Flow through pipe bend

Shubham Maurya Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, 695547, India

I.

Results and Discussion

1. Variation of wall static pressure distribution (Fig.1,2)and wall co-efficient of pressure along the flow direction and perpendicular to the flow direction for given unit Re were plotted (Fig. 3,4). As air emerges out of the bend, there is radial gradient of velocity due to centripetal acceleration (flow has to turn). Thus, pressure and Cp increase with radius.

Figure 1. Static pressure distribution on wall along flow direction (indicated by ports) for varying unit Re

2. The Cp variation with radius was theoretically found by free vortex flow assumption. The experimentally obtained Cp was compared with theoretical results and plotted against radius. (Fig. 5) The experimental results resemble free vortex flow. However, the Cp at the extremes differ by ±0.2. This is caused by boundary layer effect which leads to vortex tilting. The stream-wise component of vorticity downstream of flow causes secondary flow and the velocity profile and hence pressure distribution changes. As we had assumed inviscid irrotational flow for theoretical calculations of velocity distribution along radius, the experimental and theoretical results will certainly differ. 3. A schematic representation of Cp variation on wall is illustrated in (Fig. 6). The Cp is negative on the inner circular surface, and positive on the outer circle. This is because velocity is decreasing with radius, and hence pressure increases with radius. 4. Negative Cp on inner circular surface (Fig. 6) is the leading cause of cavitation in various pipes and ducts. Thus, knowledge of Cp is important in designing of water pipes so that pressure decrease is kept above vaporisation pressure of water. 1 of 7

Figure 2. Static pressure distribution on wall along radial direction (indicated by ports 21(outermost) and 25(innermost)) for different unit Re

Figure 3. Cp distribution on wall along flow direction (indicated by ports) for varying unit Re

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Figure 4. Cp distribution on wall with radius (indicated by ports) for varying unit Re

Figure 5. Cp distribution on wall at different radii (from r=150 mm to r=200 mm)

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Figure 6. Schematic Cp distribution on wall

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II.

Conclusion

The distribution of pressure over the curved walls of a 90 bend of rectangular duct section has been established by pressure plotting. The pressure coefficient is negative and almost constant round the inner wall, and positive and almost constant round the outer wall. Across the 45 cross-section the pressure distribution may be predicted with reasonable accuracy by assuming free-vortex velocity distribution over the section. The part of duct where it transitions from straight line to circular bend, the pressure increases with radius. But, at curved boundary of the surfaces, no slip condition exists and boundary layer effects dominate in the region close to boundary. On the bottom surface, within the boundary layer, vorticity vector points in the plane of surface perpendicular to flow and as flow progresses to the outlet, it tilts and includes a stream-wise component also. This stream-wise component is manifested as circulation often referred as secondary flow in ducts and pipes. Similar is the case with vorticity vector near upper wall surface, albeit the direction of circulation is opposite (Fig.7).

Figure 7. Secondary flow in rectangular duct

We can use the apparatus as flow meter by taking the cross-sectional area at straight section at inlet and multiplying it with velocity across the cross-section. Note that, velocity across inlet cross section can be approximated as uniform as there are no secondary flow. Discharge rate (Q) at 900 rpm =A.v = 0.05 ∗ 0.1 ∗ 22.60 = 0.113m3 /s

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