Linear sloshing frequencies in the annular region of a circular cylindrical container in the presence of a rigid baffle

Abstract

Sloshing in any type of container may invite instability to it. If some part of the free liquid surface in the annular region of a specially designed circular cylindrical container is covered with an annular baffle, the natural frequencies and the response of the liquid in the container undergo a drastic change. A partly covered free surface shifts the natural frequency above and away from the control frequency of the vehicle, in which the liquid-filled container is placed, which results in the reduction of sloshing mass participating in the dynamic motion of the system. The fundamental natural frequency of an inviscid and incompressible liquid is determined for increasing width of the baffle that is attached to the outer tank wall on the free surface. It is observed that by increasing the width of the baffle, natural frequencies can be significantly increased. Investigations are also carried out for different values of Bond number, which depicts different states of surface tension, and for varying values of the part of the radius in the fluid region. It is also observed that by increasing the fluid height inside the container, the natural frequencies can be increased, which results in reduction of sloshing.

Sloshing in vertical cylinders with circular walls: the effect of radial baffles

“…Here k 𝑝,𝑠 is the 𝑠th positive zero of 𝐽 𝑝 -the derivative of the Bessel function 𝐽 𝑝 with integer or half-integer 𝑝 ≥ 0 (again our notation differs from that in [14] for 𝑚 = 0). The twenty initial values in the increasing order are as follows: k1/2,1 = 1.1655..., k1,1 = 1.8411..., k3/2,1 = 2.4605..., k2,1 = 3.0542..., k5/2,1 = 3.6327..., k0,1 = 3.8317..., k3,1 = 4.2011..., k1/2,2 = 4.6042..., k7/2,1 = 4.7621..., k4,1 = 5.3175..., k1,2 = 5.3314..., k9/2,1 = 5.8684..., k3/2,2 = 6.0292..., k5,1 = 6.4156..., k2,2 = 6.7061..., k11/2,1 = 6.9597..., k0,2 = 7.0155..., k5/2,2 = 7.3670..., k6,1 = 7.5012..., k1/2,3 = 7.7898... (18) It should be noted that 𝑘 1,1 -the first value in (10) -coincides with k1,1 which is second here, whereas the eighth value in (10) is only fifteenth here. It is clear that every eigenvalue k2 𝑚/2,𝑠 with even 𝑚 is also an eigenvalue of problem ( 8), but for eigenvalues with odd 𝑚 this is not true.…”

“…Despite abundant numerical and analytical results (see e.g. [10] and references therein), the mechanism of the baffle effect is far from being completely understood. The aim of this note is to show the crucial role of breaking the axial symmetry in this phenomenon.…”

Coupled shallow-water fluid sloshing in an upright annular vessel

“…where D FD (ω) can be inferred from the ν = 0 limit result in [14] and P FD (ω) can be found in [17,18]. In (4.22)…”

“…They identified bifurcations where the fluid motion changed behaviour between planar sloshing, swirling and irregular sloshing motions. An annular vessel was also considered by [18] who calculated the natural sloshing frequencies in a stationary vessel when a rigid annular baffle is included at the free-surface. The study in this current article is the first such study to consider dynamically coupled sloshing in an annular vessel.…”

Liquid Vibrations in Cylindrical Tanks with and Without Baffles Under Lateral and Longitudinal Excitations

“…The dynamic analysis of fluid-filled shell structures using coupled finite and boundary element methods was discussed in [10][11]. To damp the liquid motion, reduce structural loads and prevent instability a lot of slosh-suppression devices have been proposed (Choudhary and Bora [12]). These devices are rigid or elastic ring baffles of different sizes and orientation, vertical partitions, various plates partly covering the free surface [13][14].…”