T-WAS and T-XAS algorithms for fiber-loop optical buffers

In optical packet/burst switched networks fiber loops provide a viable and compact means of contention resolution. For fixed size packets it is known that a basic void-avoiding schedule (VAS) can vastly outperform a more classical pre-reservation algorithm as FCFS. For the setting of a uniform distributed packet size and a restricted buffer size we proposed two novel forward-looking algorithms, WAS and XAS, that, in specific settings, outperform VAS up to 20% in terms of packet loss. This contribution extends the usage and improves the performance of the WAS and XAS algorithms by introducing an additional threshold variable. By optimizing this threshold, the process of selectively delaying packet longer than strictly necessary can be made more or less strict and as such be fitted to each setting. By Monte Carlo simulation it is shown that the resulting T-WAS and T-XAS algorithms are most effective for those instances where the algorithms without threshold can offer no or only limited performance improvement

Three-dimensionality in quasi-two dimensional flows: recirculations and barrel effects

A scenario is put forward for the appearance of three-dimensionality both in quasi-2D rotating flows and quasi-2D magnetohydrodynamic (MHD) flows. We show that 3D recirculating flows and currents originate in wall boundary layers and that, unlike in ordinary hydrodynamic flows, they cannot be ignited by confinement alone. They also induce a second form of three-dimensionality with quadratic variations of velocities and current across the channel. This scenario explains both the common tendency of these flows to two-dimensionality and the mechanisms of the recirculations through a single formal analogy covering a wide class of flow including rotating and MHD flows. These trans-disciplinary effects are thus active in atmospheres, oceans or the cooling blankets of nuclear fusion reactors.Comment: 6 pages, 1 Figur

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels

Stagnation–saddle points and flow patterns in Stokes flow between contra-rotating cylinders

The steady flow is considered of a Newtonian fluid, of viscosity mu, between contra-rotating cylinders with peripheral speeds U-1 and U-2 The two-dimensional velocity field is determined correct to O(H-0/2R)(1/2), where 2H(0) is the minimum separation of the cylinders and R an 'averaged' cylinder radius. For flooded/moderately starved inlets there are two stagnation-saddle points, located symmetrically about the nip, and separated by quasi-unidirectional flow. These stagnation-saddle points are shown to divide the gap in the ratio U-1 : U-2 and arise at \X\ = A where the semi-gap thickness is H(A) and the streamwise pressure gradient is given by dP/dX = mu(Ulf U-2)/H-2(A). Several additional results then follow. (i) The effect of non-dimensional flow rate, lambda: A(2) = 2RH(0)(3 lambda - 1) and so the stagnation-saddle points are absent for lambda 1/3. (ii) The effect of speed ratio, S = U-1/U-2: stagnation-saddle points are located on the boundary of recirculating flow and are coincident with its leading edge only for symmetric flows (S = i). The effect of unequal cylinder speeds is to introduce a displacement that increases to a maximum of O(RH0)(1/2) as S --> 0. Five distinct flow patterns are identified between the nip and the downstream meniscus. Three are asymmetric flows with a transfer jet conveying fluid across the recirculation region and arising due to unequal cylinder speeds, unequal cylinder radii, gravity or a combination of these. Two others exhibit no transfer jet and correspond to symmetric (S = 1) or asymmetric (S not equal 1) flow with two asymmetric effects in balance. Film splitting at the downstream stagnation-saddle point produces uniform films, attached to the cylinders, of thickness H-1 and H-2, where H-1/H-2 = S(S + 3)/3S + 1, provided the flux in the transfer jet is assumed to be negligible. (iii) The effect of capillary number, Ca: as Ca is increased the downstream meniscus advances towards the nip and the stagnation-saddle point either attaches itself to the meniscus or disappears via a saddle-node annihilation according to the flow topology. Theoretical predictions are supported by experimental data and finite element computations

Transport in finite size systems: an exit time approach

In the framework of chaotic scattering we analyze passive tracer transport in finite systems. In particular, we study models with open streamlines and a finite number of recirculation zones. In the non trivial case with a small number of recirculation zones a description by mean of asymptotic quantities (such as the eddy diffusivity) is not appropriate. The non asymptotic properties of dispersion are characterized by means of the exit time statistics, which shows strong sensitivity on initial conditions. This yields a probability distribution function with long tails, making impossible a characterization in terms of a unique typical exit time.Comment: 16 RevTeX pages + 6 eps-figures include

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

Quantifying the loss of methane through secondary gas mass transport (or 'slip') from a micro-porous membrane contactor applied to biogas upgrading

Secondary gas transport during the separation of a binary gas with a micro-porous hollow fibre membrane contactor (HMFC) has been studied for biogas upgrading. In this application, the loss or ‘slip' of the secondary gas (methane) during separation is a known concern, specifically since methane possesses the intrinsic calorific value. Deionised (DI) water was initially used as the physical solvent. Under these conditions, carbon dioxide (CO2) and methane (CH4) absorption were dependent upon liquid velocity (VL). Whilst the highest CO2 flux was recorded at high VL, selectivity towards CO2 declined due to low residence times and a diminished gas-side partial pressure, and resulted in slip of approximately 5.2% of the inlet methane. Sodium hydroxide was subsequently used as a comparative chemical absorption solvent. Under these conditions, CO2 mass transfer increased by increasing gas velocity (VG) which is attributed to the excess of reactive hydroxide ions present in the solvent, and the fast conversion of dissolved CO2 to carbonate species reinitiating the concentration gradient at the gas-liquid interface. At high gas velocities, CH4 slip was reduced to 0.1% under chemical conditions. Methane slip is therefore dependent upon whether the process is gas phase or liquid phase controlled, since methane mass transport can be adequately described by Henry's law within both physical and chemical solvents. The addition of an electrolyte was found to further retard CH4 absorption via the salting out effect. However, their applicability to physical solvents is limited since electrolytic concentration similarly impinges upon the solvents' capacity for CO2. This study illustrates the significance of secondary gas mass transport, and furthermore demonstrates that gas-phase controlled systems are recommended where greater selectivity is required

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