Turbulent diffusion of mass in circular pipe flow

An implicit finite difference scheme was used to solve the convective-diffusion equation to predict the steady-state transport of a conservative, neutrally bouyant tracer injected along the centreline into a fully developed turbulent pipe flow. Three different distributions for the radial mass diffusivity have been compared with two independent sets of experimental data. The results indicate that the distribution based on the turbulent kinematic eddy viscosity predicted by a k?l model produces the closest agreement between the numerical model predictions and the experimentally observed tracer distribution.     

Axial dispersion in pressure perturbed flow through an annular pipe oscillating around its axis

A method of moment is employed to study the axial dispersion of passive tracer molecules released in an unsteady pressure-driven flow through an annular pipe which is oscillating around its longitudinal axis. The flow unsteadiness is caused by the oscillation of the tube around its axis as well as by a periodic pressure gradient. A finite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective-diffusion equation for all time periods. The main objective is to study the nature of the dispersion coeffcient and mean concentration distribution under the sole as well as combined oscillation of the two driving forces. The behaviour of the dispersion coeffcient due to the variation of the aspect ratio, the absorption parameter for purely periodic flow has been examined and the sound response from dispersion coeffcient is found with the variation of these parameters in the sole presence of pressure pulsation. There is a remarkable difference in the behavior of the dispersion coeffcient depending on whether the ratio of two frequencies arising from the oscillations of the tube and the pressure gradient possesses a proper fraction or not. Oscillation of the tube produces much more dispersion than the pulsation of the pressure gradient and their combined effect leads to a further increase in dispersion. Tube oscillation shows a stronger effect on the dispersion coeffcient than the pressure pulsation though the effect of physical parameters are pronounced in the presence of pressure pulsation. The effect of the frequency parameter on the axial distribution of mean concentration is insensible when the oscillation of the annular tube is the only forcing. However this effect is much noticeable under the combined action of both forcing and much more effective under the sole influence of pressure pulsation.     

On the unsteady Poiseuille flow in a pipe

We show that in an unsteady Poiseuille flow of a Navier–Stokes fluid in an infinite straight pipe of constant cross-section, σ, the flow rate, F(t), and the axial pressure drop, q(t), are related, at each time t, by a linear Volterra integral equation of the second type, where the kernel depends only upon t and σ. One significant consequence of this result is that it allows us to prove that the inverse parabolic problem of finding a Poiseuille flow corresponding to a given F(t) is equivalent to the resolution of the classical initial-boundary value problem for the heat equation. G. P. Galdi: Partially supported by the NSF grant DMS–0404834. K. Pileckas: Supported by EC FP6 MCToK program SPADE2, MTKD–CT–2004–014508 A. L. Silvestre: Supported by FCT-Project POCI/MAT/61792/2004     

Numerical study of transition in a cylindrical pipe flow

We present numerical results of transition in a smooth cylindrical pipe by small periodical suction and blowing (PSB) at the inlet of a laminar pipe flow at Reynolds number 3000 based on the maximum velocity of the laminar flow and radius of the pipe. The spatial development of the PSB disturbance is simulated by means of pseudo-spectrum element method. The transitional process is described in the paper that the disturbances are growing rapidly in a short part of the pipe after they develop gradually in sufficient long distance. When the rapid growth of disturbances occurs the time step of integration should be decreased and then the flow transits to turbulent.     

Non-linear k– turbulence model results for flow over a building at full-scale

Turbulence modelling is a crucial question in the application of CFD to flows over buildings. The impinging flow and anisotropic nature of the turbulence present severe challenges. This paper presents a comparison of CFD against full-scale results. It differs from previous work which has concentrated on the wind-tunnel scale. In order to better account for the production of turbulent kinetic energy and the anisotropic nature of the turbulence a non-linear k– model is implemented. The results are discussed for different turbulence models and for the comparison of computed results with the measurements from full-scale.     

Asymptotic analysis of the nonsteady viscous flow with a given flow rate in a thin pipe

The nonsteady Navier–Stokes equations are considered in a thin infinite pipe with the small diameter ? in the case of the Reynolds number of order ?. The time-dependent flow rate is a given function. The complete asymptotic expansion is constructed and justified. The error estimate of order O(? ^J ) for the difference of the exact solution and the J-th asymptotic approximation is proved for any real J.     

Lift maximization in the flow around a contour over a screen

The problem of lift maximization for a smooth contour of given length placed in a flow near a screen is analyzed. The distance between the contour and the screen is assumed to be given. Optimal contours are constructed, and the lift coefficient is derived as a function of the contour-screen separation. The results can be useful as accurate upper bounds for the lift coefficient of actual ekranoplan airfoils.     

Computation of dilute two-phase flow in a pump

This paper is a report on a joint project between academia and industry which is concerned with computation of dilute two-phase flow through a pump in turbulent condition. The flow field for the continuous phase is computed using the Reynolds averaged Navier–Stokes equations together with mixing length turbulence modeling. The dispersed phase is treated using the Lagrangian approach by tracking it's trajectory along which the information is passed. It is found that the bubbles and small solid particles flow out of the chamber (between the rotating impeller and the casing wall) with the conveying fluid. The solid particles of relatively bigger sizes accumulate at the low pressure zones near the cashing wall or the rotating shaft.     

Global smooth resolvability for a model equations of fluid flow in a pipe

1. IntroductionWe consider here the existence of the global smooth (continuous) solution to the Cauchyproblem for the following quasilinear hyperbolic system modeling fluid flow in a pipe:Pt G., (1.1)Gi (D). P(p)' % = 0, (1 2)where p, G and p = p(p) denote, respectively, the mass density, the momentum density andthe pressure, f is the "Moody" friction factor (see [11 for details).The term --M accounts for the momentum loss due to viscous friction between thefluid and the pipe:all. S…     

Nonstationary flow for the Navier–Stokes equations in a cylindrical pipe

In cylindrical domain, we consider the nonstationary flow with prescribed inflow and outflow, modelled with Navier–Stokes equations under the slip boundary conditions. Using smallness of some derivatives of inflow function, external force and initial velocity of the flow, but with no smallness restrictions on the inflow, initial velocity neither force, we prove existence of solutions in . Copyright © 2012 John Wiley & Sons, Ltd.     

Long time behaviour of a flow in infinite pipe conforming to slip boundary conditions

The paper analyses long time behaviour of solutions of the Navier–Stokes equations in a two‐dimensional pipe‐like domain. The system is studied with perfect slip boundary conditions with arbitrary inflow conditions at infinity. The main results show the existence of global in time solutions and of an attractor for the dynamical system generated by the model. The paper also establishes an upper bound for the Hausdorff dimension of the attractor. Copyright © 2005 John Wiley & Sons, Ltd.     

On a non‐stationary fluid flow problem in an infinite periodic pipe

We study linearized, non‐stationary Navier–Stokes type equations with the given flux in an infinite pipe periodic of period length L with respect to . The existence and uniqueness of the solution is proved. Moreover, the convergence of the solution in a finite pipe of length to the L‐periodic solution as is investigated.     

Application of He's methods for laminar flow in a porous‐saturated pipe

In this paper the problem of fully developed laminar steady forced convection inside a porous‐saturated pipe with uniform wall temperature is presented and the homotopy perturbation method (HPM) and the variational iteration method (VIM) are employed to solve the differential equations governing the problem. The obtained results are valid for the whole solution domain with high accuracy. These methods can be easily extended to other linear and nonlinear equations and so can be found widely applicable in engineering and science. Copyright © 2009 John Wiley & Sons, Ltd.     

Computational modelling of slug flow in a capillary microreactor

The benefits of slug flow capillary microreactor exhibit the ability to adjust two individual transport mechanisms, i.e., convection inside the slug and diffusion between two consecutive slugs. The mass transfer rate is enhanced by internal circulation, which arises due to the shear between slug axis and continuous phase or capillary wall. The knowledge of circulation patterns within the slug plays an important role in the design of a capillary microreactor. Apart from this, well defined slug flow generation is a key activity in the development of methodology to study hydrodynamics and mass transfer. In the present paper we discuss computational fluid dynamics (CFD) modelling aspects of internal circulations (single phase) and slug flow generation (two-phase).     

Dynamic strength around a coated nanowire with surfaces/interfaces in a half solid

In this paper, the multiple scattering of anti-plane shear waves around a coated nanowire with surfaces/interfaces embedded in a half solid is studied, and the dynamic stress at the two surfaces/interfaces is presented. The boundary condition at the edge of the half solid is satisfied by the image method. The analytical solutions of displacements in the two half solids, in the coating layers, and inside the nanowire are expressed by wave function expansion method. The expanded mode coefficients are determined by satisfying the boundary conditions at the two surfaces/interfaces of the coated nanowire and the straight edge of the structure. The addition theorem for cylindrical wave function is employed to accomplish the superposition of displacement fields in the two half solids. Analyses show that the properties of the outer and inner interfaces show different effect on the dynamic stress around the nanowire. The dynamic stress distribution around the nanowire is also significantly related to the interfacial properties at the edge and the position of the nanowire.     

Minimizing flow time variance in a single machine system using genetic algorithms

In this paper, we address an n-job, single machine scheduling problem with an objective to minimize the flow time variance. We propose heuristic procedure based on genetic algorithms with the potential to address more generalized objective function such as weighted flow time variance. The development and implementation of the algorithm is supported with literature review and statistical analysis of the results. Some general guidelines to select the parameter values of the genetic algorithm are also developed using an experimental design approach.     

Strong solutions to the Stokes equations of a flow around a rotating body in weighted Lq spaces

We consider the motion of a fluid in the exterior of a rotating obstacle. This leads to a modified version of the Stokes system which we consider in the whole space ${\mathds R}^n$, n = 2 or n = 3 and in an exterior domain $D\subset {\mathds R}^3$. For every q ∈ (1, ∞) we prove existence of solutions and estimates in function spaces with weights taken from a subclass of the Muckenhoupt class A_q. Moreover, uniqueness is shown modulo a vector space of dimension 3. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Multiple solutions for the laminar flow in a porous pipe with suction at slowly expanding or contracting wall

In this paper, the asymptotic solution for the similarity equation of the laminar flow in a porous pipe with suction at expanding and contracting wall has been obtained using the singular perturbation method. However, this solution neglects exponentially small terms in the matching process. To take into account these exponentially small terms, a method involving the inclusion of exponentially small terms in a perturbation series was used to find the two solutions analytically. The series involving the exponentially small terms and expansion ratio predicts dual solutions. Furthermore, the result indicates that the expansion ratio has much important influence on the solutions. When the expansion ratio is zero, it is a special case that Terrill has discussed.     

Integrodifferential approaches to frequency analysis and control design for compressible fluid flow in a pipeline element

In this study, modelling, frequency analysis, and optimization of control processes are considered for the fluid flow in pipeline systems. A mathematical model of controlled pipeline elements with distributed parameters is proposed to describe the dynamical behaviour of compressible fluid which is transported in a long rigid tube. By exploiting specific functions representing cross-sectional forces and effective displacements as well as linear approximations of fluidic resistances, the original problem with non-uniform parameters is reduced to a partial differential equation (PDE) system with constant coefficients and homogeneous initial and boundary conditions. Three numerical approaches are applied to an efficient analysis of natural vibrations and reliable control-oriented modelling of pipeline elements. The conventional Galerkin method is compared with the method of integrodifferential relations based on a weak formulation of the constitutive laws. In the latter approach, the original initial-boundary value problem is reduced to the minimization of an error functional which provides explicit energy estimates of the solution quality. A novel projection approach is implemented on the basis of the Petrov–Galerkin method combined with the method of integrodifferential relations. This technique benefits from the advantages of the above-mentioned projection and variational approaches, namely sufficient numerical stability, a lower differential order, and an explicit quality estimation. Numerical optimization procedures, making use of a modified finite element technique, are proposed to obtain a feedforward control strategy for changing the pressure and mass flow inside the pipeline system to a desired operating state. At this given finite point of time, residual elastic oscillations inside the pipeline are minimized. Numerical results, obtained for ideal as well as viscous fluid models, are analysed and discussed.