Sheet V3 · Verification

Mass oscillation in a surge tank

Source : Independent rigid-column integration (fourth-order Runge-Kutta), verification/tests/CBELIER_test_verification_methodologie.mjs

1. The question

After a valve closure, the level in a surge tank oscillates slowly. Does CBELIER, which computes the waves, reproduce the extreme levels given by the rigid-column equation?

2. The case

upstream reservoirconduit, L = 2,000 mvalveoutletsurge tank

A reservoir feeds a 2,000 m conduit ending at a surge tank, then a valve closed at t = 1 s. CBELIER's full computation (waves and tank) is compared with a separately written rigid-column integration using the same friction and the same tank entry loss. Three geometries are tried.

3. Data and status

DataValueStatus
Conduit: length, wave speed2,000 m; 1,000 m/sDEFINED
Case 1: D, tank area, ζ2 m; 20 m²; 0DEFINED
Case 2: D, tank area, ζ2 m; 20 m²; 1DEFINED
Case 3: D, tank area, ζ1.5 m; 30 m²; 0.2DEFINED
Valve closureinstantaneous at 1 sDEFINED

4. Results

19202122050100150200time (s)level in the tank (m)CBELIER (waves + tank)RK4 rigid column
Case 2 (ζ = 1): level in the tank, CBELIER (line) and rigid column (circles). The rigid column starts at the closure (t = 1 s).

5. Differences

IndicatorCBELIERReferenceDifference
Case 1: maximum level22.097 m22.096 m0.001 m
Case 1: difference relative to the amplitude0.04 %—tolerance 1 %
Case 2: maximum level22.500 m22.506 m−0.005 m
Case 2: difference relative to the amplitude0.15 %—tolerance 1 %
Case 3: maximum level22.196 m22.201 m−0.005 m
Case 3: difference relative to the amplitude0.14 %—tolerance 1 %

The extreme levels agree within 0.2 % of the amplitude in all three geometries. CBELIER computes both the fast waves and the slow oscillation without losing mass.

6. Limitations and assumptions