Model of a Sloshing Tank

Background

• Oil tankers and transport trucks are two examples where sloshing can occur within a tank.

• If sloshing is too extreme, it can create a non-uniform distribution of weight within the tank.

• This model is a demo of free surface flow modeling using the Moving Mesh user-interface available in COMSOL Multiphysics

• The method used to move and deform the mesh in COMSOL Multiphysics is known as an Arbitray Lagrangian Eulerian (ALE) method

• The equations solved are the Navier-Stokes equations in a moving reference frame defined by the moving mesh

Model Definition

• The free surface condition (no flow cross the surface boundary) is formulated with the built in tangent and normal coordinate system boundary conditions for the moving mesh, and a neutral-stress boundary condition for Navier-Stokes equations at the top surface.

• Surface tension effects are neglected in this example, but could be included if needed

• The flow, initially at rest, is driven by an oscillating gravity vector. This is to mimic a periodic ’tank’ motion. This can be visualized using a deformation plot, where the entire frame is deformed according to the gravity vector.

• The example is made in 2D but could be generalized to 3D – you would only need a computer with more RAM compared to the 2D case.

Model Definition

• The fluid is glycerol with:= 1.49 Ns/m2

= 1270 kg/m3

The walls of the ’tank’ allow free slip.

• The gravity vector is (g_x,g_y)T, with:

g_x = g*sin(phi_0*sin(2*pi*f*t)),

g_y = -g*cos(phi_0*sin(2*pi*f*t)),

g = 9.81 m/s2

phi_0 = pi/128

f = 1 s-1

• The mesh deformation is computed according to the Navier-Stokes equations with the applied gravity load.

• Note that higher-order finite elements are used not only within the tank to represent the flow field but also to track the free fluid surface.

Model Definition – Mesh Movie** set in presentation mode to view

Results - Movie** set in presentation mode to view

• Results showing the vertical fluid velocity (y-velocty) in colors and the x-y velocity as arrows.

• The internal viscous force is the only energy dissipation mechanism in this example, therefore the wave amplitude is increasing and becomes large.

• After a while higher-order modes of oscillation become visible.

Results

• The wave height at the right side wall