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 flowdirection and perpendicular to the flow direction for given unit Re were plotted (Fig. 3,4). As airemerges out of the bend, there is radial gradient of velocity due to centripetal acceleration (flow hasto 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 exper-imentally 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 ofvorticity downstream of flow causes secondary flow and the velocity profile and hence pressure distri-bution changes. As we had assumed inviscid irrotational flow for theoretical calculations of velocitydistribution 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 onthe inner circular surface, and positive on the outer circle. This is because velocity is decreasing withradius, and hence pressure increases with radius.

4. Negative Cp on inner circular surface (Fig. 6) is the leading cause of cavitation in various pipes andducts. Thus, knowledge of Cp is important in designing of water pipes so that pressure decrease iskept above vaporisation pressure of water.

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Figure 2. Static pressure distribution on wall along radial direction (indicated by ports 21(outermost) and25(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 beenestablished by pressure plotting. The pressure coefficient is negative and almost constant round the innerwall, and positive and almost constant round the outer wall. Across the 45 cross-section the pressuredistribution may be predicted with reasonable accuracy by assuming free-vortex velocity distribution overthe 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 theregion close to boundary. On the bottom surface, within the boundary layer, vorticity vector points in theplane of surface perpendicular to flow and as flow progresses to the outlet, it tilts and includes a stream-wisecomponent also. This stream-wise component is manifested as circulation often referred as secondary flowin ducts and pipes. Similar is the case with vorticity vector near upper wall surface, albeit the direction ofcirculation 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 inletand multiplying it with velocity across the cross-section. Note that, velocity across inlet cross section canbe 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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