Log-layer mismatch and commutation error in hybrid RANS/LES simulation of channel flow

Hybrid approach combining large eddy simulation (LES) with the Reynolds-averaged Navier–Stokes equation (RANS) is expected to accurately simulate wall-bounded turbulent flows at high Reynolds numbers. As an important issue in developing hybrid methods, it is known that the log layers in the RANS and LES regions are not lined up in hybrid RANS/LES simulations of channel flow. Although several methods including additional filtering near the RANS/LES interface have been proposed to eliminate the log-layer mismatch, there is no obvious physical justification for the methods and some ad hoc tuning is necessary. In this work, the commutation error terms in the filtered velocity equations are investigated to justify the method of additional filtering. It is shown that the additional filtering can be considered as a finite difference approximation to extra terms due to the non-commutivity between the hybrid filter and the spatial derivative. Moreover, an expression determining the filter width and its location for the additional filtering is obtained. To validate the expression, a hybrid simulation of channel flow is carried out. The additional filtering with the filter width derived is shown to be effective in eliminating the log-layer mismatch and improving the mean velocity profile.     

Chiral Supramolecular Nanoarchitectures from Macroscopic Mechanical Rotations: Effects on Enantioselective Aggregation Behavior of Phthalocyanines

Fluid dynamics, resulting from the macroscopic mechanical rotation of either a rotary evaporator or a magnetic stirrer, has been shown to selectively induce one of two enantiomers (mirror‐image structures) in certain nanoscale supramolecules. As an alternative to giving a chiral twist to synthesized supramolecules or polymers, it is a challenge to reproducibly prepare chiral species by only using macroscopic mechanical rotations. Demonstrated here is a highly reproducible method for rotary‐evaporation‐induced enantioselective H‐aggregation of achiral phthalocyanines. Chiral induction mechanisms are proposed by using the chiroptical‐sign‐based absolute structures. These results will provide insight to the origin of the homochirality of life, and serves as a pioneering study in a novel scientific field in terms of admixing nanoscale molecular chemistry and macroscopic fluid dynamics.     

An Attempt to Combine Large Eddy Simulation with the k-ε Model in a Channel-Flow Calculation

Large eddy simulation (LES) is combined with the Reynolds-averaged Navier–Stokes (RANS) equation in a turbulent channel-flow calculation. A one-equation subgrid-scale model is solved in a three-dimensional grid in the near-wall region whereas the standard k–ε model is solved in a one-dimensional grid in the outer region away from the wall. The two grid systems are overlapped to connect the two models smoothly. A turbulent channel flow is calculated at Reynolds numbers higher than typical LES and several statistical quantities are examined. The mean velocity profile is in good agreement with the logarithmic law. The profile of the turbulent kinetic energy in the near-wall region is smoothly connected with that of the turbulent energy for the k–ε model in the outer region. Turbulence statistics show that the solution in the near-wall region is as accurate as a usual LES. The present approach is different from wall modeling in LES that uses a RANS model near the wall. The former is not as efficient as the latter for calculating high-Reynolds-number flows. Nevertheless, the present method of combining the two models is expected to pave the way for constructing a unified turbulence model that is useful for many purposes including wall modeling. Received 11 June 1999 and accepted 15 December 2000     

A Hybrid RANS/LES Simulation of Turbulent Channel Flow

Hybrid models combining large eddy simulation (LES) with Reynolds-averaged Navier–Stokes (RANS) simulation are expected to be useful for wall modeling in the LES of high Reynolds number flows. Some hybrid simulations of turbulent channel flow have a common defect; the mean velocity profile has a mismatch between the RANS and LES regions due to a steep velocity gradient at the interface. This mismatch is reproduced and examined using a simple hybrid model; the Smagorinsky model is switched to a RANS model increasing the filter width. It is suggested that a rapid spatial variation in the eddy viscosity is responsible for an underestimate of the grid-scale shear stress and for the steep velocity gradient. To reduce the mean velocity mismatch a new scheme is proposed; additional filtering is introduced to define two kinds of velocity components at the interface between the two regions. The two components are used to remove inconsistency in the velocity equations due to a rapid variation in the filter width. Using the new scheme, simulations of channel flow are carried out with the simple hybrid model. It is shown that the grid-scale shear stress becomes large enough and most of the mean velocity mismatch is removed. Simulations for higher Reynolds numbers are carried out with the k–ε model and the one-equation subgrid-scale model. Although it is necessary to improve the turbulence models and the treatment of the buffer region, the new scheme is shown to be effective for reducing the mismatch and to be useful for developing better hybrid simulations. Received 5 April 2002 and accepted 8 January 2003 Published online 25 March 2003 Communicated by M.Y. Hussaini     

Evaluation of nitric oxide chemical ionization mass spectra of substituted benzenes

Nitric oxide chemical ionization mass spectra of substituted benzenes obtained with the Townsend discharge technique were studied. There were four kinds of base peaks in the mass spectra, i.e. [M + NO]⁺˙, M⁺˙, [M ? H]⁺ and [M ? OR]⁺ (R = H, CH₃). The formation of the specific ion [M + NO]⁺˙ was highly dependent on the kind of substituent, and it was produced more abundantly in the case of substitutions involving electron-accepting groups. The measure of [M + NO]⁺˙ production was evaluated from the value of the ratio [M + NO]⁺˙/M⁺˙. In mono-substitutions, it was clarified that the ratios of [M + NO]⁺˙/M ⁺˙ were correlated with the Hammett substituent constant s?_p or the electrophilic substituent constant s?_p⁺. Monosubstitutions (C₆H₅R) and toluene substitutions (CH₃C₆H₄R) could be classified into six groups in terms of base peak species, [M + NO]⁺˙/M⁺˙ ratios and substituents. In disubstitutions, the mass spectral patterns were governed by the combination of substituents. Mass spectral distinctions among ortho, meta and para isomers could be made in many cases.     

Evaluation of methane negative ion chemical ionization mass spectra of polycyclic aromatic hydrocarbons and related compounds

Negative ion chemical ionization (NICI) mass spectra with methane as reagent gas and the ion abundance ratios of the negative to the positive base peak for 51 polycyclic aromatic hydrocarbons and related compounds were measured and evaluated for highly sensitive detection and isomer differentiation. Either [M ? H]^?, M^?˙ or MH^? was the base peak, except for one compound with [M ? H₂]^?˙ as its base peak. The numbers of compounds with [M ? H]^?, M^?˙ or MH^? as their base peaks were 17, 26 and 7, respectively. Many of the compounds with [M ? H]^? as the base peak had an aliphatic part in their structure. The average value of N/P (negative/positive ion abundance ratio at the base peaks) was < 1. Many of the compounds with M^?˙ as the base peak had a relatively high electron affinity. A correlation between electron affinities and ion abundances was found. In most cases, the N/P ratios were > 1, and even reached 400 in benzo [a] pyrene. Many of the compounds with MH^? as their base peaks had a phenyl group, in which cases the N/P ratios were < 1. In the case of compounds with 18 or fewer carbon atoms, in particular, it was easy to distinguish isomers by comparing their NICI mass spectra. The N/P values served as a guideline in sensitive detection. Nine compounds achieved an N/P of ≥50.     

Kinetic study of gas phase olefin polymerization with a TiCl4/MgCl2 catalyst I. Effect of polymerization conditions

This study focuses on the kinetics of ethylene/propylene (homo/co) polymerization reactions using a high activity TiCl₄/MgCl₂/AlEt₃ catalyst. The reactor system is a gas phase reactor equipped with an on-line composition control scheme. As such, important kinetic data such as the instantaneous reaction rate of each monomer is readily obtained. In the investigation, experiments are performed to study the effects of comonomer composition variations, temperature variations, hydrogen concentration variations, and variations in the Al/Ti ratio. It is observed that the ethylene and propylene instantaneous reaction rates show a rather peculiar pattern with the appearance of a second peak. Our work linked the existence of this peak to the Al/Ti ratio used. A theory based on the oxidation state change is proposed. This theory is also used to explain the effects of temperature changes and hydrogen concentration changes on the system. A variety of analytical techniques are employed to study the polymer properties and evidence is provided to support the existence of polymer partial melting at relatively high reaction temperatures. The resulting diffusion limitation is believed to be partially responsible for the observed activity decrease at such elevated temperatures. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2063–2074, 1997     

A hybrid RANS/LES simulation of high-Reynolds-number channel flow using additional filtering at the interface

A hybrid method combining large eddy simulation (LES) with the Reynolds-averaged Navier-Stokes (RANS) equation is used to simulate a turbulent channel flow at high Reynolds number. It is known that the mean velocity profile has a mismatch between the RANS and LES regions in hybrid simulations of a channel flow. The velocity mismatch is reproduced and its dependence on the location of the RANS/LES interface and on the type of RANS model is examined in order to better understand its properties. To remove the mismatch and to obtain better velocity profiles, additional filtering is applied to the velocity components in the wall-parallel planes near the interface. The additional filtering was previously introduced to simulate a channel flow at low Reynolds number. It is shown that the filtering is effective in reducing the mismatch even at high Reynolds number. Profiles of the velocity fluctuations of runs with and without the additional filtering are examined to help understand the reason for the mismatch. Due to the additional filtering, the wall-normal velocity fluctuation increases at the bottom of the LES region. The resulting velocity field creates the grid-scale shear stress more efficiently, and an overestimate of the velocity gradient is removed. The dependence of the velocity profile on the grid point number is also investigated. It is found that the velocity gradient in the core region is underestimated in the case of a coarse grid. Attention should be paid not only to the velocity mismatch near the interface but also to the velocity profile in the core region in hybrid simulations of a channel flow at high Reynolds number. PACS47.27.Eq; 47.27.Nz; 47.60.+i     

Exact transport equation for eddy diffusivity in turbulent shear flow

Two-equation models that treat the transport equations for two variables are typical models for the Reynolds-averaged Navier–Stokes equation. Compared to the equation for the turbulent kinetic energy, the equation for the second variable such as the dissipation rate does not have a theoretical analogue. In this work, the exact transport equation for the eddy diffusivity was derived and examined for better understanding turbulence and improving two-equation models. A new length scale was first introduced, which involves the response function for the scalar fluctuation. It was shown that the eddy diffusivity can be expressed as the correlation between the velocity fluctuation and the new length scale. The transport equations for the eddy diffusivity and the length-scale variance were derived theoretically. Statistics such as terms in the transport equations were evaluated using the direct numerical simulation of turbulent channel flow. It was shown that the streamwise component of the eddy diffusivity is greater than the other two components in the whole region. In the transport equation for the eddy diffusivity, the production term due to the Reynolds stress is a main positive term, whereas the pressure–length-gradient correlation term plays a role of destruction. It is expected that the analysis of the transport equations is helpful in developing better turbulence models.     

Kinetic study of gas phase olefin polymerization with a TiCl4/MgCl2 catalyst. II. Kinetic parameter estimation and model building

Monomer transport and polymerization kinetics are two key phenomena in olefin polymerization with heterogeneous transition metal catalysts. To have a better understanding of these interrelated kinetics and diffusion phenomena, a quantitative calculation of the monomer diffusion directly from experimental study is essential. In this work, a novel temperature-perturbation technique is developed to systematically study the kinetic and diffusion limitations in catalyzed gas phase olefin polymerization. A physical model of the particle growth mechanism as well as its mathematical representation is presented and the diffusion limitations occurring in the system at high temperature are characterized and quantitatively analyzed. Finally, the practical implications of the results of this study on the operation of industrial scale polyolefin reactors are examined. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 2075-2096, 1997