Influence Of Viscous Stresses Research Articles

Simplified CFD modeling for bilge keel force and hull pressure distribution on a rotating cylinder

A horizontal, circular cylinder fitted with one bilge keel is forced to rotate harmonically around its axis. The bilge keel load and hull pressure distribution are investigated. A fully submerged condition (infinite fluid), and three partly-submerged conditions are considered. A two-dimensional numerical study is performed, and the results are validated against recently published experimental data by van’t Veer et al. [30]. In addition, comparisons for mass and drag coefficients are also made with experimental data for plate in infinite fluid (Keulegan and Carpenter [8]), and wall-mounted plate (Sarpkaya and O’Keefe [9]) in oscillatory flow.A Navier–Stokes solver based on the Finite Volume Method is adopted for solving laminar flow of incompressible water. The free-surface condition is linearized by neglecting the nonlinear free-surface terms and the influence of viscous stresses in the free surface zone, while the body-boundary condition is exact. This simplified modeling of the problem required the mesh to be fine only around the bilge keels, leading to a total number of cells around N≃1×104, which reduced computational cost significantly.The influence of draft and amplitude of oscillations on the bilge keel force and hull pressure distribution are considered. The bilge keel force is presented in terms of non-dimensional drag and mass coefficients including higher harmonic components. The numerical results are also compared with the industry standard empirical method for calculation of roll damping proposed by Ikeda et al. [4]. In general, a good agreement between the results of the present numerical method and the experimental data is obtained and the differences with those predicted by the empirical method are addressed.

Stretching of a confined ferrofluid: Influence of viscous stresses and magnetic field

An analytical investigation is presented for the stretch flow of a viscous Newtonian ferrofluid highly confined between parallel plates. We focus on the development of interfacial instabilities when the upper plate is lifted at a described rate, under the action of an applied magnetic field. We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. In contrast to the great majority of works in stretch flow we take into account stresses originated from velocity gradients normal to the ferrofluid interface. The impact of such normal stresses is accounted for through a modified Young-Laplace pressure jump interfacial boundary condition, which also includes the contribution from magnetic normal traction. We study how the stability properties of the interface and the shape of the emerging patterns respond to the combined action of normal stresses and magnetic field, both in the presence and absence of surface tension. We show that the inclusion of normal viscous stresses introduces a pertinent dependence on the initial aspect ratio, indicating that the number of fingers formed would be overestimated if such stresses are not taken into account. At early linear stages it is found that such stresses regularize the system, acting as an effective interfacial tension. At weakly nonlinear stages we verified that normal stresses reduce finger competition, which can be completely suppressed with the assistance of an azimuthal magnetic field. We have also found that the magnetic normal traction introduces a purely nonlinear contribution to the problem, revealing the key role played by the magnetic susceptibility in the control of finger competition.

Equilibrium thermodynamic theory for the evaluation of temperature distributions in overdriven steady-plane wave fronts

Temperature distributions in overdriven steady wave fronts in solid 2024 Al shocked up to 80 GPa, in which no melting occurred in the wave fronts, were evaluated using the equilibrium thermodynamic theory. The effective strain increments were sufficiently small and the effective temperature rise times were sufficiently long with respect to electron–phonon relaxation times to justify using equilibrium thermodynamics. In addition, the sufficiently large viscous-stress components supported the efficacy of the thermodynamic theory. The same is true of shocks up to 250 GPa in solid Pt and 230 GPa in solid Fe. Furthermore, the influence of viscous stress was examined by evaluating the temperature distributions for inviscid 2024 Al, Pt, and Fe solids using the equations for temperature derived from the Mie–Grüneisen equation. Finally, we demonstrate that there might be a solid–liquid–solid Hugoniot between the solid and liquid–solid Hugoniots for Fe and estimate the solid–liquid–solid and liquid–solid Hugoniots.

Influence of viscous stresses on shock wave stability in gases

New shock jump conditions and the effect of curvature are derived, including viscous stresses within the shock layer and in the downstream gas flow. The main difference from the well-known Rankine–Hugoniot conditions is the existence of surface tension due to an anisotropy of viscous stresses in the layer. The classical problem of shock wave instability in gases has been solved with the new jump conditions. The surface tension is found to stabilize the shock wave generally whereas the viscous stresses in downstream flow destabilize it. The destabilizing effect dominates in the mode of spontaneous sound emission resulting in an absolute instability of the shock wave. This mode was previously considered to be neutrally stable.