Three-dimensional stress effects on time-dependent swelling behaviour of shaly rocks

2003 ◽  
Vol 40 (3) ◽  
pp. 501-511 ◽  
Author(s):  
B C Hawlader ◽  
Y N Lee ◽  
K Y Lo
Keyword(s):  
Applied Stress ◽  
Axial Stress ◽  
Three Dimensional ◽  
Biaxial Stress ◽  
Time Dependent ◽  
Stress Effect ◽  
Stress Effects ◽  
Proposed Model ◽  
Laboratory Test Results ◽  
Swelling Strain

This paper presents a time-dependent constitutive model that has been developed for the swelling of shaly rocks. Laboratory test results on many shales, including Queenston shale, show that the swelling of these rocks depends on the applied stresses. The applied stress in one principal stress direction reduces swelling strain not only in that direction but also in the perpendicular directions. It was found that swelling strain reductions are nonlinearly dependent on applied stress. The reduction in lateral swelling caused as a result of axial stress is modeled using the "pseudo-Poisson's effect". The proposed model is used to simulate the development of swelling strain with time under uniaxial and biaxial stress conditions. Comparison between the computed and experimental results shows that the pseudo-Poisson's effect is a key parameter for simulating the observed time-dependent swelling.Key words: swelling, Queenston shale, modeling, three-dimensional stress effect, nonlinearity.

Analysis of tunnels in shaly rock considering three-dimensional stress effects on swelling

2005 ◽  
Vol 42 (1) ◽  
pp. 1-12 ◽  
Author(s):  
B C Hawlader ◽  
K Y Lo ◽  
I D Moore
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Cold Water ◽  
Principal Direction ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Stress Effect ◽  
Stress Effects ◽  
Laboratory Test Results

Underground structures in shales or shaly rocks endure time-dependent swelling effects. Laboratory test results show that the swelling of these shales is dependent on three-dimensional stresses; an external stress on a specimen in one principal direction reduces the swelling not only in that direction but also perpendicularly. The effectiveness of a time-dependent swelling model that considers the three-dimensional stress effect is presented in this paper. A finite element algorithm incorporating the new constitutive model is used for a numerical analysis. The finite element program is used to analyze two tunnels in southern Ontario: the Heart Lake storm sewer tunnel, and the Darlington cold-water intake tunnel. The predicted results agree well with the records of field performance of these tunnels. The comparison between present analyses and the existing closed-form solution shows that the existing solution overestimates the time-dependent swelling effects. The three-dimensional stress effects on swelling are not considered in the closed-form solutions and are the cause of this discrepancy. The pseudo-Poisson's effect is a key parameter for modelling the observed time-dependent swelling. The use of these solutions in design is discussed.Key words: time-dependent swelling, shale, modelling, three-dimensional stress effect, finite element method, tunnel.

A parallel three-dimensional scour model to predict flow and scour below a submarine pipeline

Open Physics ◽  
2010 ◽  
Vol 8 (4) ◽  
Author(s):  
Muhammad Alam ◽  
Liang Cheng
Keyword(s):  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Time Dependent ◽  
Submarine Pipeline ◽  
Spiral Vortex ◽  
Proposed Model ◽  
Constant Rate ◽  
Shoulder Region ◽  
Lattice Unit ◽  
Speed Of Propagation

AbstractA three-dimensional Lattice Boltzmann flow and scour model is developed to simulate time-dependent scour below a submarine pipeline. The proposed model presented in this paper is able to predict streamwise and spanwise propagations of scour with respect to lattice unit of time. It is evident from this study that the existence of a spiral vortex in the proximity of the span shoulder is quite noteworthy. It is revealed that the critical regime of the 2-D scour process is found to be up to one pipe diameter away in both directions from the middle of the unsupported length of pipelines. The equilibrium maximum scour depth and the shape of streamwise equilibrium scour hole compare well with the available experimental data. The speed of propagation of scour along the pipeline length maintains an almost constant rate, which is consistent with the experimental observations found in literature. In addition, it is seen that the scour slope at the shoulder region remains fairly constant throughout the whole scour process.

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Study on the generalized k-Hilfer–Prabhakar fractional viscoelastic–plastic model

2021 ◽  
pp. 108128652110258
Author(s):  
Yi-Ying Feng ◽  
Xiao-Jun Yang ◽  
Jian-Gen Liu ◽  
Zhan-Qing Chen
Keyword(s):  
Constitutive Model ◽  
Three Dimensional ◽  
Sensitivity Analyses ◽  
Creep Process ◽  
Fractional Operator ◽  
Modified Model ◽  
Proposed Model ◽  
Accelerated Creep ◽  
The Laplace Transform ◽  
Classical Models

The general fractional operator shows its great predominance in the construction of constitutive model owing to its agility in choosing the embedded parameters. A generalized fractional viscoelastic–plastic constitutive model with the sense of the k-Hilfer–Prabhakar ( k-H-P) fractional operator, which has the character recovering the known classical models from the proposed model, is established in this article. In order to describe the damage in the creep process, a time-varying elastic element [Formula: see text] is used in the proposed model with better representation of accelerated creep stage. According to the theory of the kinematics of deformation and the Laplace transform, the creep constitutive equation and the strain of the modified model are established and obtained. The validity and rationality of the proposed model are identified by fitting with the experimental data. Finally, the influences of the fractional derivative order [Formula: see text] and parameter k on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.

Flow Mixing Enhancement from Balloon Pulsations in an Intravenous Oxygenator

2004 ◽  
Vol 127 (3) ◽  
pp. 400-415 ◽  
Author(s):  
Amador M. Guzmán ◽  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Numerical Simulations ◽  
Oxygen Transfer ◽  
Fiber Bundle ◽  
Transfer Rate ◽  
Oxygen Transfer Rate ◽  
Three Dimensional ◽  
Time Dependent ◽  
Fiber Placement ◽  
Flow Mixing ◽  
Dependent Flow

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

Biaxial stress effects on magnetization perpendicular to the stress plane

1995 ◽  
Vol 31 (6) ◽  
pp. 3665-3667 ◽  
Author(s):  
M.J. Sablik ◽  
H. Kwun ◽  
G.L. Burkhardt ◽  
R.A. Langman
Keyword(s):  
Biaxial Stress ◽  
Stress Effects ◽  
Stress Plane
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