN
CLAT
URE
:
T 1=
INLE
TTE
MPE
RATU
RETU
BESI
DE
T 2=
OU
TLET
TEM
PERA
TURE
TUBE
SID
E
t 1=
INLE
TTE
MPE
RATU
REA
IRSI
DE
t 2=
OU
TLET
TEM
PERA
TURE
AIR
SID
E
MTD
CORR
ECTI
ON
FACT
ORS
2PA
SS-C
OU
NTE
RCR
OSS
FLO
WBO
THFL
UID
SU
NM
IXED
T 1–
T 2
t 2–
t 1
R=
CORRECTIONFACTORF
CORRECTIONFACTORF
OU
TLET
INLE
T
OU
TLET
1.0 .9 .8 .7 .6 .5
1.0
.9 .8 .7 .6
t 2–
t 1
T 1–
t 1
r=r
107
54
3
21.
5
2.5
1.75
1.25
1.0
0.8
0.6
0.4
0.2
MTD
CorrectionFactors/2Pass-Cross
Flow
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure10
12
INLE
T
0.1
.2.3
.4.5
.6.7
.8.9
1.0
TYPI
CAL
TUBE
LAYO
UTS
NO
MEN
CLAT
URE
:
T 1=
INLE
TTE
MPE
RATU
RETU
BESI
DE
T 2=
OU
TLET
TEM
PERA
TURE
TUBE
SID
E
t 1=
INLE
TTE
MPE
RATU
REA
IRSI
DE
t 2=
OU
TLET
TEM
PERA
TURE
AIR
SID
E
MTD
CORR
ECTI
ON
FACT
ORS
3PA
SS-C
OU
NTE
RCR
OSS
FLO
WBO
THFL
UID
SU
NM
IXED
T 1–
T 2
t 2–
t 1
R=
CORRECTIONFACTORF
CORRECTIONFACTORF
OU
TLET
INLE
T
OU
TLET
1.0 .9 .8 .7 .6 .5
1.0
.9 .8 .7 .6
t 2–
t 1
T 1–
t 1
r=r
107
R5
43
2
1.5
2.5
1.75
1.25
1.0
0.8
0.6
0.4
0.2
MTD
CorrectionFactors/3Pass-Cross
Flow
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure11
13
CASE I. Cmin = Cair = Ccold
1. From Definition 4 above:
R = = =
=
=
Note: 1.08=0.075 lb/ft3 • 60 min/hr· 0.24 Btu/(lb • °F)
2. From Definition 5 above and by
substitution for :
E =
=
Multiplying Equation 1 by Equation 2:
3. ER =
•
=
If we let = Z, then
Z = E • R for Case I
From Definition 3 above:
Ntu= = =
=
Let k =
k = Ntu for Case 1
We can plot the expression for Case I with E • R andNtu as coordinates and R as the parameter. Knowingthat Z = E • R and that k = Ntu, we can find R on theplot.
From Equation 1, Case I:
R =
W =
t2 = + t1(T1 – T2)
R
Q • R
1.08 • FV • L • (T1–T2)
Q
FV • L • W • 1.08 • (T1–t1) FV • L • W • 1.08 • (T1–T2)
Q
Ch (T1–T2)
Cmin (T1–t1)
n • N • a
1.08 • FV • (ri + rair + rf + rm)
n • N • a
1.08 • FV • (ri + rair + rf + rm)
n • N • a • W • L • U
1.08 • W • L • FV
A•U
Cair
A•U
Cmin
T1 – T2
T1 – t1
T1 – T2
T1 – t1
Q
FV • L • W • 1.08 • (T1–t1)
FV • L • W • 1.08 • (T1–T2)
Q
Chot
Cair
FV • L • W • 1.08 • (T1–T2)
Q
FV • L • W • 1.08
[ ]Q
(T1 – T2)
scfm • 1.08
[ ]Q
(T1 – T2)
Cair
Chot
Cmin
Cmax
14
CASE II. Cmin = Ctube = Chot
From Definition 5 above:
E = = = Z
From Definition 4 above:
R = =
=
Ntu =
R • Ntu =
k = R • Ntu for Case II
CASE I or II. Selection Criteria
We can plot the expression with E and R • Ntu ascoordinates and R as the parameter on the same graphas Case I, with R = 1 common to both plots.
For values of R above the line R = 1:
W =
and t2 = R • (T1 – T2) + t1
For values of R below the line R = 1:
W =
and t2 = + t1
It can be shown that E, Ntu, and R can be related forany flow arrangement. For counter-current flow, theexpression is:
E =
Figures 12-15 show plots relating these variables forthe following cases:
1. Cross flow with both fluids unmixed (one-passACHE, Figure 12).
2. Two-pass counter cross flow with bothfluids unmixed in each pass but with the hotfluid mixed between passes (two-pass ACHE,Figure 13).
3. Three-pass counter cross flow with both fluidsunmixed in each pass but with the hot fluidmixed between passes (three-pass ACHE,figure 14).
4. Counter flow (ACHE with four or more passes,Figure 15).
The case of the isothermal exchanger is much simpler.As R goes to zero, the equation for effectivenessreduces to:
E = 1 – e–Ntu
And Ntu is as in Case I for Cmin = Cair:
Ntu =
E = =
W =Q
L • W • FV • 1.08 • (T1–t1)
Q
Qmax
Q
1.08 • (T1–t1) • FV • L • E
n • N • a
1.08 • FV • (ri + rair + rf + rm)
1 – e–Ntu • (1–R)
1 – R • e–Ntu • (1–R)
T1 – T2
R
Q • R
1.08 • (T1–T2) FV • L
Q
1.08 • R• (T1–T2) • FV • L
n • N • a • W • L
•(ri + rair + rf + rm)[ ]Q
(T1 – T2)
n • N • a
1.08 • FV • (ri + rair + rf + rm)
Q
FV • L • W • 1.08 • (T1–T2)
Chot
Cair
Cmin
Cmax
T1 – T2
T1 – t1
Ch (T1 – T2)
Cmin (T1 – t1)
15
.2.4
.6.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
1.00 .9
5
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
.15
.10
.05 0
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
M•c
p
1.08
•FV
•RFA
=
FOR
RA
BOV
ER
=1.
0
Q
(T1
–T 2)1
.08
•FV
•R=
t 2=
R(T
1–
T 2)+t 1
T1–T2
T1–t1
Z=E=
T1–T2
T1–t1
Z=E•R=
R•M
•cp
1.08
•FV
FA=
FOR
RBE
LOW
R=
1.0
R•Q
(T1
–T 2)1
.08
•FV
=
t 2=
+t 1
(T1
–T 2)
R
ON
E(1
)PA
SS
R=0.1R=0.2 R=0.3 R=0.4 R
=0.5 R
=0.6 R
=0.
7
R=
0.8
R=
0.9
R=
1.0
R=
0.9
R=
0.8
R=
0.7
R=
0.6
R=
0.5
R=
0.4
R=
0.3 R=
0.2
R=
0.1
R=
0
AirCoo
lerSizing
Cha
rt/1Pass
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure12
16
.2.4
.6.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
1.00 .9
5
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
.15
.10
.05 0
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
M•c
p
1.08
•FV
•RFA
=
FOR
RA
BOV
ER
=1.
0
Q
(T1
–T 2)1
.08
•FV
•R=
t 2=
R(T
1–
T 2)+t 1
T1–T2
T1–t1
Z=E=
T1–T2
T1–t1
Z=E•R=
R•M
•cp
1.08
•FV
FA=
FOR
RBE
LOW
R=
1.0
R•Q
(T1
–T 2)1
.08
•FV
=
t 2=
+t 1
(T1
–T 2)
R
TWO
(2)P
ASS
ES
R=0.1R=0.2
R=0.3 R=0.4 R=0.5 R=0.6 R=
0.7 R=
0.8 R=
0.9
R=
1.0
R=
0.9
R=
0.8
R=
0.7
R=
0.6
R=
0.5
R=
0.4
R=
0.3
R=
0.2
R=
0.1
R=
0
AirCoo
lerSizing
Cha
rt/2Pass
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure13
17
.2.4
.6.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
1.00 .9
5
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
.15
.10
.05 0
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
M•c
p
1.08
•FV
•RFA
=
FOR
RA
BOV
ER
=1.
0
Q
(T1
–T 2)1
.08
•FV
•R=
t 2=
R(T
1–
T 2)+t 1
T1–T2
T1–t1
Z=E=
T1–T2
T1–t1
Z=E•R=
R•M
•cp
1.08
•FV
FA=
FOR
RBE
LOW
R=
1.0
R•Q
(T1
–T 2)1
.08
•FV
=
t 2=
+t 1
(T1
–T 2)
R
THRE
E(3
)PA
SSES
R=0.1R=0.2
R=0.3R=0.4 R=0.5 R=0.6 R
=0.7 R
=0.8 R
=0.
9
R=
1.0
R=
0.9
R=
0.8
R=
0.7
R=
0.6
R=
0.5
R=
0.4
R=
0.3
R=
0.2
R=
0.1
R=
0
AirCoo
lerSizing
Cha
rt/3Pass
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure14
18
.2.4
.6.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
1.00 .9
5
.90
.85
.80
.75
.70
.65
.60
.55
.50
.45
.40
.35
.30
.25
.20
.15
.10
.05 0
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
n•N
•a•U
1.08
•FV
k=
Ntu
==
n•N
•a
1.08
•FV
(rai
r+
r i+
r f+
r m)
M•c
p
1.08
•FV
•RFA
=
FOR
RA
BOV
ER
=1.
0
Q
(T1
–T 2)1
.08
•FV
•R=
t 2=
R(T
1–
T 2)+t 1
T1–T2
T1–t1
Z=E=
T1–T2
T1–t1
Z=E•R=
R•M
•cp
1.08
•FV
FA=
FOR
RBE
LOW
R=
1.0
R•Q
(T1
–T 2)1
.08
•FV
=
t 2=
+t 1
(T1
–T 2)
R
FOU
R(4
)OR
MO
REPA
SSES
R=0.1R=0.2
R=0.3 R=0.4 R=0.5 R=0.6 R=
0.7 R=
0.8 R=
0.9
R=
1.0
R=
0.9
R=
0.8
R=
0.7
R=
0.6
R=
0.5
R=
0.4
R=
0.3
R=
0.2
R=
0.1
R=
0
AirCoo
lerSizing
Cha
rt/4Pass
HudsonProductsCorporation
•SugarLand,Texas,U
SAFigure15
19
Application of Design Method
For any ACHE service at the design stage, the giveninformation includes the process terminaltemperatures, the heat load, and the air ambienttemperature as well as desirable tube dimensions. TheNtu approach to design determines the optimumvalues for the face area of the bundle and the airsideoutlet temperature. Using this data, a cooler design isselected which must be checked rigorously, but theselection most likely will be close to the final bestdesign for a given service.
The value of Z can be calculated from the given data,and the overall heat transfer coefficient estimated fromvalues shown in Table 2. This allows the determinationof the number of tube rows and face velocitycorresponding to the value of Z • 100/U in Table 1.The value of k or Ntu is calculated and, using theassumed number of tube passes, R is read using theappropriate curve in Figures 12 through 15. This valueof R is applied in the appropriate equations to predictvalues of FA and the air outlet temperature. Thisdesign can be assumed to be accurate enough to beused for estimating purposes. An example of thisprocess is shown in the sample problem on thefollowing page.
This selection must be checked rigorously to createthe final design. This is done by application of heattransfer and pressure drop correlations that have beendeveloped empirically and confirmed byexperimentation and observation of air coolerperformance. Many of these correlations are generallyknown. Hudson Products applies criteria that havebeen developed over the past 40 years ofexperimentation and observation. The influence of thevarious parameters that affect both heat transfer andpressure drop are continually being updated byHudson Products to assure the application of the latesttechniques in the design of air-cooled heatexchangers.
TABLE 2
TYPICAL HEAT TRANSFER COEFFICIENTS FORAIR-COOLED HEAT EXCHANGERS
Condensing service U
Amine reactivator . . . . . . . . . . . . . . . . . . . . 100 – 120
Ammonia . . . . . . . . . . . . . . . . . . . . . . . . . . 105 – 125
Refrigerant 12 . . . . . . . . . . . . . . . . . . . . . . . . 75 – 90
Heavy naphtha . . . . . . . . . . . . . . . . . . . . . . . 70 – 90
Light gasoline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Light hydrocarbons . . . . . . . . . . . . . . . . . . . . 95 – 105
Light naphtha . . . . . . . . . . . . . . . . . . . . . . . . 80 – 100
Reactor effluent Platformers,Hydroformers, Rexformers . . . . . . . . . . . . . . 80 – 100
Steam (0 – 20 psig) . . . . . . . . . . . . . . . . . . . 135 – 200
Gas cooling service
Air or flue gas @ 50 psig(∆P = 1 psi) . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Air or flue gas @ 100 psig(∆P = 2 psi) . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Air or flue gas @ 100 psig(∆P = 5 psi) . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Ammonia reactor stream. . . . . . . . . . . . . . . . 90 – 110
Hydrocarbon gasses @ 15 – 50 psig(∆P = 1 psi) . . . . . . . . . . . . . . . . . . . . . . . . . . 30 – 40
Hydrocarbon gasses @ 50 – 250 psig(∆P = 3 psi) . . . . . . . . . . . . . . . . . . . . . . . . . . 50 – 60
Hydrocarbon gasses @ 250 – 1500 psig(∆P = 5 psi) . . . . . . . . . . . . . . . . . . . . . . . . . . 70 – 90
TABLE 1
Z •100
Rows FV (ft/min)0.4 4 6500.5 5 6000.7 6 5500.8 to 1.0 8 to 10 400 to 450
U
20
Liquid cooling service
Engine jacket water. . . . . . . . . . . . . . . . . . . 130 – 155
Fuel Oil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 – 30
Hydroformer andPlatformer liquids . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Light gas oil. . . . . . . . . . . . . . . . . . . . . . . . . . 70 – 90
Light hydrocarbons . . . . . . . . . . . . . . . . . . . . 90 – 120
Light naphtha . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Process Water . . . . . . . . . . . . . . . . . . . . . . . 120 – 145
Residuum . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 – 20
Tar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 – 10
Coefficients are based on outside bare tube surface for1-inch OD tubes with 10 plain extruded aluminumfins per inch, 5/8 inch high, 21.2:1 surface ratio.
Sample Problem
Cool 273,000 lb/hr of light hydrocarbon liquid from250°F to 150°F with 100°F ambient air, and withDPallowable = 5 psi, fouling = 0.001, elevation = sealevel, and properties at the average tube-sidetemperature of 200°F as follows:
cp = 0.55 Btu/lb • °F
ki = 0.055 Btu/(hr • ft • °F)
µ = 0.51 centipoise = 1.234 lb/ft • hr
The specified tube material is 0.085 inch MW (0.093inch AW) x 32 foot long carbon steel, and we select 1-inch OD tubes with 10 extruded fins per inch, 5/8inch high, with 2.5 inch transverse tube pitch.
We calculate Q = 273,000 • 0.55 • (250 – 150) =15,015,000 Btu/hr, and then use the Ntu Method toselect an exchanger size to try.
Z = • = 0.741
From Table 1, we see that proper number of tube rowsis 6, and that the face velocity should be about 550 sfm.From Table 2, the overall heat transfer coefficient shouldbe about 90 Btu/(hr • ft2 • °F). We can then calculate k:
n = Tubes per row, per foot of width
= = = 4.8
a = • OD = 0.2618
k =
= = 1.1424
We will assume three tube-side passes, and find theheat capacity ratio R from Figure 14 to be 0.70 andabove the R = 1.0 line, so the R term in FA is in thedenominator. We can then calculate the face area:
FA = = 360.8
Considering the given 32 foot long tubes,
Width = = 11.28 ft
The tube count = = 325
The width of the structural components including airseals adds about 6 inches, and we round the size upto the nearest standard size, namely 12 feet, with336 tubes.
11.28 ft • 12 in/ft • 6 rows
2.5 inch tube pitch
360.8
32
Q
FV • 1.08 • R • (T1–T2)
4.8 • 6 • 0.2618
1.08 • 550 • (1/90)
n • N • a
1.08 • FV • (1/U)
π
12
12
pitch
12
2.5
[ ]250 – 150
250 – 100
100
90
21
Fan Selection – Horsepower Requirements
The fan diameter must assure that the area occupiedby the fan is at least 40 percent of the bundle facearea. The fan diameter must be 6 inches less than thebundle width. Fan performance curves are used toselect the optimum number of blades and pitch angleas well as the horsepower.
To calculate the required horsepowerfor the fan driver:
Motor Shaft Horsepower =
Actual ft3/min (at fan) • Total Pressure Loss (inches water)
6356 • Fan (System) Efficiency • Speed Reducer Efficiency
The actual volume at the fan is calculated bymultiplying the standard volume of air (scfm) by thedensity of standard air (0.075 lb/ft3) divided by thedensity of the air at the fan. From this relationship, itcan be seen that the ratio of the fan horsepowerrequired for a forced draft unit to that required for aninduced draft unit is approximately equal to the ratioof the exit air density to the inlet air density, which is inturn equal to the ratio of absolute air temperatures (t1+ 460) / (t2 + 460). The total pressure difference acrossthe fan is equal to the sum of the velocity pressure forthe selected fan diameter, the static pressure lossthrough the bundle, (which is determined from theequipment manufacturer’s test data for a given fin typeand tube spacing), and other losses in the aerodynamicsystem. Fan diameters are selected to give good airdistribution and usually result in velocity pressures ofapproximately 0.1 inch of water.
The design of the fan, the air plenum chamber, andthe fan housing, (in particular fan tip clearance), canmaterially affect system efficiency, which is alwayslower than on fan curves based on idealized windtunnel tests. Industrial axial flow fans in properlydesigned ACHEs have fan (system) efficiencies ofapproximately 75%, based on total pressure. Poorlydesigned ACHEs may have system efficiencies as lowas 40%. Speed reducers usually have about 95%
mechanical efficiency. The value of driver outputhorsepower from the equation above must be dividedby the motor efficiency to determine input power.
For estimating purposes, refer to Figure 16 toapproximate the horsepower requirement. This chartplots bare tube surface divided by horsepower versustube bundle depth for the normal range of velocities.Applying the above criteria to our sample problem,we determine that we must use two 10-foot diameterfans to have 40% of the bundle face area. EnteringFigure 16, we find that for a 6-row bundle, thearea/horsepower is between 68 and 92 square feet ofbare tube surface. If we use an average value of 80,the horsepower requirement for each fan is(336 • .2618 • 32) / (2 • 80) = 17.5 horsepower atmaximum design ambient temperature. Powerconsumption must be calculated for the coldestexpected ambient temperature, since at a fixed fanblade angle, fan horsepower consumption is inverselyproportional to the absolute temperature. The powerrequired for this minimum ambient temperature willset the required motor size.
III. PERFORMANCE CONTROL OF ACHEs
In addition to the fact that the process flow rate,composition, and inlet temperature of the fluid mayvary from the design conditions, the ambient airtemperature varies throughout a 24-hour day and fromday to day. Since air coolers are designed formaximum conditions, some form of control isnecessary when overcooling of the process fluid isdetrimental, or when saving fan power is desired.Although control could be accomplished using by-passing of process fluid, this is rarely done, and theusual method is air flow control.
22
010
2030
4050
6070
8090
100
110
120
130
140
150
160
170
180
190
200
14 13 12 11 10 9 8 7 6 5 4 3 2 1
FOR
ESTI
MAT
ING
ON
LY–
NO
TFO
RD
ESIG
NA
/HO
RSEP
OW
ER
BUNDLEDEPTHINTUBEROWS
34
56
78
910
1112
6675
8088
9711
512
613
114
014
7
Dep
th,t
ube
row
s
Uni
twei
ght,
poun
dspe
rsq.
ft.F
ace
area
A=
BARE
TUBE
SURF
ACE,
SQ.F
T.
}}
UnitW
eigh
tAnd
SurfacePe
rUnitFanHorsepo
wer
AsAFu
nction
OfB
undleDep
thHudsonProductsCorporation
•SugarLand,Texas,U
SAFigure16
23
Varying Air Flow
Varying air flow can be accomplished by:(See Figure 17)
1. Adjustable louvers on top of bundles.
2. Two-speed fan motors.
3. Fan shut-off in sequence for multifan units.
4. AUTO-VARIABLE® fans.
5. Variable frequency for fan motor control.
Louvers operate by creating an adjustable restrictionto air flow and therefore do not save energy when airflow is reduced. In fact, louvers impose a permanentenergy loss, even in the open position.
Two-speed motors, AUTO-VARIABLE fans, andvariable frequency fan motor control do save powerwhen air flow is reduced. In temperate climates, asmuch as 67% of the design power may be saved overthe course of a year with AUTO-VARIABLE pitch fans.AUTO-VARIABLE hubs will thus pay back theiradditional cost in about one year or less.
Figure 17
Both louvers and AUTO-VARIABLE fans may beoperated automatically through an instrument thatsenses temperature or pressure in the outlet header.For extreme cases of temperature control, such asprevention of freezing in cold climates in winter, orprevention of solidification of high pour-point or highmelting point materials, more sophisticated designsare available.
Extreme Case Controls
Extreme case controls include:
1. Internal RecirculationBy using one fixed-pitch fan blowing upward andone AUTO-VARIABLE pitch fan, which is capableof negative pitch and thus of blowing airdownward, it is possible to temper the air to thecoldest portion of the tubes and thus preventfreezing. Normally forced draft units have thenegative pitch fan at the outlet end, while induceddraft units have the positive pitch fan at the outletend. In hot weather, both fans can blow upward.
2. External RecirculationThis is a more positive way of tempering coolantair, but is practical only with forced draft units.Hot exhaust air exits the bundle and enters a topplenum covered by a louver. When no circulationis required, the top louver is wide open, and theheated air exits through it. When the top louver ispartially closed, some of the hot air is diverted to aduct, through which it flows downward and backinto the fan intake, mixing with some cold ambientair. An averaging air temperature sensor below thebundle controls the amount of recirculated air, andthus the average air intake temperature, by varyingthe louver opening.
3. Co-current FlowFour high pour-point streams, it is often advisableto ensure a high tube wall temperature byarranging the flow co-currently, so that the highinlet temperature process fluid is in contact withthe coldest air and the low temperature outletprocess fluid is in contact with the warmed air.
4. Auxiliary Heating Coils – Steam or GlycolHeating coils are placed directly under bundles.Closing a louver on top of a bundle will allow theheating coil to warm the bundle or keep it warm infreezing weather, so that on start-up or shut-downthe material in the bundle will not freeze or
24
solidify. Heating coils are also occasionally used totemper very cold air to the bundles while the fan isoperating and the exhaust louver is open.
IV. NOISE CONTROL
In recent years concerns about industrial noise havegrown. Since ACHEs were not originally one of theserious sources, it has only been after the abatementof the more serious contributors that attention hasfocused on ACHEs.
ACHE noise is mostly generated by fan blade vortexshedding and air turbulence. Other contributors arethe speed reducer (high torque drives or gears) and themotor. The noise is generally broad band, except foroccasional narrow band noise produced by the motoror speed reducer, or by interaction between thesesources and the ACHE structure.
The evidence is that for efficient fans at moderate fantip speeds, this noise is proportional to the third powerof the fan blade tip speed and to the first power of theconsumed fan horsepower. It is at present quitepractical and usually economical to reduce the soundpressure level at 3 feet below an ACHE to 85 dB(A);but, below 80 dB(A), noise from the drivespredominates and special measures must be taken.
V. DESIGN OF ACHEs FORVISCOUS LIQUIDS
Film coefficients for laminar flow inside tubes are verylow and of the same order of magnitude as filmcoefficients for air flowing over the outside of baretubes. Therefore, there is generally no advantage inusing fins on the air side to increase the overall heattransfer rate since the inside laminar flow coefficientwill be controlling. Bare tube bundles with a largenumber of rows are usual.
For process fluids with outlet viscosities up to 20centipoises, it is possible by using large diametertubes and high velocities (up to 10 ft./sec) to achieve aReynolds number at the outlet above the 2,000 criticalReynolds number, and to keep the flow in the
transition region. However, this usually results inpressure drops of 30 to 100 psi. In view of thedisadvantages of designing for laminar flow, thisincreased pressure drop is normally economicallyjustifiable because the increase in the operating andcapital cost of the pump is small compared with thedecrease in the cost of the turbulent exchanger.
The biggest problem with laminar flow in tubes is thatthe flow is inherently unstable. The reasons for this canbe demonstrated by a comparison of pressure drop andheat transfer coefficient for turbulent versus laminarflow, as functions of viscosity (µ) and mass velocity (G):
In an air-cooled heat exchanger, because of imperfectair-side flow distribution due to wind, or because ofmultiple tube rows per pass, it is likely that the flowthrough some of the tubes in a given pass is cooledmore than that through other tubes.
With turbulent flow, pressure drop is such a weakfunction of viscosity (0.2 power) and such a strongfunction of mass velocity (1.8 power), that the flow inthe colder tubes must decrease only slightly in orderfor the pressure drop to be the same as that in thehotter tubes. Also, as the flow slows and the viscosityincreases, the heat transfer coefficient dropssignificantly, (-0.47 power of viscosity, 0.8 power ofG), so the over-cooling is self-correcting.
With laminar flow, pressure drop is a much strongerfunction of viscosity (1.0 power) and a much weakerfunction of mass velocity (1.0 power), so the flow inthe colder tubes must decrease much more tocompensate for the higher viscosity. Viscosity ofheavy hydrocarbons is usually a very strong functionof temperature, but with laminar flow, the heat transfercoefficient is independent of viscosity, and only a
Delta P Heat TransferFlow Type Function Function
Turbulent µ0.2, G1.8 µ-0.47, G0.8
Laminar µ1.0, G1.0 µ0.0, G0.33
25
weak function of mass velocity (0.33 power), so theself-correction of turbulent flow is absent.
The result is that many of the tubes becomevirtually plugged, and a few tubes carry most of theflow. Stability is ultimately achieved in the highflow tubes as a result of high mass velocity andincreased turbulence, but because so many tubescarry little flow and contribute little cooling, aconcurrent result is high pressure drop and lowperformance. The point at which stability isreached depends on the steepness of the viscosityversus temperature curve. Fluids with high pourpoints may completely plug most of an exchanger.
This problem can sometimes be avoided by designingdeep bundles to improve air flow distribution.Bundles should have no more than one row per passand should preferably have at least two passes perrow, so that the fluid will be mixed between passes.
When fluid has both a high viscosity and a high pourpoint, long cooling ranges should be separated intostages. The first exchanger should be designed forturbulent flow, with the outlet temperature high enoughto ensure an outlet Reynolds number above 2,000 evenwith reduced flow. The lower cooling range can beaccomplished in a serpentine coil (a coil consisting oftubes or pipes connected by 180° return bends, with asingle tube per pass). The low temperature serpentinecoil should, of course, be protected from freezing byexternal warm air recirculation ducts.
Closed loop tempered water systems are often moreeconomical, and are just as effective as a serpentinecoil. A shell and tube heat exchanger cools theviscous liquid over its low temperature range on theshell side. Inhibited water is recirculated between thetube side of the shell and tube and an ACHE, wherethe heat is exhausted to the atmosphere.
For viscous fluids which are responsibly clean, such aslube oil, it is possible to increase the tube sidecoefficient between four- and tenfold, with noincrease in pressure drop, by inserting turbulence
promoters and designing for a lower velocity. It isthen advantageous to use external fins to increase theair-side coefficient also. In addition to the increase inheat transfer coefficient, turbulence promoters havethe great advantage that the pressure drop isproportional to the 1.3 power of mass velocity, andonly to the 0.5 power of viscosity, so that non-isothermal flow are much more stable. The simplestand probably the most cost-effective promoters are theswirl strips, a flat strip twisted into a helix.
VI. COST
The approximate purchase price may be determinedfrom Figure 18, which gives the price per square footof bare tube surface as a function of the total baretube surface and the number of tube rows. The pricesindicated are FOB factory, and do not include freightor export crating charges. The prices are based on 1-inch OD X 12 BWG X 32 foot long steel tubes withextruded aluminum fins, fabricated steel headers withsteel shoulder plugs, 100 psig design pressure, TEFCmotors, and HTD drives. Price multiplication factorsare included for different tube materials.
It can be seen from these curves that the price persquare foot varies little for installations in excess of7,000 square feet of bare tube surface. It is alsoevident that the reduction in unit price as a function ofthe number of tube rows becomes progressively lessas the number of rows increases.
REFERENCES
1. Steven, R.A., J. Fernandez, and J. R. Wolf: “Mean TemperatureDifference in One, Two and Three-pass Crossflow HeatExchangers,” Trans, ASME, Paper Nos. 55-A-89 and 55-A99,1955.
2. Kays, William M., and Al. L. London, Compact Heat Exchangers,Third Edition, McGraw-Hill Book Company, New York, 1984.
3. Seider, E. N. and G. E. Tate, “Heat Transfer and Pressure Drop ofLiquids in Tubes.” Ind. Eng. Chem., Vol. 28, 1429-1435, 1936.
4. Kern Donalds Q., Process Heat Transfer, McGraw-Hill BookCompany, New York, 1950.
5. Rohsenow, Warren M., and James P. Hartnett, Handbook ofHeat Transfer, McGraw-Hill Book Company, New York, 1973.
26
20
25
30
35
40
45
50
55
60
65
02
,00
04
,00
06
,00
08
,00
01
0,0
00
12
,00
01
4,0
00
16
,00
01
8,0
00
20
,00
0
SellingPrice,Dollars/Sq.Ft.
Tota
lBar
eTu
be
Surf
ace,
Sq.F
t.
TUB
ER
OW
S
3 4 5 6 8 10
7075
Cu
rves
bas
edu
po
n1"
O.D
.x12
BW
GM
Wx
32'L
g.w
eld
edC
.St.
tub
es,
100
psi
des
ign
pre
ssu
re,c
arb
on
stee
lplu
gh
ead
ers,
TEFC
mo
tors
.W
alkw
ays,
frei
gh
t,an
dex
po
rtcr
atin
gar
en
ot
incl
ud
ed.
Ap
pro
xim
ate
pri
cead
just
men
tfa
cto
rsar
eas
follo
ws:
For2
4'tu
bes
,mu
ltip
lyb
y1.
15Fo
r40'
tub
es,m
ult
iply
by
.90
For1
6B
WG
TP-3
04st
ain
less
stee
ltu
bes
,mu
ltip
lyb
y1.
15Fo
rTP-
304
stai
nle
ssst
eelt
ub
esan
dh
ead
ers,
mu
ltip
lyb
y1.
4Fo
r250
psi
des
ign
pre
ssu
re,m
ult
iply
by
1.01
5Fo
r500
psi
des
ign
pre
ssu
re,m
ult
iply
by
1.03
*Pr
ices
sub
ject
toch
ang
e
UnitPriceAsAFu
nction
OfTotal
SurfaceAnd
Bun
dleDep
thHudsonProductsCorporation
•SugarLand,Texas,U
SAFigure18
9660 Grunwald Road
Beasley, Texas 77417-8600
Phone: (281) 275-8100
Fax: (281) 275-8211
1-800-634-9160 (24 Hours)
E-Mail: [email protected]
Internet Home Page Address:
http://www.hudsonproducts.com
Hudson Products Corporation manufactures
• Auto-Variable® fan hubs
• Combin-Aire® water- and air-cooled heat exchangers
• Exact-A-Pitch® digital protractor for setting fan pitch angles
• Fin-Fan® air-cooled heat exchangers
• Solo-Aire® air-cooled heat exchangers
• Hy-Fin® finned tubes
• Tuf-Edge® erosion resistant leading edge protection
• Tuf-Lite® fan blades
• Cofimco fan blades
HUDSONProducts Corporation
Hudson, Auto-Variable, Combin-Aire, Exact-A-Pitch, Fin-Fan, Hy-Fin, Tuf-Edge, and Tuf-Lite are registered trademarks of Hudson Products Corporation.
©2007 Hudson Products Corporation. All Rights Reserved. HPC.ACHEBROC.12.07
