ALBERT

Description: Two-dimensional, unsteady flow of a viscous, incompressible fluid in a stepped channel has been studied by the numerical solution of the Navier-Stokes equation using an accurate finite-difference method. With a sinusoidal mass flow rate, the problem has three governing parameters: the Reynolds number, the Strouhal number, and the step height. The effects on the flow of varying all three parameters has been investigated systematically. In appropriate parameter regimes, a strong vortex wave' is generated during the forward phase when the flow is over the step into the expansion. Secondary effects on the wave can result in a complex flow pattern with each major structure of the flow consisting of an eddy with more than one core. No such wave is found during the reverse phase of the flow. The generation and development of the wave is examined in some detail, and our results are compared and contrasted with those of previous studies, both experimental and theoretical, of flow in non-uniform vessels. © 1993, Cambridge University Press. All rights reserved.

Description: An experimental and numerical investigation of the density distribution produced in a container by a negatively buoyant jet has been undertaken to evaluate the effect of the forced vertical motion of the environment. Vertical motion results from inflows and exhausts above and below the jet. Three distinct cases were identified. In the first, a velocity in the environment opposed the jet and produced a steady flow. This configuration was used to measure the entrainment flux along the length of the fountain. This configuration is similar to a jet impinging on an interface for which the entrainment depends on the local Froude number. The experiments covered a wider range of local Froude numbers than previously published and have produced results which are different from those in the literature. In the second case, the environment was at rest except for the motion induced by the fountain. An interface formed at the base of the fountain and moved quickly to the top. Once there, it advanced slowly due to entrainment through the end of the fountain and the length of the fountain increased. The final case is a co-flowing environment. No interface formed if the environment velocity was greater than the advance velocity of the end of the fountain. However, one formed for a smaller environment velocity and the end of the fountain was observed to undergo a quasi-periodic jump phenomenon. The top of the fountain would advance with the environment particles for a short time and then snap back to the elevation of a fountain in an infinite environment. A new interface formed and the cycle repeated. © 1993, Cambridge University Press. All rights reserved.

Description: An exact result is calculated numerically for the dilute limiting, zero shear viscosity of bimodal suspensions of hard spheres. The required hydrodynamic functions are calculated from recent results for the resistivities of unequal spheres. Both the hydrodynamic and Brownian contributions to the Huggins coefficient exhibit a minimum that is symmetric in mixing volume fraction. The resultant minimum deepens with increasing size ratio. The results are discussed in the light of published measurements of the viscosity for bimodal suspensions and previous phenomenological theories. The reduction of viscosity upon mixing is seen to be a result of near-field hydrodynamic shielding of asymmetric particle pairs. It is also shown that the use of far-field hydrodynamic interactions yields qualitatively incorrect results for the viscosity of binary mixtures. A parametrization of the bimodal results allows an estimation of the effects of suspension polydispersity on the Huggins coefficient. For polydispersities of ten percent or less, the Huggins coefficient is essentially unchanged from the value calculated for an equivalent, monodisperse suspension at equal volume fraction. A parametrization of these results is provided for relating the reduction in Huggins coefficient to the polydispersity index. © 1994, Cambridge University Press. All rights reserved.

Description: Experimental studies have shown that convergent-divergent nozzles, when run at low pressure ratios, often undergo a flow resonance accompanied by emission of acoustic tones. The phenomenon, different in characteristics from conventional 'screech' tones, is addressed in this paper. Unlike screech, the resonant frequency (fN) increases with increasing supply pressure. There is a 'staging' behaviour; odd-harmonic stages resonate at lower pressures while the fundamental occurs in a wide range of higher pressures corresponding to a 'fully expanded Mach number' (Mj) around unity. Within a stage, fN varies approximately linearly with Mj; the slope of the variation steepens when the angle of divergence of the nozzle is decreased. Based on the data, correlation equations are provided for the prediction of fN. A companion computational study captures the phenomenon and predicts the frequencies, including the stage jump, quite well. While the underlying mechanisms are not completely understood yet, it is clear that the unsteadiness of a shock occurring within the divergent section plays a direct role. The shock drives the flow downstream like a vibrating diaphragm, and resonance takes place similarly to the (no-flow) acoustic resonance of a conical section having one end closed and the other end open. Thus, the fundamental is accompanied by a standing one-quarter wave within the divergent section, the next stage by a standing three-quarter wave, and so on. The distance from the foot of the shock to the nozzle exit imposes the pertinent length scale. The principal trends in the frequency variation are explained qualitatively from the characteristic variation of that length scale. A striking feature is that tripping of the nozzle's internal boundary layer tends to suppress the resonance. It is likely that the trip effect occurs due to a break in the azimuthal coherence of the unsteady flow.

Description: We present new laboratory data on long wave forcing over a barred beach profile under random wave breaking conditions. The data include incident and radiated wave amplitudes, wave set-up, and detailed measurements of the cross-shore variation in long wave amplitude, including shoreline (swash) amplitudes. The total surf zone width was varied via changes in both wave height and the water level over the bar crest. The data obtained from the barred beach are also compared with previous data obtained from a plane beach under essentially identical short wave forcing conditions. The presence of the bar induces a frequency downshift in the spectral peak of the radiated long waves, a consequence of the increased surf zone width on the barred beach and a clear signature of long wave forcing by a time-varying breakpoint. Further comparisons of the two data sets suggest that the bar leads to resonant trapping and amplification (or suppression) of the shoreline motion at discrete long wave frequencies. Well-defined standing long wave motion occurs at discrete frequencies inside the bar and the resonant response is consistent with a simple seiche between the bar crest and shoreline, in agreement with previous numerical model studies. The long wave structure offshore of the breakpoint depends on the relative positions of the bar, shoreline and breakpoint, and is inconsistent with a numerical solution for a free standing long wave over the barred beach profile. © 2004 Cambridge University Press.

Description: An analysis is made of solute transport through a fluid within a long, but finite, channel or pipe whose walls remain parallel but oscillate transversely. When the fluid is viscous, the wall motion causes steady streaming. Axial dispersion of solute is calculated over a wide parameter range, and mean longitudinal transport is found to be greatly enhanced when the steady-streaming Reynolds number is much greater than unity. The results are applied to low-volume high-frequency ventilation of the human lung. © 1993, Cambridge University Press

Description: Premixed H2/02/N2 flames propagating in two-dimensional turbulence have been studied using direct numerical simulations (DNS: simulations in which all fluid and thermochemical scales are fully resolved). Simulations include realistic chemical kinetics and molecular transport over a range of equivalence ratios ©〉 {& — 0.35, 0.5, 0.7, 1.0, 1.3). The validity of the flamelet assumption for premixed turbulent flames is checked by comparing DNS data and results obtained for steady strained premixed flames with the same chemistry (flamelet ‘library’). This comparison shows that flamelet libraries overestimate the influence of stretch on flame structure. Results are also compared with earlier zero-chemistry (flame sheet) and one-step chemistry simulations. Consistent with the simpler models, the turbulent flame with realistic chemistry aligns preferentially with extensive strain rates in the tangent plane and flame curvature probability density functions are close to symmetric with near-zero means. For very lean flames it is also found that the local flame structure correlates with curvature as predicted by DNS based on simple chemistry. However, for richer flames, by contrast to simple-chemistry results with non-unity Lewis numbers (ratio of thermal to species diffusivity), local flame structure does not correlate with curvature but rather with tangential strain rate. Turbulent straining results in substantial thinning of the flame relative to the steady unstrained laminar case. Heat-release and H202contours remain thin and connected (‘flamelet-like’) while species including H-atom and OH are more diffuse. Peak OH concentration occurs well behind the peak heat-release zone when the flame temperature is high (of the order of 2800 K). For cooler and leaner flames (about 1600 K and for an equivalence ratio below 0.5) the OH radical is concentrated near the reaction zone and the maximum OH level provides an estimate of the local flamelet speed as assumed by Becker et al. (1990). © 1994, Cambridge University Press. All rights reserved.

Description: A flagellated, bottom-heavy micro-organism's swimming direction in a shear flow is determined from a balance between the gravitational and viscous torques (gyrotaxis). Hitherto, the cell has been assumed to be a spheroid and the flagella have been neglected. Here we use resistive-force theory to calculate both the magnitude and the direction of a biflagellate cell's swimming velocity and angular velocity relative to the fluid when there is an arbitrary linear flow far from the cell. We present an idealized model for the flagellar beat but, in calculating the velocity of the fluid relative to an element of a flagellum, the presence of the cell body is not neglected. Results are given for the case of a spherical cell body whose flagella beat in a vertical plane, when the ambient linear flow is in the same vertical plane. Results show that resistive-force theory can be used for organisms where the cell body has significant effect on the flow past the flagella and that the viscous torque on the flagella is a significant term in the torque balance equations. A model is presented for the calculation of a cell's velocity and angular velocity in a shear flow which is valid up to high magnitudes of rate of strain or vorticity. The main application of the results will be to modify a recent continuum model for suspensions of gyrotactic micro-organisms (Pedley & Kessler 1990). © 1994, Cambridge University Press. All rights reserved.

Description: A computational study has been performed to identify the onset of transverse buoyancy-driven recirculations during laminar flow of hydrogen and nitrogen in horizontal ducts with cool upper walls, and lower walls consisting of three sections: a cool upstream section, a heated middle section and a cool downstream section. The motivation for this work stems from the need to identify operating conditions maximizing the thickness uniformity, the interface abruptness and the precursor utilization during growth of thin films and multi-layer structures of semiconductors by metalorganic chemical vapour deposition (MOCVD). A mathematical model describing the flow and heat transfer along the vertical midplane of MOCVD reactors with the above geometry has been developed and computer simulations were performed for a variety of operating conditions using the Galerkin finite-element method. At atmospheric pressure and low inlet velocities, transverse recirculations form near the upstream and downstream edges of the heated section. These can be suppressed either by increasing the inlet velocity of the gas, so that forced convection dominates natural convection, or by decreasing the operating pressure to reduce the effects of buoyancy. The onset of transverse recirculations has been determined for Grashof (Gr) and Reynolds (Re) numbers covering the following ranges: 10® 〈 Re 〈 100 and 1 〈 Gr 〈 106, with Gr and Re computed using fluid properties at the inlet conditions. The computations indicate that, for abrupt temperature changes along the lower wall (worst-case scenario), transverse recirculations are always absent if the following criteria are satisfied: (Gr/Re) 〈100 for 103 〈 Re 〈 4 and (Gr/Re2) 〈 25 for 4〈 Re 〈 100. The predicted critical values of Re, which correspond to the onset of transverse recirculations, agree well with reported experimental observations. The above criteria can be used for optimal design and operation of horizontal MOCVD reactors and may also be useful for heat transfer studies in horizontal ducts with differentially heated lower walls. © 1994, Cambridge University Press. All rights reserved.

Description: Steady and unsteady numerical simulations of two-dimensional flow in a collapsible channel were carried out to study the flow limitation which typically occurs when the upstream transmural pressure is held constant while flow rate and pressure gradient along the collapsible channel can vary independently. Multiple steady solutions are found for a range of upstream transmural pressures and Reynolds number using an arclength control method. The stability of these steady solutions is tested in order to check the correlation between flow limitation and self-excited oscillations (the latter being a consequence of unstable steady solutions). Both stable and unstable solutions are found when flow is limited. Self-excited oscillations and divergence instabilities are observed in certain solution branches. The instability of the steady solutions seems to depend on the unsteady boundary conditions used, i.e. on which parameters are allowed to vary. However, steady solutions associated with the solution branch before flow limitation where the membrane wall bulges are found to be stable for each of the three different boundary conditions employed. We conclude that there is no one to one correlation between the two phenomena in this two dimensional channel model.