Turbulence modeling for flows around convex features giving rapid eddy distortion

Reynolds averaged Navier-Stokes model performances in the stagnation and wake regions for turbulent flows with relatively large Lagrangian length scales (generally larger than the scale of geometrical features) approaching small cylinders (both square and circular) is explored. The effective cylinder (or wire) diameter based Reynolds number, ReW ≤ 2.5 × 103. The following turbulence models are considered: a mixing-length; standard Spalart and Allmaras (SA) and streamline curvature (and rotation) corrected SA (SARC); Secundov's νt-92; Secundov et al.'s two equation νt-L; Wolfshtein's k-l model; the Explicit Algebraic Stress Model (EASM) of Abid et al.; the cubic model of Craft et al.; various linear k-ε models including those with wall distance based damping functions; Menter SST, k-ω and Spalding's LVEL model. The use of differential equation distance functions (Poisson and Hamilton-Jacobi equation based) for palliative turbulence modeling purposes is explored. The performance of SA with these distance functions is also considered in the sharp convex geometry region of an airfoil trailing edge. For the cylinder, with ReW ≈ 2.5 × 103 the mixing length and k-l models give strong turbulence production in the wake region. However, in agreement with eddy viscosity estimates, the LVEL and Secundov νt-92 models show relatively little cylinder influence on turbulence. On the other hand, two equation models (as does the one equation SA) suggest the cylinder gives a strong turbulence deficit in the wake region. Also, for SA, an order or magnitude cylinder diameter decrease from ReW = 2500 to 250 surprisingly strengthens the cylinder's disruptive influence. Importantly, results for ReW ≪ 250 are virtually identical to those for ReW = 250 i.e. no matter how small the cylinder/wire its influence does not, as it should, vanish. Similar tests for the Launder-Sharma k-ε, Menter SST and k-ω show, in accordance with physical reality, the cylinder's influence diminishing albeit slowly with size. Results suggest distance functions palliate the SA model's erroneous trait and improve its predictive performance in wire wake regions. Also, results suggest that, along the stagnation line, such functions improve the SA, mixing length, k-l and LVEL results. For the airfoil, with SA, the larger Poisson distance function increases the wake region turbulence levels by just under 5%. © 2007 Elsevier Inc. All rights reserved.

Increasing the flexoelastic ratio of liquid crystals using highly fluorinated ester-linked bimesogens.

We present experimental results on the bulk flexoelectric coefficients e and effective elastic coefficients K of non-symmetric bimesogenic liquid crystals when the number of terminal and lateral fluoro substituents is increased. These coefficients are of importance because the flexoelastic ratio e/K governs the magnitude of flexoelectro-optic switching in chiral nematic liquid crystals. The study is carried out for two different types of linkage in the flexible spacer chain that connects the separate mesogenic units: these are either an ether or an ester unit. It is found that increasing the number of fluorine atoms on the mesogenic units typically leads to a small increase in e and a decrease in K, resulting in an enhancement of e/K. The most dramatic increase in e/K, however, is observed when the linking group is changed from ether to ester units, which can largely be attributed to an increase in e. Increasing the number of fluorine atoms does, however, increase the viscoelastic ratio and therefore leads to a concomitant increase in the response time. This is observed for both types of linkage, although the ester-linked compounds exhibit smaller viscoelastic ratios compared with their ether-linked counterparts. Highly fluorinated ester-linked compounds are also found to exhibit lower transition temperatures and dielectric anisotropies. As a result, these compounds are promising materials for use in electro-optic devices.