TY - GEN
T1 - Asymptotic wavefront behaviour - what outcomes are possible?
AU - Vardy, Alan E.
N1 - Publisher Copyright:
© Deltares 2026.
PY - 2026/4/16
Y1 - 2026/4/16
N2 - Wavefronts propagating along ducts tend to steepen continuously, potentially leading to the development of shocks. This extreme outcome is highly unlikely in the case of liquid flows, but it can cause significant problems in some applications of gas flows. One such example has motivated studies of various methods of limiting the steepening process, including the one presented herein. The method involves the provision of open chambers along an air duct, designed to (passively) trap and store small quantities of air as it is pressurised at the leading face of a wavefront. The cumulative influence of many such chambers causes the steepness to evolve towards a definite, finite limit, and it is shown that the same limit applies regardless of whether the wavefront is initially more-steep or less-steep. In this limiting, asymptotic state, nothing would change as the wavefront proceeds for along the duct. The crucial feature of this method is the mass sink that the chambers provide. It is shown to be unlikely that any realistic method that does not include such a sink could lead to a similar asymptotic condition. This expectation is illustrated with reference to a comparison of two cases with a distributed mass-sink. In one, friction is absent. In the other, it is greatly exaggerated. The influence of this difference is shown to be much smaller than that of the mass sink. A novel contribution of the paper, of special value for initial design purposes, is the development of a simple expression for the minimum size of chambers that has the potential to limit wavefront steepening in long ducts.
AB - Wavefronts propagating along ducts tend to steepen continuously, potentially leading to the development of shocks. This extreme outcome is highly unlikely in the case of liquid flows, but it can cause significant problems in some applications of gas flows. One such example has motivated studies of various methods of limiting the steepening process, including the one presented herein. The method involves the provision of open chambers along an air duct, designed to (passively) trap and store small quantities of air as it is pressurised at the leading face of a wavefront. The cumulative influence of many such chambers causes the steepness to evolve towards a definite, finite limit, and it is shown that the same limit applies regardless of whether the wavefront is initially more-steep or less-steep. In this limiting, asymptotic state, nothing would change as the wavefront proceeds for along the duct. The crucial feature of this method is the mass sink that the chambers provide. It is shown to be unlikely that any realistic method that does not include such a sink could lead to a similar asymptotic condition. This expectation is illustrated with reference to a comparison of two cases with a distributed mass-sink. In one, friction is absent. In the other, it is greatly exaggerated. The influence of this difference is shown to be much smaller than that of the mass sink. A novel contribution of the paper, of special value for initial design purposes, is the development of a simple expression for the minimum size of chambers that has the potential to limit wavefront steepening in long ducts.
KW - air-chambers
KW - asymptotic wavefronts
KW - mass sinks
KW - wavefront steepening
UR - https://cms.deltares.nl/assets/common/downloads/Pressure-Surge-Conference-15-Programme-FINAL.pdf
UR - https://www.deltares.nl/en/events/pressure-surge-conference-2026
UR - https://www.scopus.com/pages/publications/105040231207
M3 - Conference contribution
AN - SCOPUS:105040231207
T3 - 15th International Conference on Pressure Surges 2026
SP - 369
EP - 383
BT - 15th International Conference on Pressure Surges 2026
A2 - Jones, Sarah E. L.
PB - Deltares
T2 - 15th International Conference on Pressure Surges 2026
Y2 - 15 April 2026 through 17 April 2026
ER -