Sheet E6 · Experimental validation

Column separation at the valve (Simpson and Bergant, 1994)

Source : A. R. Simpson, A. Bergant, Journal of Hydraulic Research 32(2), 1994, pp. 183-194, figure 10

1. The question

After a very fast closure, the pressure drops to vapour pressure, a cavity forms and then collapses, creating peaks higher than Joukowsky. Does CBELIER, with its cavitation model, reproduce these peaks and their timing?

2. The case

A 37.2 m copper pipe slopes down to a valve closed in 10 ms, with an initial velocity of 0.76 m/s. Head is measured at the valve by a piezoelectric transducer. CBELIER uses the discrete gas cavity model (DGCM).

3. Data and status

Data	Value	Status
Pipe: L, D, wall thickness	37.2 m; 22 mm; 1.63 mm	PUBLISHED
Measured wave speed; initial velocity	1,328 m/s; 0.76 m/s	PUBLISHED
Closure time; upstream reservoir head	10 ms; 8.2 m	PUBLISHED
Head curve at the valve (fig. 10)	± 1 m; ± 1 ms	READ FROM FIGURE
Initial head at the valve	7.0 m	READ FROM FIGURE
Elevation drop (slope ≈ 1/20)	1.86 m	DERIVED
Roughness; open-valve loss; linear closure	1.5 µm; 0.5 m	ASSUMED

4. Results

Head at the valve: CBELIER, DGCM (line) and measurement digitised from figure 10 (circles, one in three).

5. Differences

Indicator	CBELIER	Reference	Difference
Peak no. 1	107.0 m	113.1 m	−5.4 %
Time of peak no. 1	0.029 s	0.027 s	2 ms
Peak no. 2	106.8 m	110.2 m	−3.1 %
Time of peak no. 2	0.388 s	0.402 s	−14 ms
Peak no. 3	110.9 m	98.5 m	12.6 %
Time of peak no. 3	0.702 s	0.710 s	−8 ms

The first two peaks are reproduced within 6 % and all the times within 15 ms. The third peak is overestimated by 13 %. The RMS difference is not a good indicator here: with almost vertical fronts, a 10 ms shift is enough to make it explode.

6. Limitations and assumptions

Five test data are not published and are assumed or read (roughness, exact elevation drop, valve loss, closure shape, valve head).
The third peak exceeds the 10 % target: repeated column separation remains the hardest phenomenon for every model.
The measured minimum pressure falls below the theoretical vapour pressure: an effect of the transducer or the datum, not modelled.