PSI - Issue 32

R. Tsvetkov et al. / Procedia Structural Integrity 32 (2021) 209–215 R. Tsvekov et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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values correspond to the stabilization interval close to the minimum. For longer hoses (curves 3 and 4), the system turns out to be in the region of aperiodic oscillations with a large stabilization interval. Its reduction is possible by increasing the diameter of the hose. However, this solution is not always acceptable. Another solution is to select a working fluid with a lower viscosity. According to the table, for water the value of the parameter τ (from 0.78 to 12.5) is an order of magnitude higher than for oil. With such values of τ , fluid oscillations in hoses of any length with a cross-sectional radius of more than 5 mm will be realized in the mode of periodic oscillations. However, if the hose filled with water is thin and long ( R = 2.5 mm, L > 25 m), aperiodic oscillations appear in it, and the stabilization interval increases significantly. Thus, from the analysis presented here, we can offer several practical recommendations regarding the design of the hydrostatic leveling system. We can recommend using silicone fluid (oil) for medium and short levels with segment length of L <= 10 m. In this case, the interval of liquid stabilization after the disturbance is close to the minimum possible values even if the hose has a diameter of up to 10 mm. For HLS filled with oil with a segment length of more than 25 m and a total length of more than 100 m, the hose diameter must be increased. If this is unacceptable, a less viscous fluid should be selected. 4. Conclusions The paper proposes a mathematical model of fluid movement in a multi-point hydrostatic leveling system with an arbitrary number of sensors. The model, formulated in a dimensionless form, makes it possible to analyze oscillatory processes in a HLS depending on its geometric characteristics and on the characteristic time of the system, determined by the ratio of inertial and viscous forces in liquid. On the basis of numerical experiments, the dependences of the stabilization time of fluid oscillations in a leveling device on the indicated parameters are obtained. These dependences make it possible to select the type of fluid and the combination of geometric dimensions that provide the minimum possible value of the interval of fluid stabilization after its disturbance. The analysis of the results allows one to select the silicone oil for medium and short levels with segment length about 10 m and standard hose diameter (6-10 mm). For long HLS (segment length more than 25 m) the hose diameter must be increased or less viscous fluid should be selected. Acknowledgements The study was performed as part of a government-sponsored program (the state registration number of the topic is AAAA-A19-19012290100-8). References Boudin, F., Bernard, P., Longuevergne, L., Florsch, N., Larmat, C., Courteille, C., Blum, P-A. , Vincent, T., Kammentaler, M., 2008. A silica long base tiltmeter with high stability and resolution. Review of Scientific Instruments 79, 034502. Chen, Z., Zhang, N., Zhang, X., 2011. Settlement monitoring system of pile-group foundation. Journal of Central South University of Technology 18, 2122 – 2130. d’Oreye, N., Zürn, W., 2005. Very high resolution long -baseline water-tube tiltmeter to record small signals from Earth free oscillations up to secular tilts. Review of Scientific Instruments 76, 024501. Hirt, C., Nichols, B., 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39, 201 – 225. Manukin, A., Kazantseva, O., Bekhterev, S., Matyunin, V., Kalinnikov I,. 2014. Long base hydrostatic level. Seismic Instruments 50, 238 – 243. Meier, E., Geiger, A., Ingensand, H., Licht, H., Limpach, P., Steiger, A., Zwyssig, R. 2010. Hydrostatic levelling systems: Measuring at the system limits. Journal of Applied Geodesy 42, 91 – 102. Morishita, T., Ikegami, M., 2009. The slow-ground-motion monitoring based on the hydrostatic leveling system in J-PARC linac. Nuclear Instruments and Methods in Physics Research Section A 602, 364 – 371. Sun, Z., Zhang, S., Liu, N., 2015. Application and analysis of hydrostatic level gauges in deformation monitoring of subway tunnels during operation. Modern Tunneling Technology 52, 203 – 208. Tsvetkov, R, Shardakov, I., 2020. Mathematical model and numerical analysis of the dynamic characteristics of a hydrostatic leveling system with a tank. AIP Conference Proceedings 2312, 050023. Yi, Z., Jinshen, G., Xu, W., 2019. Intelligent settlement monitoring system of high-speed railway bridge. Journal of Civil Structural Health Monitoring 9, 307 – 323.