Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐2: Time‐dependent computations

The interfacial dynamics‐based cavitation model, developed in Part‐1, is further employed for unsteady flow computations. The pressure‐based operator‐splitting algorithm (PISO) is extended to handle the time‐dependent cavitating flows with particular focus on the coupling of the cavitation and turbulence models, and the large density ratio associated with cavitation. Furthermore, the compressibility effect is important for unsteady cavitating flows because in a water–vapour mixture, depending on the composition, the speed of sound inside the cavity can vary by an order of magnitude. The implications of the issue of the speed of the sound are assessed with alternative modelling approaches. Depending on the geometric confinement of the nozzle, compressibility model and cavitation numbers, either auto‐oscillation or quasi‐steady behaviour is observed. The adverse pressure gradient in the closure region is stronger at the maximum cavity size. One can also observe that the mass transfer process contributes to the cavitation dynamics. Compared to the steady flow computations, the velocity and vapour volume fraction distributions within the cavity are noticeably improved with time‐dependent computations. Copyright © 2004 John Wiley & Sons, Ltd.     

On modifying properties of polymeric melts by nanoscopic particles

We study geometric and energetic factors that partake in modifying properties of polymeric melts via inserting well‐dispersed nanoscopic particles (NP). Model systems are cis‐1,4‐polybutadiene melts including a single atomic clusters of size varied in the range 10–150 atoms (3–7 Å in radius; 0.1–1.5% v/v). We modify the interactions between the chains and the particle by tuning attractive van der Waals interactions. Using molecular dynamics, we study equilibrium fluctuations and dynamical properties at the interface. The NPs move in the polymer matrix in two different regimes corresponding to trapped and free diffusion, depending on the NP size. Furthermore, degree of crowding around the NP by the polymer chains is quantified. Effect of NP size and interaction strength both on volume and volumetric fluctuations is manifested in mechanical properties, quantified here by bulk modulus, K. Tuning NP size and nonbonded interactions results in ～15% enhancement in K by addition of a maximum of 1.5% v/v NP. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Interfacial dynamics‐based modelling of turbulent cavitating flows,Part‐1: Model development and steady‐state computations

The merits of transport equation‐based models are investigated by adopting an enhanced pressure‐based method for turbulent cavitating flows. An analysis of the mass and normal‐momentum conservation at a liquid–vapour interface is conducted in the context of homogeneous equilibrium flow theory, resulting in a new interfacial dynamics‐based cavitation model. The model offers direct interpretation of the empirical parameters in the existing transport‐equation‐based models adopted in the literature. This and three existing cavitation models are evaluated for flows around an axisymmetric cylindrical body and a planar hydrofoil, and through a convergent–divergent nozzle. Although all models considered provide qualitatively comparable wall pressure distributions in agreement with the experimental data, quantitative differences are observed in the closure region of the cavity, due to different compressibility characteristics of each cavitation model. In particular, the baroclinic effect of the vorticity transport equation plays a noticeable role in the closure region of the cavity, and contributes to the highest level of turbulent kinetic energy there. Copyright © 2004 John Wiley & Sons, Ltd.     

Constructing infinitely many smooth structures on small 4-manifolds

The purpose of this article is two-fold. First we outline ageneral construction scheme for producing simply connected minimalsymplectic -manifolds with small Euler characteristics. Usingthis scheme, we illustrate how to obtain irreducible symplectic-manifolds homeomorphic but not diffeomorphic to for k = 1, ..., 4, or to for l = 1, ..., 6. Secondly, for each of thesehomeomorphism types, we show how to produce an infinite familyof pairwise nondiffeomorphic nonsymplectic 4-manifolds belongingto it. In particular, we prove that there are infinitely manyexotic irreducible nonsymplectic smooth structures on, and . Received April 17, 2007. Revised September 26, 2007.