Solution Of Fluid Flow Research Articles

An analytical model for the longitudinal permeability of aligned fibrous media

Abstract This paper presents an analytical series solution of the longitudinal fluid flow in porous media consisting of aligned rigid fibers, which, in turn, is used to establish a relationship for the longitudinal permeability as a function of the fiber packing geometry, fiber volume fraction and the fiber radius. The analytical series solution is developed for rectangular and staggered packing arrangements of the fibers using the boundary collocation method where the constants in the series solution are solved for numerically. As the number of boundary collocation points is increased, the analytical solution is shown to converge with a finite element solution of the identical flow situation for all fiber volume fractions and packing arrangements. In addition, the permeability results are presented in a dimensionless form as a function of the fiber volume fraction and fiber packing arrangement for a general applicability and easy use of the results for predicting the longitudinal permeability of fiber tows consisting of aligned rigid fibers.

Nonstationary poiseuille-type solutions for the second-grade fluid flow

We study solutions to the nonstationary equations describing the motion of the second-grade fluid in a twodimensional infinite channel and in a three-dimensional rotationally symmetric pipe. We prove the existence of a unique Poiseuille-type solution having a given flow rate (flux) and investigate the behavior of this solution as t → ∞.

Analysis of coherent structures in drag-reducing polymer solution flow based on proper orthogonal decomposition

Direct numerical simulation (DNS) of forcing homogeneous isotropic turbulence with polymers was performed. In order to understand the polymers effect on turbulent coherent structures, proper orthogonal decomposition was performed to identify coherent structures based on DNS data, so as to analyze the remarkable difference due to the addition of polymers. The results showed that the numbers for eigenmodes required for capturing coherent structures were 32 and 24 for the Newtonian fluid and polymer solution flows, respectively, which means the decrease of the complexity in polymer solution flow. Through the POD energy spectrum, it was found that the turbulent kinetic energy is distributed onto a large number of eigenmodes whether in the Newtonian fluid flow or polymer solution flow, suggesting that polymer solution flow is still turbulent in one aspect. Besides, the POD eigenmodes were investigated, which found that the small-scale structures are inhibited in polymer solution flow.

Modeling and Numerical Simulation of Yield Viscoplastic Fluid Flow in Concentric and Eccentric Annuli

Numerical solution of yield viscoplastic fluid flow is hindered by the singularity inherent to the Herschel-Bulkley model. A finite difference method over the boundary-fitted orthogonal coordinate system is utilized to investigate numerically the fully developed steady flow of non-Newtonian yield viscoplastic fluid through concentric and eccentric annuli. The fluid rheology is described with the Herschel-Bulkley model. The numerical simulation based on a continuous viscoplastic approach to the Herschel-Bulkley model is found in poor accordance with the experimental data on volumetric flow rate of a bentonite suspension. A strict mathematical model for Herschel-Bulkley fluid flow is established and the corresponding numerical procedures are proposed. However, only the case of flow of a Herschel-Bulkley fluid in a concentric annulus is resolved based on the presumed flow structure by using the common optimization technique. Possible flow structures in an eccentric annulus are presumed, and further challenges in numerical simulation of the Herschel-Bulkley fluid flow are suggested.

Explicit analytical solutions for fluid flow and temperature field synergy in cylindrical coordinates

The field synergy principle–an approach to find out the best convection condition–has been successfully proposed and applied. However, the case for worst convection contribution will be worthy researched also. In this paper, four groups of algebraically explicit analytical solutions with heat source or mass flow source are derived for 2D incompressible laminar flow in cylindrical coordinate. The concrete physical meanings of the solutions are analyzed. The extraordinary methods used to obtain solutions are named the method of separating variables with addition and other hybrid method. Besides theoretical meaning, the solutions can be benchmark solutions to develop the computational heat transfer.

A robust weakly compressible SPH method and its comparison with an incompressible SPH

SUMMARYThis paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering‐induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods. Copyright © 2011 John Wiley & Sons, Ltd.

Analytical solutions for pressure perturbation and fluid leakage through aquitards and wells in multilayered‐aquifer systems

Large‐scale groundwater pumping or deep fluid injection in a multilayered subsurface system may generate pressure perturbation not only in the target formation(s), but also in over‐ and underlying units. Hydraulic communication in the vertical direction may occur via diffuse leakage through aquitards and/or via focused leakage through leaky wells. Existing analytical solutions for pressure perturbation and fluid flow in such systems consider either diffuse leakage or focused leakage, but never in combination with each other. In this study, we developed generalized analytical solutions that account for the combined effect of diffuse and focused leakage. The new solutions solve for pressure changes in a system of N aquifers with alternating leaky aquitards in response to fluid injection/extraction with any number, NI, of injection/pumping (active) wells, and passive leakage/recharge in any number, NL, of leaky wells. The equations of horizontal groundwater flow in the aquifers are coupled by the vertical flow equations in the aquitards and by the flow continuity equations in the leaky wells. The solution methodology, described in detail in this paper, involves transforming the transient flow equations into the Laplace domain; decoupling the resulting ordinary differential equations (ODEs) coupled by diffuse leakage via eigenvalue analysis; solving a system of NL × N linear algebraic equations for the unknown rates of flow through leakage wells; and superposing the solution of pressure buildup/drawdown in aquifers and aquitards resulting from flow in the NI active and NL leaky wells. Verification of the new methodology was achieved by comparison with existing analytical solutions for diffuse leakage and for focused leakage, and against a numerical solution for combined diffuse and focused leakage. Application to an eight‐aquifer system with leaky aquitards and one leaky well demonstrates the usefulness and efficiency of the approach, and illustrates the pressure behavior over a spectrum of leakage scenarios and parameters.

Fluid–structure interaction analysis of flexible turbomachinery

A method for the performance computation of an expandable-impeller pump is developed and validated. Large deformations of the highly flexible pump impellers result in a strong coupling between the impeller and fluid flow. The computational method therefore requires simultaneous solution of fluid flow and structural response. OpenFOAM provides the flow and mesh motion solvers and is coupled to an author-developed structural solver in a tightly coupled approach using a fixed-point iteration. The structural deformations are time-dependent because the material exhibits stress relaxation. The time-constant of the relaxation, however, is very large, thereby allowing quasi-steady simulations. A water-tunnel test of a viscoelastic hydrofoil is employed to validate the solver. Simulations of the test problem show good agreement with the experimental results and demonstrate the need for several sub-iterations of the solver even for the quasi-steady simulations.

Wang’s shrinking cylinder problem with suction near a stagnation point

In this paper, the steady axisymmetric stagnation point flow of a viscous and incompressible fluid over a shrinking circular cylinder with mass transfer (suction) is studied. The flow is induced by a cylinder shrinking with a linear velocity distribution from the stagnation line. The fluid flow solution is an exact solution of the Navier-Stokes equation, which is reduced to a nonlinear ordinary differential equation. This equation is solved numerically for some values of the governing parameters that involves a Reynolds number R, a shrinking parameter λ, and a suction parameter γ. The effects of these governing parameters on the velocity and temperature profiles, skin friction coefficient, Nusselt number, as well as the distributions of the streamlines are investigated. The obtained results for the case of fixed cylinder are compared with those from the open literature and it is shown that they are in excellent agreement. The solutions are non-unique for some values of λ (<0). The streamlines show that the flow structures become complicated due to the shrinking and suction effects.

Homotopy analysis solution for micropolar fluid flow through porous channel with expanding or contracting walls of different permeabilities

The flow of a micropolar fluid through a porous channel with expanding or contracting walls of different permeabilities is investigated. Two cases are considered, in which opposing walls undergo either uniform or non-uniform motion. In the first case, the homotopy analysis method (HAM) is used to obtain the expressions for the velocity and micro-rotation fields. Graphs are sketched for some parameters. The results show that the expansion ratio and the different permeabilities have important effects on the dynamic characteristics of the fluid. Following Xu’s model, in the second case which is more general, the wall expansion ratio varies with time. Under this assumption, the governing equations are transformed into nonlinear partial differential equations that can also be solved analytically by the HAM. In the process, both algebraic and exponential models are considered to describe the evolution of α(t) from the initial state α0 to the final state α1. As a result, the time-dependent solutions are found to approach the steady state very rapidly. The results show that the time-dependent variation of the wall expansion ratio can be ignored because of its limited effects.

A computation of flow and heat transfer past three heated cylinders in a vee shape by a double distribution MRT thermal lattice Boltzmann model

Laminar convective flow heat transfer from a three heated square blocks arranged as a vee shaped inside a two-dimensional plane channel is numerically investigated. We propose a numerical scheme to solve the flow and the temperature fields using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively. The fluid considered here is air ( Pr = 0.71) and the analysis is carried out for Reynolds numbers ranged between 10 and 100 and for gap-to-diameter ratio 1 and 2. The velocity plots and isotherm patterns obtained are systematically presented and discussed to interpret the flow and heat transfer visualization. The variations of drag coefficient and time-averaged local Nusselt number around the surface of the three cylinders as well as the surface-averaged values of the time-averaged Nusselt number for each block are also investigated and discussed. It is found that the numerical results agree well with other numerical results. This demonstrates that the presented numerical model is a promising tool to investigate the simultaneous solution of fluid flow and heat transfer in complex geometries.

Some new exact analytical solutions for helical flows of second grade fluids

The helical flow of a second grade fluid, between two infinite coaxial circular cylinders, is studied using Laplace and finite Hankel transforms. The motion of the fluid is due to the inner cylinder that, at time t = 0 + begins to rotate around its axis, and to slide along the same axis due to hyperbolic sine or cosine shear stresses. The components of the velocity field and the resulting shear stresses are presented in series form in terms of Bessel functions J 0(•), Y 0(•), J 1(•), Y 1(•), J 2(•) and Y 2(•). The solutions that have been obtained satisfy all imposed initial and boundary conditions and are presented as a sum of large-time and transient solutions. Furthermore, the solutions for Newtonian fluids performing the same motion are also obtained as special cases of general solutions. Finally, the solutions that have been obtained are compared and the influence of pertinent parameters on the fluid motion is discussed. A comparison between second grade and Newtonian fluids is analyzed by graphical illustrations.

A high-accuracy temporal–spatial pseudospectral method for time-periodic unsteady fluid flow and heat transfer problems

A temporal–spatial pseudospectral (TSP) method is proposed for the high-accuracy solutions of time-periodic unsteady fluid flow and heat transfer problems. In this method, both the spatial and temporal derivative terms in the governing equations are computed by pseudospectral method. The spatial derivatives are computed through Chebyshev and Lagrange polynomials while the time derivatives are computed by Fourier series. The TSP method is capable of directly finding out the periodic state solutions without the necessity to resolve the initial transient state solutions, hence holds high computational efficiency and high numerical accuracy properties for the time-periodic problems. This method is validated by three 2D benchmark problems: the time-periodic incompressible flow with exact solutions; the natural convection in enclosure with time-periodic temperature on one sidewall, and on both sidewalls. The TSP results fit well the exact solutions or the benchmark solutions and the TSP accuracy is much higher than the time marching spatial pseudospectral accuracy. Some time-dependent fluid flow and heat transfer characteristic parameters are analysed. The proposed TSP method could be further extended to more complex time-periodic unsteady fluid flow and heat transfer problems where high-accuracy results are required.

Relationship Between the Hydraulic Fracture and Observed Microseismicity in the Bossier Sands of Texas

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 137936, ’Relationship Between the Hydraulic Fracture and Observed Microseismicity in the Bossier Sands, Texas,’ by A. Guest, SPE, and A. Settari, SPE, University of Calgary, prepared for the 2010 Canadian Unconventional Resources & International Petroleum Conference, Calgary, 19-21 October. The paper has not been peer reviewed. There is an increased effort to improve our understanding of hydrofracturing by use of microseismic monitoring and analysis. A numerical method was developed to predict microseismicity occurring during hydrofracturing and the influence of fracturing on the permeability of the reservoir. The core of this technique is a representative pre-fractured volume of the reservoir that deforms locally and allows the coalescence of deformation as the stress re-equilibrates. Introduction Hydraulic fracturing is used to increase the effective permeability of a producing formation and, thus, increase the production of hydrocarbons. Even though microseismicity provides a reasonable estimate of fracture parameters, our understanding of the relationship between microseismic events and the induced hydraulic fracture is not complete. Hydrofracturing of the Bossier sandstone in east Texas was studied. Early on, hydrofracturing was modeled assuming a single fracture propagating from the treatment well, with geomechanical permeability changes determined from changes of fluid pressure or stress. Reservoir properties were matched to fit the bottomhole pressure for the hydrofracturing and production for an 80-day period such that the permeability used in this model reasonably represents the permeability of the reservoir. A technique was developed to simulate the occurrence of microseismic events during hydrofracturing by numerical modeling of fracture self-localization. This technique forms fractures the size of the grid cell and allows coalescence of neighboring fractures, depending on the evolution of stress in the reservoir. The analysis of the deformation modes (seismic-moment tensors) of such fractures showed that such deformation, even though locally and temporally variable, reflects the overall macroscopic deformation that would be caused by classical hydrofracture propagation. Technique To solve for the deformation associated with hydrofracturing, mechanical equations and equations for fluid motion in porous media must be solved. The equations are coupled through pressure and permeability. In this paper, because the calculation of permeability for this technique is still not fully resolved, the mechanical and fluid-flow solutions are coupled in only one way—by treating the pressure function, generated by the flow model with pressure-dependent permeability and a hydraulic fracture, as input into the mechanical equations. Then, the local 2D geomechanical solution is based on the constitutive and geometrical equations, and mechanical equilibrium equations, which are detailed in the full-length paper. The fracture formation is solved by use of damage theory. The damage initiates when the Mohr-Coulomb or tensile-failure criteria are satisfied locally. The heterogeneity of the material can be introduced through a random function following the Weibull distribution. The heterogeneity is input for strength of the material and Young’s modulus.

Simulation of two generalised Newtonian fluids flow in micropore with dead end

This research deals with the numerical simulation of Carreau and power-law fluids flow in an open capillary of a reservoir. The capillary is connected to a dead end. The finite volume method (FVM) on a structured and co-located grid has been used. The numerical method has been validated through the comparison of numerical results against the analytical solutions of power-law fluid flow in a planar channel. The effects of fluids, the operating conditions and the aspect ratio of dead end at the low Reynolds (Re) numbers on the oil sweeping from the dead end are investigated. The simulation results show that by increasing the power-law exponent in the case of power-law fluids, the swept depth in the dead end increases. However, according to the results, the effect of Re number on the flow pattern and the oil sweeping from the dead end is insignificant at the investigated conditions. In the case of Carreau model, at the conditions investigated, the swept area increases as the power-law exponent increases, but the Reynolds number has still minor effects on the flow pattern. Also, as the aspect ratio of dead end increases, the sweep efficiency increases.

Cell face velocity alternatives in a structured colocated grid for the unsteady Navier–Stokes equations

AbstractThe use of a colocated variable arrangement for the numerical solution of fluid flow is becoming more and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity fields in this arrangement can be handled via a special interpolation procedure for the calculation of the cell face velocity named pressure‐weighted interpolation method (PWIM) (AIAA J. 1983; 21(11):1525–1532). In this paper a discussion on the alternatives to extend PWIM to unsteady flows is presented along with a very simple criterion to ascertain if a given interpolation practice will produce steady results that are relaxation dependent or time step dependent. Following this criterion it will be shown that some prior schemes presented as time step independent are actually not, although by using special interpolations can be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be presented and new formulae free of Δt dependence will be derived. Several computational exercises will accompany the theoretical discussion to support our claims. Copyright © 2009 John Wiley & Sons, Ltd.

Three dimensional modelling of lava flow using Smoothed Particle Hydrodynamics

The paper describes the use of the grid-free Smoothed Particle Hydrodynamics (SPH) method to investigate lava flow from volcanic eruptions using real three dimensional topography in the form of Digital Terrain Models (DTM). Heat transfer resulting from conduction and radiation and solidification of the lava modelled via a variable viscosity are coupled to the fluid flow solution. Simulations show that the run-out distance and the nature of the lava flow are affected significantly by the lava viscosity and that this is dependent on the scale of the volcanic eruption, with solidification effects strongest on the smallest scale. SPH appears to be a highly effective technique for predicting lava flow with very good representations of the fluid free surface, close interaction with the complex topography, easy inclusion of the thermal and solidification effects leading to very plausible flow predictions. The pile-up of the lava at the front as it solidifies and the subsequent deceleration of the flow are easily modelled by SPH.

Mass transfer in vascular access ports

Numerical simulations have been performed to evaluate the fluid flow and mass transfer processes that occur in a human-body vascular-access port. Such ports are used to facilitate the frequent introduction of cleansed blood and other drugs into the body from external sources. Each of the infusion ports studied here consists of a reservoir and an attached tube-like catheter which delivers the infused medium to its point of use. All told, three unique infusion ports were investigated. Each had a particular geometry characterized by the shape of the reservoir and the mode of attachment of the catheter to the reservoir. The numerical simulations were three-dimensional and unsteady. Both Newtonian and non-Newtonian constitutive equations were employed for the fluid flow solutions and for the subsequent mass transfer solutions. The initiation of fluid motion was the injection of a controlled volume of fluid into the reservoir. In some cases, the injected fluid was the same as that in the reservoir, and in others it was different. For all the investigated infusion systems, no hemolysis (red blood cell destruction) was in evidence when blood was passed through the catheter. Potential hemolysis was averted in two of the systems due to the very low fluid velocities. As witnessed by the mass transfer results, the use of the reservoir as a chamber to mix a secondary liquid with blood is a viable strategy.

The Computational Modeling of Transitional Flow through a Transonic Linear Turbine: Comparative Performance of Various Turbulence Models

Aero-thermal characteristics of transitional flow through a highly loaded transonic linear turbine are studied at the design incidence using computational methods. The three-dimensional compressible turbulent flow through a turbine inlet guide vane is simulated using finite-volume method-based fluid flow solutions using both Reynolds-averaged Navier Stokes (RANS) equations-based turbulence models, and a dynamic large eddy simulation (LES) approach which is based on a Smagorinsky-Lilly subgrid scale (SGS) model. The calculations are made for exit isentropic Mach numbers ranging from 0.7 to 1.1, and for Reynolds numbers ranging from 5 × 105 to 2 × 106. The numerical results obtained from different turbulence model simulations are compared with each other, and with the experimental data available in the open literature in terms of integrated flow parameters, such as pressure and heat transfer coefficients for varying exit Mach and Reynolds numbers. The present numerical approach indicates a guide line that the present LES approach can be a reliable choice for turbomachinery flows.

A stable explicit fractional step procedure for the solution of heat and fluid flow through interfaces between saturated porous media and free fluids in presence of high source terms

AbstractIn this paper, porous medium‐free fluid interface problems in the presence of high source terms are studied for the first time by using a stable, accurate and efficient Artificial Compressibility (AC) Characteristic‐Based Split (CBS) algorithm. The interest in the AC‐CBS scheme has increased, as its matrix‐inversion free procedure offers the possibility of an easy and efficient parallelization. The present algorithm, recently introduced for the solution of porous media flows, presented some difficulties in solving complex interface problems. In this paper, the AC‐CBS scheme has been specifically developed to overcome such difficulties and produce an accurate, stable, and efficient solution for the generalized porous medium flow equations for forced, free, and mixed convection through interfaces. In order to obtain the present results, a stability analysis for the AC‐CBS scheme for the solution of problems with high source terms is carried out for the first time. The efficiency and the accuracy of the AC‐CBS algorithm are verified through comparison with analytical, numerical, and experimental data available in the literature. The authors consider three different types of interface benchmark problems: (i) forced convection in a horizontal channel; (ii) mixed convection in a vertical channel; and (iii) natural convection in a vertically divided cavity. Copyright © 2010 John Wiley & Sons, Ltd.