The Sonar Flow Meter Further Results for the

The Sonar Flow Meter Further Results for the Angled Flow Meter Prepared by: Enrico Da Riva, Gennaro Bozza 11 th November 2011 11 November 2011 Gennaro Bozza 1

Summary • The velocity and pressure contours for: • Transducers max distance: alpha 15, 30 and 45 degrees • Transducers mid distance: alpha 15, 30 and 45 degrees • Transducers min distance: alpha 15, 30 and 45 degrees • Considerations about the total pressure in the domain December 24, 2021 Gennaro Bozza 2

The Angled Flow Meter D=133. 7 mm, distance max, alpha 15 degrees v Pressure contours • The simulation shows that the pressure in the upper secondary pipe is higher than the pressure in the lower secondary pipe. Indeed, the main stream act as a plunger v towards the still flow in the secondary pipe. December 24, 2021 Gennaro Bozza 3

The Angled Flow Meter D=133. 7 mm, distance max, alpha 15 degrees Uy contours The negative velocity on one side of both secondary tubes is a clear sign of the presence of a vortex. The main stream drags the fluid present in the secondary pipes, and the result is a clockwise-rotating vortex in the upper tube and a counterclockwise-rotating vortex in the lower tube. The main stream is influenced by the upper secondary tube, because of the edge facing towards the main stream. However, this doesn’t influence the measurement. December 24, 2021 Gennaro Bozza 4

The Angled Flow Meter D=133. 7 mm, distance max, alpha 30 degrees v Pressure contours December 24, 2021 Gennaro Bozza 5

The Angled Flow Meter D=133. 7 mm, distance max, alpha 30 degrees Uy contours December 24, 2021 Gennaro Bozza 6

The Angled Flow Meter D=133. 7 mm, distance max, alpha 45 degrees v Pressure contours December 24, 2021 Gennaro Bozza 7

The Angled Flow Meter D=133. 7 mm, distance max, alpha 45 degrees Uy contours December 24, 2021 Gennaro Bozza 8

The Angled Flow Meter D=133. 7 mm, distance mid, alpha 15 degrees v Pressure contours v December 24, 2021 Gennaro Bozza 9

The Angled Flow Meter D=133. 7 mm, distance mid, alpha 15 degrees Uy contours December 24, 2021 Gennaro Bozza 10

The Angled Flow Meter D=133. 7 mm, distance mid, alpha 30 degrees v Pressure contours v December 24, 2021 Gennaro Bozza 11

The Angled Flow Meter D=133. 7 mm, distance mid, alpha 30 degrees Uy contours December 24, 2021 Gennaro Bozza 12

The Angled Flow Meter D=133. 7 mm, distance mid, alpha 45 degrees v Pressure contours v December 24, 2021 Gennaro Bozza 13

The Angled Flow Meter D=133. 7 mm, distance mid, alpha 45 degrees Uy contours December 24, 2021 Gennaro Bozza 14

The Angled Flow Meter D=133. 7 mm, distance min, alpha 15 degrees v Pressure contours v December 24, 2021 Gennaro Bozza 15

The Angled Flow Meter D=133. 7 mm, distance min, alpha 15 degrees Uy contours December 24, 2021 Gennaro Bozza 16

The Angled Flow Meter D=133. 7 mm, distance min, alpha 30 degrees v Pressure contours v December 24, 2021 Gennaro Bozza 17

The Angled Flow Meter D=133. 7 mm, distance min, alpha 30 degrees Uy contours December 24, 2021 Gennaro Bozza 18

The Angled Flow Meter D=133. 7 mm, distance min, alpha 45 degrees v Pressure contours December 24, 2021 Gennaro Bozza v 19

The Angled Flow Meter D=133. 7 mm, distance min, alpha 45 degrees Uy contours December 24, 2021 Gennaro Bozza 20

The Angled Flow Meter Consideration about the total pressure The total pressure ptot is defined as the sum of the static pressure pstat and the dynamic pressure . The dynamic pressure in the secondary tube is evidently 0, and therefore it equals the total pressure. On the following page there is the comparison among static and total pressure contours: we can also see how the total pressure decreases in correspondence of the wake, where the flow is not isoentropically slowed down. December 24, 2021 Gennaro Bozza 21

The Angled Flow Meter Consideration about the total pressure December 24, 2021 Gennaro Bozza 22

The Angled Flow Meter Consideration about the total pressure We tried to manually compute the pressure in the secondary tube by assuming that the dynamic pressure equals . However this is not correct since, in fact, the u cosα component doesn’t slow down to 0 in at the border of the secondary pipe and, as a result, the main flow doesn’t transfer all the energy to the still fluid. The amount of energy transferred to the fluid in the secondary pipe is smaller than the amount as calculated above. December 24, 2021 Gennaro Bozza 23

Thank you December 24, 2021 Gennaro Bozza 24