arXiv subjects

Alexander Proskurin

Publications and source records attributed to Alexander Proskurin.

3 recordsLinked to original sources

arXiv2026

Competing instabilities in wide-gap viscoelastic Taylor-Couette flow: Taylor vs. helical vortices

This paper presents a numerical study of the stability of a polymer solution flow between concentric cylinders with a rotating inner cylinder. The case of a small-radius inner cylinder is considered. The fluid motion is described using a specific case of the Kelvin-Voigt model, often referred to as the Oskolkov model. This model is applicable to very dilute polymer solutions, where the retardation time is much smaller than the characteristic time of the problem and elastic forces are much smaller than viscous forces. The stability of the steady-state motion is investigated using a fully nonlinear approach by means of direct numerical simulation of a perturbation introduced as finite-duration white noise. Depending on the Reynolds number, the perturbation either decays or grows. The critical Reynolds numbers obtained for both Newtonian and non-Newtonian fluids are found to be in agreement with the predictions of the linear theory. It is also shown that an increase in the elastic forces makes helical perturbations more dangerous than their axisymmetric counterparts.

physics.flu-dyn↗

arXiv2021

Linear stability of flow in a 90-degree bend

The paper considers a two-dimensional flow in a channel, which consists of straight inlet and outlet branches and a circularly 90-degree curved bend. An incompressible viscous fluid flows through the elbow under the action of a constant pressure gradient between the inlet and outlet. Navier-Stokes equations were solved numerically using a high-fidelity spectral/hp element method. In a range of Reynolds numbers, an adaptive selective frequency dumping method was used to get a steady-state flow. It was found that three separation bubbles and vortex shedding can exist in the bend. The modal stability of two- and three-dimensional perturbations was investigated. Critical Reynolds number of the two-dimensional disturbances was found as extrapolation by lower Reynolds number results. It is much greater than three-dimensional one, but the two-dimensional flow could subcritically unstable with respect to the imposed small-amplitude white noise. For three-dimensional perturbations, the dependence of the critical Reynolds numbers on the bending radius is obtained. For a case of a moderate bending radius the neutral curve is provided and eigenfunctions are studied in detail: three-dimensional instability can be caused by periodic or monotonically growing mode, these unstable modes regard to the recirculation bubbles that occur after the bend.

physics.flu-dyn↗

arXiv2019

The evolution of non-linear disturbances in magnetohydrodynamic flows

In this article the stability loss of the Hartmann flow are investigated by applying the equations for disturbances. The velocity and electric potential quasi-static MHD model is used. The equations allow us to calculate time-dependent disturbance fields using a base flow and an initial disturbance. Two type of initial perturbations are considered: the eigenfunction of the linearized MHD equations and a fluid injection into the flow. These two approaches lead to identical stability results. However, we found a significant difference in the practical implementation of the two approaches. Dealing with the eigenproblem of the linearized MHD system is a laborious task. In terms of calculation costs it is equal to a series of nonlinear perturbation simulations, and if the Hartmann number is increased, the proportion becomes worse. The non-linear stability analysis produced by these two methods shows that the injection technique can also be used in numerical analysis, and that this method is less expensive in terms of calculation costs.

physics.flu-dyn↗