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Analytical and Numerical Model of Sloshing in a Rectangular Tank Subjected to a Braking

Author

Listed:
  • Oana-Maria Balaş

    (Department of Machine Building, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Cristian Vasile Doicin

    (Department of Machine Building, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Elena Corina Cipu

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    CiTi, Faculty of Applied Sciences, University Politehnica of Bucharest, 060042 Bucharest, Romania)

Abstract

This paper examines the movement of waves that occur in a fuel tank—both with and without a wave breaker—when a car is travelling at a constant speed and then suddenly brakes. This phenomenon is known as slosh noise, and the paper presents an analysis of the movement of free surfaces in relation to the level of noise generated. The paper focuses on mathematical models of the fluid flow for both tanks—one without any technical solutions for breaking waves, and the other with a solution for breaking waves. The model is constructed based on a set of initial hypotheses about the fluid flow within the tank, by developing the speed potential in a series of fundamental solutions and considering the main variables that affect the phenomenon of sloshing, such as the depth of the liquid, the tank’s geometry, and the frequency and amplitude of the initial external force acting on the tank. The analysis of free surface movement is used to find the correlation with the sound generated in the tank. Nonlinearities that arise from the sudden braking are also modelled and numerically studied using MATLAB software. Following the mathematical model, a technical wave-breaking solution was implemented and tested, and it was shown that the amplitude of the movement of the free surface is reduced by half. Further research on the correspondence between the free surface movement based on the behaviour of potential energies in the two cases may be developed.

Suggested Citation

  • Oana-Maria Balaş & Cristian Vasile Doicin & Elena Corina Cipu, 2023. "Analytical and Numerical Model of Sloshing in a Rectangular Tank Subjected to a Braking," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:949-:d:1066704
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    References listed on IDEAS

    as
    1. Emma Frosina & Adolfo Senatore & Assunta Andreozzi & Francesco Fortunato & Pino Giliberti, 2018. "Experimental and Numerical Analyses of the Sloshing in a Fuel Tank," Energies, MDPI, vol. 11(3), pages 1-24, March.
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