Gravity-driven flow in a horizontal annulus

2017 ◽  
Vol 830 ◽  
pp. 479-493 ◽  
Author(s):  
Marcus C. Horsley ◽  
Andrew W. Woods
Keyword(s):  
Horizontal Well ◽  
Outer Boundary ◽  
Equations Of Motion ◽  
Time Dependent ◽  
Two Dimensional ◽  
Narrow Gap ◽  
Dense Fluid ◽  
Annular Geometry ◽  
Gravity Driven ◽  
Gravity Driven Flow

A theory for the low-Reynolds-number gravity-driven flow of two Newtonian fluids separated by a density interface in a two-dimensional annular geometry is developed. Solutions for the governing time-dependent equations of motion, in the limit that the radius of the inner and outer boundaries are similar, and in the case that the interface is initially inclined to the horizontal, are analysed numerically. We focus on the case in which the fluid is arranged symmetrically about a vertical line through the centre of the annulus. These solutions are successfully compared with asymptotic solutions in the limits that (i) a thin film of dense fluid drains down the outer boundary of the annulus, and (ii) a thin layer of less dense fluid is squeezed out of the narrow gap between the base of the inner annulus and dense fluid. Application of the results to the problem of mud displacement by cement in a horizontal well is briefly discussed.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

Shallow, gravity-driven flow in a poro-elastic layer

2015 ◽  
Vol 778 ◽  
pp. 335-360 ◽  
Author(s):  
Duncan R. Hewitt ◽  
Jerome A. Neufeld ◽  
Neil J. Balmforth
Keyword(s):  
Coupled Model ◽  
Solid Matrix ◽  
Rigid Base ◽  
Surface Uplift ◽  
Hydrogel Particles ◽  
Dense Fluid ◽  
The Matrix ◽  
Gravity Driven ◽  
Flow Through ◽  
Gravity Driven Flow

By combining Biot’s theory of poro-elasticity with standard shallow-layer scalings, a theoretical model is developed to describe axisymmetric gravity-driven flow through a shallow deformable porous medium. Motivated in part by observations of surface uplift around $\text{CO}_{2}$ sequestration sites, the model is used to explore the injection of a dense fluid into a horizontal, deformable porous layer that is initially saturated with another, less dense, fluid. The layer lies between a rigid base and a flexible overburden, both of which are impermeable. As the injected fluid spreads under gravity, the matrix deforms and the overburden lifts up. The coupled model predicts the location of the injected fluid as it spreads and the resulting uplift of the overburden due to deformation of the solid matrix. In general, the uplift spreads diffusively far ahead of the injected fluid. If fluid is injected with a constant flux and the medium is unbounded, both the uplift and the injected fluid spread in a self-similar fashion with the same similarity variable $\propto r/t^{1/2}$. The asymptotic form of this spreading is established. Results from a series of laboratory experiments, using polyacrylamide hydrogel particles to create a soft poro-elastic material, are compared qualitatively with the predictions of the model.

A coupled variational principle for 2D interactions between water waves and a rigid body containing fluid

2017 ◽  
Vol 827 ◽  
Author(s):  
Hamid Alemi Ardakani
Keyword(s):  
Variational Principle ◽  
Potential Flow ◽  
Water Waves ◽  
Variational Principles ◽  
Equations Of Motion ◽  
The Body ◽  
Two Dimensional ◽  
Hydrodynamic Equations ◽  
Gravity Driven ◽  
Complete Set

New variational principles are given for the two-dimensional interactions between gravity-driven water waves and a rotating and translating rectangular vessel dynamically coupled to its interior potential flow with uniform vorticity. The complete set of equations of motion for the exterior water waves, the exact nonlinear hydrodynamic equations of motion for the vessel in the roll/pitch, sway/surge and heave directions, and also the full set of equations of motion for the interior fluid of the vessel, relative to the body coordinate system attached to the rotating–translating vessel, are derived from two Lagrangian functionals.

Gravity-driven reacting flows in a confined porous aquifer

2007 ◽  
Vol 588 ◽  
pp. 29-41 ◽  
Author(s):  
JAMES VERDON ◽  
ANDREW W. WOODS
Keyword(s):  
Porous Layer ◽  
Reaction Front ◽  
Numerical Solutions ◽  
Finite Depth ◽  
Injection Rate ◽  
Approximate Analytic Solution ◽  
Two Dimensional ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
Dissolution Front

We develop a model for the dynamics of a reactive gravity-driven flow in a porous layer of finite depth, accounting for the change in permeability and density across the dissolution front. We identify that the two controlling parameters are the mobility ratio across the reaction front and the ratio of the buoyancy-driven flow to the fluid injection rate. We present some numerical solutions for the evolution of a two-dimensional dissolution front, and develop an approximate analytic solution for the limit of large injection rate compared to the buoyancy-driven flow. The model predictions are compared with some new analogue laboratory experiments in which fresh water displaces a saturated aqueous solution initially confined within a two-dimensional reactive permeable matrix composed of salt powder and glass ballotini. We also present self-similar solutions for an axisymmetric gravity-driven reactive current moving through a porous layer of finite depth. The solutions illustrate how the reaction front becomes progressively wider as the ratio of the buoyancy-driven flow to the injection rate increases, and also as the mobility contrast across the front increases.

EFFECT OF FLOCCULATING AGENTS ON DRAG IN GRAVITY-DRIVEN FLOW SYSTEMS

2017 ◽  
Vol 44 (4) ◽  
pp. 339-347
Author(s):  
M. K. S. V. Raghav ◽  
Ravi Teja ◽  
Chirravuri Subbarao
Keyword(s):  
Flow Systems ◽  
Gravity Driven ◽  
Gravity Driven Flow

Drag reduction using mixed solutions of hydrotrope and surfactant in gravity driven flow systems

2013 ◽  
Vol 8 (3) ◽  
pp. 22-27
Author(s):  
M. Venkata Ramana ◽  
◽  
Ch. V. Subbarao ◽  
P. V. Gopal singh ◽  
Krishna Prasad K.M.M ◽  
...  
Keyword(s):  
Drag Reduction ◽  
Mixed Solutions ◽  
Flow Systems ◽  
Gravity Driven ◽  
Gravity Driven Flow

scholarly journals Integrable unsteady motion with an application to ocean eddies

1998 ◽  
Vol 5 (3) ◽  
pp. 145-151
Author(s):  
A. D. Kirwan, Jr. ◽  
B. L. Lipphardt, Jr.
Keyword(s):  
Potential Vorticity ◽  
Particle Motion ◽  
Gulf Stream ◽  
Incompressible Flows ◽  
Unsteady Motion ◽  
Ring System ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ocean Eddies ◽  
Multilayered Systems

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

Two-dimensional leaps in near-critical flow over isolated orography

2005 ◽  
Vol 461 (2064) ◽  
pp. 3747-3763 ◽  
Author(s):  
E.R Johnson ◽  
G.G Vilenski
Keyword(s):  
Unsteady Flow ◽  
Equations Of Motion ◽  
Fold Increase ◽  
Flow Speed ◽  
Two Dimensional ◽  
Subcritical Flow ◽  
One Dimensional ◽  
Petviashvili Equation ◽  
Lee Wave ◽  
Supercritical Flows

This paper describes steady two-dimensional disturbances forced on the interface of a two-layer fluid by flow over an isolated obstacle. The oncoming flow speed is close to the linear longwave speed and the layer densities, layer depths and obstacle height are chosen so that the equations of motion reduce to the forced two-dimensional Korteweg–de Vries equation with cubic nonlinearity, i.e. the forced extended Kadomtsev–Petviashvili equation. The distinctive feature noted here is the appearance in the far lee-wave wake behind obstacles in subcritical flow of a ‘table-top’ wave extending almost one-dimensionally for many obstacles widths across the flow. Numerical integrations show that the most important parameter determining whether this wave appears is the departure from criticality, with the wave appearing in slightly subcritical flows but being destroyed by two-dimensional effects behind even quite long ridges in even moderately subcritical flow. The wave appears after the flow has passed through a transition from subcritical to supercritical over the obstacle and its leading and trailing edges resemble dissipationless leaps standing in supercritical flow. Two-dimensional steady supercritical flows are related to one-dimensional unsteady flows with time in the unsteady flow associated with a slow cross-stream variable in the two-dimensional flows. Thus the wide cross-stream extent of the table-top wave appears to derive from the combination of its occurrence in a supercritical region embedded in the subcritical flow and the propagation without change of form of table-top waves in one-dimensional unsteady flow. The table-top wave here is associated with a resonant steepening of the transition above the obstacle and a consequent twelve-fold increase in drag. Remarkably, the table-top wave is generated equally strongly and extends laterally equally as far behind an axisymmetric obstacle as behind a ridge and so leads to subcritical flows differing significantly from linear predictions.

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