Simulation of round jets with nozzle-dependent inflow conditions using the k−ε turbulence model

In view of the “round jet initial condition anomaly”, discussed in literature, we investigate the effect of inflow conditions resulting from the use of different nozzle geometries to form the jet. RANS simulations in the framework of OpenFOAM using the k − ε turbulence model are performed. As the standard model coefficient C_ε1 = 1.44 is known to overpredict spreading rates for round jets, a value of C_ε1 = 1.6 was recommended for this case already in the 1970's. While this works well for jets issuing from long pipes, it does not give satisfactory results for other nozzle geometries. To overcome this deficiency while keeping the k − ε model, we suggest modified coefficients C_ε1 based on profiles of mean flow and turbulence at the nozzle exit. We determine optimal values of C_ε1 for three different nozzle geometries, and test them at various Reynolds numbers. Good agreement with experimental data is obtained. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photoresponsive Switches at Surfaces Based on Supramolecular Functionalization with Azobenzene–Oligoglycerol Conjugates

The synthesis, supramolecular complexation, and switching of new bifunctional azobenzene–oligoglycerol conjugates in different environments is reported. Through the formation of host–guest complexes with surface immobilized β‐cyclodextrin receptors, the bifunctional switches were coupled to gold surfaces. The isomerization of the amphiphilic azobenzene derivatives was examined in solution, on gold nanoparticles, and on planar gold surfaces. The wettability of functionalized gold surfaces can be reversibly switched under light‐illumination with two different wavelengths. Besides the photoisomerization processes and concomitant effects on functionality, the thermal cis to trans isomerization of the conjugates and their complexes was monitored. Thermal half‐lives of the cis isomers were calculated for different environments. Surprisingly, the half‐lives on gold nanoparticles were significantly smaller compared to planar gold surfaces.     

Two-cluster bifurcations in systems of globally pulse-coupled oscillators

For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all stationary two-cluster states and explain how the different states are naturally connected via bifurcations. The coupling is modeled using the phase-response-curve (PRC), which measures the sensitivity of each oscillator’s phase to perturbations. For large systems with a PRC, which is zero at the spiking threshold, we are able to find the parameter regions where multiple stable two-cluster states coexist and illustrate this by an example. In addition, we explain how a locally unstable one-cluster state may form an attractor together with its homoclinic connections. This leads to the phenomenon of intermittent, asymptotic synchronization with abating beats away from the perfect synchrony.     

A comparison of mixing rules for the combination of COSMO-RS and the Peng–Robinson equation of state

In this work, the COSMO-RS model is combined with a volume-translated Peng–Robinson equation of state (EOS) via a G^E$G^{\text{E}}$-based mixing rule. The performance of several mixing rules previously published for this purpose is compared and semi-empirical modifications to one of them are introduced to improve its performance in our application. The new mixing rule contains three internal parameters that are adjusted to achieve consistency between the mixing rule and COSMO-RS. No experimental binary data is needed for our EOS. The new COSMO-RS-based, predictive EOS introduces a density dependence into COSMO-RS and extends its applicability to higher pressures and to mixtures containing supercritical components.     

Diophantine approximation and parametric geometry of numbers

Dirichlet’s Theorem on simultaneous approximation involves a parameter Q. It can be derived from Minkowski’s geometry of numbers involving a symmetric convex body depending on Q. Therefore it is natural to study parametric Geometry of Numbers. In turn, this will shed new light on diophantine approximation.     

Large‐eddy simulation of compressible rectangular duct flow

Turbulent flow inside ducts differs significantly from the statistically one‐dimensional turbulent channel flow due to the additional confining lateral walls. Secondary flows in the corners are found which are known to affect the turbulence structure close to the walls. Most computations have been performed for incompressible or only slightly compressible flows and with square duct geometries (e.g. [1,2]). In the present study we address the effect of the aspect ratio on the flow structure in high subsonic rectangular duct flow using LES. Mean‐flow characteristics are analyzed and compared to square duct and channel flow data. We find good agreement with available incompressible DNS square duct data for low Mach number computations. For aspect ratios as high as five, the mean‐flow profile in the center of the longer side of the duct along the wall normal direction differs distinctively from channel flow for the present Mach 0.7 computations.