scholarly journals Temporal Mixing Behavior of Conservative Solute Transport through 2D Self-Affine Fractures

Processes ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 158 ◽  
Author(s):  
Zhi Dou ◽  
Brent Sleep ◽  
Pulin Mondal ◽  
Qiaona Guo ◽  
Jingou Wang ◽  
...  
Keyword(s):  
Peclet Number ◽  
Hurst Exponent ◽  
Temporal Evolution ◽  
Dominant Role ◽  
Scalar Dissipation ◽  
Péclet Number ◽  
Mixing Behavior ◽  
Power Law Function ◽  
Variable Aperture ◽  
Aperture Distribution

In this work, the influence of the Hurst exponent and Peclet number (Pe) on the temporal mixing behavior of a conservative solute in the self-affine fractures with variable-aperture fracture and constant-aperture distributions were investigated. The mixing was quantified by the scalar dissipation rate (SDR) in fractures. The investigation shows that the variable-aperture distribution leads to local fluctuation of the temporal evolution of the SDR, whereas the temporal evolution of the SDR in the constant-aperture fractures is smoothly decreasing as a power-law function of time. The Peclet number plays a dominant role in the temporal evolution of mixing in both variable-aperture and constant-aperture fractures. In the constant-aperture fracture, the influence of Hurst exponent on the temporal evolution of the SDR becomes negligible when the Peclet number is relatively small. The longitudinal SDR can be related to the global SDR in the constant-aperture fracture when the Peclet number is relatively small. As the Peclet number increases the longitudinal SDR overpredicts the global SDR. In the variable-aperture fractures, predicting the global SDR from the longitudinal SDR is inappropriate due to the non-monotonic increase of the longitudinal concentration second moment, which results in a physically meaningless SDR.

Analysis of Thermal Effects in the Yield Phase of Hydrodynamic Lubricant Film in Plane Strain Forging

1996 ◽  
Vol 118 (4) ◽  
pp. 880-885 ◽  
Author(s):  
V. K. Bhatt ◽  
D. K. Sengupta
Keyword(s):  
Film Thickness ◽  
Plane Strain ◽  
Peclet Number ◽  
Film Formation ◽  
Dominant Role ◽  
Lubricant Film ◽  
Pressure Gradients ◽  
Lubricant Film Thickness ◽  
Péclet Number ◽  
Shear Energy

A thermal Reynolds equation, which takes into account viscosity variation across the lubricant film thickness due to shear energy dissipation within the film, has been developed. It also takes into account the effect of conduction and convection on heat transfer in the lubricant film. It indicates that the pressure gradients developed in a no-slip lubricated contact are increased with an increase in Peclet number. The use of the equation is illustrated by applying it in the film formation process in the yield phase of liquid lubricated plane strain forging. The analysis indicates that the Peclet number plays a dominant role infixing the lubricant film thickness in such contacts.

HAUSDORFF DERIVATIVE MODEL FOR CHARACTERIZATION OF NON-FICKIAN MIXING IN FRACTAL POROUS MEDIA

Fractals ◽  
2019 ◽  
Vol 27 (04) ◽  
pp. 1950063 ◽  
Author(s):  
YINGJIE LIANG ◽  
ZHI DOU ◽  
ZHIFANG ZHOU ◽  
WEN CHEN
Keyword(s):  
Decay Rate ◽  
Peclet Number ◽  
Radioactive Tracer ◽  
Fickian Diffusion ◽  
Scalar Dissipation ◽  
Scalar Dissipation Rate ◽  
Péclet Number ◽  
Future Studies ◽  
Structure Changes

This study investigates the scalar dissipation rate (SDR) and dilution index of non-Fickian mixing by using the Hausdorff derivative model for conservative and first-order decaying tracers under different boundary conditions. The expressions of SDR and dilution index are derived based on the analytical solution of the Hausdorff derivative model, in which the time and space Hausdorff derivative orders, respectively capture the complexity in transport trajectory and transport scale. The properties of SDR and dilution index are discussed for different cases of Peclet number, decaying rate of the radioactive tracer, and Hausdorff derivative order, respectively. We find that the SDR of non-Fickian mixing decays more slowly than that of the Fickian diffusion, and the time scale deviates from [Formula: see text]. The evolution of the SDR has a sharp peak and decays very fast to zero when Peclet number is large. For the radioactive tracer, the larger values of decay rate, the smaller values of SDR, which decays faster to zero. The Hausdorff derivative model with larger Peclet number leads to larger dilution index. The dilution index is larger for smaller decay rate before reaching the equilibrium state. Consequently, the two metrics can be satisfactorily used to describe non-Fickian mixing based on the Hausdorff derivative model. Future studies should be designed to examine the evolution of SDR and dilution index in real geological and hydrological systems undergoing structure changes and chemical reactions.

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

Convective diffusion toward the sphere in laminar flow around the sphere

1979 ◽  
Vol 44 (4) ◽  
pp. 1218-1238
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Laminar Flow ◽  
Velocity Profile ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Péclet Number ◽  
Stability Of The Solution

The problem of convective diffusion toward the sphere in laminar flow around the sphere is solved by combination of the analytical and net methods for the region of Peclet number λ ≥ 1. The problem was also studied for very small values λ. Stability of the solution has been proved in relation to changes of the velocity profile.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

Modeling temperature rise in multi-track reciprocating frictional sliding

2021 ◽  
pp. 135065012098823
Author(s):  
Thierry A Blanchet
Keyword(s):  
Temperature Rise ◽  
Peclet Number ◽  
Maximum Temperature ◽  
Uniform Heat Flux ◽  
Heat Accumulation ◽  
Stroke Length ◽  
Péclet Number ◽  
Maximum Temperature Rise ◽  
Rectangular Patch ◽  
Accumulation Effect

As in various manufacturing processes, in sliding tests with scanning motions to extend the sliding distance over fresh countersurface, temperature rise during any pass is bolstered by heating during prior passes over neighboring tracks, providing a “heat accumulation effect” with persisting temperature rises contributing to an overall temperature rise of the current pass. Conduction modeling is developed for surface temperature rise as a function of numerous inputs: power and size of heat source; speed and stroke length, and track increment of scanning motion; and countersurface thermal properties. Analysis focused on mid-stroke location for passes of a square uniform heat flux sufficiently far into the rectangular patch being scanned from the first pass at its edge that steady heat accumulation effect response is adopted, focusing on maximum temperature rise experienced across the pass' track. The model is non-dimensionalized to broaden the applicability of the output of its runs. Focusing on practical “high” scanning speeds, represented non-dimensionally by Peclet number (in excess of 40), applicability is further broadened by multiplying non-dimensional maximum temperature rise by the square root of Peclet number as model output. Additionally, investigating model runs at various non-dimensional speed (Peclet number) and reciprocation period values, it appears these do not act as independent inputs, but instead with their product (non-dimensional stroke length) as a single independent input. Modified maximum temperature rise output appears to be a function of only two inputs, increasing with decreasing non-dimensional values of stroke length and scanning increment, with outputs of models runs summarized compactly in a simple chart.

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