Numerical modelling of quartz-biotite aggregates: Insights on strain weakening and two-phase flow laws

2021 ◽  
Author(s):  
Markus Rast ◽  
Jonas Ruh
Keyword(s):  
Numerical Experiments ◽  
Numerical Models ◽  
Fluid Pressure ◽  
Minor Importance ◽  
Two Phase ◽  
Background Strain ◽  
Ductile Flow ◽  
Multi Phase ◽  
Stress Drops ◽  
Flow Laws

<div> <div> <div> <p>Strain weakening is a prerequisite for localization of strain and therefore crucial for the understanding of shear zone evolution. In the context of progressive deformation of multi-phase aggregates, it is unclear whether the change in geometry and orientation of the involved phases leads to structural or geometric strain weakening and thus may control strain localization. Consequently, the question arises how the ductile flow of two-phase rocks can be described or determined. To contribute to a better understanding of the knowledge gaps outlined above, two-dimensional numerical shear experiments of quartz-biotite aggregates were conducted at varying temperatures, background strain rates and fluid pressure ratios. Textural variations after a shear strain of <em>γ </em>≈ 10 appear to be dependent on the viscosity contrast between the minerals involved. To estimate whether a numerical experiment is undergoing strain weakening or strain hardening (or both), the temporal evolution of the mean second invariant of the deviatoric stress tensor was tracked. The results suggest that strain weakening occurs if biotite-inclusions are distinctly isolated and that it is more effective under conditions with larger viscosity contrasts between matrix and inclusions. However, the stress drops in numerical experiments with purely structural / textural strain weakening are rather low (−1.1 to −6.4%) compared to other strain weakening processes. It appears that phase rearrangement and change in phase geometry with evolving strain is of minor importance for the occurrence of strain weakening. Based on the numerical experiments and assuming a power-law relationship between stress and strain, the flow-law parameters of quartz-biotite aggregates with different biotite contents were determined. The results are in the range of existing experimental and analytical mixed-aggregates flow-laws. However, the variations between the different flow-laws show that further research is required, for which numerical models as used in the present study could serve as basis.</p> </div> </div> </div>

scholarly journals Is complex fault zone behaviour a reflection of rheological heterogeneity?

2021 ◽  
Vol 379 (2193) ◽  
pp. 20190421 ◽  
Author(s):  
Å. Fagereng ◽  
A. Beall
Keyword(s):  
Fault Zone ◽  
Numerical Models ◽  
Finite Thickness ◽  
Fluid Pressure ◽  
Plate Boundary ◽  
Shear Zones ◽  
Fault Slip ◽  
Two Phase ◽  
Fault Properties ◽  
Stress Amplification

Fault slip speeds range from steady plate boundary creep through to earthquake slip. Geological descriptions of faults range from localized displacement on one or more discrete planes, through to distributed shearing flow in tabular zones of finite thickness, indicating a large range of possible strain rates in natural faults. We review geological observations and analyse numerical models of two-phase shear zones to discuss the degree and distribution of fault zone heterogeneity and effects on active fault slip style. There must be certain conditions that produce earthquakes, creep and slip at intermediate velocities. Because intermediate slip styles occur over large ranges in temperature, the controlling conditions must be effects of fault properties and/or other dynamic variables. We suggest that the ratio of bulk driving stress to frictional yield strength, and viscosity contrasts within the fault zone, are critical factors. While earthquake nucleation requires the frictional yield to be reached, steady viscous flow requires conditions far from the frictional yield. Intermediate slip speeds may arise when driving stress is sufficient to nucleate local frictional failure by stress amplification, or local frictional yield is lowered by fluid pressure, but such failure is spatially limited by surrounding shear zone stress heterogeneity. This article is part of a discussion meeting issue ‘Understanding earthquakes using the geological record’.

scholarly journals Two-phase CFD simulation of the monodyspersed suspension hydraulic behaviour in the tank apparatus from a circulatory pipe

2008 ◽  
Vol 10 (1) ◽  
pp. 22-27 ◽  
Author(s):  
Roch Plewik ◽  
Piotr Synowiec ◽  
Janusz Wójcik
Keyword(s):  
Cfd Simulation ◽  
Fluidised Bed ◽  
Cfd Simulations ◽  
Two Phase ◽  
Hydraulic Behaviour ◽  
Hydraulic Conditions ◽  
The One ◽  
Cfd Method ◽  
Multi Phase ◽  
The Ideal

Two-phase CFD simulation of the monodyspersed suspension hydraulic behaviour in the tank apparatus from a circulatory pipe The hydrodynamics in fluidized-bed crystallizers is studied by CFD method. The simulations were performed by a commercial packet of computational fluid dynamics Fluent 6.x. For the one-phase modelling (15), a standard k-ε model was applied. In the case of the two-phase flows the Eulerian multi-phase model with a standard k-ε method, aided by the k-ε dispersed model for viscosity, has been used respectively. The collected data put a new light on the suspension flow behaviour in the annular zone of the fluidised bed crystallizer. From the presented here CFD simulations, it clearly issues that the real hydraulic conditions in the fluidised bed crystallizers are far from the ideal ones.

Analysis of Single- and Two-Phase Flows in Turbopump Inducers

1967 ◽  
Vol 89 (4) ◽  
pp. 577-586 ◽  
Author(s):  
P. Cooper
Keyword(s):  
Equation Of State ◽  
Flow Field ◽  
Thermal Effects ◽  
Single Phase ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Pressure Rise ◽  
Recent Theory ◽  
Two Phase ◽  
Overall Efficiency

A model is developed for analytically determining pump inducer performance in both the single-phase and cavitating flow regimes. An equation of state for vaporizing flow is used in an approximate, three-dimensional analysis of the flow field. The method accounts for losses and yields internal distributions of fluid pressure, velocity, and density together with the resulting overall efficiency and pressure rise. The results of calculated performance of two sample inducers are presented. Comparison with recent theory for fluid thermal effects on suction head requirements is made with the aid of a resulting dimensionless vaporization parameter.

scholarly journals The Role of Lower Crustal Rheology in Lithospheric Delamination During Orogeny

2021 ◽  
Vol 9 ◽  
Author(s):  
Lin Chen
Keyword(s):  
Lower Crust ◽  
Numerical Models ◽  
The Tibetan Plateau ◽  
Mantle Lithosphere ◽  
Laboratory Studies ◽  
Surface Uplift ◽  
Continental Lower Crust ◽  
Lower Crustal ◽  
Flow Laws

The continental lower crust is an important composition- and strength-jump layer in the lithosphere. Laboratory studies show its strength varies greatly due to a wide variety of composition. How the lower crust rheology influences the collisional orogeny remains poorly understood. Here I investigate the role of the lower crust rheology in the evolution of an orogen subject to horizontal shortening using 2D numerical models. A range of lower crustal flow laws from laboratory studies are tested to examine their effects on the styles of the accommodation of convergence. Three distinct styles are observed: 1) downwelling and subsequent delamination of orogen lithosphere mantle as a coherent slab; 2) localized thickening of orogen lithosphere; and 3) underthrusting of peripheral strong lithospheres below the orogen. Delamination occurs only if the orogen lower crust rheology is represented by the weak end-member of flow laws. The delamination is followed by partial melting of the lower crust and punctuated surface uplift confined to the orogen central region. For a moderately or extremely strong orogen lower crust, topography highs only develop on both sides of the orogen. In the Tibetan plateau, the crust has been doubly thickened but the underlying mantle lithosphere is highly heterogeneous. I suggest that the subvertical high-velocity mantle structures, as observed in southern and western Tibet, may exemplify localized delamination of the mantle lithosphere due to rheological weakening of the Tibetan lower crust.

scholarly journals Model Calculations of Elastic Moduli in Highly Deformed Composites

1989 ◽  
Vol 10 (2) ◽  
pp. 153-164 ◽  
Author(s):  
H. J. Bunge
Keyword(s):  
Plastic Deformation ◽  
Simple Model ◽  
Elastic Moduli ◽  
Opposite Sign ◽  
Internal Stresses ◽  
Minor Importance ◽  
High Increase ◽  
Two Phase ◽  
Linear Elasticity Theory ◽  
Model Calculations

Young's modulus of heavily deformed two-phase composites shows an unusually high increase after plastic deformation. It is assumed that this is due to two reasons, i.e. texture changes and changes of the moduli of the constitutive phases on the basis of non-linear elasticity theory and internal stresses of opposite sign in the phases. Expressions of the two contributions are given on the basis of simple model assumptions. It is estimated that the changes of shape and arrangement of the phases and shape and arrangement of the crystallites in the phases are only of minor importance.

Partially Cavitating Hydrofoils: Experimental and Numerical Analysis*

2000 ◽  
Vol 44 (01) ◽  
pp. 40-58
Author(s):  
Christian Pellone ◽  
Thierry Maître ◽  
Laurence Briançon-Marjollet
Keyword(s):  
Numerical Models ◽  
Lift Coefficient ◽  
Pressure Coefficient ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Local Pressure ◽  
Two Phase ◽  
Complete Study ◽  
Flow Configurations ◽  
Potential Methods

The numerical modeling of partially cavitating foils under a confined flow configuration is described. A complete study of previous numerical models highlights that the presence of a turbulent and two-phase wake, at the rear of the cavity, has a nonnegligible effect on the local pressure coefficient, the cavitation number, the cavity length and the lift coefficient; hence viscous effects must be included. Two potential methods are used, each being coupled with a calculation of the boundary layer developed downstream of the cavity. So, an "open cavity" numerical model, as it is called, was developed and tested with two types of foil: a NACA classic foil and a foil of which the profile is obtained performing an inverse calculation on a propeller blade test section. On the other hand, under noncavitating conditions, for each method, the results are compared with the results obtained by the Navier-Stokes solver "FLUENT." The cavitating flow configurations presented herein were carried out using the small hydrodynamic tunnel at Bassin d'Essais des Carènes [Val de Reuil, France]. The results obtained by the two methods are compared with experimental measurements.

The control method for the multi-phase traffic model

2016 ◽  
Vol 27 (10) ◽  
pp. 1650111
Author(s):  
Yi Liu ◽  
Rong-Jun Cheng ◽  
Yan-Qiang Ma ◽  
Hong-Xia Ge
Keyword(s):  
Traffic Control ◽  
Control Method ◽  
Turning Points ◽  
Control Signal ◽  
Two Phase ◽  
Optimal Velocity ◽  
Car Following Model ◽  
The Stability ◽  
Improved Model ◽  
Multi Phase

Based on multi-phase car-following model proposed by Nagatani, the control theory method is used to analyze the stability of the model. The optimal velocity function is improved to have more turning points. The original optimal velocity with one turning point shows two-phase traffic, while the improved model with [Formula: see text] turning points exhibits [Formula: see text] phase traffic. Control signal is added into the model. Numerical simulation is conducted to show the results for the stability of the model with and without control signal.

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