André Bénard

Comparing the mathematical models of Lighthill to the performance of a biomimetic fish

The mathematical models for the performance of aquatic animals developed by M Lighthill are compared with the experimental performance of a biomimetic fish. The equations developed by Lighthill are evaluated at steady-state conditions. Equilibrium velocity and mechanical efficiency are calculated using Lighthills mathematical model and compared with experimental results. In both cases, a pattern is found wherein an optimum combination of tail frequency and amplitude maximizes equilibrium velocity. Differences between the theoretical and experimental results are attributed to mechanical limitations in the drive train.

Opposed-flow flame spread over polymeric materials: Influence of phase change

A numerical model for flame spread over polymeric surfaces is constructed. The dependence of the flame spread rate on phase change and thermal properties is investigated by varying three non-dimensional parameters, St, k # l, and C # Pl. Quantitative comparisons indicate that the numerical model provides excellent agreement to an analytical formula in the cases of variable latent heat of the phase change, variable liquid thermal capacity, and variable thermal conductivity. However, the deRis formula yields a constant spread rate higher than the numerical result and is independent of phase change. Qualitatively, with the increase of St ,o r with the decrease of k # l or C # Pl, the flame spread rate increases. In addition, k # l is the strongest determinant of the influence of the thickness of the liquid region. The mechanisms of flame spread at the steady state are interpreted by applying an energy balance principle for the control volume upstream of the flame leading edge. It is found that a ratio between the total heat applied to the condensed material upstream of the flame leading edge and the spread rate reveals the physical mechanisms that control the preheating of the condensed material to the ignition temperature. The dependence of flame structure on St, k # l, and C # Pl is studied. It is found that with the increase of St or k l, or with the decrease of C # Pl, the size of the flame increases. These results indicate that flame size dependence follows the magnitude of the spread rate when the properties of the condensed material are variable.

An analytical model for spherulitic growth in fiber‐reinforced polymers

An analytical model for the isothermal crystallization of fiber reinforced polymers is presented. The model is based on approximate expressions for the volume of intersection between a sphere and cylinder. These expressions are used to account for the effect of the fibers on the overall crystallization process. Expressions for the average volume of spherulites truncated by the fibers are computed. The crystallization process is divided into time frames during which specific types of fiber truncations are encountered. Three different time sequences for the occurrence of the truncations are also derived according to the fiber volume fraction. The depressing effect of the fibers on the overall crystallization process is demonstrated with simple examples.

CFD Study of Hydrodynamics and Separation Performance of a Novel Crossflow Filtration Hydrocyclone (CFFH)

This research addresses various hydrodynamic aspects and the separation performance of a novel cross-flow filtration hydrocyclone (CFFH) using computational fluid dynamics. A CFFH is a device that combines the desirable attributes of a cross-flow filter and a vortex separator into one unit to separate oil from water. The velocity and pressure fields within the CFFH are estimated by numerically solving the filtered Navier-Stokes equations (by using a Large Eddy Simulation (LES) approach). The Lagrangian approach is employed for investigating the trajectories of dispersed droplets based on a stochastic tracking method called the Discrete Phase Model (DPM). The mixture theory with the Algebraic Slip Model (ASM) is also used to compute the dispersed phase fluid mechanics and for comparing with results obtained from the DPM. In addition, a comparison between the statistically steady state results obtained by the LES with the Wall Adaptive Local Eddy-Viscosity (WALE) subgrid scale model and the Reynolds Average Navier-Stokes (RANS) closed with the Reynolds Stress Model (RSM) is performed for evaluating their capabilities with regards to the flow field within the CFFH and the impact of the filter medium. Effects of the Reynolds number, the permeability of the porous filter, and droplet size on the internal hydrodynamics and separation performance of the CFFH are investigated. Results indicate that for low feed concentration of the dispersed phase, separation efficiency obtained based on multiphase and discrete phase simulations is almost the same. Higher Reynolds number flow simulations exhibit an unstable core and thereby numerous recirculation zones in the flow field are observed. Improved separation efficiency is observed at a lower Reynolds number and for a lower permeability of the porous filter.Copyright

SIMULATIONS AND PERFORMANCE OF THE CROSSFLOW FILTRATION HYDROCYCLONE (CFFH) FOR OIL-WATER SEPARATION

A critical aspect of operating an oil well consists of separating oil from the water that is jointly produced. This paper describes modeling of a crossflow filtration hydrocyclone (CFFH), a device that combines desirable attributes of a crossflow filter and a vortex separator into one unit to separate oil from produced water. A porous media is incorporated around the crossflow outlet region of the cylindrical CFFH so as to achieve the desired separation efficiency. The main purpose of this work is to predict the fluid dynamic behavior of a particular CFFH design and its separation efficacy based on 3D computational fluid dynamics (CFD) simulations. The velocity field in the fluid phase is obtained using a Reynolds Stress Model (RSM) for closing the Reynolds Average Navier. Stokes (RANS) equation. The Lagrangian Discrete Phase Model (DPM) is used to investigate the trajectories of particles mimicking oil droplets and grade efficiency of the CFFH. The effect of the Reynolds and the Stokes numbers on the grade efficiency and particle residence time is studied. The effective length of the porous media and the vortex strength for different operating conditions is also investigated. Results indicate that the separation efficiency is significantly influenced by the porous media. Hydrocyclones with an aspect ratio greater than 4.0 exhibit lower grade efficiency due to a weaker swirl. NOMENCLATURE

Energy balance analysis of ignition over a melting polymer subjected to a high radiation heat flux in a channel cross flow

A two-dimensional ignition model is examined for two different flow patterns, one with a Navier-Stokes calculation and one with an Oseen approximation. The physical phenomena include channel flow and combustion reaction in the gas phase, pyrolysis and melting in the condensed phase, and radiation heat loss and fuel injection flow at the interface. Ignition is studied by means of an integral energy balance analysis, where various heat transfer mechanisms are evaluated. It is found that the flow pattern has an influence on the ignition process though the qualitative dependence is unchanged except for some isolated (though important) features of the problem. Generally, the Oseen approximation results in a shorter ignition delay. The influence of condensed phase material properties such as latent heat, conductivity, and heat capacity are investigated based on the energy barrier concept. Based on the numerical observations, a simple theory is derived to determine the ignition delay time by employing the energy balance principle. The predicted ignition delay agrees well with the direct numerical results. The external radiation is studied by changing its magnitude over a wide range. It influences the ignition behavior by mainly changing the ignition delay, whose results indicate that the polymer under investigation belongs to in the category of thermally thick polymers. In addition, the surface temperature is observed to increase with increasing external radiation heat flux.

Opposed-flow ignition and flame spread over melting polymers with Navier-Stokes gas flow

A numerical model is constructed to predict transient opposed-flow flame spread behaviour in a channel flow over a melting polymer. The transient flame is established by initially applying a high external radiation heat flux to the surface. This is followed by ignition, transition and finally steady opposed-flow flame spread. The physical phenomena under consideration include the following: gas phase: channel flow, thermal expansion and injection flow from the pyrolyzed fuel; condensed phase: heat conduction, melting, and discontinuous thermal properties (heat capacity and thermal conductivity) across the phase boundary; gas-condensed phase interface: radiation loss. There is no in-depth gas radiation absorption in the gas phase. It is necessary to solve the momentum, species, energy and continuity equations in the gas along with the energy equation(s) in the liquid and solid. Agreement is obtained between the numerical spread rate and a flame spread formula. The influence of the gas flow is explored by comparing the Navier-Stokes (NS) and Oseen (OS) models. An energy balance analysis describes the flame-spread mechanism in terms of participating heat transfer mechanisms.

Numerical Study of Internal Flow Structures Within Hydrocyclones With Parabolic and Hyperbolic Swirl Chambers

In this work we examine the internal flow structures within hydrocyclones used for liquid-liquid separation, especially those used for the removal of oil droplets from water. The internal flow structures and patterns are greatly influenced by the geometric shape of the swirl chamber. The effects of parabolic and hyperbolic wall profiles of the swirl chamber on the reverse flow vortex core, short circuit flows, and the separation efficiency are investigated numerically by solving the Reynolds Average Navier-Stokes equations closed by an equation of change for the Reynolds stress. Droplets (forming the dispersed phase) trajectories are predicted by solving a kinematic equation of motion and force balance. Internal flow structures for different geometric conditions have partially motivated the redesign of the hydrocyclone geometry so as to support a longer and stable reverse flow vortex core and for greater separation efficiency. Results indicate that both the parabolic and hyperbolic swirl chambers provide improved separation efficiency. However, the hyperbolic swirl chamber has a greater potential for the reduction of effective length of the hydrocyclone with maintaining the same separation efficiency.Copyright

Motion of a deformed sphere with slip in creeping flows

The motion of a rigid particle whose surface is a slightly deformed sphere is studied for creeping flows with the assumption of slip on the particle. Expressions are obtained for the hydrodynamic force and torque exerted by the fluid on a deformed sphere using an asymptotic method introduced by H. Brenner, wherein the normalized amplitude of the deviation from sphericity is assumed to be a small parameter. The Stokes’ resistance calculated by this method is validated by comparing with existing solutions the limiting cases of no slip and perfect slip. The equations describing the motion of a deformed sphere with a slip surface in a simple shear flow are also derived and solved. The motion of the deformed sphere is shown to differ significantly from the no-slip case for low values of a dimensionless parameter that incorporates the slip coefficient. The period of rotation of the deformed sphere is longer, and for cases where the slip coefficient is low, the spheroid rotates to a fixed angle and reaches a quasi-steady orientation.Copyright

Topology Optimization of Heat-Resistant Structures

The standard problem of finding the optimal layout of structural material associated with maximum stiffness is expanded to include consideration of thermal criteria. The problem is posed as a three-phase layout problem where the phases include an insulating or fire retardant material and an unknown distribution of heat sources, in addition to the structural material. The model used is simple, yet results suggest that the introduction of measures to control the temperature in the structure when subjected to significant heat transfer rates can result in layouts that differ substantially from solutions where thermal issues are ignored.Copyright