Critical Reynolds Number Rec Research Articles

Characterizing the Relationship Between Non‐Darcy Effect and Hydraulic Aperture in Rough Single Fractures

AbstractHydraulic aperture (eh) which is independent of inertial effect has been widely used as an important parameter to study the geometric properties of single fractures in previous studies. However, the inertial effect dependence of hydraulic aperture was gradually revealed in recent studies. Therefore, hydraulic aperture could provide a new method to characterize the non‐Darcy effect. In this study, 2D numerical simulations based on Navier‐Stokes equation were carried out to explore the feasibility of characterizing non‐Darcy effect based on hydraulic aperture. The results showed that the onset of flow regimes transition from Darcy to non‐Darcy could be well characterized by the hydraulic aperture. Before the non‐Darcy flow appeared, the initial hydraulic aperture (eh0) maintained constant regardless of the inertial effect (quantified by non‐Darcy effect factor E), once the non‐Darcy effect emerged, the hydraulic aperture decreased with the increase of inertial effect. The increased volume of low‐velocity zone in the rough single fractures was considered as the mechanism of non‐Darcy effect. And the existence of critical relative roughness (Rc) was found and it would affect the critical non‐Darcy effect factor (Ed) or critical Reynolds number (Rec) by affecting the development of low velocity region and preferential flow paths. From the overall trend, the hydraulic aperture decreased with the increase of E, and it fluctuated due to the development of recirculation zones (RZs). Moreover, the predictive model of non‐Darcy effect factor (E) based on hydraulic aperture was obtained and the validity of the model was preliminarily verified.

Effect of confinement on the rotation of a two-dimensional elliptical porous particle in shear flow

The rotation of non-spherical porous particles in fluid flows is of practical relevance in various natural and industrial processes. However, despite the increasing interest in micro-scale channels and reactors, the understanding of rotation of non-spherical porous particles in a confined fluid flow is, if not blank, far from complete. In this work, we present a numerical study on the rotation of an elliptical porous particle in a confined shear flow by solving the governing equations using a lattice Boltzmann method. The particles with varying aspect ratios AR, Darcy number Da, and Reynolds number Re are examined for different confinement ratios B. Akin to its solid counterpart, the elliptical porous particle either exhibits time-periodic rotation with a non-uniform angular rate or takes a stationary orientation for different B. With finite fluid inertia, both the maximum and minimum angular rate decrease with B. For the elliptical porous particle, a higher B promotes the increasing rate of rotation period against Re, resulting in a smaller critical Reynolds number Rec (if observed) at which the particle ceases to rotate. A scaling law for solid particles was extended to correlate the rotation period and Re for porous particles, where B has a negligible effect. An empirical formula to predict Rec as a function of B, AR, and Da is established using the symbolic regression. The transition from rotating to stationary at different B can be explained by the net torque exerted on the elliptical porous particle.

Influence of cylinder breadth and shape on the onset of flow unsteadiness and the aeolian tone level

The Reynolds number for the onset of flow unsteadiness is determined for several canonical geometries (triangles, rectangles, ellipses and lozenges) at different sectional breadth (L) to height (d) ratios (aspect ratio AR=L∕d), for more than 70 shapes. The flow is modeled using a direct Navier–Stokes incompressible two-dimensional solver and the shape is defined by an Immersed Boundary Method. The employed procedure takes the fluctuation of the velocity in the wake as the criterion to define the unsteadiness and a binary search to find the transition. This procedure yields critical Reynolds number Rec values in agreement with available data in the literature. When AR approaches zero, the five shapes lead to almost the same value of 31, which corresponds to Rec for a flat plate normal to the flow. It is then found that Rec grows exponentially with the aspect ratio, the influence of the cross section shape being accounted for by a single regression parameter. For all aspect ratios, the ellipse exhibits the highest Rec, and the front-pointing triangle the lowest, the three other geometries laying in between those two. The physics of the influence of cross-section shape on Rec is analyzed, considering its link with recirculation length in particular. An exploitation of the results is outlined for the analysis of recent aeroacoustic shape optimizations at fixed Re=150, through correlation between the lift fluctuation at this regime with the distance to the onset of unsteadiness it corresponds to.

Critical parameters for non-Newtonian shear-thickening power-law fluids flow across a channel confined circular cylinder

In this work, the critical parameters for an incompressible flow of non-Newtonian shear-thickening power-law fluids across a channel confined circular cylinder have been investigated numerically. The governing equations have been solved by using the finite volume method for the wide range of power-law (1≤n≤1.8) fluids and for two values of wall blockage ratio (β=2 and 4). The present methodology has extensively been validated with numerical and experimental results available for limited conditions. Transitional insights of channel confined cylinder, in particular, critical parameters indicating the transitions from creeping to separating flows (i.e., onset of steady symmetric wake formation), and from steady symmetric wake to unsteady asymmetric wake formation (i.e., onset of vortex formation) are investigated and presented in terms of the critical Reynolds numbers (Rec and Rec). The relative impacts of unconfined and confined flows on these critical parameters have also been explored. In general, both onsets of the flow separation and wake asymmetry delayed with an increasing values of the power-law index (n) and the wall confinement (λ). The dependence of critical Re on n for the confined (finite β) flow are, however, completely opposite to that for unconfined (β=∞) flow, i.e., critical Re decreased with increasing n. The influence of power-law index on the onset of vortex is quite stronger to that on the onset of wake formation. For instance, Rec for β=(2,4,∞) altered from (12.5, 7.25, 6.25) to (30.5, 9.25, 0.75) and the corresponding changes with Rec are noted from (84.5, 70.25, 46.5) to (449.5, 179.5, 33.5) as n varied from 1 to 1.8, respectively. The Stokes paradox (i.e., no creeping flow even as Re→0) apparent with unconfined flow of power-law fluids is irrelevant in confined flows, under otherwise identical conditions. Finally, the predictive correlations for critical Re as a function of dimensionless parameters (n and β) are presented for their easy use in engineering analysis.

Characterizing shear-thinning fluids transitioning from rheology- to inertia-dominated flow regimes in porous media

Understanding and predicting non-Newtonian fluid flows in porous media is crucial for many geophysical and environmental problems. Although extensive studies have investigated nonlinear flow for shear thinning fluids, the critical Reynolds number (Rec) for identifying nonlinearity in transition from rheology-dominated to inertia-dominated flows remains unclear. To determine Rec, we conducted hundreds of direct numerical simulations of power law fluids with diverse fluid rheology (quantified by a power law exponent n) through a variety of pore geometries which are characterized by a non-dimensional hydraulic shape factor (β). The numerically-derived pressure gradient and fluid flux were used to compute the bulk viscosity ~ Reynolds number curves, which were further employed to determine Rec. With knowing Rec, we established a predictive function between Rec and (β, n). This function allows for the estimation of Rec based on the measurable properties (β, n) via imaging technique. Our mechanistic modelling work sheds light on predicting nonlinear flow for non-Newtonian fluids at the continuum scale by knowing under what conditions the inertial effects are significant.

Influence of aspect ratio on vortex formation in X-junctions: Direct numerical simulations and eigenmode decomposition

We study numerically the appearance and number of axial vortices in the outlets of X-shaped junctions of two perpendicular channels of rectangular sections with facing inlets. We explore the effect of the aspect ratio of the cross section, AR, on the number of vortices created at the center of the junction. Direct numerical simulations (DNSs) performed for different values of the Reynolds number Re and AR demonstrate that vortices with their axis parallel to the outlets, referred to as axial vortices, appear above critical Reynolds numbers Rec. As AR increases from 1 to 11, the number of vortices observed increases from 1 to 4, independently of Re. For AR = 1, the single axial vortex induces an interpenetration of the inlet fluids in the whole section; instead, for larger AR’s for which more vortices appear, the two inlet fluids remain largely segregated in bands, except close to the vortices. The linear stability analysis demonstrates that only one leading eigenmode is unstable for a given set of values of AR and Re. This mode provides a simplified model of the flow field, reproducing its key features such as the number of vortices and their distance. Its determination with this method requires a much smaller computational load than the DNS. This approach is shown to allow one to determine quickly and precisely the critical Reynolds number Rec and the sensitivity function S, which characterizes the influence of variations of the base flow on the unstable one.

Investigation on Nonlinear Flow Behavior through Rock Rough Fractures Based on Experiments and Proposed 3-Dimensional Numerical Simulation

Rock fractures as the main flow channels, their morphological features, and spatial characteristics deeply influence the seepage behavior. Reservoir sandstones as a case study, four splitting groups of fractures with different roughness were scanned to get the geometric features, and then the seepage experiments were taken to analyze the relationship of the pressure gradient ∇ P and flow rate Q , and the critical Reynolds number( Re c ) and wall friction factor ( f ) were determined to explain the translation of linear seepage to nonlinear seepage condition. Based on the scanning cloud data of different rough fractures, the fractures were reconstructed and introduced into the COMSOL Multiphysics software; a 3-dimensional seepage model for rough fractures was calibrated and simulated the seepage process and corresponding pressure distribution, and explained the asymmetry of flow velocity. And also, the seepage characteristics were researched considering aperture variation of different sample fractures; the results indicated that increasing aperture for same fracture decreased the relative roughness, the fitting coefficients by Forchheimer formula based on the data ∇ P ~ Q decreased, and the figures about the coefficients and corresponding aperture described nonlinear condition of the above rough fractures. In addition, the expression of wall friction factor was derived, and relationship of f , Re , and relative roughness indicated that f increased with increasing fracture roughness considering the same aperture, resulting in nonlinear flow more easily, otherwise is not, showing that f could be used to describe the seepage condition and corresponding turning point. Finally, it can be seen from the numerical results that the nonlinearity of fluid flow is mainly caused by the formation of eddies at fracture intersections and the critical pressure gradient decreases with increasing angle. And also, analysis about the coefficient B in the Forchheimer law corresponding to fracture intersections considering the intersecting angle and surface roughness is proposed to reveal the flow nonlinearity. The above investigations give the theoretical support to understand and reveal the seepage mechanism of the rock rough fractures.

On the Thrust Generation from an Elliptic Airfoil in Plunging and Translating Motion at Low Reynolds Numbers

In this paper, numerical simulation elliptic airfoil model, which mimics the biological locomotion, is studied. Elliptic airfoil undergoes a combined plunging and translating at low Reynolds number is simulated by using body fitted coordinate system. The moving mesh in the physical domain is mapped to a regular fixed mesh in the computational domain through a time dependent transformation between the physical and computational co-ordinates. The governing equations of laminar incompressible flow are transformed in the computational plane by incorporating the time dependent transformation, which naturally accounts for the mesh velocities. The transformed equations are discretized on the structured, collocated, o-type elliptic grid using the finite difference methodology. The unsteady equations are marched in time by using a semi-implicit pressure correction (projection) scheme. Along with the time marching of the governing equations, utilizing the mesh velocities and the forward Eulertime integration also moves the mesh points. The effect of Reynolds number (Re) is investigated on the flapping flight propulsion is investigated. It is found that there exists a critical Reynolds number (Rec) for every frequency after which there exists a thrust force. The effect of Rec is related to transformation of neutral wake to thrust generating wake. It is also found that the optimal frequency corresponds to a reduced frequency parameter of 0.7 where a lock in exists. It is also found that this Stc is independent of Re and the mode of vortex shedding is same at Re = 100 and 200 for Stc = 0.7. Further, it is shown that the mode of vortex shedding present is always helpful in thrust generation.

Stability of flow in a deformable channel with an unrestrained boundary

We report results from a linear stability analysis of Newtonian plane Poiseuille flow through a deformable linear elastic channel with an unrestrained boundary wherein the deformable wall is not rigidly bonded to a substrate and is free to undergo motion. The objective of this study is to address the experimental observations of instabilities for this configuration [S. S. Srinivas and V. Kumaran, “Transitions to different kinds of turbulence in a channel with soft walls,” J. Fluid Mech. 822, 267–306 (2017)]. We analyze the role of an unrestrained deformable boundary on the stability of channel flow using both asymptotic and numerical methods. Our results show that when the solid to fluid layer thickness ratio is O(1), both wall modes (whose critical Reynolds number Rec ∝ G3/4, with G being the shear modulus of the solid) and inviscid modes (whose Rec ∝ G1/2) are significantly destabilized by the presence of an unrestrained boundary when compared to channels with completely bonded deformable boundaries. In agreement with experimental observations, the eigenfunctions corresponding to both these unstable modes exhibit a pronounced asymmetric behavior, thereby highlighting the influence of the unrestrained deformable boundary on the stability of the flow. The asymptotic predictions for the wall mode instability are shown to be in excellent agreement with our numerical results. However, for the solid to fluid thickness ratio ∼7.7 (used in the aforementioned experiments), our results show that the reduction in the critical Reynolds number due to the unrestrained boundary is only moderate; we provide possible reasons for the same.

Passive control of the onset of vortex shedding in flow past a circular cylinder using slit

This study investigates the passive flow control phenomena over a two-dimensional circular cylinder using numerical simulations in the laminar regime. The aim is to explore one of the passive control techniques, which involves the introduction of a slit to the geometry of the cylinder. The two parameters, slit width ratio S/D (slit width/diameter) and slit angle (measured with respect to the incoming flow direction), play an essential role in determining the trend of critical Reynolds number (Rec). Most of the analysis invokes flow visualization and saturation amplitude methods to obtain the critical Reynolds number (indicative of the onset of vortex shedding) for different cases. Furthermore, Hopf bifurcation analysis using the Stuart-Landau equation and global stability analysis confirm the accuracy and consistency in the predicted solutions. The additional amount of flow through the slit increases the pressure downstream of the cylinder, which consequently leads to an increase in Rec of the modified cylinder. The critical Reynolds number increases with S/D of the modified cylinder at 0° slit angle (as an additional amount of flow grows with S/D). The critical Reynolds number shows an increasing trend with the slit angle in the range of S/D = 0.05–0.15 as the fluctuation intensity reduces with the slit angle in this range. For S/D = 0.15–0.25, the extra amount of flow through the slit induces instability in the wake, which causes a decrease in Rec with the slit angle. A correlation is obtained, which estimates the critical Reynolds number for a given S/D and slit angle.

Effects of Pr and pool curvature on thermocapillary flow instabilities in annular pool

We linearly analyzed the effect of the Prandtl number (Pr) on the stability of thermocapillary flow in shallow annular pools with an aspect ratio Γ = (Ro - Ri)/d = 20 and two radius ratios ΓR = Ri/Ro= 0.50 and 0.98039, where d, Ro, and Ri are the liquid depth and the radii of the heated outer wall and the cooled inner wall, respectively. The results for Pr ∈ [0, 102] show that the steady axisymmetric thermocapillary flows in these annular pools become unstable against oscillatory instability modes, OSC1, OSC2 and hydrothermal wave (HTW). Two co-dimension-two bifurcations occur at Pr*1 and Pr*2. The critical mode for Pr ≤ Pr*1 is OSC2 with almost constant critical Reynolds number Rec, large wave number and high frequency. OSC1 with smaller wave number and lower frequency is the critical mode for Pr*1 ≤ Pr ≤ Pr*2 and Rec slightly decreases with increasing Pr. HTW is the critical mode for Pr ≥ Pr*2 and Rec decreases with increasing Pr. The values of (Pr*1, Pr*2) are (0.00953, 0.03054) for ΓR = 0.50, and (0.01919, 0.01946) for ΓR = 0.98039. Energy-budget analyses reveal that the instabilities in low-Pr range are caused by instabilities in the steady toroidal vortex (or vortices) near the cold wall.

Relationship between the critical Reynolds number and aperture for flow through single fractures: Evidence from published laboratory studies

An evaluation of published laboratory studies of flow through single rough fractures was conducted to establish a relationship between aperture (2b) and critical Reynolds number (Rec) under controlled conditions for physically measured fractures. Of the relevant 47 published laboratory studies, only six reported physically measured apertures along with adequate hydraulic testing information to determine the corresponding Rec value and show that the fractures follow the cubic law reasonably well. Our analysis indicates a logarithmic relationship between 2b and Rec for cubic-law fractures in the reported aperture range (100–500 µm), consistent with theoretical and modeling studies. Discrete fracture network models used for simulating flow and transport in fractured rock aquifers require reliable values for 2b, usually obtained from the cubic law, using T values from straddle-packer hydraulic tests. The cubic law requires specification of the number of permeable fractures (N) in each test interval, but, distinguishing the permeable from the impermeable fractures is problematic. The relationship between 2b and Rec determined from the laboratory tests provides a fluid-mechanics basis for estimating the number of permeable fractures in straddle-packer tests. Constant-head step-tests carefully done with many steps provide precise identification of the flow rate at the onset of nonlinear flow, and numerous tests have shown that flow deviates from linearity at larger flow rates for larger values of transmissivity (T). A procedure was previously developed to relate N, 2b, and Rec using hydraulic test data, but this approach requires knowledge of the relation between 2b and Rec, thereby motivating this work.

Experimental Investigation of Grout Nonlinear Flow Behavior through Rough Fractures

This research experimentally analyzed the impacts of various water cement (W/C) ratios of ultrafine cement grout material and normal loads FN applied to fractures on grout nonlinear flow behavior through a rough plexiglass fractured sample. An effective self-made apparatus was designed and manufactured to conduct the stress-dependent grout flow tests on the plexiglass sample containing rough fractures. At each W/C ratio, the grout pressure P increased from 0 to 0.9 MPa, and the normal loads FN ranged from 666.3 to 1467.8 N. The results of the experiments indicate that (1) the Forchheimer’s law can be used to express the results of grout nonlinear flow through rough fractures. Moreover, both nonlinear coefficient a and linear coefficient b in Forchheimer’s law decreased with the increase of the W/C ratio, but increased with the increase of the FN value. (2) For normalized transmissivity, with the increase of Re, the decline of the T/T0–Re curves means that the grout flow behavior through the fracture mainly went through three stages: the viscosity effect, then the weak inertia effect, and finally the strong inertia effect. The three stages showed that with the increase of Re, the grout flow state changed from linear to nonlinear. Moreover, with the increase of the W/C ratio, the Forchheimer coefficient β decreased. (3) At a given FN, the critical grout hydraulic gradient Jc decreased, but the critical Reynolds number Rec increased as the W/C ratio increased; at a given W/C ratio, Jc increased, but Rec decreased as FN increased.

Theoretical and numerical study of Couette‐Taylor flow with an axial flow using lattice Boltzmann method

SummaryIn this study, the numerical models for swirling flows developed by Li et al and Zhou for lattice Boltzmann method (LBM) are chosen. These models were firstly validated using the Couette‐Taylor flow between two concentric cylinders simulations. Numerical results showed the efficiency of the Zhou's model. Numerical simulation results using LBM are in good agreement for the steady and unsteady regimes compared to the literature review. In a second step, the Zhou model was then adopted to our study to determine the Couette‐Taylor instabilities with an axial flow. Two protocols are tested. The first one (direct protocol) starts with an azimuthal flow without any axial flow (Re = 0). Once the regime is established, an axial flow is then superposed to the Couette‐Taylor flow (with a sudden or a progressive manner). The second protocol (inverse protocol) starts with an axial flow at a given Reynolds number (Poiseuille flow). Once the regime is established, an azimuthal flow is the executed (with a sudden or a progressive manner). The effect of various parameters controlling the physical situation is also discussed. The increase of the azimuthal velocity mainly led to the emergence and development of Taylor vortices. Its influence decreases when the axial Reynolds number increases. The relevant result for this study is the change of the critical axial Reynolds number Rec (total disappearance of instabilities) with both protocols and both manners.

Flow instability in weakly eccentric annuli

A temporal linear stability analysis of laminar flow in weakly eccentric annular channels has been performed. It has been shown that, even for eccentricities ε and Reynolds numbers that were much smaller than those considered in previous studies, flow instability occurred in the form of travelling waves having characteristics that are very different from those of Tollmien-Schlichting waves and which were triggered at mid-gap by an inviscid mechanism that is associated with the presence of inflection points in azimuthal profiles of the base velocity. The critical stability conditions have been determined for 0 ≤ ε ≤ 0.1 and for diameter ratios 0 < γ < 1. The critical Reynolds number Rec decreased with increasing γ for 0 < γ ≲ 0.13, reached a minimum at γ ≈ 0.13, and increased with further increase in γ. The lowest observed Rec was 529 and occurred for ε = 0.1 and γ ≈ 0.13. As ε → 0, Rec ∝ ε−2. The critical wave number and the critical frequency of the disturbances decreased with increasing γ and approached zero as γ → 1, whilst their ratio was nearly constant in the range of parameters considered in this study. The most unstable regions were found to be at roughly mid-gap on the two flanks of the annulus, and the phase speed of the disturbances was close to the base flow velocity at these regions.

Magnetically Induced Flow Focusing of Non-Magnetic Microparticles in Ferrofluids under Inclined Magnetic Fields.

The ability to focus biological particles into a designated position of a microchannel is vital for various biological applications. This paper reports particle focusing under vertical and inclined magnetic fields. We analyzed the effect of the angle of rotation (θ) of the permanent magnets and the critical Reynolds number (Rec) on the particle focusing in depth. We found that a rotation angle of 10° is preferred; a particle loop has formed when Re < Rec and Rec of the inclined magnetic field is larger than that of the vertical magnetic field. We also conducted experiments with polystyrene particles (10.4 μm in diameter) to prove the calculations. Experimental results show that the focusing effectiveness improved with increasing applied magnetic field strength or decreasing inlet flow rate.

Effects of screw pitches and rotation angles on flow and heat transfer characteristics of nanofluids in spiral tubes

Flow and heat transfer characteristics of nanofluids in spiral tubes are experimentally studied. The effects of screw pitches (s = 10 cm, s = 12.5 cm, s = 15 cm), rotation angles (β = 0°, β = 45°, β = 90°) and nanoparticle mass fractions (ω = 0.0 wt%, ω = 0.1 wt%, ω = 0.3 wt%, ω = 0.5 wt%) on the flow and heat transfer performances are analyzed. Results show that Nusselt number increases with the decreasing screw pitch and the increasing nanoparticle mass fraction. It is also found that spiral tube with rotation angle β = 45° shows the largest heat transfer enhancement ratio, followed by rotation angle β = 0°, and the spiral tube with rotation angle β = 90° shows the smallest heat transfer enhancement ratio. In addition, a comprehensive evaluation index is applied to analyze the thermo-hydraulic performances of spiral tubes. One conclusion is obtained that there is a critical Reynolds number (Rec = 10,000) for the highest evaluation index, and the evaluation index increases with the decreasing screw pitch and increasing nanoparticle mass fraction. The evaluation index of nanofluids in the spiral tube can reach 1.24–1.25 at best.

Sensitivity of wake parameters to diameter changes for a circular cylinder

Two-dimensional, incompressible fluid flow past a circular cylinder, having a variable diameter, is analyzed numerically at low Reynolds numbers (Re). The Reynolds number is based on the cylinder diameter and free-stream velocity. Numerical outcomes demonstrate that at low Reynolds number, the flow remains steady. Analysis of the flow evolution also shows that with enhancing Re beyond a certain critical value, the flow becomes unstable and undergoes a Hop bifurcation. The critical Reynolds number beyond which the flow becomes unsteady is determined for each configuration by an extrapolation procedure. A nonuniform variation of the critical Reynolds number (Rec) with the diameter is observed. On the other hand, it is observed that elongating the diameter of the cylinder leads to increasing the critical Reynolds number. It was also noted that the variation of the diameter value has a significant influence on the different regimes criteria as well as on the vortex detachment. Besides, it is seen that the diameter variation may lead to the birth of vortices with different oscillating frequencies due to the increase of the cylinder diameter that modifies considerably the Strouhal number.

Instability of MHD couette flow of an electrically conducting fluid

We study the electrically conducting fluid stability of magnetohydrodynamic flow between parallel plates by Chebyshev collocation method by applied transverse magnetic field. Temporal growth is obtained by the governing equations. The results show that the dominating factor is the change in shape of the undisturbed velocity profile caused by the magnetic field, which depends only on the Hartmann number. The stability equations is solved by QZ-algorithm to find the eigenvalue problem. The numerical calculation show that Magnetic field with particular magnitude destabilizes Couette flow while other magnitude stabilize the flow. It is also analyzed that Rec decreases rapidly to the minimum value for Hartmann number Ha greater than 3.887 and increases steadily from Hartmann number Ha (&amp;gt;5.559). It is observed that critical Reynolds number Rec is larger as Hartmann number decreases from Ha=3.887. The two critical Reynolds numbers in the elliptic curves are found for different values of Hartmann number.

Quantitative Estimates of Nonlinear Flow Characteristics of Deformable Rough-Walled Rock Fractures with Various Lithologies

The existence of surface roughness, various contact conditions and the occurrence of flow nonlinearity make the flow process in natural rock fractures more complicated. To evaluate the fluid flow regimes in deformable rough-walled rock fractures, a great many hydromechanical tests were conducted on nine real fractures artificially produced from a wide range of lithological diversity. For fractures with a certain JRC (fracture roughness coefficient) value, the confining pressure varied from 5 to 20 MPa, and the hydraulic pressure was increased from 0.4 to 6.0 MPa. The experimental results display that (i) regression analyses of the raw experimental data indicate that the Forchheimer’s law provides a perfect description for flow process through the fractures. The coefficients of viscous and inertial pressure drops undergo a growth of 2–3 orders of magnitude with an increase in the confining pressure; (ii) the hydraulic aperture decreases by approximately 87.41–92.81% as the confining pressure increases, and experiences a decrease of 1.52–2.96 times with the JRC values. A power-law function is used to evaluate the hydraulic aperture as a function of the nonlinear coefficient. The nonlinear coefficient decreases with increasing hydraulic aperture; (iii) using Forchheimer equation, the critical Reynolds number Rec was successfully assessed by choosing E percentage (generally 10%) of the nonlinear effect as the critical value between the linear and nonlinear flow regimes. The obtained Rec steadily increases with increasing confining pressure, while it diminishes with the JRC values; and (v) the transmissivity decreases as the pressure gradient increases. Additionally, transmissivity also exhibits a decreasing trend with both the confining pressures and JRC values due to fracture closure and tortuous and channeling flow paths in rougher fractures, and the rate of its decrease for a smaller confining pressure (5, 10 MPa) is more significant.