Entry and exit flows of Bingham fluids

On the Numerical Simulation of Viscoplastic Fluid Flow

“…The method is easy to implement because the regularized problem involves a differentiable nonlinear viscosity operator. Unfortunately, the criterion to decide whether a flow region is yielded or unyielded has become less clear-cut as pointed out in Abdali, Mitsoulis and Markatos [1992], Mitsoulis, Abdali and Markatos [1993]; indeed, if the regularization related strain-rate tensor (namely D(u ε ), u ε being the velocity solution of the regularized problem) vanishes, it is on a set of measure zero. Thus, with regularization methods, the determination of the yielded and unyielded regions relies on a Von Mises stress criterion (namely, x belongs to the unyielded region if |D(u ε (x))| is "small enough").…”

“…The first approach relies on regularization; it has been widely used for many years by many practitioners (see, among many others, Beris, Tsamopoulos, Armstrong and Brown [1985], Papanastasiou [1987], Abdali, Mitsoulis and Markatos [1992], Mitsoulis, Abdali and Markatos [1993], Burgos and Alexandrou [1999], Mitsoulis and Zisis [2001], Liu, Muller and Denn [2002], and Mitsoulis and Huilgol [2004]). The key idea behind regularization methods is to approximate the (nonsmooth) constitutive law by a differentiable one.…”

“…These problems have been thoroughly investigated when the fluid is viscoelastic because in that case, the viscoelastic extra-stress tensor develops a singularity at re-entrant corners; less attention has been given to their viscoplastic analogs. Let us mention, however, the following contributions: Abdali, Mitsoulis and Markatos [1992], Mitsoulis, Abdali and Markatos [1993], Mitsoulis andHuilgol [2004], all using regularization, andCoupez, Zine andAgassant [1994] using an augmented Lagrangian method. The flow pattern is pretty simple: upstream and downstream of the contraction the flow is of the Poiseuille type with a central plug region, however the recirculation region of the Newtonian case becomes a stagnant zone with zero velocity.…”

Numerical modeling of helical flow of viscoplastic fluids in eccentric annuli

“…panastasiou 1987 proposed a constitutive equation for fluids with yield stress, where a material parameter controls the exponential growth of stress which is valid for both yielded and unyielded regions. 1990, Abdali et al 1992, Mitsoulis et al 1993, Pham and Ž . Ž .…”

A numerical investigation of inertia flows of Bingham-Papanastasiou fluids by an extra stress-pressure-velocity galerkin least-squares method

“…As a weakness, its dependence on a non-rheological (numerical) parameter, which controls the exponential growth of the yield-stress term of the classical Bingham model in regions subjected to very small strain-rates, may be pointed. Abdali et al (1992) simulated Bingham-Papanastasiou fluid flows through a one-to-four sudden contraction, in axisymmetric and planar channels, by a finite element methodology. The authors also considered exit flows aiming to determine yielded and unyielded regions in extrusion dies.…”