| Περίληψη: | In the present thesis, we examine the pressure-driven flow of a thixotropic elastoviscoplastic fluid (TEVP) through a cylindrical pipe. Although this flow has been studied extensively in fluid mechanics with yield stress materials and Newtonian fluids, recent studies have stressed the importance of thixotropy and elasticity to accurately describe it. The objective of this work is to examine the behavior of a TEVP fluid through a pipe, by solving the transient problem, until steady state is reached. This is quintessential, as it will give us an insight into how the flow evolves over time to appreciate the thixotropic, viscoelastic and viscoplastic effects that take place.
In the first and introductory chapter, emphasis is given on the omnipresence of yield stress materials in everyday life and nature and applications ranging from industrial processes to biological tissues and cosmetic products. What distinguishes these materials is their characteristic transition from a solid to a liquid state, when subjected to stress, once they surpass a critical threshold, the so-called yield stress.
Furthermore, in Chapter 2 a wide class of yield stress materials is presented and the debate of the existence of “real” yield stress is discussed. Recent studies though have underlined the importance of including elastic and thixotropic effects when modeling them. This necessity led to more research regarding the flow of EVP materials, materials that exhibit characteristics of viscoelastic solids before yielding, and viscoplastic liquids upon yielding. Moreover, the concept of thixotropy, regarding the time-dependent evolution of the fluid’s viscosity is introduced and briefly discussed. In the last sections of this chapter, we define the constitutive models that will be used extensively throughout this work. In particular, we present a recently proposed thixotropic elastoviscoplastic model (TEVP), that combines the Saramito with the linear Phan-Thien-Tanner model (LPTT) while introducing thixotropy via a structure parameter. We use this model to derive simpler models, that describe the behavior of EVP, elastoviscoplastic, viscoelastic and Newtonian fluids. Specifically, the derived models are the modified Saramito (SRM-LPTT), the linear Phan-Thien-Tanner (LPTT), the Oldroyd-B, the Bingham, and the Newtonian.
In Chapter 3 the Poiseuille flow of a TEVP fluid through a cylindrical pipe is considered. The governing equations and the boundary conditions are stated and the necessity of the transient approach to the problem is stressed. In Chapter 4 the Galerkin Finite Element Method is employed to discretize the velocity and the stress fields into a nodal grid. It is asserted that the computed solution converges for different numbers of finite elements. Moreover, for the time integration, the Newton-Raphson method was used and it is deduced that there is time convergence of the solution for various timesteps.
An extensive parametric analysis is performed in Chapter 5. Each constitutive model was used to examine the parameters that affect the flow behavior. In particular, for the Newtonian model the impact of Reynolds on the flow profile was examined. For the Oldroyd-B model the effect of the Weissenberg number on the flow characteristics was assessed. Subsequently, for the LPTT model we analyzed the effect of the LPTT parameter on the flow development, and we also examined the role of yield stress, via the Bingham number, in the time evolution of the flow considering the Bingham and the SRM-LPTT model. Another case involved the effect of thixotropic parameters on the flow, using the TEVP model to study a fumed silica suspension using material data from a recent study [1].
This work is concluded with useful remarks regarding the results of the parametric analysis and suggestions for future investigations.
|
|---|
