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.

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.

A 3D Unsteady Flow Analysis in a Doubly Constricted Tube

2000 ◽  
Author(s):  
B. V. Rathish Kumar ◽  
T. Yamaguchi ◽  
H. Liu ◽  
R. Himeno
Keyword(s):  
Pressure Drop ◽  
Unsteady Flow ◽  
Stokes Equations ◽  
Vortex Formation ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
In Series ◽  
3D Unsteady Flow

Abstract Unsteady flow dynamics in a doubly constricted vessel is analyzed by using a time accurate Finite Volume solution of three dimensional incompressible Navier-Stokes equations. Computational experiments are carried out for various values of Reynolds number in order to assess the criticality of multiple mild constrictions in series and also to bring out the subtle 3D features like vortex formation. Studies reveal that pressure drop across a series of mild constrictions can get physiologically critical. Further this pressure drop is found to be sensitive to the spacing between the constrictions and also to the oscillatory nature of the inflow profile.

scholarly journals Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

2018 ◽  
Vol 8 (9) ◽  
pp. 1413 ◽  
Author(s):  
Dan Yao ◽  
Kwongi Lee ◽  
Minho Ha ◽  
Cheolung Cheong ◽  
Inhiug Lee
Keyword(s):  
Boundary Conditions ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Jet Pump ◽  
Two Phase

A new pump, called the hybrid airlift-jet pump, is developed by reinforcing the advantages and minimizing the demerits of airlift and jet pumps. First, a basic design of the hybrid airlift-jet pump is schematically presented. Subsequently, its performance characteristics are numerically investigated by varying the operating conditions of the airlift and jet parts in the hybrid pump. The compressible unsteady Reynolds-averaged Navier-Stokes equations, combined with the homogeneous mixture model for multiphase flow, are used as the governing equations for the two-phase flow in the hybrid pump. The pressure-based methods combined with the Pressure-Implicit with Splitting of Operators (PISO) algorithm are used as the computational fluid dynamics techniques. The validity of the present numerical methods is confirmed by comparing the predicted mass flow rate with the measured ones. In total, 18 simulation cases that are designed to represent the various operating conditions of the hybrid pump are investigated: eight of these cases belong to the operating conditions of only the jet part with different air and water inlet boundary conditions, and the remaining ten cases belong to the operating conditions of both the airlift and jet parts with different air and water inlet boundary conditions. The mass flow rate and the efficiency are compared for each case. For further investigation into the detailed flow characteristics, the pressure and velocity distributions of the mixture in a primary pipe are compared. Furthermore, a periodic fluctuation of the water flow in the mass flow rate is found and analyzed. Our results show that the performance of the jet or airlift pump can be enhanced by combining the operating principles of two pumps into the hybrid airlift-jet pump, newly proposed in the present study.

scholarly journals Performance investigation of a volute porous tongue of a turbocharger turbine

2020 ◽  
Vol 40 (1) ◽  
pp. 59-66
Author(s):  
Abderrahmane Chachoua ◽  
Mohamed Kamal Hamidou ◽  
Mohammed Hamel
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Turbines ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Recirculation Flow ◽  
Recirculating Flow ◽  
Show Evidence ◽  
The Right

The design for better performance of the spiral housing volute used commonly in radial and mixed inflow gas turbines is of prime importance as it affects the machine stage at both design and off design conditions. The tongue of the scroll divides the flow into two streams, and represents a severe source of disturbances, in terms of thermodynamic parameter uniformity, maximum kinetic energy, the right angle of attack to the rotor and minimum losses. Besides, the volute suffers an undesirable effect due to the recirculating mass flow rate in near bottom vicinity of the tongue. The present project is an attempt to design a tongue fitted with cylindrical holes traversing normal to the stream wise direction, where on account of the large pressure difference between the top and the bottom sides of the tongue will force the recirculating flow to go through the rotor inlet. This possibility with its limitations has not yet been explored. A numerical simulation is performed which might provide our suitable objectives. To achieve this goal the ANSYS code is used to build the geometry, generate the mesh, and to simulate the flow by solving numerically the averaged Navier Stokes equations. Apparently, the numerical results show evidence of favorable impact in using porous tongue. The realization of a contact between the main and recirculation flow by drilled holes on the tongue surface leads to a flow field uniformity, a reduction in the magnitude of the loss coefficient, and a 20 % reduction in the recirculating mass flow rate.

Effect of Blade Numbers on Pressure Drop of Axial Cyclone Separators by CFD

2011 ◽  
Vol 55-57 ◽  
pp. 343-347 ◽  
Author(s):  
Yi Gang Luan ◽  
Hai Ou Sun
Keyword(s):  
Pressure Drop ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Three Dimensional Model ◽  
Navier Stokes Equations ◽  
Pressure Drops ◽  
Computational Fluid Dynamics Cfd ◽  
Cfd Method ◽  
Resistance Performance

In this article, computational fluid dynamics(CFD) method is used to predict the effect of blade numbers on the pressure drop of axial cyclone separators. A three-dimensional model is built to acquire the resistance of axial cyclone separators with different blade numbers. The flow field inside cyclone separators is calculated using 3D Reynolds-averaged Navier-Stokes equations. And turbulence model is used to simulate the Reynold stress. Also pressure drop of cyclone separators with different blade numbers is expressed as a function of different inlet velocities. At the same inlet velocity with increasing the blade numbers, pressure drops of cyclones reduce greatly. And changing the blade number of cyclone separator is an effective method to improve its resistance performance.

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.

Design of a Fractal Tree-Like Microchannel Net Heat Sink for Microelectronic Cooling

2006 ◽  
Author(s):  
F. J. Hong ◽  
P. Cheng ◽  
H. Ge ◽  
Teck Joo Goh
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Heat Sink ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Electronic Cooling ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Result ◽  
Parallel Microchannels

In this paper, a numerical simulation is carried to study pressure drop and heat transfer in a fractal tree-like microchannel net heat sink of 10mm×12.5mm×0.5mm in dimensions. The numerical result is obtained by solving three-dimensional Navier-Stokes equations and energy equation, taking into consideration conjugate heat transfer in the microchannel walls. A comparison of fractal tree-like microchannel net heat sink with 6 branch levels to parallel microchannels heat sink, with respect to the pressure drop, thermal resistance and temperature uniformity, was also performed under the condition of the same heat sink dimensions. The results indicates that for a mass flow rate of water less than 0.00175kg/s, the fractal tree-like microchannel is much better than parallel channel heat sink with respect to all of three aspects. Therefore, the fractal tree-like microchannels net heat sink using water as the coolant is promising to be used in the future electronic cooling industry.

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

Steady streaming in a turbulent oscillating boundary layer

2007 ◽  
Vol 571 ◽  
pp. 265-280 ◽  
Author(s):  
PIETRO SCANDURA
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Time Average

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

Pressure drop and power dissipation in oscillatory wavy-walled-tube flows

1988 ◽  
Vol 187 ◽  
pp. 573-588 ◽  
Author(s):  
M. E. Ralph
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Power Dissipation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Frequency Parameter ◽  
Mean Power ◽  
Pressure Drops ◽  
The Mean

Pressure drops occurring in oscillatory viscous flows in wavy-walled tubes have been studied experimentally, for Reynolds numbers up to 1500 and Strouhal numbers in the range 0.005 to 0.02, and by numerical solution of the Navier-Stokes equations, for Reynolds numbers up to 200 and Strouhal numbers between 0.005 and 0.1. Agreement was good for values of the mean modulus of the pressure drop at lower Strouhal numbers and for values of the mean power dissipation at all Strouhal numbers.Numerical solutions have shown that the pressure drop may vary non-sinusoidally, even though the imposed variation in flow rate is sinusoidal. This cannot be explained by the nonlinearity of the steady pressure drop-flow rate relationship, and arises because the velocity field is not quasi-steady. In particular energy may be stored in strong vortices formed during the acceleration phase of the flow cycle, and partially returned to the main flow later. The peak pressure drops in such flows, which are associated with the formation of these vortices, can be almost twice as large as values predicted by adding the appropriate quasi-steady and unsteady inertial contributions. This finding is important in the wider context of unsteady conduit flow.The dependences of the mean modulus of the pressure drop and the mean power dissipation on the Strouhal number and frequency parameter were investigated in detail numerically for two geometries. It was not possible to reduce either dependence to a function of a single parameter. The ‘equivalent’ straight-walled tube for power dissipation was found to have a smaller bore than that for pressure drop, leading to smaller ‘phase angles’ than might have been expected at large values of the frequency parameter. This is because as the pressure drop becomes increasingly dominated by unsteady inertia, there remain relatively large recirculations in which energy is dissipated.

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