EFFECTS OF TENSOR CLOSURE MODELS AND 3-D ORIENTATION ON THE STABILITY OF FIBER SUSPENSIONS IN A CHANNEL FLOW

IntroductionFlowoffibresuspensionshasbeenveryfamiliarinmanyindustrialfields.Fibreadditivesplayanimportantroleindragreductioninmanytypesofflow[1- 3].Inthesuspensions,somebehavioroftheflowmaybealteredbythefibres.Oneoftheimportantexamplesisthehydrodynamicsta…     

Review of Drucker’s postulate and the issue of plastic stability in metal forming

Drucker’s postulate defines a class of stable work hardening materials that are classified as non-energetic and is equivalent to the associated flow rule (AFR). The postulate has been shown to be a sufficient condition for plastic stability. However, experiments indicate that plastic deformation of aluminum and steel alloys does not adhere to the constraints of the AFR. Therefore, the requirement for accuracy suggests that the metal forming industry should also consider material models that are based on non-associated flow. But Drucker’s work raises the issue of stability when considering the use of non-associated flow in material models. While this concern is merited and many types of instability arises from certain types of non-associated flow, this has led to a widely accepted view that Drucker’s postulate is a necessary condition for stability. This perception is inhibiting the acceptance or consideration of more accurate material models that are suggested from the experimental observations about violations of the AFR. This paper proposes a specific class of material models based on non-associated flow and derives the constraints on this class of models to ensure stability. The existence of this class of non-AFR models proves that Drucker’s postulate is a sufficient but not necessary condition for stability. Furthermore, the class of models described in this paper is quite general and provides a framework for consideration of potentially more accurate material models while guaranteeing the same level of stability as typically associated with materials that satisfy Drucker’s postulate.     

On the suitability of first-order differential models for two-phase flow prediction

The stability features of a general elass of one-dimensional two-phase flow models are examined. This class of models is characterized by the presence of first-order derivatives and algebraic functions of the flow variables, higher-order differential terms being absent, and can accommodate a variety of physical effects such as added mass and unequal phase pressures in some formulations. By taking a general standpoint, a number of results are obtained applicable to the entire class of models considered. In particular, it is found that, despite the presence of algebraic terms in the equations (describing, e.g. drag effects) the stability criteria are independent of the wavenumber of the perturbation. As a consequence, reality of characteristics is necessary, although not sufficient, for stability. To illustrate the theory, three specific models are considered in detail.     

A systematic procedure for constructing critical state models in three dimensions

A general procedure for developing constitutive models for frictional materials possessing a critical state is developed in a three-dimensional context. The procedure starts from the laws of thermo-dynamics, so that the first and second laws of thermo-dynamics are automatically satisfied. There is hence no need to invoke any extraneous stability postulates. The models involve a number of parameters, which can be interpreted in terms of micro-mechanical energy storage and dissipative mechanisms. In most cases non-associated flow rules are predicted and in some cases the yield surfaces are seen to have concave segments. The procedure is more general than that traditionally used for materials with non-associated flow rules, in that plastic potentials are not needed and not presumed to exist. In illustration, examples of families of models are given in which the critical state surface is either the Drucker–Prager or the Matsuoka–Nakai cone.     

Stability of a compressible swirling flow in a circular pipe

The stability of an axisymmetric flow of viscous gas in a circular pipe, which models the Burgers vortex in the pipe axis neighborhood, is studied within the linear theory framework. Neutral curves for the most unstable disturbances are calculated. The influence of the characteristic Mach number on the flow stability is investigated. It is shown that for a given model velocity distribution the Mach number affects only the temperature and pressure profiles of the main undisturbed flow. In this case, for the disturbance types considered, as the Mach number increases, the critical Reynolds number corresponding to loss of stability decreases. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 35–41, January–February, 1999. The work received financial support from the Russian Foundation for Basic Research (project No. 96-01-00586).     

Numerical stabilities of loosely coupled methods for robust modeling of lightweight and flexible structures in incompressible and viscous flows

The growing interest to examine the hydroelastic dynamics and stabilities of lightweight and flexible materials requires robust and accurate fluid–structure interaction(FSI)models. Classically, partitioned fluid and structure solvers are easier to implement compared to monolithic methods;however, partitioned FSI models are vulnerable to numerical("virtual added mass") instabilities for cases when the solid to fluid density ratio is low and if the flow is incompressible.As a partitioned method, the loosely hybrid coupled(LHC)method, which was introduced and validated in Young et al.(Acta Mech. Sin. 28:1030–1041, 2012), has been successfully used to efficiently and stably model lightweight and flexible structures. The LHC method achieves its numerical stability by, in addition to the viscous fluid forces, embedding potential flow approximations of the fluid induced forces to transform the partitioned FSI model into a semi-implicit scheme. The objective of this work is to derive and validate the numerical stability boundary of the LHC. The results show that the stability boundary of the LHC is much wider than traditional loosely coupled methods for a variety of numerical integration schemes. The results also show that inclusion of an estimate of the fluid inertial forces is the most critical to ensure the numerical stability when solving for fluid–structure interaction problems involving cases with a solid to fluid-added mass ratio less than one.     

Stability of an inhomogeneous vibrationally-nonequilibrium flow in a waveguide

The stability of an inhomogeneous subsonic vibrationally-nonequilibrium flow is examined in the linear approximation. It is shown that the nonequilibrium flow stability is reduced with increase in the initial flow velocity and the energy pumping zone width. This is attributed to the effect of the feedback due to acoustic disturbances propagating counter to the flow. Calculations are carried out for different pumping models.     

Instability and waves during generalized Newtonian fluid film flow down a vertical wall

The problem of linear stability of a non-Newtonian fluid film flowing down a vertical plane under the action of gravity is considered. The linear stability of steady-state flow with a plane free boundary and the nonlinear waves that arise if this flow is unstable are investigated. The results obtained for two rheological models, the power-law and Eyring fluids, are compared.     

Uncertainty quantification and global sensitivity analysis of mechanistic one-dimensional models and flow pattern transition boundaries predictions for two-phase pipe flows

The prediction of uncertainties is a growing interest in flow assurance industrial applications, but only few works have been presented on this topic. In this work, an uncertainty quantification and a global sensitivity analysis are performed to quantify the level of confidence in predictions of one-dimensional mechanistic models considering different two-phase flow regimes. A method is proposed for this purpose accounting for the effect of several variables on pressure drop and hold-up predictions by the well-known one-dimensional two-fluid model, such as fluid flow rates, geometry (the inclination angle and the pipe diameter), and fluid properties (density and viscosity); the case of a non-Newtonian shear-thinning fluid behaviour is also considered. Flow pattern transition boundaries, including the stability of the stratified flow regime, are included in this analysis. Monte Carlo simulations were used for the uncertainty quantification while different approaches for the sensitivity analysis (scatter plot, linear regression, the Morris’s method, and the Sobol’s Method) were used and compared to identify the best tool for this family of models. The Sobol’s method appears to be the most convenient approach and a discussion is provided considering different practical cases for gas/liquid and liquid/liquid systems. The most critical input parameters in terms of uncertainty are rigorously identified case by case. A way to reduce the output uncertainty is indicated by the interpretation of the results of the global sensitivity analysis. The conclusions of this analysis gives new insights regarding the degree of uncertainties in predictions of one-dimensional mechanistic models.     

Suppression or enhancement of interfacial instability in two-layer plane Couette flow of FENE-P fluids past a deformable solid layer

The linear stability of two-layer plane Couette flow of FENE-P fluids past a deformable solid layer is analyzed in order to examine the effect of solid deformability on the interfacial instability due to elasticity and viscosity stratification at the two-fluid interface. The solid layer is modeled using both linear viscoelastic and neo-Hookean constitutive equations. The limiting case of two-layer flow of upper-convected Maxwell (UCM) fluids is used as a starting point, and results for the FENE-P case are obtained by numerically continuing the UCM results for the interfacial mode to finite values of the chain extensibility parameter. For the case of two-layer plane Couette flow past a rigid solid surface, our results show that the finite extensibility of the polymer chain significantly alters the neutral stability boundaries of the interfacial instability. In particular, the two-layer Couette flow of FENE-P fluids is found to be unstable in a larger range of nondimensional parameters when compared to two-layer flow of UCM fluids. The presence of the deformable solid layer is shown to completely suppress the interfacial instability in most of the parameter regimes where the interfacial mode is unstable, while it could have a completely destabilizing effect in other parameter regimes even when the interfacial mode is stable in rigid channels. When compared with two-layer UCM flow, the two-layer FENE-P case is found in general to require solid layers with relatively lower shear modulii in order to suppress the interfacial instability. The results from the linear elastic solid model are compared with those obtained using the (more rigorous) neo-Hookean model for the solid, and good agreement is found between the two models for neutral stability curves pertaining to the two-fluid interfacial mode. The present study thus provides an important extension of the earlier analysis of two-layer UCM flow [V. Shankar, Stability of two-layer viscoelastic plane Couette flow past a deformable solid layer: implications of fluid viscosity stratification, J. Non-Newtonian Fluid Mech. 125 (2005) 143–158] to more accurate constitutive models for the fluid and solid layers, and reaffirms the central conclusion of instability suppression in two-layer flows of viscoelastic fluids by soft elastomeric coatings in more realistic settings.     

Higher order stability effects in a natural convection boundary layer over a vertical heated wall

 The stability of a laminar boundary layer flow under natural convection on a vertical isothermally heated wall is studied analytically. The analysis is performed by using two different two-dimensional linear models: (1) The non-parallel flow model in which the steady mean flow as well as the disturbance amplitude functions can change in the streamwise direction; (2) The parallel flow model in which the effects of the mean flow and disturbance changes in the streamwise direction are neglected. The linear non-parallel stability analysis is based on the so-called parabolised stability equations (PSEs) which have been successfully applied to the stability analysis of forced convection boundary layers. In this study the PSE equations are applied to natural convection boundary layers in order to show the difference between parallel and non-parallel stability analysis. A second part of this study deals with the effects of variable properties, which are always present in natural convection flows. They are analysed by an extended version of the Orr–Sommerfeld equation (EOSE). Received on 31 May 2000     

On Rayleight instability in decaying plane Couette flow

The inflexion point criterion of Rayleigh is one of the most well-known results in hydrodynamic stability theory but cannot easily be demonstrated experimentally in wall bounded flows. For plane Couette flow, where both walls move with equal speed in opposite directions, it is possible to establish a (time-dependent) inflectional velocity profile if both walls are brought momentarily to rest. If the Reynolds number is high enough a growing stationary instability develops. This situation is ideally suited for flow visualization of the instability. In this paper we show flow visualization experiments and stability calculations of the developing transverse roll cell instability in such a flow at low Reynolds numbers. Although the stability calculations are based on a quasi-stationary velocity profile, the measured and most amplified wave length obtained from the calculations are in excellent agreement.     

An investigation of jet trajectory in flow through scaled vocal fold models with asymmetric glottal passages

Pulsatile two-dimensional flow through asymmetric static divergent models of the human vocal folds is investigated. Included glottal divergence angles are varied between 10° and 30°, with asymmetry angles between the vocal fold pairs ranging from 5° to 15°. The model glottal configurations represent asymmetries that arise during a phonatory cycle due to voice disorders. The flow is scaled to physiological values of Reynolds, Strouhal, and Euler numbers. Data are acquired in the anterior–posterior mid-plane of the vocal fold models using phase-averaged Particle Image Velocimetry (PIV) acquired at ten discrete locations in a phonatory cycle. Glottal jet stability arising from the vocal fold asymmetries is investigated and compared to previously reported work for symmetric vocal fold passages. Jet stability is enhanced with an increase in the included divergence angle, and the glottal asymmetry. Concurrently, the bi-modal jet trajectory and flow unsteadiness diminishes. Consistent with previous findings, the flow attachment due to the Coanda effect occurs when the acceleration of the forcing function is zero.     

Stability of steady-state non-Newtonian fluid layer flow

The stability of the steady-state plane-parallel flow of a non-Newtonian fluid layer in the gravity field along an inclined rigid surface is investigated. It is shown that the most dangerous are the long-wave perturbations propagating over the free surface. The stability maps are plotted for such perturbations in the Reynolds number — gravity parameter plane. With increase in the gravity number the layer flow becomes less stable. The layer deviation from the vertical lines stabilizes the flow.     

A time-periodic approach for fluid-structure interaction in distensible vessels

The analysis of periodic unsteady incompressible flow inside compliant vessels is of considerable interest for the simulation of blood flow in arteries. Weakly coupled fluid-structure interaction (FSI) models seem to be most suitable for this purpose. For weakly coupled solution methods, however, often convergence may not be achieved for compliant vessels with an axial length scale that is large compared to the characteristic radius. In this study, a time-periodic method for weakly coupled FSI models is presented. Approximate solutions of subsequent time-periods are obtained using the solution of the previous time-period as an initial solution. For the first period, not only suitable boundary conditions are derived from a 1-D wave propagation model, but also the initial axial pressure distribution. The time-periodic method was successfully applied to straight, curved and bifurcating geometries. The new approach proves to have a far better computational stability than weakly coupled methods based on timestep-wise coupling, especially in vessels with a length that is an order of magnitude larger than the radius.     

Forward roll coating flows of viscoelastic liquids

Roll coating is distinguished by the use of one or more gaps between rotating cylinders to meter and apply a liquid layer to a substrate. Except at low speed, the two-dimensional film splitting flow that occurs in forward roll coating is unstable; a three-dimensional steady flow sets in, resulting in more or less regular stripes in the machine direction. For Newtonian liquids, the stability of the two-dimensional flow is determined by the competition of capillary and viscous forces: the onset of meniscus nonuniformity is marked by a critical value of the capillary number. Although most of the liquids coated industrially are non-Newtonian polymeric solutions and dispersions, most of the theoretical analyses of film splitting flows relied on the Newtonian model. Non-Newtonian behavior can drastically change the nature of the flow near the free surface; when minute amounts of flexible polymer are present, the onset of the three-dimensional instability occurs at much lower speeds than in the Newtonian case.Forward roll coating flow is analyzed here with two differential constitutive models, the Oldroyd-B and the FENE-P equations. The results show that the elastic stresses change the flow near the film splitting meniscus by reducing and eventually eliminating the recirculation present at low capillary number. When the recirculation disappears, the difference of the tangential and normal stresses (i.e., the hoop stress) at the free surface becomes positive and grows dramatically with fluid elasticity, which explains how viscoelasticity destabilizes the flow in terms of the analysis of Graham [M.D. Graham, Interfacial hoop stress and instability of viscoelastic free surface flows, Phys. Fluids 15 (2003) 1702–1710].     

Flow field around the flapping flag

The flapping flag is a canonical fluid–structure interaction problem that describes a cantilever plate with flow along its elastic axis. When the flapping flag loses stability it enters a large amplitude Limit Cycle Oscillation (LCO). While theoretical models can accurately predict the flutter velocity and frequency, there are still discrepancies between the experimental observations and the theoretical predictions of the post-critical LCO response. This note provides recent flow field visualizations in a single longitudinal plane for a cantilevered aluminum plate in axial flow during its LCO. Particle Image Velocimetry (PIV) techniques are used to show that the flow over the midspan of the plate is attached even during the violent LCO motion. This observation suggests that potential flow aerodynamic models may be able to capture the essential features in the flow field.     

Instability of sintering of porous bodies

Sintering models are discussed and used to analyze flow instabilities that may arise during preliminary compaction of powders. These instabilities can be at the origin of heterogeneities in the densification. The material is modeled as a viscoplastic thermal sensitive porous material. The modeling includes the limit case of a linear viscous material. The effects of sintering conditions (temperature and pressure in the case of pressure sintering) and the effects of material characteristics such as porosity, heat capacity, theoretical density, surface tension, particle size and creep parameters on stability of sintering are investigated. The heat release associated with the plastic flow is shown to sometimes have an important role. Stability criteria are derived and applied to the analysis of sintering and hot isostatic pressing, using various sintering models. These stability criteria can be used to optimize the densification process; one can control, for example, temperature so as to avoid any instability. Stability maps enabling an optimization of temperature–pressure regime in hot isostatic pressing are built for sample metal (nickel) powder.     

Nonlinear stability of two-dimensional steady flows of an ideal fluid with constant vorticity and their axisymmetric analogs

Flows with constant vorticity are widely used as local models of more complicated flows [1]. In many cases, such flows are stable against finite two-dimensional perturbations. In particular, the inviscid plane-parallel Couette flow has the property of nonlinear stability. Similar treatment of a class of axisymmetric flows yields nonlinear stability of a spherical Hill vortex and inviscid Poiseuille flow in a circular tube with respect to axisymmetric perturbations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 16–21, October–December, 1981.