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

Oana-Maria Balaş (), Cristian Vasile Doicin and Elena Corina Cipu
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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

Mathematics, 2023, vol. 11, issue 4, 1-16

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.

Keywords: slosh noise; rectangular tank; mathematical modelling; potential flow; spectral methods; fundamental solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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