Chapter 3 Single-Phase Shell-Side Flows and Heat Transfer

Transcription

1 Chapter 3 Single-Phase Shell-Side Flos and Heat Transfer SUMMARY: The design method of Taborek (1983) for single-phase shell-side flos of shell-and-tube heat exchangers ith single segmental baffles is presented here. The Taborek version of the Delaare method is thought to be the most accurate, reliable and complete method available in the open literature. The basic theory of single-phase shell-side flo in baffled heat exchangers is presented and then a complete treatment of the Taborek method for application to plain tubes and integral lo finned tubes, such as the Wolverine Tube S/T Trufin tubes. The method predicts both heat transfer coefficients and pressure drops as a function of the tube bundle geometry and its dimensional description. 3.1 Introduction Single-phase flo of liquids and gases over tube bundles is an important heat transfer process confronted in numerous types of heat exchanger applications. In contrast to single-phase heat transfer inside tubes, shell-side flos (i.e. those across the outside of the tubes in a baffled tube bundle confined by a heat exchanger shell) are particularly complex because of the many geometrical factors involved and the many possible fluid flo paths. Tinker (1951) as the first to give a physical description of this process, hich as used in the development of hat is often referred to as the Delaare method, proposed by Bell (1960, 1963) and republished in Bell (1986). Taborek (1983) proposed a ne version of this design method for single-phase shell-side flos of shell-and-tube heat exchangers ith single segmental baffles (essentially for hat is called a TEMA E-shell) and described ho to extended it to TEMA J-shells and F- shells and to E-shells ith no-tubes-in-the-indo. The basic theory of single-phase shell-side flo in baffled E-shell heat exchangers is presented here and then a more complete treatment of the Taborek method. This method is for flo over tube bundles ith single-segmental baffles. Other types of baffles used in special applications include double-segmental baffles, triple-segmental baffles, disk-and-donut baffles, rod baffles and helical baffles; these alternative, less used geometries are not addressed here. In this chapter, first the method for plain tubes is described and then its extension to integral lo finned tubes. 3.2 Stream Analysis of Flo Distribution in a Baffled Heat Exchanger In a baffled shell-and-tube heat exchanger, only a fraction of the fluid flo through the shell-side of a heat exchanger actually flos across the tube bundle in the idealized path normal to the axis of the tubes. The remaining fraction of the fluid flos through "bypass" areas. As can be expected, the fluid seeks the flo path of less resistance from the inlet to the outlet of the exchanger. In a typical design, the non-ideal flos represent up to 40% of the total flo and hence it is imperative to account for their effects on heat transfer and pressure drop. These flo paths in an actual heat exchanger ith single-segmental baffles ere first intuitively described by Tinker (1951) as depicted in his schematic diagram shon in Figure 3.1. The total flo is divided into individual streams designated by the letters shon in the diagram as follos: Single-Phase Shell-Side Flos and Heat Transfer 3-1

2 Figure 3.1. Shell-side flo paths in a baffled heat exchanger according to Tinker (1951). The total flo is divided into individual streams designated by the letters shon in the diagram as follos: Stream A: The tube hole leakage stream represents the flo from one baffle compartment to the next that passes through the annular openings beteen the oversized holes for the tubes in the baffles and the outside of the tubes, as illustrated in Figure 3.2. The flo is driven by the pressure drop from one baffle compartment to the next. The leakage occurs through the diametral clearance beteen the diameter of the baffle hole minus the outside diameter of the tube. If the tubes are expanded into the baffles, then the diametral clearance is zero. This bypass stream is minimized by reducing the diametral clearance and completely eliminated if the clearance becomes zero. Figure 3.2. Diagram of tube hole leakage stream A. Stream B: The crossflo stream is the idealized cross flo over the tube bundle normal to the axis of the tubes. This is the preferred flo in a baffled shell-and-tube heat exchanger and is illustrated in Figure 3.1. Single-Phase Shell-Side Flos and Heat Transfer 3-2

3 Stream C: The bundle bypass stream flos through the annular opening beteen the outside of the tube bundle and the inner shell all as illustrated in Figure 3.3. The diametral clearance for this flo to pass through is equal to the shell internal diameter minus the outer tube limit diameter of the tube bundle. The bundle bypass stream is reduced by minimizing the diametral clearance beteen the shell internal diameter and the outer tube limit diameter of the tube bundle and by installing pairs of sealing strips around the perimeter of the tube bundle to block this flo path and thereby force the fluid back into the tube bundle. Figure 3.3. Schematic of bundle bypass stream C. Stream E: The shell-to-baffle bypass stream refers to the flo through the gap beteen the outer edge of the baffle and the inner shell all as depicted in Figure 3.4. The diametral clearance is equal to the shell internal diameter minus the diameter of the baffle and is minimized by decreasing the construction clearance beteen the shell and the baffle to its feasible minimum. Stream F: The pass partition bypass stream refers to the flo through the open lanes in a tube bundle formed by omission of tubes in the bundle and tubesheet for placement of tubepass partition plates in the heads of multi-pass heat exchangers. It is illustrated in Figure 3.1. This stream only refers to those openings oriented in the direction of the fluid flo. Pass partition openings oriented normal to the flo path do not cause a bypass. This bypass stream thus only occurs in some multi-pass tube layouts and they can be eliminated by placement of several dummy tubes in each bypass lane to drive the fluid back into the tube bundle. Single-Phase Shell-Side Flos and Heat Transfer 3-3

4 Figure 3.4. Schematic of shell-to-baffle bypass stream E. 3.3 Definition of Bundle and Shell Geometries Figure 3.5. Single-segmental shell-and-tube heat exchanger shoing baffle spacings. Figure 3.5 depicts a single-segmental shell-and-tube bundle geometry ith fixed tubesheets at both heads in hich the shell-side flo makes one shell pass from one end of the tube bundle to the other ith the flo directed across the tube bundle by the baffles. This is a common configuration used in refrigeration and petrochemical heat exchangers. The inlet, central and outlet baffle spacings are shon and are identified as L bi, L bc and L bo, respectively. L bi and L bo, are often equal in length to L bc, except hen the first and last baffle compartments must be enlarged to allo for the placement of the respective shell-side Single-Phase Shell-Side Flos and Heat Transfer 3-4

5 nozzles. The baffle layout is determined from the inlet, central, and outlet baffle spacings and the effective tube length. The effective tube length L ta is equal to the total tube length less the combined thickness of the to tubesheets. The number of baffles (an integer) and baffle spacings can be determined from these values. The effective length for determining the baffle spacing for a U-tube exchanger includes the straight length of the tube plus D s /2, here D s is the shell internal diameter. Thus the baffle spacing at the U-bend should include the tube straight length in this compartment plus (D s /2). Figures 3.5, 3.6 and 3.7 reproduced from Taborek (1983) define the principal heat exchanger dimensions. D otl is the outer tube limit diameter and D ctl is the centerline tube limit diameter (note: D ctl = D otl - D t here D t is the outside diameter of the tubes). The baffle cut height is shon as a height L bch ; the value of the baffle cut B c is (L bch /D s ) x 100%, i.e. given in terms of the percent of the shell internal diameter. The diametral clearance beteen the shell internal diameter D s and outer tube limit diameter D otl is L bb. Onehalf of L bb is the idth of this bypass channel. A pass partition lane is shon ith a idth of L p. The diametral clearance beteen the shell internal diameter D s and the diameter of the baffle D b is L sb, here the gap is equal to L sb /2. Figure 3.6. Baffle and tube bundle geometry. Single-Phase Shell-Side Flos and Heat Transfer 3-5

6 Figure 3.7. Baffle cut and clearance. The above dimensions D s, D otl, baffle cut (% of D s ), L bb and L sb can be obtained from a tube layout draing of the heat exchanger. If the value of D otl is not knon, L bb can be assumed to be equal to mm (3/8 in.) for D s < 300 mm (11.81 in.) and L bb can be assumed to be mm (5/8 in.) for D s > 1000 mm (39.37 in.). For D s from 300 to 1000 mm inclusive, L bb can be assumed to be 12.7 mm (1/2 in.). These values are typical of TEMA heat exchanger specifications but are often smaller for directexpansion evaporators. If L sb is not knon, it can be assumed that L sb = 2.0 mm for D s < 400 mm (15.75 in.) hile for larger shells L sb = D S (mm). If the diametral clearance beteen the baffle holes and the outside of the tube is not knon, the maximum TEMA value can be assumed mm (1/32 in.) or a smaller value in the range from mm (1/64 in.) to mm. This clearance is equal to the baffle hole diameter minus D t. Thermal performance is significantly improved by minimizing this clearance. The three tube layouts addressed by the Taborek design method are shon in Figure 3.8: 30, 45 and 90. The 60 layout is not included. The tube pitch is L tp and is defined as the distance center-to-center beteen tubes in the bundle. The pitch parallel to the direction of flo is L pp hile that pitch normal to the direction of the flo is L pn. Single-Phase Shell-Side Flos and Heat Transfer 3-6

7 Figure 3.8. Tube layouts. The number of tubes that fit ithin a shell depends on a number of geometrical factors, dimensions and clearances, principally the type of tube layout (triangular, square or rotated square) and the tube pitch. Single-Phase Shell-Side Flos and Heat Transfer 3-7

8 The simple estimation method presented by Taborek (1983) for fixed tubesheets for single tubepass units ithout any tubes removed in the nozzle entrance and exit areas is: D N tt = [3.3.1] C L 2 ctl 2 1 tp here N tt is the number of tubes, D ctl is the centerline tube limit diameter and L tp is the tube pitch. The constant C 1 = 1.0 for square (90 ) and rotated square tube (45 ) layouts and C 1 = for triangular (30 ) tube layouts. Designs ith multiple tubepasses (2, 4, ) are commonly used and they ill have feer tubes than given by the above expression. Use of a tube count softare program is highly recommended for an accurate estimate since tubes are often removed at the inlet nozzle to permit placement of an impingement plate and the number removed depends on the nozzle diameter. An accurate tube count improves the accuracy of the heat transfer and pressure drop calculations. 3.4 Stream Analysis of Heat Transfer in a Baffled Heat Exchanger The stream analysis shell-side heat transfer coefficient for single-phase flo α ss is ss ( JCJLJBJRJSJ ) αi α = μ [3.4.1] here α I is the ideal tube bank heat transfer coefficient calculated for all the flo across the tube bundle (that is all flo assumed to be in stream B). J C, J L, J B, B JR and J S are the correction factors for the leakage and bypass flo effects and J μ is the all viscosity correction factor. The corrections factors and ideal tube bank heat transfer correlations are described in the sections belo. The value of α ss is the mean value for the hole tube bundle applied to the outside heat transfer surface area of the tubes. Mean bulk physical properties are used for evaluating the correlations Baffle Cut Correction Factor (J C ) The baffle cut correction factor J C accounts for the non-ideal flo effects of indo flo on heat transfer since the velocity through the indo (that of the baffle cut) is not the same as that for cross-flo over the bundle. The indo flo velocity can be larger or smaller than for cross-flo depending on the size of the cut and the baffle spacing. In addition, the indo flo is partially longitudinal to the tubes, hich is less effective than cross-flo. Therefore, J C is a function of the baffle cut, the outer tube limit diameter and the indo flo area and is calculated as follos: J = [3.4.2] C F C here F C is F = 1 2 [3.4.3] C F F is the fraction of the cross-sectional area occupied by the indo: Single-Phase Shell-Side Flos and Heat Transfer 3-8

9 θctl sin θctl F = [3.4.4] 360 2π The angle of the baffle cut relative to the centerline of the heat exchanger is θ ctl (in degrees): 1 D s Bc θctl = 2cos 1 2 [3.4.5] Dctl 100 The above expression is valid for baffle cuts from 15% to 45% of the shell diameter. Use of baffle cuts outside this range is not normally recommended because of the ensuing maldistribution of the flo. J C typically ranges in value from 0.65 to in a ell-designed unit Baffle Leakage Correction Factor (J L ) The pressure difference beteen neighboring baffle compartments forces a fraction of the flo through the baffle-to-tubehole gaps in the baffles (Stream A) and through the annular gap beteen the shell and the baffle edge (Stream E). These streams reduce the part of the flo that passes over the tube bundle as cross-flo (Stream B), reducing both the heat transfer coefficient and the pressure drop. Stream E is very detrimental to thermal design because it is not effective for heat transfer. The baffle leakage correction factor is calculated from the folloing expression: J L ( r ) + [ ( 1 r )] exp( 2.2r ) = [3.4.6] s s lm here r s is r s S S + S sb = [3.4.7] sb tb and r lm is r lm S + S S sb tb = [3.4.8] m The shell-to-baffle leakage area S sb, the tube-to-baffle hole leakage area S tb for N tt (1-F ) tube holes and the cross-flo area at the bundle centerline S m are determined as follos: S sb DsLsb( 360 θds = ) [3.4.9] S tb 2 2 [( Dt + Ltb ) Dt ] Ntt ( 1 F π = ) [3.4.10] 4 D ctl S m = Lbc Lbb + ( Ltp Dt ) [3.4.11] Ltp,eff Single-Phase Shell-Side Flos and Heat Transfer 3-9

10 B Engineering Data Book III In the above expressions, L sb is the diametral shell to baffle clearance and the baffle cut angle θ ds in degrees is 1 Bc θds = 2cos 1 2 [3.4.12] 100 here L bc is the central baffle spacing and L bb is the bypass channel diametral gap, both described earlier. The effective tube pitch is L tp,eff, hich is equal to L tp for 30 and 90 tube layouts hile for 45 staggered layouts L tp,eff is equal to 0.707L tp. For a ell-proportioned heat exchanger, J L > hile values of J L < 0.6 should be avoided. The maximum value of J L is 1.0. For refrigeration chillers and ater-cooled condensers, a value of 0.85 to 0.90 is achievable because of their tighter construction tolerances and smaller clearances than TEMA standards Bundle Bypass Correction Factor (J B ) B The bundle bypass correction factor J B accounts for the adverse effect of the flo beteen the inner shell all and the tube bundle (Stream C) and the bypass lane created by any pass partition lanes (Stream F) in the direction of flo. Stream F is not alays present and it can be eliminated completely by placing dummy tubes in the pass partition lanes. Stream C is reduced by a tighter fit of the tube bundle into the shell and also by placing sealing strips (in pairs) around the bundle perimeter, up to a maximum of one pair of strips for every to tube ros passed by the flo beteen the to baffle cuts. The bundle bypass correction factor J is BB J B [ C F ( 1 )] 3 2r = exp [3.4.13] bh sbp ss The empirical factor C bh = 1.35 for laminar flo (100 Re) and C bh = 1.25 for transition and turbulent flos (Re > 100). To evaluate this expression, one requires the ratio of the bypass to the crossflo area F sbp, and the ratio r ss of the number of sealing strips N ss (number of pairs if any) passed by the flo to the number of tube ros crossed beteen baffle tips in one baffle section N tcc. First of all, F sbp is given by S b F sbp = [3.4.14] Sm here S m as given above and S b is the bypass area: b bc [( D D ) L ] S = L + [3.4.15] s otl pl here L pl represents the idth of the bypass lane beteen tubes. For situations ithout a pass partition lane or for such a lane normal to the flo direction, set L pl = 0 hile for a pass partition lane parallel to the flo direction L pl is equal to ½ the actual dimension of the lane or can be assumed to be equal to the tube diameter D t. The ratio r ss is N ss r ss = [3.4.16] Ntcc The value of N tcc is obtained from Single-Phase Shell-Side Flos and Heat Transfer 3-10

11 Ds Bc Ntcc = 1 2 L [3.4.17] pp 100 here L pp = 0.866L tp for a 30 layout, L pp = L tp for a 90 layout and L pp = 0.707L tp for a 45 layout. This expression has a maximum limit of J B B = 1 at rss ½ Unequal Baffle Spacing Correction Factor (J S ) The unequal baffle spacing correction factor J S accounts for the adverse effect of an inlet baffle spacing L bi and/or outlet baffle spacing L bo larger than the central baffle spacing L bc. Some exchangers have a larger baffle spacing in the inlet and outlet nozzle compartments compared to the central baffle spacing, alloing placement of the shell-side nozzles ithout interference ith the body flanges and ithout overlapping the first baffle. The flo velocity in these compartments is thus loered and has an adverse influence on heat transfer. For larger inlet and outlet spacings than the central baffle spacing, the correction factor J S < 1.0. For inlet and outlet baffle spacings equal to the central baffle spacing, no correction is required and J S = 1.0. The value for J S is determined directly from the effect on the flo velocity and is given by the folloing expression: J S = 1 n ( Nb 1) + ( Lbi Lbc ) + ( Lbo Lbc ) ( N 1) + ( L L ) + ( L L ) b bi bc bo bc 1 n [3.4.18] here n = 0.6 for turbulent flo and n = 1/3 for laminar flo. The number of baffle compartments N b is determined from the effective tube length and the baffle spacings Laminar Flo Correction Factor (J R ) In laminar flos, heat transfer is reduced by the adverse temperature gradient formed in the boundary layer as the flo thermally develops along the flo channel. The laminar flo correction factor J R accounts for this effect. For laminar shell-side flo J R < 1.0 (i.e. for 100 Re) hile for Re > 100, no correction is needed and J R = 1.0. For 20 Re, the value of J R is given by J R ( JR ) 20 N = = [3.4.19] c here N c is the total number of tube ros crossed by the flo in the entire heat exchanger: N ( N + N )( N 1 = ) [3.4.20] c tcc tc b + The number of tuberos crossed N tcc beteen baffle tips has been noted above hile the number of tube ros crossed in the indo area N tc is 0.8 Bc Ds Dctl Ntc = Ds L [3.4.21] pp For Re > 20 but Re < 100, the value is prorated as Single-Phase Shell-Side Flos and Heat Transfer 3-11

12 20 Re = ( JR ) + [( JR ) 1 20 ] [3.4.22] 80 JR 20 The minimum value of J R in all cases is Wall Viscosity Correction Factor (J μ ) Heat transfer and pressure drop correlations are normally evaluated using bulk physical properties obtained at the mean of the inlet and outlet temperatures. For heating and cooling of liquids, the effect of variation in properties beteen the bulk fluid temperature and the all temperature is corrected by the viscosity ratio J μ, hich is the ratio of the bulk viscosity μ to the all viscosity μ all : m μ J μ = [3.4.23] μ all The correction factor is greater than 1.0 for heating the shell-side fluid and vice-versa for cooling the shell-side fluid. The exponent for heating and cooling of liquids is usually set to m = For gases, no correction is required for a gas being cooled hile a correction based on temperature rather than viscosity is used for gases being heated as follos: 0.25 T J T all 273 μ = [3.4.24] + here T is the bulk temperature and T all is the all temperature. The all temperature must be calculated from a preliminary heat transfer calculation to determine the viscosity at the all Ideal Tube Bank Heat Transfer Coefficient (α I ) The ideal tube bank heat transfer coefficient α I is calculated for all the flo across the tube bundle (that is as if all the flo in the exchanger ere in Stream B ithout any bypass flos) as: 2 / 3 α I = jicpm& Pr [3.4.25] The mass velocity of the fluid m & is based on the total flo M through the minimum flo area normal to the flo and is in units of kg/m 2 s. Pr is the Prandtl number. The heat transfer factor j I is obtained as follos: j I 1.33 a a = a 2 1 Re [3.4.26] L tp / D t a a 3 = [3.4.27] a Re The values of a 1, a 2, a 3 and a 4 are listed in Table 3.1 given by Taborek (1983). For the above methods, the shell-side cross-flo mass velocity at the maxumum cross-section of the tube bundle is Single-Phase Shell-Side Flos and Heat Transfer 3-12

13 M m & = [3.4.28] S m here M is the shell-side flo rate in kg/s and S m as defined earlier. The shell-side Reynolds number is then Re = D m μ t & [3.4.29] The Prandtl number is defined as c Pr = pμ [3.4.30] k The physical properties (viscosity μ, specific heat c p and thermal conductivity k) are evaluated at the mean bulk fluid temperature. The effective tube length L ta is used to calculate the actual heat transfer surface area A o as A = πd L N [3.4.31] o t ta tt for the number of tubes in the bundle N tt. Table 3.1. Empirical coefficients for calculation of j I and f I. Layout Re a 1 a 2 a 3 a 4 b 1 b 2 b 3 b < < < Single-Phase Shell-Side Flos and Heat Transfer 3-13

14 3.5 Stream Analysis of Shell-Side Pressure Drop in a Baffled Heat Exchanger Figure 3.9. Pressure drop regions in shell-side flo. The pressure drop for shell-side flo is equal to the sum of the inlet nozzle pressure drop, the bundle pressure drop and the outlet nozzle pressure drop. The inlet and outlet nozzle pressure drops can be Single-Phase Shell-Side Flos and Heat Transfer 3-14

15 approximated as being equal to 2 velocity heads each. The bundle pressure drop is equal to the sum of the cross-flo pressure drops Δp c, the indo pressure drops Δp, and the to end zone pressure drops (first and last baffle compartments) Δp as illustrated in Figure 3.9. The bundle pressure drop Δp total, excluding nozzles or impingement plates, is Δ p = Δp + Δp + Δp [3.5.1] total c e The pressure drop Δp c across tube bundle beteen the baffle tips is based on the ideal tube bank pressure drop Δp bi for one baffle compartment ith the central baffle spacing L bc. The zones covered by this pressure drop are the central baffle compartments for flo beteen the baffle cuts. The pressure drop in all the central baffle compartments (N b -1) is c bi ( Nb 1) R BR L Δ p = Δp [3.5.2] here Δp bi is the ideal bundle pressure drop for one baffle compartment of the N b compartments and is based on the mass velocity defined earlier. The expression for Δp bi is: Δp bi = 0.002f N I tcc m& ρ 2 R μ [3.5.3] The friction factor f I is obtained from f I b 1.33 b b = 2 1 Re [3.5.4] Ltp / D t here b b Re 3 = [3.5.5] b 4 The empirical constants for b, b 1, b 2, b 3 and b 4 are taken from Table 3.1. The viscosity correction factor R μ on pressure drop is R μ m μ = [3.5.6] μ The values of m ere cited earlier. The bypass correction factor R B B is R B [ C F ( 1 )] 3 2r = exp [3.5.7] bp sbp ss ith the limit of R B B = 1 for rss ½ hile F sbp as defined earlier. For the empirical factor C bp, use C bp = 4.5 for laminar flo (100 Re) and C bh = 3.7 for transition and turbulent flos (Re > 100). The leakage correction factor R L is L p [ 1.33( 1 r ) r ] R = exp + [3.5.8] s lm Single-Phase Shell-Side Flos and Heat Transfer 3-15

16 here r s and r lm ere defined earlier and the exponent p is ( 1 + r ) 0. 8 p = 0.15 s + [3.5.9] The pressure drop and mass velocity in all N b indo zones for turbulent flo (Re > 100) are Δp = N b 0.001m& 2ρ ( Ntc ) R LR μ 2 [3.5.10] M m & = [3.5.11] S S m here M is the shell-side flo rate in kg/s. The areas S m and S are found from their appropriate expressions presented earlier. The 0.6 in the above expression accounts for the frictional effects and the factor 2 accounts for the velocity heads for the flo turnaround in the indo. For laminar flo (100 Re), the equivalent expression is Δp = N b m& μ Ntc 26 ρ Ltp D t L + D bc m& + 2ρ 2 R LR μ [3.5.12] The first term in brackets refers to the cross flo and the second term refers to the longitudinal flo. The hydraulic diameter of the baffle indo is D = 4S πd N + [3.5.13] t t ( πd θ 360) s ds θ ds as defined earlier. N t is the number of tubes in the indo and is determined from the total number of tubes N tt as N = N F [3.5.14] t tt here F as defined earlier. S is the net flo area in the indo, given as S = S S [3.5.15] g t The area occupied by the N t tubes in the indo is S t and is calculated as π 2 S t = Nt Dt [3.5.16] 4 The gross indo flo area ithout tubes in the indo is S g, given as Single-Phase Shell-Side Flos and Heat Transfer 3-16

17 2 πds θds sin θds Sg = [3.5.17] π The pressure drop Δp e in the to end zones of the tube bundle is p p N 1 + R R Δ tc e = Δ bi B S [3.5.18] Ntcc The pressure drop correction for unequal baffle spacings at the inlet and/or outlet ith respect to the central baffle spacing is R S, calculated as follos: R S L L 2 n bi 2 n bc bc = [3.5.19] bo L + L The tube numbers N tc and N tcc ere defined earlier as ere methods for calculating Δp bi, R B B and Rμ. For all baffle spacings of equal length, R S = 2. In the above expression, N = 1 for laminar flo (Re < 100) and n = 0.2 for turbulent flo. 3.6 Stream Analysis Applied to Lo Finned Tube Bundles In this section, the above plain tube method is applied to integral lo finned tube bundles using the modifications proposed by Taborek (1983) Lo Finned Tubes and Applications Figure Geometric description of integral lo finned tube. Lo finned tubes are an excellent heat transfer enhancement to apply to single-phase shell-side flos, for both liquid flos and even more so for gas flos. Figure 3.10 shos a geometric sketch of an integral lo Single-Phase Shell-Side Flos and Heat Transfer 3-17

18 finned tube that is defined by its folloing dimensions. The characteristic dimensions are: tube diameter at the plain unfinned end D t, the tube diameter of the fin tips D fo (typically equal to D t ), the root diameter at the base of the fins D fr, the tube internal diameter in the finned zone D ti, the fin thickness L fs, the number of fins per meter N f and finally the actual etted surface area per unit length A of. Figure 3.11 shos a photograph of a selection of Wolverine Tube lo finned tubes. Integral lo finned tubes are available in nearly every common heat exchanger tube material. Common fin densities range from 630 to over 1000 fins per meter (commonly defined as their number of fins per inch, such as 19 fpi, 26 fpi, 28 and 30 fpi tubes). Typically fin heights are up to about a maximum of 1.5 mm (0.059 in.) hile fin thickness is commonly about 0.3 mm (0.012 in.). Tables of integral lo finned tubes ith their dimensions are available from the Wolverine Tube Inc. ebsite. For many single-phase flos, it is advantageous to use integral lo finned tubes rather than plain tubes. Lo finned tubes are appropriate for applications here the shell-side (outside) heat transfer coefficient is small compared to the tube-side coefficient and/or hen the shell-side fouling factor is controlling the design. The first situation most often occurs (a) hen the shell-side flo is at the lo end of the turbulent flo regime, in the transition regime or in the laminar flo regime, (b) hen the alloable pressure drop is small, requiring use of large baffle cuts and baffle spacings, or (c) hen a heat transfer augmentation is used on the inside of the tube, such as helical fins or ribs inside Wolverine Tube lo finned tubes. Figure A selection of lo finned tubes of Wolverine Tube Inc. Another very important benefit of lo finned tubes is their positive effect on the shell-side fouling resistance. Since the shell-side fouling factor is applied to the total etted surface area (hich is about 3 to 4 times that of a plain tube), the effective fouling resistance is reduced by a factor of 3 to 4 using the same fouling factor value as for the plain tube design. For large fouling factors or here the fouling resistance is significant (quite typical situation even for modest fouling factor values), the effect of the large surface area ratio of a lo finned tube can dramatically increase the overall heat transfer coefficient. Hence, one uses a lo finned tube to increase the shell-side heat transfer coefficient, to decrease the shellside fouling resistance and to increase the tube-side velocity and heat transfer coefficient (also D ti is less than that of the plain ends of the tube). It is important to remember that hen an external lo finned tube is used, the internal diameter of the finned section of the tube D ti should be used for determining the tube-side heat transfer coefficient and pressure drop. The most effective lo finned tube geometry can be determined by trying several different fin densities. If corrosion alloances are important, thick fins should be used. For large corrosion alloances, fins may not be appropriate since they may be orn aay Heat Transfer and Pressure Drops ith Lo Finned Tubes The stream analysis method of Taborek (1983) for plain tubes as extended by Taborek in the same publication to application to integral lo finned tube bundles. The changes to the above design equations are presented belo. The heat transfer coefficient for the shell-side of a lo finned tube bundle is used to Single-Phase Shell-Side Flos and Heat Transfer 3-18

19 then calculate the overall heat transfer coefficient, at hich point the fin efficiency of the lo fins must be taken into account. Input data. The folloing additional information is required for calculating the shell-side thermal performance of a lo finned tube bundle: Diameter over the fins: Fin root diameter: Number of fins per unit of tube length: Average fin thickness (assuming rectangular profile): Wetted surface area of finned tube per unit of tube length: Tube-to-baffle hole clearance: D fo D fr N f L fs A of L tb To determine L tb, use D fo in place of D t. Normally, D fo is equal to or slightly less than D t. Heat transfer and flo geometries. The total heat transfer surface area upon hich to apply the shell-side heat transfer coefficient of the finned tube bundle α ss is A o, hich for the finned tube is obtained from the folloing expression: A = A L N [3.6.1] o of ta tt The equivalent projected area of an integral lo finned tube is less than that of a plain tube of the same diameter because of the openings beteen adjacent fins in the direction of flo. Hence, the melt don or equivalent projected diameter D req is a function of the tube geometry and density as: D = D + 2L N L [3.6.2] req fr fh f fs and the fin height L fh is L fh Dfo Dfr = [3.6.3] 2 Thus, herever the plain tube diameter D t appeared in the correlations and geometrical equations for the plain tube bank, it is replaced by D req or as noted belo: S m calculations: use D req in place of D t. Re calculation: use D req in place of D t. S t calculation: use D fo in place of D t. Ideal tube bank values of j I. The method for plain tubes is applicable to lo finned tubes ithout modification ith Re determined using D req rather than D t for Re >1000. When Re < 1000, a laminar boundary layer overlap on the fins begins to adversely affect the heat transfer. This is accounted for by the folloing expression, applicable only hen Re <1000: j = J j [3.6.4] I f I,plain Single-Phase Shell-Side Flos and Heat Transfer 3-19

20 In Taborek (1983), a graph is given for the variation in J f versus log Re from Re = 20 to Re = 1000, here J f = 1.0 at Re = This curve has been fitted here as follos: ( Re 20) ( ) 20 log J f = [3.6.5] log 1000 Ideal tube bank values of f I. The equivalent cross-flo area is larger for a finned tube bundle relative to an identical plain tube bundle because of the additional flo area beteen the fins. For finned tubes the friction factor is about 1.4 times larger than for a plain tube; hoever, the loer velocity due to the larger flo area from the open area beteen fins in the direction of flo is also taken into account in the Reynolds number Re. To calculate the friction factor for the lo finned tube bank, first calculated f I,plain using the finned tube values of Re and D req from the plain tube correlation and then multiply this value by 1.4 as follos: f I = 1.4f I,plain [3.6.6] Example calculation: a detailed six-page example calculation is available in Taborek (1983) that is recommended to the reader. Single-Phase Shell-Side Flos and Heat Transfer 3-20