Viscoplastic flow in an extrusion damper

Abstract

Numerical simulations of the flow in an extrusion damper are performed using a finite volume method. The damper is assumed to consist of a shaft, with or without a spherical bulge, oscillating axially in a containing cylinder filled with a viscoplastic material of Bingham type. The response of the damper to a forced sinusoidal displacement is studied. In the bulgeless case the configuration is the annular analogue of the well-known lid-driven cavity problem, but with a sinusoidal rather than constant lid velocity. Navier slip is applied to the shaft surface in order to bound the reaction force to finite values. Starting from a base case, several problem parameters are varied in turn in order to study the effects of viscoplasticity, slip, damper geometry and oscillation frequency to the damper response. The results show that, compared to Newtonian flow, viscoplasticity causes the damper force to be less sensitive to the shaft velocity; this is often a desirable damper property. The bulge increases the required force on the damper mainly by generating a pressure difference across itself; the latter is larger the smaller the gap between the bulge and the casing is. At high yield stresses or slip coefficients the amount of energy dissipation that occurs due to sliding friction at the shaft-fluid interface is seen to increase significantly. At low frequencies the flow is in quasi steady state, dominated by viscoplastic forces, while at higher frequencies the fluid kinetic energy storage and release also come into the energy balance, introducing hysteresis effects.

A finite volume method for the simulation of elastoviscoplastic flows and its application to the lid-driven cavity case

“…2). It can be seen that both D τ + f,i and D τ − f,i equal a characteristic viscosity, given by (25) or (26), times the velocity gradient in the direction d f , albeit calculated differently: the gradient as computed in D τ + f,i is sensitive to velocity oscillations whereas that computed in D τ − f,i is not. The mechanism of oscillation suppression is similar to that for momentum interpolation: in the presence of spurious velocity oscillations, the smooth part of D τ + f,i is cancelled out by D τ − f,i , but the oscillatory part produces oscillations in the operator image (in F h (φ h ), in the terminology of Eq.…”

“…The "velocities" u p+ f and u p− f are functions of local pressure variations, and attempt to quantify the contributions of these pressure variations to the velocity field. Pressure and velocity are connected through the momentum equation, so consider this equation in the following non-conservative form, where we assume that the stress tensor can be approximated through the use of a characteristic viscosity such as (25) or (26) as τ ≈ η(∇u + (∇u) T ):…”

“…In the latter case, the solid and dash-dot lines correspond to the use of Eqs. (25) and (26), respectively. Dashed lines with short or long dashes correspond, respectively, to replacing S by S/2 or 2S in (25).…”

“…An alternative, very popular discretisation / solution method in Computational Fluid Dynamics is the Finite Volume Method (FVM); it has been successfully applied to viscoplastic (e.g. [24,25]) and viscoelastic (e.g. [26][27][28][29]) flows individually, but not to EVP flows, to the best of our knowledge (a hybrid FE/FV method was used in [30]).…”

Theoretical study of the flow in a fluid damper containing high viscosity silicone oil: Effects of shear-thinning and viscoelasticity

“…A possible reason for the lack of such prior studies is that viscoelastic simulations are much more expensive than those involving generalised Newtonian fluids such as the CY, as additional differential equations have to be solved (one per stress component), which are unwieldy at high elasticity (the notorious high-Weissenberg number problem -see e.g. [21]), while also much smaller time steps are needed in order to capture the elastic phenomena (whereas if the flow is assumed generalised Newtonian, it is also quasi-steady due to the high viscosity of typical damper fluids and one can employ large time steps without loss of accuracy -see [22]).…”