Axial Couette flow of a generalized Oldroyd-B fluid due to a longitudinal time-dependent shear stress

2010 ◽  
Vol 33 (4) ◽  
pp. 429-441 ◽  
Author(s):  
A. U. Awan ◽  
Corina Fetecau ◽  
Qammar Rubbab
Keyword(s):  
Shear Stress ◽  
Couette Flow ◽  
Time Dependent

Couette Flow of a Generalized Oldroyd-B Fluid due to Constantly Accelerated Shear Stress Coupled with the Pressure Gradient

2011 ◽  
Vol 354-355 ◽  
pp. 179-182
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang ◽  
Jia Jia Niu
Keyword(s):  
Shear Stress ◽  
Laplace Transform ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Hankel Transform ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Finite Hankel Transform

This paper presented an analysis for the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress with the influence of the internal constantly decelerated pressure gradient. The exact solutions are established by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform and presented by integral and series form in terms of the Mittag-Leffler function. Moreover, the effects of various parameters are analyzed in detail by graphical illustrations.

Exact Solutions for the Fractional Time-Dependent Oldroyd-B Fluid Model Subject to a Constantly Accelerated Shear Stress

2014 ◽  
Vol 518 ◽  
pp. 114-119 ◽  
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Fluid Model ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Model Subject

In this paper, based on the fractional model, we present an investigation on the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress which is affected by the internal constantly decelerated pressure gradient. By using the fractional derivatives Laplace and finite Hankel transforms, the obtained solutions for the velocity field and shear stress, written in terms of generalized R function, are presented the similar characteristics with Newtonian and non-Newtonian fluids. Moreover, the effects of various parameters are systematically analyzed.

scholarly journals Time-Dependent Response of a Recycled C&D Material-Geotextile Interface under Direct Shear Mode

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3070
Author(s):  
Fernanda Bessa Ferreira ◽  
Paulo M. Pereira ◽  
Castorina Silva Vieira ◽  
Maria de Lurdes Lopes
Keyword(s):  
Shear Stress ◽  
Stress Relaxation ◽  
Shear Displacement ◽  
Time Dependent ◽  
Shear Behaviour ◽  
Displacement Rate ◽  
Shear Mode ◽  
Direct Shear ◽  
Constant Displacement ◽  
Shear Box

Geosynthetic-reinforced soil structures have been used extensively in recent decades due to their significant advantages over more conventional earth retaining structures, including the cost-effectiveness, reduced construction time, and possibility of using locally-available lower quality soils and/or waste materials, such as recycled construction and demolition (C&D) wastes. The time-dependent shear behaviour at the interfaces between the geosynthetic and the backfill is an important factor affecting the overall long-term performance of such structures, and thereby should be properly understood. In this study, an innovative multistage direct shear test procedure is introduced to characterise the time-dependent response of the interface between a high-strength geotextile and a recycled C&D material. After a prescribed shear displacement is reached, the shear box is kept stationary for a specific period of time, after which the test proceeds again, at a constant displacement rate, until the peak and large-displacement shear strengths are mobilised. The shear stress-shear displacement curves from the proposed multistage tests exhibited a progressive decrease in shear stress with time (stress relaxation) during the period in which the shear box was restrained from any movement, which was more pronounced under lower normal stress values. Regardless of the prior interface shear displacement and duration of the stress relaxation stage, the peak and residual shear strength parameters of the C&D material-geotextile interface remained similar to those obtained from the conventional (benchmark) tests carried out under constant displacement rate.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Due to a Time-Dependent Couple

2011 ◽  
Vol 66 (1-2) ◽  
pp. 40-46 ◽  
Author(s):  
Corina Fetecau ◽  
Muhammad Imran ◽  
Constantin Fetecau
Keyword(s):  
Exact Solutions ◽  
Couette Flow ◽  
Bessel Functions ◽  
Time Dependent ◽  
Second Grade ◽  
Governing Equations ◽  
Material Parameters ◽  
Taylor Couette ◽  
Similar Solutions ◽  
Taylor Couette Flow

Taylor-Couette flow in an annulus due to a time-dependent torque suddenly applied to one of the cylinders is studied by means of finite Hankel transforms. The exact solutions, presented under series form in terms of usual Bessel functions, satisfy both the governing equations and all imposed initial and boundary conditions. They can easily be reduced to give similar solutions for Maxwell, second grade, and Newtonian fluids performing the same motion. Finally, some characteristics of the motion, as well as the influence of the material parameters on the behaviour of the fluid, are emphasized by graphical illustrations.

Numerical Analysis of Flow and Heat Transfer Characteristics on Micro Couette Flow

2014 ◽  
Vol 960-961 ◽  
pp. 551-554
Author(s):  
Lei Huang ◽  
Yang Cui
Keyword(s):  
Shear Stress ◽  
Couette Flow ◽  
Velocity Slip ◽  
Flow And Heat Transfer ◽  
Knudsen Numbers ◽  
Pressure Profiles ◽  
Viscous Heat ◽  
Temperature And Pressure ◽  
In The Beginning ◽  
Stream Direction

In this paper, Couette flow is mainly discussed by studying the general flow behaviour mechanism and importing the velocity slip and temperature jump boundary condition. By analyzing velocity, temperature and pressure profiles at different Knudsen numbers, we concluded that Couette flow is driven by shear stress. The shear stress lies in stream direction. Viscous heat causes the increasing of the fluid’s temperature. With the increasing of Knudsen numbers, the increasing speed increases. It’s in the beginning of transition region that the heat flux has the maximum.

On the principle of exchange of stabilities

1969 ◽  
Vol 310 (1502) ◽  
pp. 341-358 ◽  
Keyword(s):  
Growth Rate ◽  
Couette Flow ◽  
Equations Of State ◽  
Travelling Waves ◽  
Time Dependent ◽  
Heat Sources ◽  
Constant Heat ◽  
Perturbation Theorem ◽  
Adjoint Operators ◽  
Real Self

A perturbation theorem is proved: a class of real, bounded (non-self-adjoint) perturbations of norm ϵ to real self-adjoint operators preserve the reality of the simple eigenvalues for ϵ sufficiently small. A bound is obtained on ϵ. Application is made to Bénard convection with constant heat sources, radiation, particular time-dependent profiles and nonlinear equations of state and to instability of circular Couette flow for a range of gap widths. In each case the growth rate is the eigenvalue and hence if ϵ < ϵ c , travelling waves (either growing or decaying) are forbidden.

Nonlinear dynamics of viscoelastic Taylor–Couette flow: effect of elasticity on pattern selection, molecular conformation and drag

2009 ◽  
Vol 620 ◽  
pp. 353-382 ◽  
Author(s):  
D. G. THOMAS ◽  
B. KHOMAMI ◽  
R. SURESHKUMAR
Keyword(s):  
Shear Rate ◽  
Linear Stability ◽  
Couette Flow ◽  
Drag Force ◽  
Molecular Conformation ◽  
Vortex Structures ◽  
Time Dependent ◽  
Pattern Selection ◽  
Stability Threshold ◽  
Flow Transitions

Three-dimensional and time-dependent simulations of viscoelastic Taylor–Couette flow of dilute polymer solutions are performed using a fully implicit parallel spectral time-splitting algorithm to discover flow patterns with various spatio-temporal symmetries, namely rotating standing waves (RSWs), disordered oscillations (DOs) and solitary vortex structures referred to as oscillatory strips (OSs) and diwhirls (DWs). A detailed account of the impact of flow transitions on molecular conformation and viscoelastic stress, velocity profiles, hydrodynamic drag force and energy spectra of time-dependent flow states is presented. Overall, predicted pattern selection and flow features compare very favourably with experimental observations. For elasticity number E, that signifies the ratio of elastic to viscous forces, >0.1, and when the shear rate (cylinder rotation speed) is increased above the linear stability threshold, the circular Couette flow (CCF) becomes unstable to RSWs which are characterized by a checkerboard-like pattern in the space–time plot of radial velocity, implying symmetry between inflow/outflow (I/O) regions. As the shear rate is further increased, perturbations that break the I/O symmetry are amplified leading to DOs and/or flame-like patterns with spectral mechanical energy transfer reminiscent of elastically induced low-Reynolds-number turbulence. However, when the shear rate is decreased from those at which such chaotic states are observed, the radially inward acting polymer body force created by flow-induced molecular stretching causes the development of narrow inflow regions surrounded by much broader weak outflow domains. This promotes the formation of solitary vortex structures, which can be stationary and axisymmetric (DWs) or time-dependent (OSs). The dynamics of the formation of these structures by merging and coalescence of vortex pairs and the implication of such events on instantaneous hydrodynamic force are studied. For O(1) values of E, OSs and DWs appear approximately at constant values of the We, defined as the ratio of polymer relaxation time to the inverse shear rate in the gap. As shear rate is decreased further, DWs decay to CCF although at We values less than the linear stability threshold. The flow transitions are hysteretic with respect to We, as evidenced by a plot of drag force versus We.

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