Computer modelling of liquid sloshing in tanks under periodic loads
Abstract
The paper aims on developing the computer methodology for taking damping into account when analysing the stability of fluid movement in reservoirs and fuel tanks under periodic external loads
Relevance. Damping plays a critical role in providing stability and reducing potential hazards in tanks partially filled with liquid. Lack of cushioning can lead to motion instability. In liquid tanks, any movement disturbances such as sudden acceleration, deceleration or turning can cause sloshing. Without damping, sloshing can even increase, potentially leading to uncontrolled and dangerous situations, especially in vehicles or at industrial processes. Damping provides control over the clapping dynamics, providing smoother and more predictable behaviour. By damping out excessive vibrations, engineers can ensure that the fluid remains stable inside the fuel tank, reducing the risk of excessive dynamic loads on the tank structure or the vehicle carrying it. Therefore, studies devoted to the study of clapping damping are relevant.
Research methods. The methods of integral equations, the method of given forms, and the method of boundary elements were used to solve the problem of damping splashes.
The results. The spectral boundary value problem was solved and the frequencies and forms of natural oscillations of the fluid were found. Combined horizontal and vertical loads were studied, and zones of stable and unstable movement were found depending on the load parameters. The effect of damping using the Rayleigh matrix was studied. The importance of the obtained results on fluid splashing in rigid tanks is to clarify the critical role of damping in providing stability and reducing potential hazards to the stability of launch vehicle fuel tanks during flight.
Conclusions. The method for determining the time-varying level of the liquid free surface in rigid shells of revolution has been developed. The spectral problem of determining the frequencies and modes of liquid oscillations in a truncated conical tank is solved by reducing it to the system of one-dimensional integral equations. With the help of the Ince-Strutt diagram, the zones of instability of fluid movement under harmonic vertical loads were found. The effect of Rayleigh damping on the growth of the free surface level has been clarified. In the future, it is planned to study the oscillations of elastic shells of rotation with liquid, using various composite materials
Downloads
References
/References
A. Karaiev, E. Strelnikova, (2020). Liquid Sloshing in Circular Toroidal and Coaxial Cylindrical Shells. In: Ivanov, V., Pavlenko, I., Liaposhchenko, O., Machado, J., Edl, M. (eds) Advances in Design, Simulation and Manufacturing III. DSMIE 2020. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-50491-5_1
O.-M. Balas C. V. Doicin and E. C. Cipu, (2023). Analytical and Numerical Model of Sloshing in a Rectangular Tank Subjected to a Braking, Mathematics, Vol. 11, P. 949-955, DOI:10.3390/math11040949
J. Liu Q. Zang, W. Ye, G. Lin, (2020). High performance of sloshing problem in cylindrical tank with various barrels by isogeometric boundary element method”, Engineering Analysis with Boundary Elements, , Vol. 114, P. 148-165, DOI:10.1016/j.enganabound.2020.02.014
D. V. Krutchenko, Е. А. Strelnikova, Shuvalova Y. S. (2017). Discrete singularities method in problems of seismic and impulse impacts on reservoirs. Bulletin of VN Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems», vol. 35, pp. 31-37. http://lib.kart.edu.ua/bitstream/123456789/13113/1/Krutchenko.pdf.
P. Lampart, A. Rusanov, S. Yershov, S. Marcinkowski, A. Gardzilewicz, (2005).Validation of a 3D BANS solver with a state equation of thermally perfect and calorically imperfect gas on a multi-stage low-pressure steam turbine flow, Journal of Fluids Engineering, Transactions of the ASME, vol. 127(1), pp. 83–93,2005. DOI: 10.1115/1.185249.
A. Malykhina, D. Merkulov, O. Postnyi, N. Smetankina, (2019). Stationary problem of heat conductivity for complex-shape multilayer plates. Bulletin of VN Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems», vol. 41, pp. 46-54,. DOI:10.26565/2304-6201-2019-41-05.
K.Murawski, (2020). Technical Stability of Very Slender Rectangular Columns Compressed by Ball-And-Socket Joints without Friction, Int. Journal of Structural Glass and Advanced Materials Research, vol, 4(1), pp. 186-208, DOI: 10.3844/sgamrsp.2020.186.208
C.Tong, Y. Shao, H. B. Bingham, & FC. W. Hanssen, (2021). An Adaptive Harmonic Polynomial Cell Method with Immersed Boundaries: Accuracy, Stability and Applications. International Journal for Numerical Methods in Engineering, , Vol. 122, P. 2945–2980. https://doi.org/10.1002/nme.6648.
E. Strelnikova, D. Kriutchenko, V. Gnitko, A. Tonkonozhenko, (2020).Liquid Vibrations in Cylindrical Tanks with and Without Baffles Under Lateral and Longitudinal Excitations, International Journal of Applied Mechanics and Engineering, Vol. 25, Issue 3, P. 117-132, DOI: 10.2478/ijame-2020-0038.
S. K. Poguluri, Il H. Cho, (2023).Effect of vertical porous baffle on sloshing mitigation of two-layered liquid in a swaying tank, Ocean Engineering, vol. 289, Part 1, 115952, https://www.sciencedirect.com/science/article/pii/S0029801823023363
N. Choudhary, S.N. Bora and E. Strelnikova, (2021). Study on liquid sloshing in an annular rigid circular cylindrical tank with damping device placed in liquid domain, J. Vib. Eng. Tech., vol. 9, pp. 1–18, DOI:10.1007/s42417-021-00314-w
N. Choudhary, N. Kumar, E. Strelnikova, V. Gnitko, D. Kriutchenko, K. Degtyariov, (2021). Liquid vibrations in cylindrical tanks with flexible membranes. Journal of King Saud University – Science, vol. 33(8), 101589, doi.org/10.1016/j.jksus.2021.101589.
O. Sierikova, E. Strelnikova, Gnitko V, Degtyarev K. (2021).Boundary Calculation Models for Elastic Properties Clarification of Three-dimensional Nanocomposites Based on the Combination of Finite and Boundary Element Methods. IEEE 2nd KhPI Week on Advanced Technology (KhPIWeek), pp. 351–356,.doi: 10.1109/KhPIWeek53812.2021.9570086
M. Konopka, F., De Rose, H. Strauch, C. Jetzschmann, N. Darkow, J. Gerstmann, (2019). “Active slosh control and damping - Simulation and experiment, Acta Astronautica, vol. 158, pp. 89 - 102, https://doi.org/10.1016/j.actaastro.2018.06.055.
Y. Zhang, D. Wan, (2018), MPS-FEM coupled method for sloshing flows in an elastic tank”, Ocean Engineering, vol. 152, pp. 416-427, https://doi.org/10.1016/j.oceaneng.2017.12.008
V. Gnitko, A. Karaiev, K.Degtyariov, E.Strelnikova, (2019). Singular boundary method in a free vibration analysis of compound liquid-filled shells, WIT Transactions on Engineering Sciences, Vol. 126, P. 189-200, WIT Press, DOI:10.2495/BE420171.
I. A. Raynovskyy and A. N. Timokha, (2020). Sloshing in Upright Circular Containers: Theory, Analytical Solutions, and Applications, CRC Press/Taylor and Francis Group, https://doi.org/10.1201/9780429356711
R. A. 1brahim, Liquid Sloshing Dynamics. Theory and Applications. Cambridge University Press. 2005, 984 p.
K. Pradeepkumar, V. Selvan, K.Satheeshkumar, (2020). Review of Numerical Methods for Sloshing, International Journal for Research in Applied Science & Engineering Technology, Vol. 8, Issue XI, doi.org/10.22214/ijraset.2020.32116.
Gavrilyuk I., Hermann M., Lukovsky I., Solodun O., Timokha A. (2008). Natural Sloshing frequencies in Truncated Conical Tanks, Engineering Computations, vol. 25, no. 6, pp. 518 – 540, DOI: 10.1108/02644400810891535
O. Sierikova, E. Strelnikova and K. Degtyariov, (2022). Srength Characteristics of Liquid Storage Tanks with Nanocomposites as Reservoir Materials, 2022 IEEE 3rd KhPI Week on Advanced Technology (KhPIWeek), Kharkiv, Ukraine, pp. 1-7, DOI:10.1109/KhPIWeek57572.2022.9916369.
Karaiev A., Strelnikova E. Liquid Sloshing in Circular Toroidal and Coaxial Cylindrical Shells. In: Ivanov, V., Pavlenko, I., Liaposhchenko, O., Machado, J., Edl, M. (eds) Advances in Design, Simulation and Manufacturing III. DSMIE 2020. Lecture Notes in Mechanical Engineering. Springer, Cham. 2020. https://doi.org/10.1007/978-3-030-50491-5_1
Balas O.-M., Doicin C. V. and Cipu E. C. Analytical and Numerical Model of Sloshing in a Rectangular Tank Subjected to a Braking, Mathematics, vol. 11, pp. 949-955, 2023. DOI:10.3390/math11040949
Liu J., Zang Q., Ye W., Lin G. High performance of sloshing problem in cylindrical tank with various barrels by isogeometric boundary element method, Engineering Analysis with Boundary Elements, vol.114, pp.148-165, 2020. DOI:10.1016/j.enganabound.2020.02.014.
Krutchenko D. V., Strelnikova Е. А., Shuvalova Y. S. Discrete singularities method in problems of seismic and impulse impacts on reservoirs. Вісник Харківського національного університету імені В.Н.Каразіна, сер. «Математичне моделювання. Інформаційні технології. Автоматизовані системи управління», т. 35, С. 31-37, 2017, http://lib.kart.edu.ua/bitstream/123456789/13113/1/Krutchenko.pdf.
Lampart P., Rusanov A., Yershov S., Marcinkowski S., Gardzilewicz A. Validation of a 3D BANS solver with a state equation of thermally perfect and calorically imperfect gas on a multi-stage low-pressure steam turbine flow, Journal of Fluids Engineering, Transactions of the ASME, vol. 127(1), pp. 83–93,2005. DOI: 10.1115/1.185249.
Malykhina A., Merkulov D., Postnyi O., Smetankina N. Stationary problem of heat conductivity for complex-shape multilayer plates, Вісник Харківського національного університету імені В.Н.Каразіна, сер. «Математичне моделювання. Інформаційні технології. Автоматизовані системи управління», т. 41, С. 46-54, 2019. DOI:10.26565/2304-6201-2019-41-05.
Murawski K. Technical Stability of Very Slender Rectangular Columns Compressed by Ball-And-Socket Joints without Friction, Int. Journal of Structural Glass and Advanced Materials Research, vol. 4(1), pp. 186-208, 2020. DOI: 10.3844/sgamrsp.2020.186.208
Tong C., Shao Y., Bingham H.B. & Hanssen, FC. W., An Adaptive Harmonic Polynomial Cell Method with Immersed Boundaries: Accuracy, Stability and Applications. International Journal for Numerical Methods in Engineering, vol. 122, pp. 2945–2980, 2021. https://doi.org/10.1002/nme.6648
Strelnikova E., Kriutchenko D., Gnitko V. Tonkonozhenko A., Liquid Vibrations in Cylindrical Tanks with and Without Baffles Under Lateral and Longitudinal Excitations. International Journal of Applied Mechanics and Engineering, vol. 25(3), pp.117-132, 2020. DOI:10.2478/ijame-2020-0038
Poguluri S. K., Cho Il H., Effect of vertical porous baffle on sloshing mitigation of two-layered liquid in a swaying tank, Ocean Engineering, vol. 289, Part 1, 2023,115952, https://www.sciencedirect.com/science/article/pii/S0029801823023363
Choudhary N., Bora S.N. and Strelnikova E., Study on liquid sloshing in an annular rigid circular cylindrical tank with damping device placed in liquid domain, J. Vib. Eng. Tech., vol. 9, pp. 1–18, 2021. DOI:10.1007/s42417-021-00314-w
Choudhary N., Kumar N., Strelnikova E., Gnitko V., Kriutchenko D., Degtyariov K. Liquid vibrations in cylindrical tanks with flexible membranes. Journal of King Saud University – Science, vol. 33(8), 101589, 2021. doi.org/10.1016/j.jksus.2021.101589.
Sierikova O, Strelnikova E, Gnitko V, Degtyarev K., Boundary Calculation Models for Elastic Properties Clarification of Three-dimensional Nanocomposites Based on the Combination of Finite and Boundary Element Methods. IEEE 2nd KhPI Week on Advanced Technology (KhPIWeek), pp. 351–356, 2021. doi: 10.1109/KhPIWeek53812.2021.9570086
Konopka M., De Rose F., Strauch H., Jetzschmann C., Darkow N., Gerstmann J., Active slosh control and damping - Simulation and experiment, Acta Astronautica, vol. 158, pp. 89-102, 2019, https://doi.org/10.1016/j.actaastro.2018.06.055.
Zhang Y., Wan D., MPS-FEM coupled method for sloshing flows in an elastic tank, Ocean Engineering, vol. 152, pp. 416-427, 2018, https://doi.org/10.1016/j.oceaneng.2017.12.008.
Gnitko V., Karaiev A., Degtyariov K., Strelnikova E. Singular boundary method in a free vibration analysis of compound liquid-filled shells, WIT Transactions on Engineering Sciences, vol.126, pp.189-200, 2019. WIT Press, DOI:10.2495/BE420171.
Raynovskyy I. A. and Timokha A. N. Sloshing in Upright Circular Containers: Theory, Analytical Solutions, and Applications, 2020, CRC Press/Taylor and Francis Group, https://doi.org/10.1201/9780429356711
1brahim R. A., 2005. Liquid Sloshing Dynamics. Theory and Applications. Cambridge University Press.
Pradeepkumar K., Selvan V., Satheeshkumar K., Review of Numerical Methods for Sloshing. International Journal for Research in Applied Science & Engineering Technology. vol.8, Issue XI, 2020, doi.org/10.22214/ijraset.2020.32116.
Gavrilyuk I., Hermann M., Lukovsky I., Solodun O., Timokha A., Natural Sloshing frequencies in Truncated Conical Tanks, Engineering Computations, vol. 25, no. 6, pp.518 – 540, 2008, DOI: 10.1108/02644400810891535.
Sierikova O., Strelnikova E. and Degtyariov K., Srength Characteristics of Liquid Storage Tanks with Nanocomposites as Reservoir Materials, 2022 IEEE 3rd KhPI Week on Advanced Technology (KhPIWeek), Kharkiv, Ukraine, pp. 1-7, 2022, doi: 10.1109/KhPIWeek57572.2022.9916369
