Eddy correlations for water flow in a single fracture with abruptly changing aperture

Qian, Jiazhong; Liang, Min; Zhou, C.; Zhan, Hongbin

doi:10.1002/hyp.8332

Cited by 31 publications

(13 citation statements)

References 49 publications

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“…The main flow channel becomes narrow due to the expansion of the eddy domain. Several previous works [28][29][30][31][32] showed similar results for the growth of eddies due to the increasing Reynolds number. At high Reynolds number (Re=170), it can be seen clearly that the eddy-controlled domain occupies a large portion of the fracture.…”

Section: Flow Field and Eddies Formationsupporting

confidence: 68%

“…Since the mean aperture and the length of fracture were specific, the advection time scale and diffusion time scale only depended on the average velocity and diffusion, respectively. Due to the sudden expansion of the aperture, the eddies usually form in the vicinity of the rough fracture wall [28]. Thus, to capture the influence of eddies on the spreading and mixing of the solute, the relatively large diffusion time scale was assumed for both the nonreaction and reaction transport, which resulted from a relatively large diffusion = 2.1 × 10 −7 2 / .…”

Section: Problem Setupmentioning

confidence: 99%

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Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

et al. 2018

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This pore-scale modeling study in single self-affine fractures showed that the heterogeneous flow field had a significant influence on the mixing-induced reaction transport. We generated the single self-affine fracture by the successive random additions (SRA) technique. The pore-scale model was developed by coupling the Navier-Stoke equation (NSE) and advection-diffusion equation with reaction (ADER). Eddies were captured in the self-affine fracture due to the increasing Reynolds number and the sudden expansion of aperture. The flux-weighted breakthrough curves (BTCs) of reaction product showed the typical non-Fickian characteristics (i.e., "early arrival" and "heavy tail"). It was found that the reactant was involved in eddies and then reacted inside the eddy-controlled domain. Consequently, eddies played a significant role in delaying the mass exchange process between the eddycontrolled domain and the main flow channel, which resulted in the "heavy tail" in BTCs. As the Reynolds number increased, the breakthrough time increased while the concentration peaks of BTCs decreased. Furthermore, the dilution index presenting the exponential of the Shannon entropy of a concentration probability distribution was used to quantify the degree of reactant mixing. The results showed that the quantification of dilution for nonreaction transport was in good agreement with the outcomes of mixing-induced reaction transport. The high Reynolds number and Peclet number had a negative influence on the mixing process at the early time whereas they led to the enhanced mixing process at the late time.

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Section: Flow Field and Eddies Formationsupporting

confidence: 68%

Section: Problem Setupmentioning

confidence: 99%

Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

et al. 2018

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“…It is generally accepted that flow through a symmetric SF with a sudden expansion becomes asymmetric around the plane of symmetry when the Reynolds number (Re) increases. This phenomena was experimentally reported by many investigators including Durst et al (1974), Restivo and Whitelaw (1978), Sobey (1985), Fearn et al (1990), Shapira et al (1990), Foumeny et al (1996), Hawa and Rusak (1999), Rusak and Hawa (1999), and Qian et al (2012). Figure 1(a) is a schematic diagram showing the recirculation zone of flow in an SF with abruptly changing apertures (SF-ACA).…”

Section: Introductionsupporting

confidence: 61%

The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Qian

Zhan

et al. 2015

Hydrol. Process.

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Flow in a single fracture (SF) is an important research subject in groundwater hydrology, hydraulic engineering, radioactive nuclear waste repository and geotechnical engineering. An abruptly changing aperture is a unique type of SF. This study discusses the relation between the values of the critical Reynolds number (Rec) for the onset of symmetry breaking of flow and the expansion ratio (E) of SF, which is defined as the ratio between the outlet (D) and inlet (d) apertures. This study also investigates the effect of inlet aperture d on Rec for flow in an SF with abruptly changing apertures (SF‐ACA) using the finite volume method. Earlier numerical and experimental results showed that flow is symmetric in respect to the central plane of the SF‐ACA at small Reynolds number (Re) but becomes asymmetric when Re is sufficiently large. Our simulations show that the value of Rec decreases with the increasing E, and the relationship between the logarithm of Rec and E can be described accurately using either a quadratic polynomial function or a logarithmic function. However, the relationship of Rec and d for a given E value is vague, and Rec becomes even less sensitive to d when E increases. This study also reveals that the hydraulic gradient (J) and flow velocity (v) follow a super‐linear relationship that can be fitted almost perfectly by the Forchheimer equation. The inertial component (Ji) of J increases monotonically with Re, whereas the viscous component (Jv) of J decreases monotonically with Re. The Re value corresponding to equal inertial and viscous components of J (named as the transitional point Re) decreases when E increases, and such a transitional point Re should be closely related to the critical Reynolds number Rec, although a rigorous theoretical proof is not yet available. Copyright © 2015 John Wiley & Sons, Ltd.

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“…The LCL is not strictly valid under all circumstances. At large Reynolds or Peclet numbers (Detwiler et al, 2000;Konzuk and Kueper, 2004), in the presence of asperities or inclusions in the aperture that may create eddies (Konzuk and Kueper, 2004;Liu and Fan, 2012;Oron and Berkowitz, 1998;Qian et al, 2012) or under conditions of hydromechanical dilation and/or normal stress (Cornet et al, 2003;Gentier et al, 2013;Liu et al, 2013;Witherspoon et al, 1980), the rate of flow may not scale with the cube of the local aperture. However, for the development herein we do not need to invoke the LCL directly; we assume only small variations in aperture will cause large variations local advective velocity.…”

Section: Introductionmentioning

confidence: 99%

Power law breakthrough curve tailing in a fracture: The role of advection

Fiori

Becker

2015

Journal of Hydrology

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Keywords:Solute transport Single fracture Breakthrough curve Powerlaw tailing s u m m a r yWe offer an explanation of the strongly tailed solute breakthrough curve typically observed when a tracer test is conducted in fractured bedrock. In this example, we limit the model to a single planar fracture of varying aperture. Flow heterogeneity derives from variable fracture aperture, which implies variable transmissivity (T). The analysis employs a physically based model well-suited to strong heterogeneity and relies only upon advective transport. The purely advective model is able to explain a power-law trend of magnitude À2 to À3 in the breakthrough curve tail; a range that has been found in field tracer experiments. The principle cause of this trend is the comparatively slow transport in zones of small transmissivity (tight aperture). Slow advection occurs when either heterogeneity (variance of ln T) is strong or when the assumed heterogeneity distribution is non-Gaussian. Thus, we link breakthrough tailing to the statistical parameters for the transmissivity field.

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Eddy correlations for water flow in a single fracture with abruptly changing aperture

Cited by 31 publications

References 49 publications

Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

Pore-Scale Modeling of Mixing-Induced Reaction Transport through a Single Self-Affine Fracture

The effect of expansion ratio on the critical Reynolds number in single fracture flow with sudden expansion

Power law breakthrough curve tailing in a fracture: The role of advection

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