FRACTAL ANALYSES OF ANISOTROPIC FRACTURE SURFACES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 547-559 ◽  
Author(s):  
B.L. COX ◽  
J.S.Y. WANG
Keyword(s):  
Area Ratio ◽  
Affine Scaling ◽  
Rock Fractures ◽  
Flow Models ◽  
Anisotropic Fracture ◽  
Fractal Analyses ◽  
Dixie Valley ◽  
Flow Through ◽  
Self Similar ◽  
Simulated Flow

Natural surfaces of rock fractures often have anisotropic asperity distributions, especially for shear fractures or faults. The asperity distributions could be treated as self-affine fractals with directional dependent scaling in the plane of the rock surfaces. Different fractal analyses (divider, slit-island, variogram) are applied to surface distributions of asperity data (topography): (1) a granitic fracture from the Stripa mine in Sweden; (2) a faulted and geothermally altered fracture from Dixie Valley, Nevada, USA. The cutoff patterns (indicator maps) of the granitic fracture show a radial pattern, while those of the faulted fracture show a very anisotropic stretched pattern of shapes. Different cutoff patterns of the same surface generally yield the same fractal dimension with the slit-island technique. The slit-island technique assumes that the cut-off patterns are self-similar in the plane of the surface, with the perimeter versus area analyzed for the entire population of contours, regardless of aspect ratio. We measure the variance in the two coordinate directions as a function of perimeter/area ratio for the anisotropic fracture from Dixie Valley to determine a self-affine scaling ratio for the slit-island analysis. We compare this ratio with anisotropy ratios obtained from simulated flow models based on channeling of flow through the largest openings. The possible applications of fractal analyses to both the geometry and flow are evaluated.

Micro- and macro-behaviour of fluid flow through rock fractures: an experimental study

2013 ◽  
Vol 21 (8) ◽  
pp. 1717-1729 ◽  
Author(s):  
Zhenyu Zhang ◽  
Jan Nemcik ◽  
Shuqi Ma
Keyword(s):  
Experimental Study ◽  
Fluid Flow ◽  
Rock Fractures ◽  
Flow Through

An Investigation Into the Performance of Two ISA Metering Nozzles of Finite and Zero Area Ratio

1965 ◽  
Vol 87 (2) ◽  
pp. 525-529 ◽  
Author(s):  
S. Soundranayagam
Keyword(s):  
Reynolds Number ◽  
Potential Flow ◽  
Discharge Coefficient ◽  
Flow Model ◽  
Reynolds Numbers ◽  
Area Ratio ◽  
Flow Through

The flow through two ISA nozzles of area ratio zero and 0.4 was investigated to determine the nature of the flow and its variation with Reynolds number. Separation occurs within the nozzle of zero area ratio, the size of the bubble increasing with decreasing Reynolds number. The predicted discharge coefficient based on a simplified flow model agrees with experiment for large Reynolds numbers. Upstream influences affect the performance of the nozzle of area ratio 0.4. The flows through the two nozzles are not comparable, and potential-flow results cannot be used to explain flow in venturis and nozzles in pipes. The discharge-coefficient curve for area ratio 0.4 shows a distinct hump when based on the head differential measured as for venturis, but no hump when based on the head differential across the corner taps.

Fluid flow through rough-walled rock fractures with hydrophobic surfaces

2014 ◽  
Vol 18 (4) ◽  
pp. 375-380 ◽  
Author(s):  
Hang Bok Lee ◽  
In Wook Yeo ◽  
Kang-Kun Lee
Keyword(s):  
Fluid Flow ◽  
Rock Fractures ◽  
Hydrophobic Surfaces ◽  
Flow Through

Effect of small asymmetries on axisymmetric stenotic flow

2013 ◽  
Vol 721 ◽  
Author(s):  
Martin D. Griffith ◽  
Thomas Leweke ◽  
Mark C. Thompson ◽  
Kerry Hourigan
Keyword(s):  
Velocity Profile ◽  
Experimental Test ◽  
Reynolds Numbers ◽  
Wake Flow ◽  
Machining Precision ◽  
Severe Effect ◽  
Highly Sensitive ◽  
Flow Through ◽  
Simulated Flow

AbstractFlow through axisymmetric and eccentric sinuous stenoses is investigated numerically, for Reynolds numbers up to 400. The eccentricity consists of an offset of the stenosis throat. A range of stenosis eccentricity is tested; the wake flow is found to be highly sensitive to small eccentricities in the stenosis geometry, even with stenosis offsets of the order of the machining precision of experimental test-sections. Comparisons are made between the numerically simulated flow through stenoses with small eccentricities and results from the literature of non-axisymmetric flows through nominally axisymmetric geometries. The effect of distortion to the inlet Poiseuille velocity profile is also investigated and found to have a significantly less severe effect on the downstream wake flow than geometric eccentricity.

scholarly journals Air Permeability of Thick Foams: Flow Numerical Simulations

2018 ◽  
Vol 10 (3) ◽  
pp. 41
Author(s):  
Karel Adámek
Keyword(s):  
Flow Field ◽  
Air Permeability ◽  
Measured Data ◽  
Main Flow ◽  
Flow Simulations ◽  
Foam Volume ◽  
Car Seats ◽  
Good View ◽  
Flow Through ◽  
Simulated Flow

From measured data are determined permeability parameters of thick perforated foam samples, used as car seats cushions. Parameters are used for numerical flow simulations in foam samples. Model of detailed geometry gives good view about detailed flow field (pressure and velocity) in foam volume, influenced by perforations and grooves. However, simulated flow is several times different from measured one. The main flow is through perforations (99%) and flow through foam is of two orders lower. Using homogenous geometry with “averaged” permeability parameters, evaluated from measured values, the coincidence of measured and simulated flow is very good, difference of 1-5%. However, it is not possible to get any details of flow in foam volume. Using inlet layer, the flow is decreasing, first in perforations and the ratio between perforation and foam flows is more balanced.

Experimental Study of Entrance Effects on Laminar Gas Flow Through Silicon Orifices

2005 ◽  
Author(s):  
Aaron J. Knobloch ◽  
Joell R. Hibshman ◽  
George Wu ◽  
Rich Saia
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Flow Area ◽  
Fully Developed Flow ◽  
Flow Rates ◽  
Flow Models ◽  
Entry Length ◽  
Orifice Flow ◽  
Measured Flow ◽  
Flow Through

This study summarizes a fundamental investigation of flow through an array of silicon micromachined rectangular slots. The purpose of the study is to evaluate the effect of entrance pressure, flow area, orifice thickness, slot length, and slot width of the orifice on flow rate. These orifices were fabricated using a simple frontside through wafer DRIE process on a 385 μm thick wafer and wafer bonding to create thicker orifices. The dies were then packaged as part of a TO8 can and flow tested. To complement the results of this experimental work, two simple flow models were developed to predict the effect of geometrical and entrance conditions on the flow rate. These models were based on macroscale assumptions that were not necessarily true in the case of thin orifices. One relationship was based on Pouiselle flow which assumes fully developed flow conditions. Calculation of the entry length required for fully developed flow indicate that in the low Reynolds Number regime (32-550) evaluated, the entry flow development requires 2-8 times the thickness of the thickest orifices used for this study. Therefore, calculations of orifice flow based on a Pouiselle model are an overestimate of the actual measured flow rates. Another model examined typical orifice relationships using head loss at the entrance and exit of the slots did not accurately capture the particular flow rates since it overestimated the expansion or constriction losses. A series of experiments where the pressure was varied between 75 and 1000 Pa were performed. A comparison of the Pouiselle flow solution with experimental results was made which showed that the Pouiselle flow model overpredicts the flow rates and more specifically, the effect of width on the flow rates. The results of these tests were used to develop a transfer function which describes the dependence of flow rate on orifice width, thickness, length, and inlet pressure.

Applicability of Choking Flow Models for Subcooled Flashing Flow Through Tube Cracks

2011 ◽  
Author(s):  
Brian Wolf ◽  
Shripad T. Revankar ◽  
Jovica R. Riznic
Keyword(s):  
Mechanistic Model ◽  
Channel Length ◽  
Two Phase ◽  
Experimental Conditions ◽  
Flow Rates ◽  
Flow Models ◽  
Model Predictions ◽  
Flow Through ◽  
The Difference ◽  
Non Equilibrium

Recently there is some database available on choking flow through cracks relevant to steam generator (SG) tubes to model the critical flow. These data are used in assessing the key choking flow models. Based on this assessment a mechanistic choking model is developed. The model is used to predict the choking flow rates for various experimental conditions for subcooled flashing flow through narrow slits with L/D varying from small values (∼5) to large values (100). Results are presented on the effects of thermal and mechanical non-equilibrium on the choking flow for small L/D channels. A mechanistic model was developed to model two-phase choking flow through slits. A comparison of model results to experimental data shows that the homogeneous equilibrium based models markedly under predict choking flow rates in such geometries. As subcooling increases, and channel length decreases the non-equilibrium effects play a greater role in the choking phenomenon, therefore the difference in model predictions and experimental results increases.

A One-Dimensional Viscous-Inviscid Strong Interaction Model for Flow in Indented Channels With Separation and Reattachment

2003 ◽  
Vol 125 (3) ◽  
pp. 355-362 ◽  
Author(s):  
S. G. C. Kalse ◽  
H. Bijl ◽  
B. W. van Oudheusden
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Present Model ◽  
Interaction Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Flow Models ◽  
Flow Through ◽  
Layer Flow ◽  
Semi Empirical

A new one-dimensional model is presented for the calculation of steady and unsteady flow through an indented two-dimensional channel with separation and reattachment. It is based on an interactive boundary layer approach, where the equations for the boundary layer flow near the channel walls and for an inviscid core flow are solved simultaneously. This approach requires no semi-empirical inputs, such as the location of separation and reattachment, which is an advantage over other existing one-dimensional models. Because of the need of an inviscid core alongside the boundary layers, the type of inflow as well as the length of the channel and the value of the Reynolds number poses some limitations on the use of the new model. Results have been obtained for steady flow through the indented channel of Ikeda and Matsuzaki. In further perspective, it is discussed how the present model, in contrast to other one-dimensional flow models, can be extended to calculate the flow in nonsymmetrical channels, by considering different boundary layers on each of the walls.

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