The problem of decaying rotation of a disk floating on the surface of a viscoelastic fluid in a cylindrical container is solved by numerical methods. The motion is found to have the form of decaying oscillations observed previously for water. In addition to the viscosity coefficient, the constructed mathematical model of the viscoelastic fluid has two more independent parameters: shear modulus and time of relaxation of elastic stresses. Elastic parameters of water are determined through comparisons with experimental data.Introduction. Rotational motion of a floater made in the form of a disk floating on the fluid surface in a cylindrical container is studied in the present work by numerical methods (Fig. 1). The disk is instantaneously set into motion (rotation around its own centerline coinciding with the container centerline). When the disk acquires steady-state rotation, the action of the external moment is terminated, and the disk motion starts to decay owing to viscous friction on the fluid. It was found in the experiments [1] that the decay has an oscillating character (Fig. 2). Based on this fact, water may be assumed to have viscoelastic properties, though it is normally considered as a Newtonian fluid. The problem considered here was numerically solved in [2] in the approximation of the Newtonian fluid; changes in the initial conditions and physical parameters of the disk and the container were found to initiate no backward motion of the disk. The data of [1] are interpreted in the present work on the basis of several linear models of a viscoelastic fluid. The most suitable model turned out to be the model of viscoelasticity [3] with an exponential function of decaying of elastic stresses. As compared with the Newtonian fluid model, the model developed in [3] has two more independent parameters: shear modulus G and time of relaxation of elastic stresses T . The fluid considered is interpreted as a substance with the stress dependent on the strain and strain rate. In turn, the strain is determined by the differences in the material configuration at consecutive times.Mathematical Model. The stress tensor of the examined fluid is presented as σ = σ vis + σ el . The elastic part of the stress tensor of the isotropic fluid with the convective elasticity

No abstract

No abstract