6 CORRELATION DEVELOPMENT
6.1 Introduction to the data base
A database containing published experimental data on heat transfer and pressure drop was established for serrated and solid-fin tube bundles having a staggered layout. Table 6-1 gives an overview of the data from the literature included in the database. The data is also shown in Figure 6-1 (serrated-fin heat transfer), Figure 6-2 (solid-fin heat transfer), Figure 6-3 (serrated-fin pressure drop) and Figure 6-4 (solid-fin pressure drop).
The data used for the correlation development was restricted to Reynolds numbers below 50 000, a minimum of four longitudinal tube rows and a tube bundle arrangement angle below 45° (with the ratio of the tube pitches (Pt/Pl) <
2). The Reynolds number limitation was based on the findings of Stasiulevičius et al. (1988) who showed that for a higher Reynolds number, flow transition may occur, which changes the Reynolds number dependency for both heat transfer and pressure drop. Also, for most heat recovery operations, the Reynolds number will normally be below 50 000. The limitation to at least four longitudinal tube rows is based on the argument that the flow structure and hence the heat transfer coefficient develops through the first tube rows (PFR (1976), Zozulya et al. (1973)) as discussed in chapter 5.4. Therefore, shallow tube bundles may experience a different behaviour and are excluded. Næss (2005) showed that for transversal-to-longitudinal-tube-pitch ratios (Pt/Pl) above ca. 2, heat transfer and pressure drop experienced a decrease with increasing pitch ratio.
However, data covering this area is at present very limited, and has therefore been excluded from this investigation. Also, from a thermal-hydraulic design perspective, the most attractive tube-pitch ratios are close to 1.15 (30° layout angle), which provides the most heat transfer surface area per unit volume, combined with the highest heat transfer coefficient (Næss (2007)).
CORRELATION DEVELOPMENT 113 In the interpretation of the fin-side heat transfer coefficient from the experimental
data, all sources with the exception of Ma et al. (2012) and Næss (2010) assumed uniform heat transfer coefficient distribution on the heat transfer surface. However, the correction made by Ma et al. (2012) and Næss (2010) for uneven heat transfer coefficient distribution was moderate, in the range of 3 to 7%, and the data were therefore accepted without modifications. The results from Ma et al. (2012) and Næss (2010) were therefore about 3%-7% higher than they would have appeared assuming uniform heat transfer coefficient distribution.
From Table 6-2 it can be seen that the experimental data expand the database data. The fin-height-to-tube-diameter ratio increased from 0.63 to 0.91 for the serrated-fin and from 0.71 to 0.74 for the solid-fin tube bundles. Note that the tested tube bundles were arranged in a more compact manner. The extended-surface ratio Ar and the heat-transfer-extended-surface-to-minimum-flow-area ratio Aht/Af,min for the tested tube bundles is in the upper range of all tube bundles of the database.
Figure 6-5 to Figure 6-8 compare the experimental data of this study with data from the database. The heat transfer data of the serrated-fin tubes (Figure 6-5) extends the database data both on the upper and lower limits. The solid-fin heat transfer experimental data (Figure 6-6) is in the same range as the literature data. However, this is not the case for the pressure drop. The Euler number of the new experiments is generally higher for both the serrated-fin data (Figure 6-7) and solid-fin data (Figure 6-8). Only Geometry 8, which has the smallest tube diameter of 13.5mm, is in the range of the literature data.
114 CORRELATION DEVELOPMENT Table 6-1: Experimental data from the literature included in the databases and used for correlation development with the experimental data of this study
Reference
Serrated fins Solid fins Heat
transfer Pressure
drop Heat
transfer Pressure drop Ackerman and Brunsvold (1970) X X
Brauer (1964) X
Briggs and Young (1963) X X
Cox (1973) X
Hashizume (1981) X X X X
Hofmann (2009) X X
Kawaguchi et al. (2004) X X
Kawaguchi et al. (2005) X X
Kawaguchi et al. (2006a) X X
Kawaguchi et al. (2006b) X X
Kays and London (1984) X X
Ma et al. (2012) X X
Næss (2007) X X
Robinson and Briggs (1966) X
Stasiulevičius et al. (1988) X X
Vampola (1966) X X
Ward and Young (1959) X X
Weierman (1977) X X
Weierman et al. (1978) X X Worley and Ross (1960) X X
CORRELATION DEVELOPMENT 115 Table 6-2: Range of parameters from the database and test bundles. Data in
parentheses are from the present investigation.
Parameter Range*
Serrated fins Solid fins Tube diameter do 17.20 / 12.83 – 63.50 Fin height to tube diameter -
hf/do
Fin pitch to tube diameter - sf/do
0.08 – 0.33 (0.11 – 0.20)
0.08 – 0.36 (0.12 – 0.21) Transversal tube pitch to
tube diameter - Pt/do
1.75 – 3.50 (2.20 – 3.41)
1.72 – 3.13 / 3.43 (2.20 – 2.87) Transversal tube pitch to
longitudinal tube pitch - Pt/Pl
0.75 – 2.00 Heat transfer surface to
minimum flow area ratio - Aht/Af,min
8.2 – 60.6 / 61.7 (30.2 – 59.1)
7.45 – 64.42 / 55.08 (26.8 – 58.5) Minimum flow area ratio to
flow area between the fins - Af,min/Af,fin
1.00 – 3.24 (1.00 – 1.38)
1.07 / 1.05 – 3.39 / 4.52 (1.00 – 1.38)
* Database: Minimum (heat transfer / pressure drop) - Maximum (heat transfer / pressure drop)
Test bundles: Minimum – Maximum
** For L-foot fins, the degree of serration was set to 0.99 instead of 1
116 CORRELATION DEVELOPMENT
Figure 6-1: Serrated-fin heat transfer data from the literature used for correlation development
Figure 6-2: Solid-fin heat transfer data from the literature used for correlation development
0 10000 20000 30000 40000 50000 Nu∙Pr‐1/3[‐]
0 10000 20000 30000 40000 50000 Nu∙Pr‐1/3[‐]
CORRELATION DEVELOPMENT 117
Figure 6-3: Serrated-fin pressure drop data from the literature used for correlation development
Figure 6-4: Solid fin pressure drop data from the literature used for correlation development
0 10 000 20 000 30 000 40 000 50 000
Euler number [‐]
0 10000 20000 30000 40000 50000
Euler number [‐]
118 CORRELATION DEVELOPMENT
Figure 6-5: Comparison of the experimental serrated-fin heat transfer data to the database data
Figure 6-6: Comparison of the experimental solid-fin heat transfer data to the database data
0 50 100 150 200 250 300
0 10000 20000 30000 40000 50000 Nu∙Pr‐1/3[‐]
Reynolds number [‐]
Database Geometry 1 Geometry 4 Geometry 5 Geometry 6 Geometry 7
0 50 100 150 200 250 300
0 10000 20000 30000 40000 50000 Nu∙Pr‐1/3[‐]
Reynolds number [‐]
Database Geometry 2 Geometry 3 Geometry 8
CORRELATION DEVELOPMENT 119
Figure 6-7: Comparison of the experimental serrated-fin pressure drop data to the database data
Figure 6-8: Comparison of the experimental solid -fin pressure drop data to the database data
0 10 000 20 000 30 000 40 000 50 000
Euler number [‐]
0 10000 20000 30000 40000 50000
Euler number [‐]
120 CORRELATION DEVELOPMENT