The growth and structure of this tape-induced swirl in the laminar flow regime, as characterized by experimental flow visualization Manglik and Ranganathan, 1997 and computational simulati
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exchangerfora specified heat duty, significant reduction in size can be achieved
The ease of fitting multitube bundles with tape inserts and their removal, as depicted
in Fig 14.30a, makes them particularly useful in fouling situations, where frequent
tube-side cleaning may be required
The characteristic geometrical features of a twisted tape, as shown in Fig 14.30b,
include the 180° twist pitchH, tape thickness δ, and tape width w (which is
usu-ally about the same as the tube inside diameterd in snug- to tight-fitting tapes) The
severity of tape twist is described by the dimensionless twist ratioy(= H/d), and
depending on the tube diameter and tape material, inserts with a very small twist ratio can be employed When placed inside a circular tube, the flow field gets altered in sev-eral different ways: increased axial velocity and wetted perimeter due to the blockage and partitioning of the flow cross section, longer effective flow length in the helically twisting partitioned duct, and tape’s helical curvature–induced secondary fluid circu-lation or swirl Of these, the most dominant mechanism is swirl generation, which effects transverse fluid transport across the tape-partitioned duct, thereby promoting greater fluid mixing and higher heat transfer coefficients The growth and structure of this tape-induced swirl in the laminar flow regime, as characterized by experimental flow visualization (Manglik and Ranganathan, 1997) and computational simulations
Figure 14.30 Twisted-tape inserts: (a) typical application in a shell-and-tube heat exchanger (courtesy of Brown Fintube Company); (b) characteristic geometrical features.
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(Manglik and You, 2002), are depicted in Fig 14.31 The fully developed laminar swirl flows, which consist of two asymmetrical counter-rotating helical vortices, have been shown (Manglik and Bergles, 1993a; Manglik et al., 2001a) to scale by a dimen-sionless swirl parameter defined on the basis of a primary force balance as
where
Res =ρV s d
µ V s=
G
ρ
1+
π
2y
21/2
(14.31b)
Figure 14.31 Structure of swirl produced by twisted-tape inserts in laminar flows in
circu-lartubes: (a) experimental visualization of secondary flow patterns (from Manglik and Ran-ganathan, 1997); (b) results of numerical simulations (From Manglik and You, 2002).
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Based on this scaling of the swirl behavior in the laminar flow regime, the
follow-ing correlation for predictfollow-ing the isothermal Fannfollow-ing friction factor has been proposed (Manglik and Bergles, 1993a):
f s= 15.767
Res
π + 2 − 2(δ/d)
π − 4(δ/d)
2
1+ 10−6Sw2.551/6
(14.32) wheref sis based on the effective swirl velocity and swirl flow length, or
2ρV2
s L s L s = L
1+
π
2y
21/2
(14.33)
Equation (14.32) has been shown to predict within±10% a fairly large set of
exper-imental data for a very wide range of flow conditions and tape geometry: 0≤ Sw ≤
2000, 1.5 ≤ y ≤ ∞, 0.02 ≤ (δ/d) ≤ 0.12 (Manglik and Bergles, 1993a; Manglik
et al., 2001a) Forlaminarflow heat transferin tubes maintained at a uniform wall temperature (UWT), the following correlation developed by Manglik and Bergles (1993a) is recommended:
Num = 4.612(µ b /µ w )0.14
fully developed flow
(1 + 0.0951Gz0.894 )2.5
thermal entrance
+ 6.413 × 10−9(Sw · Pr0.391 )3.835
swirl flows
2
+ 2.132 × 10−14(Re a · Ra)2.23
free convection
0.1
(14.34)
Here each of the terms that account for various convection effects is highlighted, and the interplay between thermal entrance effects and fully developed tape-induced swirl flows is depicted in Fig 14.32 With Ra∼ 0, their respective asymptotes are
represented by Sw → 0, Gz → ∞ (entrance effects), and Sw → ∞, Gz → 0
(swirl-dominated flows) Similarly, in flows where Gr> Sw2, free convection effects dominate and they are scaled by the grouping (Rea · Ra), as shown in Fig 14.33
For tubes with the uniform heat flux (UHF) condition, the correlation devised by Hong and Bergles (1976) for fully developed swirl flows may be considered after incorporating the classical viscosity-ratio correction factor to account for viscous property variations as follows:
Nuz = 5.172
1+ 5.484 × 10−3Pr0.7
Rea
y
1.250.5
µb
µw
0.14
(14.35)
Furthermore, to account for the influence of free convection on swirl flows in UHF tubes, Bandyopadhyay et al (1991) have extended the Hong and Bergles correlations
to include mixed convection as
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Figure 14.32 Influence of twisted-tape-generated swirl and tube partitioning on the average Nusselt numberin thermal developing and fully developoed laminarflows in circulartubes with uniform wall temperature (From Manglik and Bergles, 1993a.)
Nuz="Nu9z,HB + 1.17Ra∗0.1819#1/9
(14.36) For predicting friction factors under the more practical diabatic (heating or cooling) conditions, based on the theoretical results of Harms et al (1998) for the limiting case
of a straight-tape insert (y = ∞, δ = 0) for liquids and the experimental results of Watanabe et al (1983), a first-order correction to the isothermal results of eq (14.32) can be made as
f
fiso =
µ
b
µw
m
forliquids
T
b
T w
0.1
forgases
(14.37a)
where
m(UWT) =
$0.65 heating
$0.61 heating
In the turbulent flowregime, which is characterized inherently by fluctuating
velocities, a well-mixed cross-stream eddy structure, and flow instabilities in the transition process, the scaling of swirl flows due to twisted-tape inserts with Sw is
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Figure 14.33 Mixed convection effects in laminarfully developed twisted-tape-induced swirl-flow heat transfer in circular tubes with uniform wall temperature (From Manglik and Bergles, 1993a.)
found to be inapplicable (Manglik and Bergles, 1993b) Instead, the friction factor correlates with a power law reciprocal of the twist ratio as
f = 0.0791
Re0.25
1+2.752y1.29
π
π − (4δ/d)
1.75π + 2 − (2δ/d)
π − (4δ/d)
1.25
(14.38)
and it describes the available experimental data within±5% (Manglik and Bergles,
1993b; Tong et al., 1996; Manglik and Bergles, 2002a) Again, to correct for heating and cooling conditions in predicting the friction factors, the following recommenda-tions given by Lopina and Bergles (1969) for liquids, and by Watanabe et al (1983) forgases, may be adopted:
f
fiso
=
µb
µw
0.35(d h /d)
forliquids
T b
T w
0.1
forgases
(14.39)
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For turbulent flow heat transfer with Re ≥ 104, Manglik and Bergles (1993b) have proposed a Nusselt number correlation that is expressed as
Nu= 0.023Re0.8· Pr0.4
1+0.769y
π + 2 − (2δ/d)
π − (4δ/d)
0.2 π
π − (4δ/d)
0.8
φ
(14.40a) where the property correction factorφ is given by
φ =
µ
b
µw
n
or
T
b
T w
m
(14.40b) where
n =
$
0.18 liquid heating
$
0.45 gas heating
0.15 gas cooling (14.40c)
The predictions of eq (14.40) have been found (Manglik and Bergles, 1993b; 2002a)
to describe within±10% the majority of experimental data for a very wide range
of tape-twist ratios (2 ≤ y ≤ ∞) reported in the literature for both gas and liquid
turbulent flows in circular tubes with twisted-tape inserts
Of all the swirl flow devices, twisted tapes have also found extensive use in boiling applications Two recent reviews (Shatto and Peterson, 1996; Manglik and Bergles, 2002a) have covered most aspects of their thermal–hydraulic performance, which includes bulk boiling with net vapor generation, subcooled boiling, and critical heat flux A schematic synopsis of the effects of twisted-tape inserts on the heat transfer in
a uniformly heated tube with once-through boiling (typically encountered in power boilers and refrigerant evaporators) is given in the bulk fluid and tube wall tempera-ture map of Fig 14.34 Variations in the wall temperatempera-ture of an empty smooth tube and one fitted with a twisted tape and in the bulk fluid temperature are depicted for
a typical case of fixed mass flux, inlet temperature, and pressure level in a uniformly heated tube The heat transfer enhancement due to the tape insert is reflected in the reduced wall temperature along the tube length in the single-phase liquid, subcooled boiling, bulk boiling, dispersed-flow film boiling, and post-dryout single-phase va-por regimes Also, dryout is delayed to significantly higher quality The primary en-hancement mechanism is perhaps tape-induced swirl, which tends to improve vapor removal and wetting of the heated surface
Enhancement of subcooled boiling is of particular interest for cooling and ther-mal management of high-heat-flux devices (e.g., electrical machines, electronic and microelectronic devices, and nuclear reactors cores) Gambill et al (1961), Feinstein and Lundberg (1963), and Lopina and Bergles (1973) have reported a limited set
of experimental data, and the typical boiling curves for the influence of a tape-twist
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106
2
3 4
5
6 7 8 9
106
(T w⫺Tsat) [K]
y = 2.48
y = 3.15
y = 5.26
y = 9.20
Empty tube
Degassed, demineralized water
L Nickel tubes, Inconel tapes Swirl tubes = 4.915 mm Empty tube = 5.029 mmd d i i
= 344.73 kPa
= 2.743 7.925 m/s
p V
sat exit in
⫺
b
Figure 14.35 Boiling curves for fully developed subcooled flow boiling heat transfer in a tube with twisted-tape inserts of different twist severity (From Lopina and Bergles, 1973.)
ratio, as characterized by the results of Lopina and Bergles (1973), are depicted in Fig 14.35 The slight leftward shift of the swirl flow boiling curves relative to that foran empty tube suggests some heat transferenhancement, although the change in they values seems to have no significant effect.
A more effective use of twisted tapes in subcooled boiling has been shown for increasing the critical heat flux (Bergles, 1998; Manglik and Bergles, 2002a) Higher wall heat fluxes are essentially sustained because swirl-induced radial pressure gradi-ents promote greater vapor removal from and transport of liquid droplets to the heated
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Figure 14.36 Enhanced CHF in subcooled boiling due to twisted-tape-induced swirl flows
(From Gambill et al., 1961.)
surface This enhancement is seen in the experimental data of Gambill et al (1961)
in Fig 14.36, where increase in CHF of up to 100% is seen In fact, Gambill et al
(1961) have shown that the CHF is higherby a factorof 2 in tubes with twisted-tape inserts compared to that in smooth empty tubes for the same pumping power Driˇzius
et al (1978) measured CHF in a 1.6-mm-diameter tube fitted with 2≤ y ≤ 10 tapes,
and found the data to be independent of subcooling but dependent on mass fluxy and
heated length In a more recent study, Gaspari and Cattadori (1994) reconfirmed the
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enhanced performance of twisted tapes with their CHF data, which is 1.4 to 2.1 times higherwith twist ratios ofy = 2.0 and 1.0, respectively Similarly, in their
experi-ments with small-diameter(2.44 ≤ d ≤ 6.54 mm) stainless steel tubes and different twist ratio (1.9 ≤ y ≤ ∞) tapes, Tong et al (1996) found the CHF enhanced by a factorof 1.5 with the tightest twisted tape and a mass flux of 15,000 kg/m2· s They
also deduced that CHF was inversely proportional toy, d, T i, andl/d, but directly
proportional toG and p e Based on this parametric analysis, the following empirical correlation has been proposed:
q
cr= 31.554 (G/G o )0.6657 (p e /p e,o )0.2787
(y/y o )0.2412 (d/d o )0.0735
(L h /d) o
(L h /d)
0.2191
Tsub,e − T i
Tsat,e − T i,o
1.041
(14.41)
Here the variables with the subscripto pertain to a reference condition (see Tong et
al for details), and the predictions of eq (14.41) have been shown to describe within
±25% most of theirown experimental data as well as those of Gambill et al (1961),
Driˇzius et al (1978), Inasaka et al (1991), and Gaspari and Cattadori (1994)
For the pressure drop in subcooled flow boiling, needed to size the pumping system, determine the exit pressure, and assess the thermal–hydraulic stability of the system (Manglik and Bergles, 2002a), Pabisz and Bergles (1997) have devised an empirical correlation Their equation is based on the Tong et al (1996) data, where any gravitational component has been subtracted from the measured pressure drop and is expressed as
∆p = (∆p
fluid only+ ∆p
subcooled boiling)1/n (14.42)
The details of procedures for calculating the single-phase fluid only and subcooled boiling contributions can be found in Pabisz and Bergles (1997), and the predic-tions of this correlation have been shown to describe most of the experimental data within±15%
In bulk or saturated boiling conditions, twisted-tape inserts have been shown to en-hance the heat transfer coefficient throughout the entire quality region (0≤ x ≤ 1), as
well as to increase the CHF (or dryout quality) and the heat transfer coefficients in the post-dryout dispersed-flow film boiling region (Shatto and Peterson, 1996; Manglik and Bergles, 2002a) Enhanced performance data have been reported for a variety of fluids, including water, refrigerants, cryogenic fluids, and liquid metals (Bergles et al., 1995; Manglik and Bergles, 2002a) As reviewed by Shatto and Peterson (1996), several different correlations have been proposed by different investigators (Gambill
et al., 1961; Blatt and Adt, 1963; Jensen and Bensler, 1986; Agarwal et al., 1986;
Kedzierski and Kim, 1997) For predicting the CHF, Jensen (1984) provides an em-pirical correlation based on data for water and R-22 that describes the experimental results within an average deviation of±10% Bergles et al (1971) have considered the
dispersed flow (post-dryout) regime and have devised a rather elaborate correlation
Their equation is based on several variables that affect and describe swirl flow behav-iorand on the assumption that the vaporremains at saturated conditions Blatt and Adt (1963), and Agarwal et al (1982) have also given correlations for the two-phase flow pressure drop in bulk boiling that are based on their respective data for R-11 and R-12
... generation, subcooled boiling, and critical heat flux A schematic synopsis of the effects of twisted-tape inserts on the heat transfer ina uniformly heated tube with once-through boiling (typically... shown to en-hance the heat transfer coefficient throughout the entire quality region (0≤ x ≤ 1), as
well as to increase the CHF (or dryout quality) and the heat transfer coefficients... vapor removal and wetting of the heated surface
Enhancement of subcooled boiling is of particular interest for cooling and ther-mal management of high -heat- flux devices (e.g., electrical