Next Article in Journal
Bathymetry Time Series Using High Spatial Resolution Satellite Images
Previous Article in Journal
Assessment of the Soil Erosion Response to Land Use and Slope in the Loess Plateau—A Case Study of Jiuyuangou
Previous Article in Special Issue
Oblique Wave Attack on Rubble Mound Breakwater Crest Walls of Finite Length
Open AccessArticle

Mathematical Model of Small-Volume Air Vessel Based on Real Gas Equation

College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China
College of Water Conservancy and Civil Engineering, Xinjiang Agricultural University, Urumqi 830052, China
Authors to whom correspondence should be addressed.
Water 2020, 12(2), 530; (registering DOI)
Received: 22 January 2020 / Revised: 9 February 2020 / Accepted: 10 February 2020 / Published: 13 February 2020
(This article belongs to the Special Issue Physical Modelling in Hydraulics Engineering)
The gas characteristics of an air vessel is one of the key parameters that determines the protective effect on water hammer pressure. Because of the limitation of the ideal gas state equation applied for a small-volume vessel, the Van der Waals (VDW) equation and Redlich–Kwong (R–K) equation are proposed to numerically simulate the pressure oscillation. The R–K polytropic equation is derived under the assumption that the volume occupied by the air molecules themselves could be ignored. The effects of cohesion pressure under real gas equations are analyzed by using the method of characteristics under different vessel diameters. The results show that cohesion pressure has a significant effect on the small volume vessel. During the first phase of the transient period, the minimum pressure and water depth calculated by a real gas model are obviously lower than that calculated by an ideal gas model. Because VDW cohesion pressure has a stronger influence on the air vessel pressure compared to R–K air cohesion pressure, the amplitude of head oscillation in the vessel calculated by the R–K equation becomes larger. The numerical results of real gas equations can provide a higher safe-depth margin of the water depth required in the small-volume vessel, resulting in the safe operation of the practical pumping pipeline system. View Full-Text
Keywords: small volume air vessel; R–K equation; VDW equation; pressure fluctuation small volume air vessel; R–K equation; VDW equation; pressure fluctuation
Show Figures

Figure 1

MDPI and ACS Style

Ni, W.; Zhang, J.; Shi, L.; Wang, T.; Zhang, X.; Chen, S. Mathematical Model of Small-Volume Air Vessel Based on Real Gas Equation. Water 2020, 12, 530.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

Back to TopTop