Flow limitation in convective dominated open capillary channel flows

In this work the flow rate limitation of convective dominated flows in open capillary channels is investigated experimentally. Since irreversible flow losses are small in this type of flow, the flow variables are approximately symmetrical with respect to the middle of the channel. Therefore a very precise proof of the origin of the limitation is possible. A new technique for the determination of the key property, the speed index, is presented. The speed index confirms that also in convective dominated flows the flow limitation occurs due to a choking-effect. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

TVD scheme for computing open channel wave flows

For the shallow water equations in the first approximation (Saint-Venant equations), a TVD scheme is developed for shock-capturing computations of open channel flows with discontinuous waves. The scheme is based on a special nondivergence approximation of the total momentum equation that does not involve integrals related to the cross-section pressure force and the channel wall reaction. In standard divergence difference schemes, most of the CPU time is spent on the computation of these integrals. Test computations demonstrate that the discontinuity relations reproduced by the scheme are accurate enough for actual discontinuous wave propagation to be numerically simulated. All the qualitatively distinct solutions for a dam collapsing in a trapezoidal channel with a contraction in the tailwater area are constructed as an example.     

Oscillating two-phase channel flows

Zusammenfassung Die in einem Kreisrohr durch pulsierende Kräfte in Bewegung gesetzte Strömung einer inkompressiblen Flüssigkeit mit schwebenden kugelförmigen Teilchen wird analysiert. Das Lösungsverfahren beruht auf der Zusammenfassung der Teilchen- und Flüssigkeit-Impulsgleichungen zu einer einzelnen Integrodifferentialgleichung, die durch die Laplace-Transformation gelöst wird. Die Geschwindigkeit von Teilchen und Flüssigkeit und der Reibungswiderstand werden als Polynome angegeben und durch einen Computer numerisch berechnet. Überraschenderweise ergibt sich, dass im Gleichgewichtsgrenzfall das Teilchen-Flüssigkeit-System, das durch eine stetige Massenkraft in Bewegung gesetzt wird, sich wie ein Teilchenloses verhält. Es wird auch gezeigt, dass die Wirkung der Massen- und Druckkräfte etwa gleich ist, wenn die Dichte des Teilchenmaterials viel grösser als die Dichte der Flüssigkeit ist. Die Wirkung dieser Kräfte ist verschieden, wenn diese beiden etwa gleich sind.     

Energy stability of channel flows

Zusammenfassung Die Energiemethode wird zur Untersuchung der Stabilität einer beliebigen Kanalströmung angewandt. Es wird eine auf Eigenwertabschätzungen basierte qualitative Beschreibung der Fläche (, ) gegeben, welche die Schranke für den Instabilitätsbereich in Abhängigkeit von Längs- bzw. Querwellenzahl der Störungen darstellt. Eine allgemeine untere Grenze für die minimalisierende Querwellenzahl und den zugehörigen Eigenwert (0, ) wird angegeben. Das Problem der Energiestabilität wird dann für eine Klasse von Geschwindigkeitsprofilen mit Wendepunkt gelöst. Die durch numerische Integration erhaltenen Ergebnisse werden mit den Ergebnissen der linearen Stabilitätstheorie verglichen.     

Randomly oscillating turbulent channel flows

The velocity response to a sinusoidally oscillating pressure gradient is obtained for turbulent flow in a two-dimensional channel. The statistical relations between a spectrum of such pressure pulsations and the resulting spectrum of velocity oscillations are then written in terms of a spectral transfer function. This function, which incorporates the dynamic solution is complicated, but is well approximated with a simple expression.

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Zusammenfassung Für turbulente Strömung in einem zweidimensionalen Kanal wird die Geschwindigkeitsverteilung, die durch einen sinusoidal oszillierenden Druckgradient verursacht ist,

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Nomenclature A, B coefficients defined by comparison of Equation (1) with the appropriate dynamical equation foru - a half width of channel, or radius of pipe - b rate of increase of withy - c defined in Equation (31) - d defined in Equation (32) - f normalized spectral density of pressure oscillations - g normalized spectral density of velocity oscillations - h turbulent viscosity parameter defined in Equation (26) - I - K _n amplitude of the individual pressure oscillations - L ₁,L ₂,L ₃,L ₄,L ₅,L ₆ functions defined by Equations (18) (19) (20) (21) (24) (25) - m defined in Equation (30) - n frequency of pressure and velocity oscillations - p pressure - p _x defined in Equation (2) - R _p autocorrelation coefficient for pressure oscillations - R _u autocorrelation coefficient for velocity oscillations - t time - u axial velocity - w variable defined after Equation (15) - x axial position coordinate - y transverse position coordinate - z variable defined after Equation (15) - eddy diffusivity for momentum - dimensionless frequency, defined in Equation (7), for laminar case - _t dimensionless frequency, defined after Equation (16), for turbulent case - function defined in Equation (13) - laminar kinematic viscosity - variable displacement in time - fluid density - spectral transfer function - variable defined after Equation (16) This study was supported in part by the R. L. Albrook Hydraulic Laboratory of the Wash. State Univ. Division of Industrial Research.     

Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method

Centre manifold method is an accurate approach for analytically constructing an advection–diffusion equation (and even more accurate equations involving higher-order derivatives) for the depth-averaged concentration of substances in channels. This paper presents a direct numerical verification of this method with examples of the dispersion in laminar and turbulent flows in an open channel with a smooth bottom. The one-dimensional integrated radial basis function network (1D-IRBFN) method is used as a numerical approach to obtain a numerical solution for the original two-dimensional (2-D) advection–diffusion equation. The 2-D solution is depth-averaged and compared with the solution of the 1-D equation derived using the centre manifolds. The numerical results show that the 2-D and 1-D solutions are in good agreement both for the laminar flow and turbulent flow. The maximum depth-averaged concentrations for the 1-D and 2-D models gradually converge to each other, with their velocities becoming practically equal. The obtained numerical results also demonstrate that the longitudinal diffusion can be neglected compared to the advection.     

Symplectic flows on the open ball

We construct a complete, infinitesimally symplectic vectorfield on the open unit ball in R⁴ with no zeros. This shows that there are symplectic diffeomorphisms of the ball with no fixed points.     

Similarity of homoclinic tangles in open planar flows

An invariance of the structure of the homoclinic tangle with respect to a simultaneous rescaling of the perturbation amplitude and the coordinates in the neighborhood of the saddle was recently studied in low dimensional chaotic Hamiltonian systems. A similar property exists in open systems with transient chaotic behaviour. The scaling constant depends on the ratio of the perturbation frequency and the eigenvalue of the linearized system at the saddle. This result can be used to analyze the structure of the mixing layers in time-dependent two-dimensional open flows. The invariance of the homoclinic tangle is demonstrated numerically for a weakly perturbed flow of ideal fluid around a cylinder.     

Surfactant-driven instability in two-fluid pipe and channel flows

Recent work on the stability of two-layer channel flow, with either smooth or corrugated walls, and core-annular flow is discussed with the emphasis on the potentially destabilising effect of an insoluble surfactant. Linearised normal mode analyses are conducted to identify unstable parametric conditions, and these are followed up by computer simulations which confirm the linear results and, furthermore, reveal a rich array of dynamical behaviour in the nonlinear regime. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

河渠非定常流的精确边界能控性

借助于一阶拟线性双曲型方程组混合初边值问题的半整体C^1解理论对单个河道及弦状网络河道中的非定常流动分别讨论了在闸门边界条件下的精确边界能控性问题,并对在泄洪边界条件下的精确边界能控性进行了相应的讨论。     

Semiclassical lattice hydrodynamics of rarefied channel flows

The two-dimensional channel flows of gas of arbitrary statistics in the slip and transition regimes as characterized by the Knudsen number are studied using a newly developed semiclassical lattice Boltzmann method. The method is directly derived by projecting the Uehling-Uhlenbeck Boltzmann-BGK equations onto the tensor Hermite polynomials using moment expansion method. The intrinsic discrete nodes of the Gauss-Hermite quadrature provide the natural lattice velocities for the semiclassical lattice Boltzmann method. The mass flow rates and the velocity profiles are calculated for the three particle statistics over wide range of Knudsen numbers and the Knudsen minimum can be captured. The results indicate distinct characteristics of the effects of quantum statistics.     

Separation of magnetic particles in channel flows by BEM

In-line separation of suspensions can become difficult in case of particles with comparable values of densities. For flows in micro devices in such cases gravitational settling is inefficient, and other separation techniques must be applied. In case of magneto active particles, the action of Kelvin magnetic force in a non-uniform magnetic field could be used in order to achieve a higher degree of particles separation. The contribution therefore deals with Euler-Lagrangian formulation of dilute two-phase flows. The Boundary element based computational algorithm solves the incompressible Navier-Stokes equations written in velocity-vorticity formulation. The non-uniform magnetic field is defined analytically for the case of a set of long thin wires. The particle trajectories are computed by applying the 4th order Runge-Kutta method. The computed test case consists of a narrow channel with laminar flow of suspension under Re = 1 − 10. Particle trajectories under the influence of a non-uniform magnetic field are computed for the case of magnetite and aluminium particles suspended in water. The efficiency of separation on basis of particle trajectories for different values of Re number and magnetic field strength is performed, clearly indicating superior separation of magneto active particles. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global controllability between steady supercritical flows in channel networks

We consider a tree‐like network of open channels with outflow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the flow is modelled by the de St. Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in finite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in the class of C1‐functions, so no shocks occur. Copyright 2004 John Wiley & Sons, Ltd.     

Stochastic flows of diffeomorphisms on an open set in rn

In this paper, we will give sufficient conditions for the solution to a stochastic differential equation (SDE) on an open set D in R" to define a stochastic flow of diffeomorphisms of D onto itself. Since a necessary and sufficient condition for the solution to determine a stochastic flow of diffeomorphisms is that the original SDE and its adjoint SDE are both strictly conservative, we will concentrate our attention on finding sufficient conditions for the SDE to be strictly conservative. It will be etablished that the strict conservativeness follows if the vector fields governing the SDE decay suitably near the boundary dD in the direction transversal to 3D and some additional assumptions are satisfied.     

Poisson flows in single class open networks of quasireversible queues

This paper analyzes open networks of quasireversible nodes with a single class of customers and in equilibrium. A simple argument shows, under a stability conditions, that a flow on a link of such a network is Poisson if and only if the link is not part of a loop. This loop criterion is shown to apply to the usual quasireversible networks with bounded service rates.     

Thin visco–capillary film flows in inclined rectangular channels

Starting from an exact solution for the velocity profile and the free surface the influence of side walls on a gravity driven thin film flow is studied in detail. A parameter study shows the ‘velocity overshoot’ — a structural change in the velocity profile and its dependence to the capillary elevation of the fluid at the side walls.     

Vortex control in channel flows using translational invariant cost functionals

The use of translation invariant cost functionals for the reduction of vortices in the context of shape optimization of fluid flow domain is investigated. Analytical expressions for the shape design sensitivity involving different cost functionals are derived. Channel flow problems with a bump and an obstacle as possible control boundaries are taken as test examples. Numerical results are provided in various graphical forms for relatively low Reynolds numbers. Striking differences are found for the optimal shapes corresponding to the different cost functionals, which constitute different quantification of a vortex.     

Sub-optimal constant-volume control for open channel networks

A state variable mathematical model for use in the synthesis of automatic control systems for open-channel networks is presented. The system considered here consists of n-cascaded reaches joined by control gates.The linear time invariant model consists of a controllable and observable representation where the state variables are the stored water volume variations in each reach and the control signals are the variations of the control gates opening sections. The model derives, through appropriate simplifications, from a more complex one in terms of transfer functions which was derived by linearizing the Saint-Venant equations.The problem of a linear quadratic optimal regulator is formulated in classical terms for the canal system and the constant-volume control laws obtained for the simplified model have been imposed on the complex one: such a control is therefore to be considered sub-optimal.The results of a digital simulation of the controlled system behaviour indicate that the system operates with practically constant stored water volumes in each reach and that such behaviour is fairly close to that of a pressure-water pipe system.