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

Towards understanding the design of dual-modal MR/fluorescent probes to sense zinc ions

A series of gadolinium complexes were synthesised in order to test the design of dual-modal probes that display a change in fluorescence or relaxivity response upon binding of zinc. A dansyl-DO3ATA gadolinium complex [GdL1] displayed an increase and a slight blue-shift in fluorescence in the presence of zinc; however, a decrease in relaxation rate was observed. Consequently, the ability of the well-known zinc chelator, BPEN, was assessed for relaxivity response when conjugated to the gadolinium chelate. The success of this probe [GdL2], lead to the inclusion of the same zinc-probing moiety alongside a longer wavelength emitting fluorophore, rhodamine [GdL3], to arrive at the final iteration of these first generation dual-modal zinc-sensing probes. The compounds give insight into the design protocols required for the successful imaging of zinc ions

Functional ionic liquids and deep eutectic solvents for luminescence sensing applications and carbon capture

Title from PDF of title page (University of Missouri--Columbia, viewed on September 12, 2013).The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Thesis advisor: Dr Sheila BakerIncludes bibliographical references.M.S. University of Missouri-Columbia 2013.Dissertations, Academic -- University of Missouri--Columbia -- Chemical engineering."May 2013"Novel functional Ionic Liquids (ILs) and Deep Eutectic Solvents (DESs), containing unique properties, were investigated. Eight new salts based on four different β-diketonate anions, each coupled with the choline or tetrabutylphosphonium cation were prepared and fully characterized via ESI-MS, FTIR, and 1H/13C NMR. The thermal stabilities and transitions for these β-diketonate salts were explored using DSC and TGA. The inherent binding capability of the β-diketonate allowed for lanthanide recognition in which the coordination with Eu3+ resulted in a intensification of luminescence. Additionally, these ILs display prominent color change of the β-diketonate in the presence of an acid source, permitting the visual transduction of local pH changes. Utility for carbon capture was also considered, however, these ILs were essentially incapable of binding CO2. Computational studies revealed that the association of CO2 to the β-diketonate anion was thermodynamically unfavored and sterically hindered. A DES of choline chloride (ChCl) and glycerol (Gly) along with a superbase was shown to capture up to 124 mg of CO2 per g of reagents (1.00 mole CO2 per mole of ChCl and Gly). Different bases and mixture composition were also investigated. The system could also be easily reversed upon heating under nitrogen. The optimal system for CO2 capture was found to contain a 1:2 ChCl:Gly DES mixture mixed with the superbase, DBN, in a 1:3.5 Gly:DBN molar ratio. Overall, these newly introduced β-diketonate ILs and DES and superbase mixture showed interesting and useful physicochemical properties applicable to a number of applications

Precision cosmology from future lensed gravitational wave and electromagnetic signals

The standard siren approach of gravitational wave cosmology appeals to the direct luminosity distance estimation through the waveform signals from inspiralling double compact binaries, especially those with electromagnetic counterparts providing redshifts. It is limited by the calibration uncertainties in strain amplitude and relies on the fine details of the waveform. The Einstein Telescope is expected to produce $10^4-10^5$ gravitational wave detections per year, $50-100$ of which will be lensed. Here we report a waveform-independent strategy to achieve precise cosmography by combining the accurately measured time delays from strongly lensed gravitational wave signals with the images and redshifts observed in the electromagnetic domain. We demonstrate that just 10 such systems can provide a Hubble constant uncertainty of $0.68\%$ for a flat Lambda Cold Dark Matter universe in the era of third generation ground-based detectors