Analysis of fluid flow in constricted tubes and ducts using body-fitted non-staggered grids

A finite volume method for the calculation of laminar and turbulent fluid flows inside constricted tubes and ducts is described. The selected finite volume method is based on curvilinear non-orthogonal co-ordinates (body-fitted co-ordinates) and a non-staggered grid arrangement. The grids are either generated by transfinite interpolation or an elliptic grid generator. The method is employed for calculation of laminar flows through a tube, a converging-diverging duct and different constricted tubes by both a two- and a three-dimensional computer program. In addition, turbulent flow through an axisymmetric constricted tube is calculated. Both the power law scheme and the second-order upwind scheme are used. The calculated results are compared with the experimental data and with other numerical solutions.     

Numerical solution of a casson fluid flow in the entrance of annular tubes

The solution of the momentum equation for a Casson fluid flowing in the entrance region of an annular tube has been obtained. The results have been presented for a large range of radii ratio and dimensionless yield stress. The mathematical accuracy of the numerical procedure is demonstrated by comparing the asymptotic velocity profiles at large axial distance with fully developed solution [1]. In addition, the results of the numerical solution for the case of yield stress equal to zero are compared with the entrance flow solution for a Newtonian fluid [2].     

Numerical simulation of vortical ideal fluid flow through curved channel

A numerical algorithm to study the boundary‐value problem in which the governing equations are the steady Euler equations and the vorticity is given on the inflow parts of the domain boundary is developed. The Euler equations are implemented in terms of the stream function and vorticity. An irregular physical domain is transformed into a rectangle in the computational domain and the Euler equations are rewritten with respect to a curvilinear co‐ordinate system. The convergence of the finite‐difference equations to the exact solution is shown experimentally for the test problems by comparing the computational results with the exact solutions on the sequence of grids. To find the pressure from the known vorticity and stream function, the Euler equations are utilized in the Gromeka–Lamb form. The numerical algorithm is illustrated with several examples of steady flow through a two‐dimensional channel with curved walls. The analysis of calculations shows strong dependence of the pressure field on the vorticity given at the inflow parts of the boundary. Plots of the flow structure and isobars, for different geometries of channel and for different values of vorticity on entrance, are also presented. Copyright © 2003 John Wiley & Sons, Ltd.     

Numerical and experimental study of turbulent impinging twin-jet flow

The two dimensional impinging circular twin-jet flow with no-cross flow is studied numerically and experimentally. The theoretical predications are carried out through numerical procedure based on finite volume method to solve the governing mass, momentum, turbulent kinetic energy and turbulent kinetic energy dissipation rate. The parameters studied were jet Reynolds number (9.5 × 10⁴  Re  22.4 × 10⁴), nozzle to plate spacing (3  h/d  12), nozzle to nozzle centerline spacing (l/d = 3, 5 and 8) and jet angle (0°  θ  20°). It is concluded that the stagnation primary point moves away in the radial main flow direction by increasing the jet angle. This shift becomes stronger by increasing the nozzle to nozzle centerline spacing (l/d). A secondary stagnation point is set up between two jets. The value of pressure at this point decreases by decreasing Reynolds number and/or increasing the jet angle.

The sub atmospheric region occurs on the impingement plate. It increases strongly by increasing Reynolds number and decreases as the jet angle and/or a nozzle to plate spacing increases. The spreading of jet decreases by increasing nozzle to plate spacing. The intensity of re-circulation zone between two jets decreases by increasing of h/d and jet angle. The increase of turbulence kinetic energy occurs within high gradient velocity.     

Gradients at a curved shock in reacting flow

The inviscid equations of motion for the flow at the downstream side of a curved shock are solved for the shock–normal derivatives. Combining them with the shock–parallel derivatives yields gradients and substantial derivatives. In general these consist of two terms, one proportional to the rate of removal of specific enthalpy by the reaction, and one proportional to the shock curvature. Results about the streamline curvature show that, for sufficiently fast exothermic reaction, no Crocco point exists. This leads to a stability argument for sinusoidally perturbed normal shocks that relates to the formation of the structure of a detonation wave. Application to the deflection–pressure map of a streamline emerging from a triple shock point leads to the conclusion that, for non–reacting flow, the curvature of the Mach stem and reflected shock must be zero at the triple point, if the incident shock is straight. The direction and magnitude of the gradient at the shock of any flow quantity may be written down using the results. The sonic line slope in reacting flow serves as an example. Extension of the results – derived in the first place for plane flow – to three dimensions is straightforward. Received 12 February 1997 / Accepted 10 June 1997     

On the physics of viscoplastic fluid flow in non-circular tubes

Flow of Bingham plastics through straight, long tubes is studied by means of a versatile analytical method that allows extending the study to a large range of tube geometries. The equation of motion is solved for general non-circular cross-sections obtained via a continuous and one-to-one mapping called the shape factor method. In particular the velocity field and associated plug and stagnant zones in tubes with equilateral triangular and square cross-section are explored. Shear stress normal to equal velocity lines, energy dissipation distribution and rate of flow are determined. Shear-thinning and shear-thickening effects on the flow, which cannot be accounted for with the Bingham model, are investigated using the Hershey-Bulkley constitutive formulation an extension of the Bingham model. The existence and the extent of undeformed regions in the flow field in a tube with equilateral triangular cross-section are predicted in the presence of shear-thinning and shear-thickening as a specific example. The mathematical flexibility of the analytical method allows the formulation of general results related to viscoplastic fluid flow with implications related to the design and optimization of physical systems for viscoplastic material transport and processing.     

Dynamics of the flow around colliding spheres

An investigation of the flow resulting from the collision of two spheres at low Reynolds numbers is presented. Each sphere starts from rest and traverses a distance of 5 sphere diameters to the point of contact. Experimental and numerical results are compared for a symmetric collision; that is, a collision between two spheres of the same diameter and travelling with the same velocity. The flow consists of two axisymmetric recirculation zones which become a pair of colliding vortex rings, expanding radially from the collision point. Several examples of unbalanced collisions are also presented numerically, with one or both of the velocity and diameter of the spheres altered. These collisions break the symmetry, altering the post-collision expansion of the vortex rings.     

Reservoir fluid flow through vertical fracture of thick stratum with underlying fluid interface

An exact solution is obtained for the problem of steady-state filtration of a heavy dense incompressible fluid in a thin, infinitely deep, inclined reservoir having a crack of given depth along the reservoir rise. The region of filtration of the lighter liquid (oil) has an impermeable upper boundary in the form of a horizontal fault line. Below the filtration region there is a free boundary, below which lies the region of stationary fluid (bottom water). The interface of the fluids, the fissure profile, and the reservoir fluid flow rate are determined from the solution of the problem on the basis of the given parameters (permeability of the reservoir and of the material filling the fissure, viscosity of the filtering fluid, specific weight of the upper and lower fluids, depth of the fissure, pressure differential between a point at the fissure and a point at the interface of the fluids). In the case when the thin reservoir is a vertical filtering layer, the considered flow is interpreted as the motion of the reservoir fluid through a vertical fissure of a thick reservoir (half-space) in the presence of an underlying fluid interface. The problem is solved in finite form with the aid of known analytic functions using integrals of the Cauchy type. The fundamental solution is first found of the special problem of flow with a point singularity. The fundamental solution is also of independent importance as an extension of the solution of certain known problems [1–4].     

Unsteady flow of an elastico-viscous fluid in tubes of uniform cross-section

In this paper, the uniqueness of solution for internal bounded unsteady flows of a shortmemory fluid is first established. Closed-form solutions are then obtained for the equations characterizing flows of such fluids in circular and rectangular tubes of uniform cross-section under an arbitrary pressure gradient. Special cases including the oscillatory flow between two parallel plates are discussed.     

Numerical study of effects of pulsatile amplitude for transitional turbulent pulsatile flow in pipes with ring‐type constrictions

The effects of pulsatile amplitude on sinusoidal transitional turbulent flows through a rigid pipe in the vicinity of a sharp‐edged mechanical ring‐type constriction have been studied numerically. Pulsatile flows were studied for transitional turbulent flow with Reynolds number (Re) of the order of 10⁴, Womersley number (Nw) of the order of 50 with a corresponding Strouhal number (St) of the order of 0.04. The pulsatile flow considered is a sinusoidal flow with dimensionless amplitudes varying from 0.0 to 1.0. Transitional laminar and turbulent flow characteristics in an alternative manner within the pulsatile flow fields were observed and studied numerically. The flow characteristics were studied through the pulsatile contours of streamlines, vorticity, shear stress and isobars. It was observed that fluid accelerations tend to suppress the development of flow disturbances. All the instantaneous maximum values of turbulent kinetic energy, turbulent viscosity, turbulent shear stress are smaller during the acceleration phase when compared with those during deceleration period. Various parametric equations within a pulsatile cycle have also been formulated through numerical experimentations with different pulsatile amplitudes. In the vicinity of constrictions, the empirical relationships were obtained for the instantaneous flow rate (Q), the pressure gradient (dp/dz), the pressure loss (P_loss), the maximum velocity (V_max), the maximum vorticity (ζ_max), the maximum wall vorticity (ζ_w,max), the maximum shear stress (τ_max) and the maximum wall shear stress (τ_w,max). Elliptic relation was observed between flow rate and pressure gradient. Quadratic relations were observed between flow rate and the pressure loss, the maximum values of shear stress, wall shear stress, turbulent kinematic energy and the turbulent viscosity. Linear relationships exist between the instantaneous flow rate and the maximum values of vorticity, wall vorticity and velocity. The time‐average axial pressure gradient and the time average pressure loss across the constriction were observed to increase linearly with the pulsatile amplitude. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical investigation of tube flow with suction through permeable walls

The dependence of turbulent tube flow parameters on the suction intensity and the suction region length is determined by numerical simulation. The comparison of the calculated results with the available experimental data shows mainly their agreement reflecting the main distinctive features of fairly complicated processes of flow rearrangement under suction.     

棱柱绕流流动的数值模拟

利用数值方法对长宽比为1／3, 1和3的棱柱绕流在雷诺数为100的非稳态流动特性进行了分析和研究。采用有限体积法对棱柱绕流的二维流动N-S方程进行离散求解,分析和研究了非稳态的棱柱绕流流场,升力系数,阻力系数和涡动特性,数值模拟的结果与相关文献的数据比较吻合。通过上述研究能够为了解棱柱绕流的非稳态流动特性提供有力的帮助。而对棱柱三维流动的模拟分析和对雷诺数的变化对棱柱流动特性的影响进行研究,将为掌握棱柱绕流的工程特性打下基础。     

Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions

The subgrid-scale (SGS) model in a large-eddy simulation (LES) operates on a range of scales which is marginally resolved by discretization schemes. Accordingly, the discretization scheme and the subgrid-scale model are linked. One can exploit this link by developing discretization methods from subgrid-scale models, or the converse. Approaches where SGS models and numerical discretizations are fully merged are called implicit LES (ILES). Recently, we have proposed a systematic framework for the design, analysis, and optimization of nonlinear discretization schemes for implicit LES. In this framework parameters inherent to the discretization scheme are determined in such a way that the numerical truncation error acts as a physically motivated SGS model. The resulting so-called adaptive local deconvolution method (ALDM) for implicit LES allows for reliable predictions of isotropic forced and decaying turbulence and of unbounded transitional flows for a wide range of Reynolds numbers. In the present paper, ALDM is evaluated for the separated flow through a channel with streamwise-periodic constrictions at two Reynolds numbers Re = 2,808 and Re = 10,595. We demonstrate that, although model parameters of ALDM have been determined for isotropic turbulence at infinite Reynolds number, it successfully predicts mean flow and turbulence statistics in the considered physically complex, anisotropic, and inhomogeneous flow regime. It is shown that the implicit model performs at least as well as an established explicit model.      

Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.     

The transient two-dimensional flow through double porous media

This paper presents the analytical solutions in Laplace domain for two-dimensionalnonsteady flow of slightly compressible liquid in porous media with double porosity by usingthe methods of integral transforms and variables separation.The effects of the ratio ofstorativities ω,interporosity flow parameter λ,on the pressure behaviors for a verticallyfractured well with infinite conductivity are investigated by using the method of numericalinversion.The new log-log diagnosis graph of the pressures is given and analysed.     

Multifield computational fluid dynamics model of particulate flow in curved circular tubes

Limitations of mass transfer resulting from non-optimized fluid mechanics can severely affect the performance of synthetic membrane filtration systems. To improve membrane efficiency, modern applications of this technology have extensively used curved membrane ducts that take advantage of Dean vortices (i.e., curvature-induced secondary flows) to minimize membrane fouling. This paper is concerned with a complete three-dimensional analysis of single-phase and two-phase particle/liquid flows around a curved membrane tube. The proposed multidimensional model was implemented in an advanced (next-generation) multiphase computational fluid dynamics (CFD) solver, NPHASE. The results of simulations have been validated against experimental data and compared against other findings available in the literature. The consistency and accuracy of the present approach have been demonstrated. The novel aspects of this work include: the demonstration that azimuthal vortices may bifurcate at Dean numbers lower than previously anticipated, the use of vorticity magnitude as a measure of vortex strength, and the explanation of the role that Dean vortices play to mitigate the effect of gravity on particle settling. The overall results have direct relevance to synthetic membrane fouling during filtration of particle suspensions.     

Unsteady fluid flow and heat transfer over a bank of flat tubes

Transient numerical simulations of fluid flow and heat transfer over a bank of flat tubes have been carried for both in-line and staggered configurations for the following boundary conditions: (a) isothermal and (b) isoflux. The effect of Reynolds number, Prandtl number, length ratio, and the height ratio, on the Nusselt number, and the dimensionless pressure drop are elucidated. Correlations are proposed for both pressure drop and Nusselt number and optimum configurations have been determined.     

Turbulent flow of mildly elastic fluids through rotating straight circular tubes

The turbulent flow of mildly elastic drag reducing fluids through a straight tube rotating around an axis perpendicular to its own is analysed using boundary layer approximations. The momentum integral approach is used and the governing equations have been solved numerically using the Runge-Kutta-Merson method. The influence of the Deborah number on the velocity distribution and the boundary layer thickness has been exemplified through the analysis. NCL Communication No. 3354.     

Generalized flow analysis of non-Newtonian visco-elastic fluid flow through fractal reservoir

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