Simultaneous Invariants of Strain and Rotation Rate Tensors and Their Admitted Region

The purpose of this paper is to establish the admitted region for five simultaneous, functionally independent invariants of the strain rate tensor S and rotation rate tensor Ω and calculate some simultaneous invariants of these tensors which are encountered in the theory of constitutive relations for turbulent flows. Such a problem, as far as we know, has not yet been considered, though it is obviously an integral part of any problem in which scalar functions of the tensors S and Ω are studied. The theory provided inside this paper is the building block for a derivation of new algebraic constitutive relations for three-dimensional turbulent flows in the form of expansions of the Reynolds-stress tensor in a tensorial basis formed by the tensors S and Ω, in which the scalar coefficients depend on simultaneous invariants of these tensors

Attenuation of low-frequency pressure fluctuations within the test section of an aeroacoustic wind tunnel using Helmholtz resonators

A new aeroacoustic wind tunnel with an open test section was built at the University of Siegen. During the operation, infrasound tonal components and overtones reaching almost 110 dB in amplitude could be observed, sometimes influencing the measurements due to induced vibration of the wind tunnel structure. The present paper demonstrates the application of Helmholtz resonators on a pilot basis, which successfully attenuated these low-frequency peaks drastically. A systematic analysis using Helmholtz resonators with varying neck lengths was conducted. A single Helmholtz resonator, though able to tackle a target frequency, wasn't enough to get rid of other low-frequency components, leading to the use of two resonators. Additionally, the first application of the wind tunnel is shown to get an idea of its capabilities

Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-optimization

Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing 100.000s of evaluations. Even with the assistance of surrogate models, quality diversity needs 100s or even 1000s of evaluations, which can make it use infeasible. In this study we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.Comment: This is the final version and has been accepted for publication in Evolutionary Computation (MIT Press

The influence of forcing schemes on the diffusion properties in pseudopotential-based Lattice Boltzmann models for multicomponent flows

In dem Vortrag wird gezeigt, wie die Wahl eines Forcing Schemas (bspw. von Shan & Doolen (1995) oder He & Doolen (1998)) über die Chapman-Enskog Entwicklung zu einem vom Forcing abhängigen Diffusionskoeffizienten für Mehrphasenströmungen führt. Der kritische Wert von G wird danach bestimmt und bekannte in der Literatur ad hoc verwendete Beziehungen abgeleitet (Huan et al. (2007)), sowie für tau=1 der bisher nicht erklärbare Shift um den Faktor 2 abgeleitet. Simulationen zeigen die exzellente Übereinstimmung des Diffusionskoeffizienten bspw. mit dem Fick’schen Gesetz für unterschiedliche Werte von G.The talk presents the influence of the choice of forcing schemes in pseudopotential-based LBM methods for multi-phase flows (e.g. Shan & Doolen (1995) or He & Doolen (1998)) on the diffusion coefficient, obtained via Chapman-Enskog analysis. The critical value of G is obtained und known relations used in the literature are subsequently derived based on this theory (e.g. Huan et al. (2007)). The often observed shift at tau=1 for the critical value of G can be directly derived. Simulation show excellent agreement between the diffusion coefficient and Fick’s law for various values of G

High-order semi-Lagrangian kinetic scheme for compressible turbulence

Turbulent compressible flows are traditionally simulated using explicit Eulerian time integration applied to the Navier-Stokes equations. However, the associated Courant-Friedrichs-Lewy condition severely restricts the maximum time step size. Exploiting the Lagrangian nature of the Boltzmann equation's material derivative, we now introduce a feasible three-dimensional semi-Lagrangian lattice Boltzmann method (SLLBM), which elegantly circumvents this restriction. Previous lattice Boltzmann methods for compressible flows were mostly restricted to two dimensions due to the enormous number of discrete velocities needed in three dimensions. In contrast, this Rapid Communication demonstrates how cubature rules enhance the SLLBM to yield a three-dimensional velocity set with only 45 discrete velocities. Based on simulations of a compressible Taylor-Green vortex we show that the new method accurately captures shocks or shocklets as well as turbulence in 3D without utilizing additional filtering or stabilizing techniques, even when the time step sizes are up to two orders of magnitude larger compared to simulations in the literature. Our new method therefore enables researchers for the first time to study compressible turbulent flows by a fully explicit scheme, whose range of admissible time step sizes is only dictated by physics, while being decoupled from the spatial discretization