Model for laminar and turbulent flows of viscous and nonlinear viscous non-Newtonian fluids

Abstract

We develop a model that describes laminar and turbulent flows of viscous and nonlinear viscous fluids. A basis for the model is a characteristic, which we call a local Reynolds number, and which is calculated at each point of the domain of flow. In the subdomain wherein the local Reynolds number does not exceed some value, the flow is laminar; otherwise it is turbulent, i.e., the model identifies the areas of laminar and turbulent flows. The model predicts the existence of a laminar boundary layer at turbulent flows. It enables us to describe special features of turbulent flows such as a drastic increase in the resistance to flow and the variation of the velocity profile with the increase of the Reynolds number, and so on. The model is mathematically grounded. We prove the existence of global solutions to stationary and nonstationary flow problems with the nonhomogeneous Dirichlet and mixed boundary conditions, where velocities and surface forces are given on different parts of the boundary. Numerical methods for solving stationary and nonstationary flow problems are investigated.

Existence of Optimal Control for a Nonlinear-Viscous Fluid Model

“…It should be mentioned at this point that a lot of studies have been conducted towards mathematical models of nonlinear-viscous fluids (see monograph [8] and [9][10][11][12]). Nevertheless, there are very few results on the existence and properties of solutions of control problems for nonlinearviscous fluid flows.…”

Solvability of the Non-Linearly Viscous Polymer Solutions Motion Model

“…In general, many types of function have been proposed in the literature, but most of them have been applied to the study of one–dimensional models. In the paper [ 23 ] it is shown that the given restrictions on the function are natural for real fluids and that the numerical results for this model is very close to the results of experimental studies.…”

“…At this paper we will consider some of the natural viscosity constraints for real fluids proposed by V.G. Litvinov [ 23 ]: where the tensor is defined by the relation . Here we use the notation for arbitrary square matrices and of the same order.…”

FSI Computation and Experimental Verification of Fluid Flow in Flexible Tubes

“…In the follow-up work should be tested liquid, which falls into the category of non-Newtonian similar to blood. However, the turbulent behavior of non-Newtonian fluids is not yet sufficiently described [14], [15], [16]. From this point of view, it is more certain to consider only laminar flow, even with regard to the experience gained for the follow-up work.…”