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Photo: Emily Ranquist
The use of 90° elbows upstream of a pump inlet can distort the approach flow resulting in spatial and temporal velocity variations and swirling flow that negatively affect pump performance and increase maintenance requirements.
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Figures 3b and d show the cross-sectional mean velocity distributions at different positions for Setups 2 and 3, respectively. Upstream of the first elbow, the velocity profile is fully developed. At the elbow outlet, as observed by previous investigators (e.g., Sudo et al. 1992), there is a shift of the peak velocity toward the outer wall of the elbow due to the outward secondary flow, and a region having very low velocity is formed between the inner wall and the center of the pipe. The water with low velocity near the inner wall shifts toward the central region of the pipe, increasing gradually the velocity of the water near the inner wall. The region of low velocity moves farther toward the outer wall, and the secondary flow weakens gradually, its cores shifting to the central part of the pipe. Further downstream, the secondary flow breaks down and the longitudinal velocity shows a smooth distribution without unevenness. However, a further longitudinal distance is required for the flow to exhibit a symmetric velocity distribution, as shown in the upstream tangent. Fig. 3 Setup 2: a Contour map of swirl angle S, and b streamwise velocity U*; Setup 3: c Contour map of swirl angle S, and d streamwise velocity U* Full size image The spatial non-uniformity of the velocity at the pump inlet can cause pressure fluctuations on the pump impeller and, consequently, a loading imbalance on the pump shaft, possibly causing vibration or pre-mature bearing wear (Khan and Islam 2012). The overall acceptability of the velocity profile at the pump inlet has been based on the ratio of the minimum and maximum velocities, U min and U max , respectively, to the average velocity, U m (U* max = U max /U m and U* min = U min /U m ). The velocity profile is acceptable for the pump inlet once a cross section is able to produce velocities that are within 10% of the average velocity. Figure 4 shows U* max and U* min in function of x/D. Initially the curves distanced themselves from the dashed line (10% of the average velocity), then for a short-space, the curves remain inside the 10% region, and, finally, they tend to the values of the fully developed flow. Fig. 4 a Maximum and b minimum time-averaged velocities along the pipe after a long elbow (Setup 2). The velocities should be within 10% of the cross-sectional area average velocity. ● Rey = 5,000; ■ Rey = 10,000; ♦ Rey = 50,000;▲ Rey = 100,000; ► Rey = 250,000;◄ Rey = 425,000; ▼ Rey = 500,000 Full size image Figure 5 presents U* max and U* min in function of Reynolds number (Rey) for different curvature radius (Rc/D in ) and distances from the elbow. Although in general U* max decreases with increasing Reynolds, and U* min increases with increasing Reynolds, the values of U* max and U* min are never concomitantly within 10% of the average velocity. Enayet et al. (1982), Sudo et al. (1992), Ono et al. (2011), Hellström et al. (2013), and Kim et al. (2014) also observed velocity variation bigger than 10% of the cross-sectional average velocity Reynolds between 25,000 and 115,000, and for distances up to 50D downstream of the curve. It is worth to mention that we are ignoring the boundary layer effects. Fig. 5 Maximum and minimum time-averaged velocities along the pipe after a 90-degree elbow. The velocities should be within 10% of the cross-sectional area average velocity. ax/D = 0; bx/D = 5; cx/D = 10; dx/D = 50. ○ Rc/D = 1.0 (Hellström et al., 2013); ● Rc/D = 1.0 (Ono et al., 2011); ■ Rc/D = 1.0 (present work); ▲ Rc/D = 1.296 (present work); ♦ Rc/D = 1.5 (Ono et al., 2011); ▬ Rc/D = 2.0 (Sudo et al., 1992); x Rc/D = 3.0 (Kim et al., 2014) Full size image In order to explain these velocities bigger than 10% of the cross-sectional average velocity, we considered the empirical power-law equation as a good approximation for the velocity profile for fully developed turbulent flow through a smooth pipe (e.g., Fox et al. 2008), as follows
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$$ \frac{u}{{U_{ \hbox{max} } }} = \left( {1 - \frac{r}{R}} \right)^{{\frac{1}{n}}} $$ (1)
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Read More »Fig. 9 Distances (Ls) in which each Setup reached 5° for the swirl angle in function of the Reynolds number. ● Setup 1; ■ Setup 2; ♦ Setup 3; ▲ Setup 4 Full size image As already mentioned, Steenbergen and Voskamp (1998) showed that for turbulent swirling flows in straight pipes with smooth wall the dependence of the swirl decay rate on the Reynolds number is similar to that of the friction factor. Since the friction factor decreases with increasing Reynolds, the swirl angle also decreases. This means that as the Reynolds number increases, the rate of decrease in the friction factor diminishes. In a similar way, the swirl angle decay rate should also diminish with increasing Reynolds numbers. Consequently, the increase in Ls with Rey for a given setup should become smaller for increasing Reynolds numbers, as observed for Rey > 5.104 (Fig. 9). Note that the effect of wall roughness was not investigated. The discussion above was for smooth pipes. However, if we consider that the swirl decay rate is proportional to the friction factor, and that the friction factor is almost independent of the Reynolds number (valid only for a region of the Moody diagram), then Ls would have a similar behavior then that found in Fig. 9. However, since the influence of wall roughness was not modeled, this result should be taken cautiously, and included as a future work. For the two-elbow setups, the swirl is much more complicated, being a composite of two types of swirl, depending on the pipe length between the two elbows (Mattingly and Yeh 1991). For a long pipe length between the two elbows, the swirl should approach that of a single elbow case. The comparison of Ls from Setup 2 with Setup 3 show that, for Setup 3, the swirl produced by the first elbow still has an influence upon the swirl produced by the second elbow, tending to 11D. Finally, Setup 4, with the highest Rc, promoted the lowest swirl angle values of all setups and Reynolds numbers, reaching an angle of 5° within 5D for all Reynolds numbers. These numerical results can be used to evaluate the current specifications of ANSI/HI 9.8 (2012). Firstly, it can be observed that all elbows (or Setups) fall outside of the acceptance criteria, mainly because the velocity variation along the cross section is more than 10% of the average velocity along the cross section, i.e., this criterion must either be reviewed or better specified by the norm. This concern agrees with the conclusions presented by Verhaart et al. (2015), who stated that the criteria of the norm are not sufficiently clearly defined. Secondly, to reduce the swirl angle to less than 5° for short radius elbows, a length from 3D to 16D would be required. The ANSI/HI 9.8 (2012) specification of 5D for short radius elbows is not sufficient. Furthermore, long radius elbows cannot be considered as not flow-disturbing fittings as assumed by the norm, since they fall outside of two acceptance criteria, namely that the average swirl angle should be less than 5°, and that the time-averaged velocities at the pump suction shall be within 10% of the cross-sectional area average velocity.
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