scholarly journals Flow Classification and Its Application to Fluid Processing

2021 ◽  
Vol 333 ◽  
pp. 02001
Author(s):  
Yasuya Nakayama ◽  
Toshihisa Kajiwara
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Classification Scheme ◽  
Strain Rate Tensor ◽  
Spatial Distributions ◽  
Process Performance ◽  
Fluid Element ◽  
Flow Classification ◽  
Analysis Technique ◽  
Deformation Rate Tensor

Mathematically, the problem of flow field classification can be analyzed by the eigenanalysis of the deformation-rate tensor; however, such analysis technique have not been commonly applied in fluid processing. We derive a simplified objective flow classification scheme based on the invariants of the strain-rate tensor and the vorticity tensor. Multiaxiality of flow, which is related to the type of elongation, and converging/bifurcating flow, is characterized by the strain-rate tensor, while rotation contribution that protects fluid element from stretching is characterized by the relative intensity of an objective vorticity to the strain-rate. The spatial distributions of flow classification quantities offer an essential tool in understanding the flow pattern structure, and therefore can be useful to get insights into the connection between the geometry and the process performance.

scholarly journals Crevasse patterns and the strain-rate tensor: a high-resolution comparison

1998 ◽  
Vol 44 (146) ◽  
pp. 68-76 ◽  
Author(s):  
J. T. Harper ◽  
N. F. Humphrey ◽  
W. T. Pfeffer
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Principal Strain ◽  
Length Scale ◽  
Strain Rate Tensor ◽  
Regional Flow ◽  
Orthogonal Grid ◽  
Valley Glacier ◽  
Longitudinal Strain Rate

AbstractValues of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2 reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate (x) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e. x > 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

scholarly journals Crevasse patterns and the strain-rate tensor: a high-resolution comparison

1998 ◽  
Vol 44 (146) ◽  
pp. 68-76 ◽  
Author(s):  
J. T. Harper ◽  
N. F. Humphrey ◽  
W. T. Pfeffer
Keyword(s):  
Flow Field ◽  
Strain Rate ◽  
Longitudinal Strain ◽  
Principal Strain ◽  
Length Scale ◽  
Strain Rate Tensor ◽  
Regional Flow ◽  
Orthogonal Grid ◽  
Valley Glacier ◽  
Longitudinal Strain Rate

AbstractValues of the strain-rate tensor represented at a 20 m length scale are found to explain the pattern and orientation of crevasses in a 0.13 km2reach of Worthington Glacier, Alaska, U.S.A. The flow field of the reach is constructed from surveyed displacements of 110 markers spaced 20-30 m apart. A velocity gradient method is then used to calculate values of the principal strain-rate axes at the nodes of a 20 m x 20 m orthogonal grid. Crevasses in the study reach are of two types, splaying and transverse, and are everywhere normal to the trajectories of greatest (most tensile) principal strain rate. Splaying crevasses exist where the longitudinal strain rate (x) is ≤ 0 and transverse crevasses are present under longitudinally extending flow (i.e.x> 0). The orientation of crevasses changes in the down-glacier direction, but the calculated rotation by the flow field does not account for this change in orientation. Observations suggest that individual crevasses represent local values of the regional flow field and are transient on the time-scale of 1-2 years; they are not persistent features that are translated and rotated by flow. Crevasse patterns are thus found to be a useful tool for mapping the strain-rate tensor in this reach of a temperate valley glacier.

scholarly journals Modeling and Simulation Techniques Used in High Strain Rate Projectile Impact

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 274
Author(s):  
Derek G. Spear ◽  
Anthony N. Palazotto ◽  
Ryan A. Kemnitz
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Smoothed Particle Hydrodynamics ◽  
High Strain ◽  
Lagrangian Analysis ◽  
Computational Performance ◽  
Lagrangian Modeling ◽  
Analysis Technique ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

A series of computational models and simulations were conducted for determining the dynamic responses of a solid metal projectile impacting a target under a prescribed high strain rate loading scenario in three-dimensional space. The focus of this study was placed on two different modeling techniques within finite element analysis available in the Abaqus software suite. The first analysis technique relied heavily on more traditional Lagrangian analysis methods utilizing a fixed mesh, while still taking advantage of the finite difference integration present under the explicit analysis approach. A symmetry reduced model using the Lagrangian coordinate system was also developed for comparison in physical and computational performance. The second analysis technique relied on a mixed model that still made use of some Lagrangian modeling, but included smoothed particle hydrodynamics techniques as well, which are mesh free. The inclusion of the smoothed particle hydrodynamics was intended to address some of the known issues in Lagrangian analysis under high displacement and deformation. A comparison of the models was first performed against experimental results as a validation of the models, then the models were compared against each other based on closeness to experimentation and computational performance.

LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

2018 ◽  
Author(s):  
Jean-François Monier ◽  
Nicolas Poujol ◽  
Mathieu Laurent ◽  
Feng Gao ◽  
Jérôme Boudet ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Strain Rate Tensor ◽  
Separation Flow ◽  
Compressor Cascade ◽  
Corner Separation ◽  
Reynolds Stress Tensor ◽  
Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

scholarly journals Seismic deformation at the Alban Hills volcano during the 1989-1990 seismic sequence

1998 ◽  
Vol 41 (2) ◽  
Author(s):  
G. Selvaggi ◽  
F. D'Ajello Caracciolo
Keyword(s):  
Strain Rate ◽  
Fluid Pressure ◽  
Strain Rate Tensor ◽  
Seismic Structure ◽  
Fault Plane Solutions ◽  
Alban Hills ◽  
Shear Failures ◽  
One Year ◽  
The One ◽  
Seismic Moment Release

We analysed the one-year-long seismic swarm at the Alban Hills volcano which occurred during 1989-1990. We portray spatial distribution of seismic moment release, better delineating the activated volume during the swarm. The seismic structure is imaged as a 7-km long, 3-km wide, and 3-km thick volume, located between 2 and 5 km depth, and NW-SE striking. Fault plane solutions and scalar seismic moments for the largest earthquakes provide the description of the average strain rate tensor. The principal strain rate axes show a dominant extension in NE-SW direction, a SE-NW direction of compression and a negligible thickening rate. P and T axes direction of the smaller earthquakes suggests that the same mode of deformation is distributed all over the activated volume. These results are discussed in terms of seismic deforming processes active at the Alban Hills volcano, in the frame of magmatic inflation recently invoked to explain the rapid vertical uplift affecting part of the volcano. The observed average deformation is consistent with shear failures occurring on faults connecting stress-oriented dykes in response to an increasing fluid pressure.

scholarly journals Strain Rates On Rutford Ice Stream, Antarctica (Abstract)

1986 ◽  
Vol 8 ◽  
pp. 207
Author(s):  
N. Stephenson ◽  
C.S.M. Doake
Keyword(s):  
Strain Rate ◽  
Velocity Gradient ◽  
Surface Strain ◽  
Lateral Strain ◽  
Strain Rate Tensor ◽  
Strain Rates ◽  
Average Value ◽  
Divergent Flow ◽  
Ice Stream ◽  
Thickness Variations

In a study of the Rutford Ice Stream, strain rates were measured on a transverse section. Magnitudes ranged up to 40 × 10−3 a−1 but were typically in the order of 3 × 10−3 a−1 with an error of 0.1 χ 10−3 a−1. Variations in the strain rate between adjacent stakes of 0.2 χ 10−3 a−1 to 2 × 10−3 a−1 were matched to the thickness variations on the glacier. For each set of three adjacent stakes, the velocity gradient components of the surface strain rate tensor were calculated by assuming that the gradients were linear over the distance between adjacent stakes. When plotted against distance across the ice stream, each strain rate component revealed different aspects of the flow field. The longitudinal strain rate was compressive, with an almost constant magnitude of 10−3 a−1. The lateral strain rate is extensive, with an average value of 1.1 × 10−3 a−1 which agreed with the angle between the divergent flow lines observed on a Landsat image. Peaks in the lateral strain rate, corresponding to longitudinal bands of thicker ice, showed that these thicker bands were spreading more rapidly at the expense of thinner areas. The two velocity gradient components of the shear rate tensor also reflected differences in ice thickness.

scholarly journals How to Realize Volume Conservation During Finite Plastic Deformation

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Heling Wang ◽  
Dong-Jie Jiang ◽  
Li-Yuan Zhang ◽  
Bin Liu
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Strain Rate ◽  
Strain Rate Tensor ◽  
Cauchy Stress ◽  
Volume Conservation ◽  
Tangential Stiffness ◽  
Manufacture Process ◽  
Universal Approach

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

A computer-aided method for calculating the distributions of strain-rate and strain from an experimental flow field

1976 ◽  
Vol 11 (1) ◽  
pp. 26-31 ◽  
Author(s):  
L E Farmer ◽  
P L B Oxley
Keyword(s):  
Flow Field ◽  
Computer Program ◽  
Strain Rate ◽  
Plane Strain ◽  
Strain Rates ◽  
Simple Geometry ◽  
Punch Velocity ◽  
Computer Aided ◽  
Intersection Points

A method of calculating strain-rates and strains from an experimental flow field is developed using simple geometry with polynomials used to represent small segments of the experimental streamlines and the corresponding distance/time along streamline curves. The method is applied to an experimental flow field for plane strain extrusion obtained using printed grids (0.002 inch square), the input to the computer program being the co-ordinates of the grid intersection points and the punch velocity.

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