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: 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: Cavitation inception in a turbulent shear layer was studied at Reynolds numbers up to 2 × 106. Flash photography, high-speed motion pictures and holography were used to study the relation of cavitation inception to the shear-layer turbulent structure. Both spanwise and streamwise vortices were clearly visualized by the cavitation. Cavitation inception consistently occurred in the streamwise vortices and more fully developed cavitation was visible in both structures, with the streamwise cavities typically confined to the braid regions between adjacent spanwise vortices. The strength of the streamwise vortices was estimated using a Rankine vortex model, which showed that their strength was always less than 10 % of that of the spanwise vortices. Measurements of fluctuating pressures were made by holographically monitoring the size of air bubbles injected into the non-cavitating shear flow. The measured pressure fluctuations had positive and negative peaks as high as 3 times the freestream dynamic pressure, sufficient to explain cavitation inception at high values of the inception index. The occurrence of inception in the streamwise vortices of the shear layer, combined with previous reports of velocity dependence of the streamwise vortex strength, may explain the commonly observed Reynolds-number scaling of the cavitation inception index in shear flows. © 1990, Cambridge University Press. All rights reserved.

Description: In the vicinity of a caustic of a dispersive wave system, where the group velocity is stationary and hence dispersive effects are relatively weak, the nonlinear Schrodinger equation (NLS) breaks down, and the propagation of the envelope of a finite-amplitude wavepacket is governed by a modified nonlinear Schrodinger equation (MNLS). On the basis of the MNLS, a search for wave envelopes of permanent form is made near a caustic. It is shown that possible solitary wave envelopes satisfy a nonlinear eigenvalue problem. Numerical evidence is presented of symmetric, double-hump solitary-wave solutions. Also, a variety of periodic envelopes are computed. These findings are discussed in connection with previous analytical and numerical work. © 1990, Cambridge University Press. All rights reserved.

Description: This paper treats a liquid-metal flow through a sharp elbow connecting two constant-area, rectangular ducts with thin metal walls. There is a uniform, strong magnetic field in the plane of the centrelines of the ducts. An analytical solution, with a series of eigenfunctions is possible for two sectors of the geometry, while a finite-difference relaxation solution is used for the third sector. The analytical and numerical solutions are coupled at the common boundaries by a combination of a Galerkin minimization of a residual and of integrals of the basic conservation laws over cells adjacent to each boundary. Results are presented for the three-dimensional pressure, electric potential function and fluid velocity. The pressure drop due to the three-dimensional effects near the elbow is also presented. The eigenfunction series represents a quite general solution for any three-dimensional flow in a rectangular duct with a skewed magnetic field. © 1990, Cambridge University Press. All rights reserved.