scholarly journals Effect of Lower Surface Roughness on Nonlinear Hydraulic Properties of Fractures

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jinglong Li ◽  
Xianghui Li ◽  
Bo Zhang ◽  
Bin Sui ◽  
Pengcheng Wang ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Regimes ◽  
Lower Surface ◽  
Nonlinear Flow ◽  
Hydraulic Pressure

This study investigates the effect of fracture lower surface roughness on the nonlinear flow behaviors of fluids through fractures when the aperture fields are fixed. The flow is modeled with hydraulic pressure drop = 10 − 4 ~ 10 5   Pa / m by solving the Navier-Stokes equations based on rough fracture models with lower surface roughness varying from JRC = 1 to JRC = 19 . Here, JRC represents joint roughness coefficient. The results show that the proposed numerical method is valid by comparisons between numerically calculated results with theoretical values of three parallel-plate models. With the increment of hydraulic pressure drop from 10-4 to 105 Pa/m spanning ten orders of magnitude, the flow rate increases with an increasing rate. The nonlinear relationships between flow rate and hydraulic pressure drop follow Forchheimer’s law. With increasing the JRC of lower surfaces from 1 to 19, the linear Forchheimer coefficient decreases, whereas the nonlinear Forchheimer coefficient increases, both following exponential functions. However, the nonlinear Forchheimer coefficient is approximately three orders of magnitude larger than the linear Forchheimer coefficient. With the increase in Reynolds number, the normalized transmissivity changes from constant values to decreasing values, indicating that fluid flow transits from linear flow regimes to nonlinear flow regimes. The critical Reynolds number that quantifies the onset of nonlinear fluid flow ranges from 21.79 to 185.19.

scholarly journals Effects of Contact Area and Contact Shape on Nonlinear Fluid Flow Properties of Fractures by Solving Navier-Stokes Equations

Lithosphere ◽  
2021 ◽  
Vol 2021 (Special 3) ◽  
Author(s):  
Hanqing Yang ◽  
Xiaolin Wang ◽  
Liyuan Yu ◽  
Richeng Liu
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Contact Area ◽  
Stokes Equations ◽  
Hydraulic Gradient ◽  
Navier Stokes ◽  
Hydraulic Pressure ◽  
Flow Paths ◽  
Critical Hydraulic Gradient ◽  
Contact Shape

Abstract The influences of contact shape and contact area on nonlinear fluid flow properties through fractures are investigated by solving Navier-Stokes equations. The evolutions of nonlinear relationships between flow rate and hydraulic pressure drop, Forchheimer coefficients, nonlinear factor, critical hydraulic gradient, distributions of flow streamlines, and tracer flow paths at different times are systematically estimated. The results show that the nonlinear relationships between flow rate and hydraulic pressure drop can be well described by Forchheimer’s law, in which the nonlinear term coefficient b is approximately three orders of magnitude larger than the linear term coefficient a. The smaller contact area corresponds to smaller variations in many aspects such as flow rate, critical hydraulic gradient, flow streamlines, and tracer flow paths. The critical hydraulic gradient decreases with the increasing degree of contact shape variations while the contacts have the same mean area. The increase in hydraulic pressure drop can induce significant eddies and decrease the permeability and/or conductivity of fractures. However, the distributions of streamlines and tracer flow paths are not dramatically disturbed under a large hydraulic pressure drop.

Experimental Analysis of Poiseuille Number in Square Microchannels

2009 ◽  
Author(s):  
T. J. John ◽  
B. Mathew ◽  
H. Hegab
Keyword(s):  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Friction Factor ◽  
Flow Rate ◽  
Liquid Flow ◽  
Liquid Flow Rate ◽  
Microfluidic Devices ◽  
Total Uncertainty ◽  
Poiseuille Number

The applications involving fluid flow through microchannels in industry and research have increased significantly with the evolution of microfluidic devices such as lab-on-chip systems. Most of the previous studies concerning fluid flow were done using circular microchannels. However, there is an increased usage of noncircular microchannels, especially square microchannels, in microfluidic devices. Thus there is need for experimental studies on the behavior of fluid flow in square microchannels, and the comparison of the results with the results obtained from the conventional fluid flow equations is relevant. In this study the authors are focusing on the analysis of the friction factor associated with square microchannels of rounded edges under laminar flow conditions. Microchannels with hydraulic diameters of 200, 300, 400 and 500 micrometers and length of 10 cm and 5 cm are used in the analysis. DI-water and ethylene glycol at room temperature is used as the liquid for experiments. A constant liquid flow rate is achieved in the channels using a syringe pump that can pump from 50 μl/hr to 7,500 ml/hr using a 60 ml syringe, and a high precision pressure gauge is used to measure the pressure drop across the channel. The Reynolds number of the liquid flow in all the channels is kept constant between 20 and 120 by varying the flow rate. The friction factor at each Reynolds number is calculated and the results are compared with the friction factor of conventional channels. Experiments are conducted to measure the pressure drop across the channels. The pressure drop obtained across the 5 cm channel is subtracted from the pressure drop obtained across the 10 cm channel so that the effect of entrance effect can be eliminated from the results. The fiction factor obtained from the experiments is used to calculate the Poiseuille number. The experimental values of Poiseuille number are showing a median deviation of around 9% from the conventional values for all the different channels. The uncertainty is observed to be ca.9% for all the channels at all values of Reynolds numbers. The major factor contributing towards the total uncertainty is the uncertainty in the measurement of liquid flow rate.

Study of fluid flow through a channel deformed by piezoelement

2018 ◽  
Vol 13 (3) ◽  
pp. 1-10 ◽  
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh Nasibullaeva ◽  
O.V. Darintsev
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Flow Rate ◽  
Contact Surface ◽  
Piezoelectric Element ◽  
Neumann Boundary ◽  
Differential Pressure ◽  
Physical Parameters ◽  
Flow Through

The flow of a liquid through a tube deformed by a piezoelectric cell under a harmonic law is studied in this paper. Linear deformations are compared for the Dirichlet and Neumann boundary conditions on the contact surface of the tube and piezoelectric element. The flow of fluid through a deformed channel for two flow regimes is investigated: in a tube with one closed end due to deformation of the tube; for a tube with two open ends due to deformation of the tube and the differential pressure applied to the channel. The flow rate of the liquid is calculated as a function of the frequency of the deformations, the pressure drop and the physical parameters of the liquid.

Pressure Drop Measurements for Air Flow Through Open-Cell Aluminum Foam

2004 ◽  
Author(s):  
Nihad Dukhan ◽  
Angel Alvarez
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Aluminum Foam ◽  
Flow Direction ◽  
The Other ◽  
Turbulent Regime ◽  
Thick Sample ◽  
Open Cell ◽  
Two Samples

Wind-tunnel pressure drop measurements for airflow through two samples of forty-pore-per-inch commercially available open-cell aluminum foam were undertaken. Each sample’s cross-sectional area perpendicular to the flow direction measured 10.16 cm by 24.13 cm. The thickness in the flow direction was 10.16 cm for one sample and 5.08 cm for the other. The flow rate ranged from 0.016 to 0.101 m3/s for the thick sample and from 0.025 to 0.134 m3/s for the other. The data were all in the fully turbulent regime. The pressure drop for both samples increased with increasing flow rate and followed a quadratic behavior. The permeability and the inertia coefficient showed some scatter with average values of 4.6 × 10−8 m2 and 2.9 × 10−8 m2, and 0.086 and 0.066 for the thick and the thin samples, respectively. The friction factor decayed with the Reynolds number and was weakly dependent on the Reynolds number for Reynolds number greater than 35.

Experimental Investigation of Effect of Tip Coolant Ejection on Internal Flow Characteristics Within a Realistic Blade Coolant Channel

2013 ◽  
Author(s):  
Jian Pu ◽  
Zhaoqing Ke ◽  
Jianhua Wang ◽  
Lei Wang ◽  
Hongde You
Keyword(s):  
Experimental Investigation ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Turbine Blade ◽  
Flow Rate ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Flow Ratio ◽  
Lp Turbine ◽  
Mass Flow Ratio

This paper presents an experimental investigation on the characteristics of the fluid flow within an entire coolant channel of a low pressure (LP) turbine blade. The serpentine channel, which keeps realistic blade geometry, consists of three passes connected by a 180° sharp bend and a semi-round bend, 2 tip exits and 25 trailing edge exits. The mean velocity fields within several typical cross sections were captured using a particle image velocimetry (PIV) system. Pressure and flow rate at each exit were determined through the measurements of local static pressure and volume flow rate. To optimize the design of LP turbine blade coolant channels, the effect of tip ejection ratio (ER) from 180° sharp bend on the flow characteristics in the coolant channel were experimentally investigated at a series of inlet Reynolds numbers from 25,000 to 50,000. A complex flow pattern, which is different from the previous investigations conducted by a simplified square or rectangular two-pass U-channel, is exhibited from the PIV results. This experimental investigation indicated that: a) in the main flow direction, the regions of separation bubble and flow impingement increase in size with a decrease of the ER; b) the shape, intensity and position of the secondary vortices are changed by the ER; c) the mass flow ratio of each exit to inlet is not sensitive to the inlet Reynolds number; d) the increase of the ER reduces the mass flow ratio through each trailing edge exit to the extent of about 23–28% of the ER = 0 reference under the condition that the tip exit located at 180° bend is full open; e) the pressure drop through the entire coolant channel decreases with an increase in the ER and inlet Reynolds number, and a reduction about 35–40% of the non-dimensional pressure drop is observed at different inlet Reynolds numbers, under the condition that the tip exit located at 180° bend is full open.

Letterbox Trailing Edge Heat Transfer: Effects of Blowing Rate, Reynolds Number, and External Turbulence on Heat Transfer and Film Cooling Effectiveness

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
N. J. Fiala ◽  
I. Jaswal ◽  
F. E. Ames
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Film Cooling ◽  
Suction Surface ◽  
Trailing Edge ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio ◽  
Adiabatic Effectiveness

Heat transfer and film cooling distributions have been acquired for a vane trailing edge with letterbox partitions. Additionally, pressure drop data have been experimentally determined across a pin fin array and a trailing edge slot with letterbox partitions. The pressure drop across the array and letterbox trailing edge arrangement was measurably higher than for the gill slot geometry. Experimental data for the partitions and the inner suction surface region downstream from the slot have been acquired over a four-to-one range in vane exit condition Reynolds number (500,000, 1,000,000, and 2,000,000), with low (0.7%), grid (8.5%), and aerocombustor (13.5%) turbulence conditions. At these conditions, both heat transfer and adiabatic film cooling distributions have been documented over a range of blowing ratios (0.47≤M≤1.9). Heat transfer distributions on the inner suction surface downstream from the slot ejection were found to be dependent on both ejection flow rate and external conditions. Heat transfer on the partition side surfaces correlated with both exit Reynolds number and blowing ratio. Heat transfer on partition top surfaces largely correlated with exit Reynolds number but blowing ratio had a small effect at higher values. Generally, adiabatic film cooling levels on the inner suction surface are high but decrease near the trailing edge and provide some protection for the trailing edge. Adiabatic effectiveness levels on the partitions correlate with blowing ratio. On the partition sides adiabatic effectiveness is highest at low blowing ratios and decreases with increasing flow rate. On the partition tops adiabatic effectiveness increases with increasing blowing ratio but never exceeds the level on the sides. The present paper, together with a companion paper that documents letterbox trailing edge aerodynamics, is intended to provide engineers with the heat transfer and aerodynamic loss information needed to develop and compare competing trailing edge designs.

Lateral-Flow Effect on Endwall Heat Transfer and Pressure Drop in a Pin-Fin Trapezoidal Duct of Various Pin Shapes

2000 ◽  
Vol 123 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Chau-Ching Lu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Lateral Flow ◽  
Transfer Enhancement ◽  
Pin Fin ◽  
Flow Reynolds Number ◽  
Outlet Flow ◽  
Flow Through

The effects of lateral-flow ejection 0<ε<1.0, pin shapes (square, diamond, and circular), and flow Reynolds number (6000<Re<40,000) on the endwall heat transfer and pressure drop for turbulent flow through a pin-fin trapezoidal duct are studied experimentally. A staggered pin array of five rows and five columns is inserted in the trapezoidal duct, with the same spacings between the pins in the streamwise and spanwise directions: Sx/d=Sy/d=2.5. Three different-shaped pins of length from 2.5<l/d<4.6 span the distance between two endwalls of the trapezoidal duct. Results reveal that the pin-fin trapezoidal duct with lateral-flow rate of ε=0.3-0.4 has a local minimum endwall-averaged Nusselt number and Euler number for all pin shapes investigated. The trapezoidal duct of lateral outlet flow only (ε=1.0) has the highest endwall heat transfer and pressure drop. Moreover, the square pin results in a better heat transfer enhancement than the diamond pin, and subsequently than the circular pin. Finally, taking account of the lateral-flow rate and the flow Reynolds number, the work develops correlations of the endwall-averaged heat transfer with three different pin shapes.

Prototype Reynolds Number Vortex-Induced Vibration Tests on a Full-Scale Rigid Riser

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Decao Yin ◽  
Halvor Lie ◽  
Rolf J. Baarholm
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Flow Regime ◽  
Amplitude Ratio ◽  
Flow Regimes ◽  
Offshore Structures ◽  
Full Scale ◽  
Displacement Amplitude ◽  
Small Scale ◽  
Supercritical Flow

Slender offshore structures in deep water subjected to currents may experience vortex-induced vibrations (VIV), which can cause significant fatigue damage. Extensive experimental researches have been conducted to study the VIV in the past several decades. However, most of the experimental works have small-scale models and relatively low Reynolds number (Re)—“subcritical” or even lower Reynolds number regime. There is a lack of full understanding of the VIV in prototype Re flow regime. Applying the results with low Re to a full-scale riser with prototype Re might have uncertainties due to the scaling effects. In addition, the surface roughness of the riser is also an important parameter, especially in critical Re regime, which is the case for prototype risers. In the present study, two full-scale rigid riser models with different surface roughness ratios were tested in the towing tank of MARINTEK in 2014. Stationary tests, pure crossflow (CF) free oscillation tests, and forced/controlled motion tests were carried out. Several conclusions could be made: The drag coefficient is dependent on the Re number and surface roughness ratio. At critical and supercritical flow regimes, the displacement amplitude ratio is less sensitive to Re than that at lower Re. The displacement amplitude ratio in subcritical flow regime is significantly larger than that in critical and supercritical flow regimes. Two excitation regions for the ‘smooth riser’ and one excitation region for the “rough riser” are identified.

Lubrication analysis and boundary integral simulations of a viscous micropump

2000 ◽  
Vol 416 ◽  
pp. 197-216 ◽  
Author(s):  
RICHARD F. DAY ◽  
H. A. STONE
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Direction ◽  
Maximum Flow ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Micropump ◽  
Analytical Relations ◽  
Rate Optimization

Several recent papers discuss a viscous micropump consisting of Poiseuille flow of fluid between two plates with a cylinder placed along the gap perpendicular to the flow direction (e.g. Sen, Wajerski & Gad-el-Hak 1996). If the cylinder is not centred, rotating it will generate a net flow and an additional pressure drop along the channel, due to the net tangential viscous stresses along its surface. The research reported here complements existing work by examining the lubrication limit where the gaps between the cylinder and the walls are small compared to the cylinder radius. Lubrication analysis provides analytical relations among the flow rate, torque, pressure drop and rotation rate. Optimization of the flow parameters is shown in order to determine the optimal geometry of the device, which can be used by micro-electrical-mechanical systems designers. It is also shown, for example, that a device cannot be developed that achieves maximum flow rate and rotation simultaneously. In addition, since the Reynolds number can be smaller than 1, the Stokes equations are solved for this configuration using a numerical boundary integral method. The numerical results match the lubrication solution for small gaps, and determine the limits of validity for using the lubrication results.

Prototype Reynolds Number VIV Tests on a Full-Scale Rigid Riser

2017 ◽  
Author(s):  
Decao Yin ◽  
Halvor Lie ◽  
Rolf J. Baarholm
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Flow Regime ◽  
Amplitude Ratio ◽  
Flow Regimes ◽  
Offshore Structures ◽  
Full Scale ◽  
Displacement Amplitude ◽  
Small Scale ◽  
Supercritical Flow

Slender offshore structures in deep water subjected to currents may experience vortex-induced vibrations (VIV), which can cause significant fatigue damage. Extensive experimental researches have been conducted to study the VIV in the past several decades. However, most of the experimental works have small-scale models and relatively low Reynolds number (Re) - ‘subcritical’ or even lower Reynolds number regime. There is a lack of full understanding the VIV in prototype Re flow regime. Applying the results with low Re to a full scale riser with prototype Re might have uncertainties due to the scaling effects. In addition, the surface roughness of the riser is also an important parameter, especially in prototype Re regime. In present study, two full-scale rigid riser models with different surface roughness ratios were tested in the towing tank of MARINTEK in 2014. Stationary tests, pure cross-flow (CF) free oscillation tests and forced/controlled motion tests were carried out. Several conclusions could be made: • The drag coefficient is dependent on the Re number and surface roughness ratio. • At critical and supercritical flow regimes, the displacement amplitude ratio is less sensitive to Re than that at lower Re. The displacement amplitude ratio in subcritical flow regime is significantly larger than that in critical and supercritical flow regimes. • Two excitation regions for the ‘smooth riser’ and one excitation region for the ‘rough riser’ are identified.

Sign in / Sign up

Export Citation Format

Share Document