Release of a viscous power-law fluid over an inviscid ocean

2012 ◽  
Vol 700 ◽  
pp. 63-76 ◽  
Author(s):  
Samuel S. Pegler ◽  
John R. Lister ◽  
M. Grae Worster
Keyword(s):  
Power Law ◽  
Large Time ◽  
Three Dimensional ◽  
Shear Thinning ◽  
Capillary Forces ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Initial Shape ◽  
Algebraic Decay

AbstractWe consider the two- and three-dimensional spreading of a finite volume of viscous power-law fluid released over a denser inviscid fluid and subject to gravitational and capillary forces. In the case of gravity-driven spreading, with a power-law fluid having strain rate proportional to stress to the power $n$, there are similarity solutions with the extent of the current being proportional to ${t}^{1/ n} $ in the two-dimensional case and ${t}^{1/ 2n} $ in the three-dimensional case. Perturbations from these asymptotic states are shown to retain their initial shape but to decay relatively as ${t}^{\ensuremath{-} 1} $ in the two-dimensional case and ${t}^{\ensuremath{-} 3/ (n+ 3)} $ in the three-dimensional case. The former is independent of $n$, whereas the latter gives a slower rate of relative decay for fluids that are more shear-thinning. In cases where the layer is subject to a constraining surface tension, we determine the evolution of the layer towards a static state of uniform thickness in which the gravitational and capillary forces balance. The asymptotic form of this convergence is shown to depend strongly on $n$, with rapid finite-time algebraic decay in shear-thickening cases, large-time exponential decay in the Newtonian case and slow large-time algebraic decay in shear-thinning cases.

Turbulent Flow Simulation of Power-Law Fluid in Annular Channel

2020 ◽  
Author(s):  
Andrey Gavrilov ◽  
Yaroslav Ignatenko ◽  
Oleg Bocharov ◽  
Roger Aragall
Keyword(s):  
Steady State ◽  
Power Law ◽  
Drill Pipe ◽  
Three Dimensional ◽  
Annular Channel ◽  
Shear Stresses ◽  
Two Dimensional ◽  
Power Law Fluid ◽  
Pressure Losses ◽  
Viscous Shear

Abstract Transient three-dimensional flow simulations of power–law fluid in a long axisymmetric annular channel considering 0.5 diameter ratio were performed. An in–house CFD code considering URANS (Unsteady Reynolds Averaged Navier–Stokes), 2D RANS (steady-state axially uniform 2D RANS) and LES (Large Eddy Simulation) approaches were compared to perform the simulations. Flow structure was analyzed. Numerical experiments showed that rotation of the inner cylinder (drill pipe) leads to two effects: decrease of apparent viscosity in the region close to the rotating cylinder, thus decreasing viscous shear stresses; development of secondary vorticity structures increasing energy loss. First mechanism decreases pressure losses and dominates when Re < 300. At Re ∼ 300 the mechanisms compete with each other and pressure losses depends on power–law index n. At Re > 300 mechanism of second vortex structured dominates and increases pressure loss with rotation. Pressure losses for two-dimensional steady-state and three-dimensional transient problems were compared. Pressure losses using a two-dimensional approach can be underestimated by up to 30%.

scholarly journals Modelling of Power-Law Fluid Flow Inside a Piezoelectric Inkjet Printhead

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2441
Author(s):  
Ju Peng ◽  
Jin Huang ◽  
Jianjun Wang
Keyword(s):  
Fluid Flow ◽  
Power Law ◽  
Inkjet Printing ◽  
Three Dimensional ◽  
Equivalent Circuit Model ◽  
Shear Thinning ◽  
Power Law Fluid ◽  
Heterogeneous Objects ◽  
High Level ◽  
Inkjet Printhead

Piezoelectric three-dimensional inkjet printing has been used to manufacture heterogeneous objects due to its high level of flexibility. The materials used are non-Newtonian inks with complex rheological properties, and their behavior in the context of inkjet printing has not been fully understood: for example, the fact that the shear-thinning viscosity affects the droplet generation. Therefore, a control strategy coping with shear-thinning behaviors is needed to ensure printing consistency. In this paper, a novel model-based approach is presented to describe the shear-thinning ink dynamics inside the piezoelectric inkjet printhead, which provides the basis to design the excitation parameters in a systematic way. The dynamic equation is simplified into a quasi-one-dimensional equation through the combination of the boundary layer theory and the constitutive equation of the power-law fluid, of which the viscosity is shear-thinning. Based on this, a nonlinear time-varying equivalent circuit model is presented to simulate the power-law fluid flow rate inside the tube. The feasibility and effectiveness of this model can be evaluated by comparing the results of computational fluid dynamics and the experimental results.

Three-dimensional disturbances to a mixing layer in the nonlinear critical-layer regime

1995 ◽  
Vol 291 ◽  
pp. 57-81 ◽  
Author(s):  
S. M. Churilov ◽  
I. G. Shukhman
Keyword(s):  
Travelling Waves ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Critical Layer ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Theory ◽  
New Type ◽  
Two Stages

We consider the nonlinear spatial evolution in the streamwise direction of slightly three-dimensional disturbances in the form of oblique travelling waves (with spanwise wavenumber kz much less than the streamwise one kx) in a mixing layer vx = u(y) at large Reynolds numbers. A study is made of the transition (with the growth of amplitude) to the regime of a nonlinear critical layer (CL) from regimes of a viscous CL and an unsteady CL, which we have investigated earlier (Churilov & Shukhman 1994). We have found a new type of transition to the nonlinear CL regime that has no analogy in the two-dimensional case, namely the transition from a stage of ‘explosive’ development. A nonlinear evolution equation is obtained which describes the development of disturbances in a regime of a quasi-steady nonlinear CL. We show that unlike the two-dimensional case there are two stages of disturbance growth after transition. In the first stage (immediately after transition) the amplitude A increases as x. Later, at the second stage, the ‘classical’ law A ∼ x2/3 is reached, which is usual for two-dimensional disturbances. It is demonstrated that with the growth of kz the region of three-dimensional behaviour is expanded, in particular the amplitude threshold of transition to the nonlinear CL regime from a stage of ‘explosive’ development rises and therefore in the ‘strongly three-dimensional’ limit kz = O(kx) such a transition cannot be realized in the framework of weakly nonlinear theory.

On the Hydrodynamic Interaction Between Ship and Free-Surface Motions on Vessels With Moonpools

2019 ◽  
Author(s):  
Senthuran Ravinthrakumar ◽  
Trygve Kristiansen ◽  
Babak Ommani
Keyword(s):  
Free Surface ◽  
Flow Separation ◽  
Coupling Effect ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Navier Stokes ◽  
Linear Potential ◽  
Two Dimensional ◽  
Sloshing Mode ◽  
Vessel Motion

Abstract Coupling between moonpool resonance and vessel motion is investigated in two-dimensional and quasi three-dimensional settings, where the models are studied in forced heave and in freely floating conditions. The two-dimensional setups are with a recess, while the quasi three-dimensional setups are without recess. One configuration with recess is presented for the two-dimensional case, while three different moonpool sizes (without recess) are tested for the quasi three-dimensional setup. A large number of forcing periods, and three wave steepnesses are tested. Boundary Element Method (BEM) and Viscous BEM (VBEM) time-domain codes based on linear potential flow theory, and a Navier–Stokes solver with linear free-surface and body-boundary conditions, are implemented to investigate resonant motion of the free-surface and the model. Damping due to flow separation from the sharp corners of the moonpool inlets is shown to matter for both vessel motions and moonpool response around the piston mode. In general, the CFD simulations compare well with the experimental results. BEM over-predicts the response significantly at resonance. VBEM provides improved results compared to the BEM, but still over-predicts the response. In the two-dimensional study there are significant coupling effects between heave, pitch and moonpool responses. In the quasi three-dimensional tests, the coupling effect is reduced significantly as the moonpool dimensions relative to the displaced volume of the ship is reduced. The first sloshing mode is investigated in the two-dimensional case. The studies show that damping due to flow separation is dominant. The vessel motions are unaffected by the moonpool response around the first sloshing mode.

Pipe Response Under Concentrated Lateral Loads and External Pressure

2005 ◽  
Author(s):  
Spyros A. Karamanos ◽  
Charis Eleftheriadis
Keyword(s):  
Three Dimensional ◽  
External Pressure ◽  
Absorption Capacity ◽  
Pressure Effects ◽  
Analytical Models ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Lateral Loads ◽  
Offshore Pipelines ◽  
Different Levels

The present paper examines the denting deformation of offshore pipelines and tubular members (D/t≤50) subjected to lateral (transverse) quasi-static loading in the presence of uniform external pressure. Particular emphasis is given on pressure effects on the ultimate lateral load of tubes and on their energy absorption capacity. Pipe segments are modeled with shell finite elements, accounting for geometric and material nonlinearities, and give very good predictions compared with test data from non-pressurized pipes. Lateral loading between two rigid plates, a two-dimensional case, is examined first. Three-dimensional case, are also analyzed, where the load is applied either through a pair of opposite wedge-shaped denting tools or a single spherical denting tool. Load-deflection curves for different levels of external pressure are presented, which indicate that pressure has significant influence on pipe response and strength. Finally, simplified analytical models are proposed for the two-dimensional and three-dimensional load configurations, which yield closed-form expressions, compare fairly well with the finite element results and illustrate some important features of pipeline response in a clear and elegant manner.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

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