اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA calculus for flows in periodic domains
283
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present a constructive procedure for the calculation of 2-D potential flows in periodic domains with multiple boundaries per period window. The solution requires two steps: (i) a conformal mapping from a canonical circular domain to the physical target domain, and (ii) the construction of the complex potential inside the circular domain. All singly periodic domains may be classified into three distinct types: unbounded in two directions, unbounded in one direction, and bounded. In each case, we relate the target periodic domain to a canonical circular domain via conformal mapping and present the functional form of prototypical conformal maps for each type of target domain. We then present solutions for a range of potential flow phenomena including flow singularities, moving boundaries, uniform flows, straining flows and circulatory flows. By phrasing the solutions in terms of the transcendental Schottky--Klein prime function, the ensuing solutions are valid for an arbitrary number of obstacles per period window. Moreover, our solutions are exact and do not require any asymptotic approximations.
قيم البحث
اقرأ أيضاً
We study generation of magnetic fields involving large spatial scales by time- and space-periodic small-scale parity-invariant flows. The anisotropic magnetic eddy diffusivity tensor is calculated by the standard procedure involving expansion of magn
etic modes and their growth rates in power series in the scale ratio. Our simulations, conducted for flows with random harmonic composition and exponentially decaying energy spectra, demonstrate that enlargement of the spatial scale of magnetic field is beneficial for generation by time-periodic flows. However, they turn out, in general, to be less efficient dynamos, than steady flows.
Understanding mixing and transport of passive scalars in active fluids is important to many natural (e.g. algal blooms) and industrial (e.g. biofuel, vaccine production) processes. Here, we study the mixing of a passive scalar (dye) in dilute suspens
ions of swimming Escherichia coli in experiments using a two-dimensional (2D) time-periodic flow and in a simple simulation. Results show that the presence of bacteria hinders large scale transport and reduce overall mixing rate. Stretching fields, calculated from experimentally measured velocity fields, show that bacterial activity attenuates fluid stretching and lowers flow chaoticity. Simulations suggest that this attenuation may be attributed to a transient accumulation of bacteria along regions of high stretching. Spatial power spectra and correlation functions of dye concentration fields show that the transport of scalar variance across scales is also hindered by bacterial activity, resulting in an increase in average size and lifetime of structures. On the other hand, at small scales, activity seems to enhance local mixing. One piece of evidence is that the probability distribution of the spatial concentration gradients is nearly symmetric with a vanishing skewness. Overall, our results show that the coupling between activity and flow can lead to nontrivial effects on mixing and transport.
A series of benchmarks based on the physical situation of phase inversion between two immiscible liquids is presented. These benchmarks aim at progressing toward the direct numerical simulation of two-phase flows. Several CFD codes developed in Frenc
h laboratories and using either Volume-of-Fluid or Level-Set interface tracking methods are used to provide physical solutions of the benchmarks, convergence studies and code comparisons. Two typical configurations are retained, with integral scale Reynolds numbers of 13.700 and 433.000, respectively. The physics of the problem are probed through macroscopic quantities such as potential and kinetic energies, or enstrophy. In addition, scaling laws for the temporal decay of the kinetic energy are derived to check the physical relevance of the simulations. Finally the droplet size distribution is probed. Additional test problems are also reported to estimate the influence of viscous effects in the vicinity of the interface.
We develop a stochastic model for the velocity gradients dynamics along a Lagrangian trajectory. Comparing with different attempts proposed in the literature, the present model, at the cost of introducing a free parameter known in turbulence phenomen
ology as the intermittency coefficient, gives a realistic picture of velocity gradient statistics at any Reynolds number. To achieve this level of accuracy, we use as a first modelling step a regularized self-stretching term in the framework of the Recent Fluid Deformation (RFD) approximation that was shown to give a realistic picture of small scales statistics of turbulence only up to moderate Reynolds numbers. As a second step, we constrain the dynamics, in the spirit of Girimaji & Pope (1990), in order to impose a peculiar statistical structure to the dissipation seen by the Lagrangian particle. This probabilistic closure uses as a building block a random field that fulfils the statistical description of the intermittency, i.e. multifractal, phenomenon. To do so, we define and generalize to a statistically stationary framework a proposition made by Schmitt (2003). These considerations lead us to propose a non-linear and non-Markovian closed dynamics for the elements of the velocity gradient tensor. We numerically integrate this dynamics and observe that a stationary regime is indeed reached, in which (i) the gradients variance is proportional to the Reynolds number, (ii) gradients are typically correlated over the (small) Kolmogorov time scale and gradients norms over the (large) integral time scale (iii) the joint probability distribution function of the two non vanishing invariants $Q$ and $R$ reproduces the characteristic teardrop shape, (iv) vorticity gets preferentially aligned with the intermediate eigendirection of the deformation tensor and (v) gradients are strongly non-Gaussian and intermittent.
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle approximation. A
family of regular configurations is found with periodic oscillations of all the settling particles. The oscillations are shown to be robust under some out-of-phase rearrangements of the particles. In the presence of an additional particle above such a regular configuration, the particle periodic trajectories are horizontally repelled from the symmetry axis, and flattened vertically. The results are used to propose a mechanism how a spherical cloud, made of a large number of particles distributed at random, evolves and destabilizes.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
