9,110 research outputs found
RANS Equations with Explicit Data-Driven Reynolds Stress Closure Can Be Ill-Conditioned
Reynolds-averaged Navier--Stokes (RANS) simulations with turbulence closure
models continue to play important roles in industrial flow simulations.
However, the commonly used linear eddy viscosity models are intrinsically
unable to handle flows with non-equilibrium turbulence. Reynolds stress models,
on the other hand, are plagued by their lack of robustness. Recent studies in
plane channel flows found that even substituting Reynolds stresses with errors
below 0.5% from direct numerical simulation (DNS) databases into RANS equations
leads to velocities with large errors (up to 35%). While such an observation
may have only marginal relevance to traditional Reynolds stress models, it is
disturbing for the recently emerging data-driven models that treat the Reynolds
stress as an explicit source term in the RANS equations, as it suggests that
the RANS equations with such models can be ill-conditioned. So far, a rigorous
analysis of the condition of such models is still lacking. As such, in this
work we propose a metric based on local condition number function for a priori
evaluation of the conditioning of the RANS equations. We further show that the
ill-conditioning cannot be explained by the global matrix condition number of
the discretized RANS equations. Comprehensive numerical tests are performed on
turbulent channel flows at various Reynolds numbers and additionally on two
complex flows, i.e., flow over periodic hills and flow in a square duct.
Results suggest that the proposed metric can adequately explain observations in
previous studies, i.e., deteriorated model conditioning with increasing
Reynolds number and better conditioning of the implicit treatment of Reynolds
stress compared to the explicit treatment. This metric can play critical roles
in the future development of data-driven turbulence models by enforcing the
conditioning as a requirement on these models.Comment: 35 pages, 18 figure
(1S*,4aR*,5S*,6S*,8aR*)-3-Benzyl-1-methyl-5,6-diphenyl-3,4,4a,5,6,8a-hexahydro-1H-2,3-benzoxazin-4-one
In the title compound, C28H27NO2, the oxazinone ring adopts a twist-boat conformation and the cyclohexene ring has a twisted envelope conformation. The crystal structure is stabilized by weak non-classical intermolecular C—H⋯O hydrogen bonds
Ethyl 4-methyl-1,3-dioxo-1,2,3,4-tetrahydroisoquinoline-4-carboxylate
In the title compound, C13H13NO4, the fused-ring system is nearly planar, with an r.m.s. deviation of 0.0408 Å. In the crystal, molecules are linked into centrosymmetric dimers by a pair of N—H⋯O hydrogen bonds. The ethyl group is disordered over two positions in a ratio of 0.758 (6):0.242 (6)
Synthesis of a ditopic homooxacalix[3]arene for fluorescence enhanced detection of heavy and transition metal ions
A pyrene-appended ratiometric fluorescent chemosensor L based on a synthetic approach of insulating the fluorophore from the ionophore by a specific molecular spacer has been synthesised and characterised. The fluorescence spectra changes of L suggested that the chemosensor can detect heavy and transition metal (HTM) ions ratiometrically and with variable sensitivity according to the substituents present. ¹H NMR titration experiments indicated that the three triazole ligands prefer binding with Hg²⁺, Pb²⁺ and Zn²⁺, resulting in a conformational change that produces monomer emission of the pyrene accompanied by the excimer quenching. However, the addition of Fe³⁺, which may be accommodated by the cavity of L, makes the pyrene units move closer to each other, and a discernible increase in the emission intensity of the static excimer is observed. Therefore, it is believed that the ditopic scaffold of the calix[3]arene as a specific molecular spacer here plays an important role in the blocking of the heavy atom effect of HTM ions by insulating the fluorophore from the ionophore given the long distance between the metal cation and the pyrene moiety
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