Nested separatrices in simple shear flows: the effect of localized disturbances on stagnation lines

The effects of localized two-dimensional disturbances on the structure of shear flows featuring a stagnation line are investigated. A simple superposition of a planar Couette flow and Moffatt's [J. Fluid Mech. 18, 1--18 (1964)] streamfunction for the decay of a disturbance between infinite stationary parallel plates shows that in general the stagnation line is replaced by a chain of alternating elliptic and hyperbolic stagnation points with a separation equal to 2.78 times the half-gap between the plates. The flow structure associated with each saddle point consists of a homoclinic separatrix and two other separatrices which locally diverge but become parallel far from the disturbance. This basic structure repeats to give a sequence of nested separatrices permitting the streamfunction to approach that of simple shear flow far from the disturbance. Using the finite element method, the specific disturbance caused by a stationary cylinder placed on the stagnation line is considered, and results confirm the existence of the stagnation point chain, with computed separations and velocity damping ratios in very good agreement with those obtained from the Couette-Moffatt superposition. Numerical solutions also illustrate that while Reynolds number greatly affects the stagnation point separation and velocity damping ratio, these two quantities are the same for any pair of adjacent stagnation points in a given chain. Insight gained from the analysis of planar shear flows is applied to the flow in a half-filled horizontal annulus between rotating coaxial cylinders, and is used to explain why only certain flow patterns from the range of mathematically possible structures arise in previous numerical solutions. By way of contrast, the concentric annulus solution is then perturbed to allow for a small eccentricity. The non-uniformity of the inter-cylinder gap is shown to destroy the chain of stagnation points, but also to unfold additional flow structures not realizable when the gap is uniform

Flow in a double-film-fed fluid bead between contra-rotating rolls, Part 1: equilibrium flow structure

In multiple-roll coaters thin liquid films are transferred from roll to roll by means of liquid ‘beads’ which occupy the small gaps between adjacent rolls. Double-Film-Fed (DFF) beads are those which feature two ingoing films instead of the usual one, and arise in the intermediate stages of certain types of roll coater. One of the ingoing films, h1, is supplied from the previous inter-roll gap while the other, h2, ‘returns’ from the subsequent gap. Such a flow is investigated here under the conditions of low flow rate, small capillary number and negligible gravity and inertia, using lubrication theory and finite element analysis. The thickness of film h1 is fixed independently, while that of h2 is specified as a fraction, [zeta], of the film output on the same roll. This simple approach allows a degree of feedback between the output and input of the bead, and enables one to simulate different conditions in the subsequent gap. Predictions of outgoing film thicknesses made using the two models agree extremely well and show that, for each value of [zeta] < 1, one outgoing film thickness decreases monotonically with speed ratio, S, while the other features a maximum. Good agreement is also seen in the pressure profiles, which are entirely sub-ambient in keeping with the small capillary number conditions. The finite element solutions reveal that in the ‘zero-flux’ case (when [zeta] = 1) the flow structures are very similar to those seen in an idealized cavity problem. In the more general ([zeta] < 1) situation, as in single-film-fed meniscus roll coating, several liquid transfer-jets occur by which liquid is conveyed through the bead from one roll to the other. The lubrication model is used to calculate several critical flow rates at which the flow is transformed, and it is shown that when the total dimensionless flow rate through the bead exceeds 1/3, the downstream flow structure is independent of the relative sizes of the ingoing films

Stokes flow in a half-filled annulus between rotating coaxial cylinders

A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii R-i,R-0 rotating with peripheral speeds U-i,U-0). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, phi, as a function of radius ratio (R) over bar = R-i/R-0 and speed ratio S = U-i/U-0. Results show that for S > 0 (S 1, a sequence of 'flow bifurcations' leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gap limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S 0 and aspect ratios are small (except near S = 1). For S > 0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both (R) over bar and S

Stirring and transport enhancement in a continuously modulated free-surface flow

The transport of fluid from a recirculation region adjacent to a free surface is studied using a numerical method validated with experimental flow visualization. The flow is an example of a liquid film coating process, and consists of two counter-rotating rolls placed side-by-side and half-submerged in a bath of fluid. In the gap between the rolls a recirculation zone exists just below the free surface, around which the flow splits into two films. Fluid recirculating for long periods has been identified as a source of coating defects, so this paper considers a possible method of inducing stirring. The flow is modulated by driving one of the rolls through a Hooke's joint, which delivers a well-characterized periodic perturbation to the roll speed. In response to this speed modulation, the free surface undergoes a periodic change in position and shape which drives an exchange of fluid between the recirculation region and the surrounding flow. The amplitude of the free-surface motion is strongly dependent on modulation frequency. The dynamics of the free surface preclude a quasi-steady approach, even in the small-frequency limit, and so a fully time-dependent analysis based on the finite element method is employed. Trigonometric temporal interpolation of the finite element data is used to make passive tracer advection calculations more efficient, and excellent agreement is seen between simulation and experiment. Computations of the stable and unstable invariant manifolds associated with periodic points on the free surface reveal that the exchange of fluid is governed by a self-intersecting turnstile mechanism, by which most fluid entrained during a modulation cycle is ejected later in the same cycle. Transport over several cycles is explored by observation of the evacuation of passive tracers initially distributed uniformly in the recirculation zone. Results demonstrate the persistence of unmixed cores whose size is dependent on the modulation frequency. By considering the percentage of tracers remaining after a fixed number of cycles, contours in frequency-amplitude space show that for each modulation amplitude there is a frequency which produces the most effective transport, with up to 80 % of tracers removed by a modulation which produces only a 5 % change in film thickness. Finally it is shown how modulation of both rolls at slightly different phases can reduce the film thickness variation to about 1 % while maintaining the level of transport

Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver. Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography. Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function. An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion

A methodology for determining the dynamic exchange of resources in nuclear fuel cycle simulation

Simulation of the nuclear fuel cycle can be performed using a wide range of techniques and methodologies. Past efforts have focused on specific fuel cycles or reactor technologies. The CYCLUS fuel cycle simulator seeks to separate the design of the simulation from the fuel cycle or technologies of interest. In order to support this separation, a robust supply–demand communication and solution framework is required. Accordingly an agent-based supply-chain framework, the Dynamic Resource Exchange (DRE), has been designed implemented in CYCLUS. It supports the communication of complex resources, namely isotopic compositions of nuclear fuel, between fuel cycle facilities and their managers (e.g., institutions and regions). Instances of supply and demand are defined as an optimization problem and solved for each timestep. Importantly, the DRE allows each agent in the simulation to independently indicate preference for specific trading options in order to meet both physics requirements and satisfy constraints imposed by potential socio-political models. To display the variety of possible simulations that the DRE enables, example scenarios are formulated and described. Important features include key fuel-cycle facility outages, introduction of external recycled fuel sources (similar to the current mixed oxide (MOX) fuel fabrication facility in the United States), and nontrivial interactions between fuel cycles existing in different regions

Aerodynamic shape optimization of a low drag fairing for small livestock trailers

Small livestock trailers are commonly used to transport animals from farms to market within the United Kingdom. Due to the bluff nature of these vehicles there is great potential for reducing drag with a simple add-on fairing. This paper explores the feasibility of combining high-fidelity aerodynamic analysis, accurate metamodeling, and efficient optimization techniques to find an optimum fairing geometry which reduces drag, without significantly impairing internal ventilation. Airflow simulations were carried out using Computational Fluid Dynamics (CFD) to assess the performance of each fairing based on three design variables. A Moving Least Squares (MLS) metamodel was built on a fifty-point Optimal Latin Hypercube (OLH) Design of Experiments (DoE), where each point represented a different geometry configuration. Traditional optimization techniques were employed on the metamodel until an optimum geometrical configuration was found. This optimum design was tested using CFD and it matched closely to the metamodel prediction. Further, the drag reduction was measured at 14.4% on the trailer and 6.6% for the combined truck and trailer

Ventilation of small livestock trailers

A large number of livestock is transported to market in small box trailers. The welfare of animals transported in this way is now assuming greater importance with the onset of tougher EU legislation. This paper presents the first study into the ventilation of small livestock trailers using experimental and computational methods. Wind tunnel studies, using a 1/7th scale model, highlight the important influence of the towing vehicle and trailer design on the airflow within the trailer. Detailed CFD analysis agrees well with the wind tunnel data and offers the ability to assess the impact of design changes

White sorghum grain (Funk\u27s G766W) and elevator-run red sorghum grain compared for fattening cattle

An new white variety of sorghum grain (Funk\u27s G766W) has been reported to be higher in digestible dry matter and protein than elevator-run, rod sorghum grain. A 120-day field trial was conducted on the George and Vernon Miller farm near Great Bend to compare the two sorghum grain types under feed-lot conditions

Simulations with different lattice Dirac operators for valence and sea quarks

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a "mixed" action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to O(a), and the appropriate low energy chiral effective Lagrangian is constructed, including the leading O(a) contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.Comment: 17 pages, 1 ps figure (2 clarification paragraphs added