A review on slip models for gas microflows

Accurate modeling of gas microflow is crucial for the microfluidic devices in MEMS. Gas microflows through these devices are often in the slip and transition flow regimes, characterized by the Knudsen number of the order of 10-2∼100. An increasing number of researchers now dedicate great attention to the developments in the modeling of non-equilibrium boundary conditions in the gas microflows, concentrating on the slip model. In this review, we present various slip models obtained from different theoretical, computational and experimental studies for gas microflows. Correct descriptions of the Knudsen layer effect are of critical importance in modeling and designing of gas microflow systems and in predicting their performances. Theoretical descriptions of the gas-surface interaction and gas-surface molecular interaction models are introduced to describe the boundary conditions. Various methods and techniques for determination of the slip coefficients are reviewed. The review presents the considerable success in the implementation of various slip boundary conditions to extend the Navier-Stokes (N-S) equations into the slip and transition flow regimes. Comparisons of different values and formulations of the first- and second-order slip coefficients and models reveal the discrepancies arising from different definitions in the first-order slip coefficient and various approaches to determine the second-order slip coefficient. In addition, no consensus has been reached on the correct and generalized form of higher-order slip expression. The influences of specific effects, such as effective mean free path of the gas molecules and viscosity, surface roughness, gas composition and tangential momentum accommodation coefficient, on the hybrid slip models for gas microflows are analyzed and discussed. It shows that although the various hybrid slip models are proposed from different viewpoints, they can contribute to N-S equations for capturing the high Knudsen number effects in the slip and transition flow regimes. Future studies are also discussed for improving the understanding of gas microflows and enabling us to exactly predict and actively control gas slip. © Springer-Verlag 2012.

LES of heat transfer in electronics

Numerical methods based on the Reynolds Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) equations are applied to the thermal prediction of flows representative of those found in and around electronics systems and components. Low Reynolds number flows through a heated ribbed channel, around a heated cube and within a complex electronics system case are investigated using linear and nonlinear LES models, hybrid RANS-LES and RANS-Numerical-LES (RANS-NLES) methods. Flow and heat transfer predictions using these techniques are in good agreement with each other and experimental data for a range of grid resolutions. Using second order central differences, the RANS-NLES method performs well for all simulations. © 2011 Elsevier Inc.

Numerical simulation of single-stream jets from a serrated nozzle

Hybrid large-eddy type simulations for cold jet flows from a serrated nozzle are performed at an acoustic Mach number Ma ac = 0.9 and Re = 1.03×10 6. Since the solver being used tends towards having dissipative qualities, the subgrid scale (SGS) model is omitted, giving a numerical type LES (NLES) or implicit LES (ILES) reminiscent procedure. To overcome near wall streak resolution problems a near wall RANS (Reynolds averaged Navier-Stokes) model is smoothly blended to the LES making a hybrid RANS-ILES. The geometric complexity of the serrated nozzle is fully considered without simplification or emulation. An improved but still modest hexahedral multi-block grid with circa 20 million grid points (with respect to 12.5 million in Xia et al.; Int J Heat Fluid Flow 30:1067-1079, 2009) is used. Despite the modest grid size, encouraging and improved results are obtained. Directly resolved mean and second-order fluctuating quantities along the jet centerline and in the jet shear layer compare favorably with measurements. The radiated far-field sound predicted using the Ffowcs Williams and Hawkings (FW-H) surface integral method shows good agreement with the measurements in directivity and sound spectra. © 2011 Springer Science+Business Media B.V.

Nonlinear optics in Silicon photonic crystal cavities

Silicon is known to be a very good material for the realization of high-Q, low-volume photonic cavities, but at the same it is usually considered as a poor material for nonlinear optical functionalities like second-harmonic generation, because its second-order nonlinear susceptibility vanishes in the dipole approximation. In this work we demonstrate that nonlinear optical effects in silicon nanocavities can be strongly enhanced and even become macroscopically observable. We employ photonic crystal nanocavities in silicon membranes that are optimized simultaneously for high quality factor and efficient coupling to an incoming beam in the far field. Using a low-power, continuous-wave laser at telecommunication wavelengths as a pump beam, we demonstrate simultaneous generation of second- and third harmonics in the visible region, which can be observed with a simple camera. The results are in good agreement with a theoretical model that treats third-harmonic generation as a bulk effect in the cavity region, and second-harmonic generation as a surface effect arising from the vertical hole sidewalls. Optical bistability is also observed in the silicon nanocavities and its physical mechanisms (optical, due to two-photon generation of free carriers, as well as thermal) are investigated. © 2011 IEEE.

A body force-based method for prediction of multiple-pure-tone noise: Validation

Emissions, fuel burn, and noise are the main drivers for innovative aircraft design. Embedded propulsion systems, such as for example used in hybrid-wing body aircraft, can offer fuel burn and noise reduction benefits but the impact of inlet flow distortion on the generation and propagation of turbomachinery noise has yet to be assessed. A novel approach is used to quantify the effects of non-uniform flow on the creation and propagation of multiple pure tone (MPT) noise. The ultimate goal is to conduct a parametric study of S-duct inlets to quantify the effects of inlet design parameters on the acoustic signature. The key challenge is that the effects of distortion transfer, noise source generation and propagation through the non-uniform flow field are inherently coupled such that a simultaneous computation of the aerodynamics and acoustics is required to capture the mechanisms at play. The technical approach is based on a body force description of the fan blade row that is able to capture the distortion transfer and the blade-to-blade flow variations that cause the MPT noise while reducing computational cost. A single, 3-D full-wheel CFD simulation, in which the Euler equations are solved to second-order spatial and temporal accuracy, simultaneously computes the MPT noise generation and its propagation in distorted inlet flow. A new method of producing the blade-to-blade variations in the body force field for MPT noise generation has been developed and validated. The numerical dissipation inherent to the solver is quantified and used to correct for non-physical attenuation in the far-field noise spectra. Source generation, acoustic propagation and acoustic energy transfer between modes is examined in detail. The new method is validated on NASA's Source Diagnostic Test fan and inlet, showing good agreement with experimental data for aerodynamic performance, acoustic source generation, and far-field noise spectra. The next steps involve the assessment of MPT noise in serpentine inlet ducts and the development of a reduced order formulation suitable for incorporation into NASA's ANOPP framework. © 2010 by Jeff Defoe, Alex Narkaj & Zoltan Spakovszky.

A novel MPT noise prediction methodology for highly-integrated propulsion systems with inlet flow distortion

Embedded propulsion systems, such as for example used in advanced hybrid-wing body aircraft, can potentially offer major fuel burn and noise reduction benefits but introduce challenges in the aerodynamic and acoustic integration of the high-bypass ratio fan system. A novel approach is proposed to quantify the effects of non-uniform flow on the generation and propagation of multiple pure tone noise (MPTs). The new method is validated on a conventional inlet geometry first. The ultimate goal is to conduct a parametric study of S-duct inlets in order to quantify the effects of inlet design parameters on the acoustic signature. The key challenge is that the mechanism underlying the distortion transfer, noise source generation and propagation through the non-uniform flow field are inherently coupled such that a simultaneous computation of the aerodynamics and acoustics is required. The technical approach is based on a body force description of the fan blade row that is able to capture the distortion transfer and the MPT noise generation mechanisms while greatly reducing computational cost. A single, 3-D full-wheel unsteady CFD simulation, in which the Euler equations are solved to second-order spatial and temporal accuracy, simultaneously computes the MPT noise generation and its propagation in distorted mean flow. Several numerical tools were developed to enable the implementation of this new approach. Parametric studies were conducted to determine appropriate grid and time step sizes for the propagation of acoustic waves. The Ffowcs-Williams and Hawkings integral method is used to propagate the noise to far field receivers. Non-reflecting boundary conditions are implemented through the use of acoustic buffer zones. The body force modeling approach is validated and proof-of-concept studies demonstrate the generation of disturbances at both blade-passing and shaft-order frequencies using the perturbed body force method. The full methodology is currently being validated using NASA's Source Diagnostic Test (SDT) fan and inlet geometry. Copyright © 2009 by Jeff Defoe, Alex Narkaj & Zoltan Spakovszky.

The vibro-acoustic analysis of built-up systems using a hybrid method with parametric and non-parametric uncertainties

An existing hybrid finite element (FE)/statistical energy analysis (SEA) approach to the analysis of the mid- and high frequency vibrations of a complex built-up system is extended here to a wider class of uncertainty modeling. In the original approach, the constituent parts of the system are considered to be either deterministic, and modeled using FE, or highly random, and modeled using SEA. A non-parametric model of randomness is employed in the SEA components, based on diffuse wave theory and the Gaussian Orthogonal Ensemble (GOE), and this enables the mean and variance of second order quantities such as vibrational energy and response cross-spectra to be predicted. In the present work the assumption that the FE components are deterministic is relaxed by the introduction of a parametric model of uncertainty in these components. The parametric uncertainty may be modeled either probabilistically, or by using a non-probabilistic approach such as interval analysis, and it is shown how these descriptions can be combined with the non-parametric uncertainty in the SEA subsystems to yield an overall assessment of the performance of the system. The method is illustrated by application to an example built-up plate system which has random properties, and benchmark comparisons are made with full Monte Carlo simulations. © 2012 Elsevier Ltd. All rights reserved.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.

2.1 GHz MOS mixer linearisation approach for IIP2 enhancement using multiple factor compensation

An integrated downconversion CMOS mixer incorporating a comprehensive compensation scheme is presented which aims to minimise second-order intermodulation distortion (IMD2). Unlike previously reported IMD2 calibration schemes which tune only one nonlinear factor at a time, the presented solution allows simultaneous adjustment of several different factors thus achieving a better compensation. The mixer has been implemented in UMC 0.18 μm CMOS to verify the proposed scheme and for comparison with alternative compensation methods. Measurements show that the solution described can improve the input intercept point (IIP2) by over 20 dB while maintaining good amplification and noise performance. IMD2 calibration results are presented and show useful advantages over other approaches. To the best of the authors' knowledge, this scheme for IMD2 calibration has not been previously reported. © The Institution of Engineering and Technology 2013.

Cabaret finite-difference schemes for the one-dimensional Euler equations

In the present paper we consider second order compact upwind schemes with a space split time derivative (CABARET) applied to one-dimensional compressible gas flows. As opposed to the conventional approach associated with incorporating adjacent space cells we use information from adjacent time layer to improve the solution accuracy. Taking the first order Roe scheme as the basis we develop a few higher (i.e. second within regions of smooth solutions) order accurate difference schemes. One of them (CABARET3) is formulated in a two-time-layer form, which makes it most simple and robust. Supersonic and subsonic shock-tube tests are used to compare the new schemes with several well-known second-order TVD schemes. In particular, it is shown that CABARET3 is notably more accurate than the standard second-order Roe scheme with MUSCL flux splitting.

Computations of turbulent lean premixed combustion using conditional moment closure

Conditional Moment Closure (CMC) is a suitable method for predicting scalars such as carbon monoxide with slow chemical time scales in turbulent combustion. Although this method has been successfully applied to non-premixed combustion, its application to lean premixed combustion is rare. In this study the CMC method is used to compute piloted lean premixed combustion in a distributed combustion regime. The conditional scalar dissipation rate of the conditioning scalar, the progress variable, is closed using an algebraic model and turbulence is modelled using the standard k-e{open} model. The conditional mean reaction rate is closed using a first order CMC closure with the GRI-3.0 chemical mechanism to represent the chemical kinetics of methane oxidation. The PDF of the progress variable is obtained using a presumed shape with the Beta function. The computed results are compared with the experimental measurements and earlier computations using the transported PDF approach. The results show reasonable agreement with the experimental measurements and are consistent with the transported PDF computations. When the compounded effects of shear-turbulence and flame are strong, second order closures may be required for the CMC. © 2013 Copyright Taylor and Francis Group, LLC.

Low-rank optimization with trace norm penalty

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges superlinearly to the global solution while maintaining complexity that is linear in the number of rows and columns of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach that outperforms the naive warm-restart approach on the fixed-rank quotient manifold. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. © 2013 Society for Industrial and Applied Mathematics.

Kinetic study of the 2-methyl-3-methoxy-4-phenylbutanoic acid produced by oxidation of microcystin in aqueous solutions

Microcystins (MCs) are a family of related cyclic hepatotoxic heptapeptides, of which more than 70 types have been identified. The chemically unique nature of the C20 beta-amino acid, (2S, 3S, 8S, 9S)-3-amino-9-methoxy-2,6,8-trimethyl-10-phenyldeca4,6-dienoic acid (Adda), portion of the MCs has been exploited to develop a strategy to analyze the entirety. Oxidation of MCs causes the cleavage of MC Adda to form 2-methyl-3-methoxy-4-phenylbutanoic acid (MMPB). In the present study, we investigated the kinetics of MMPB produced by oxidation of the most-often-studied MC variant, MC-LR (L = leucine, R = arginine), with permanganate-periodate. This investigation allowed insight regarding the influence of the reaction conditions (concentration of the reactants, temperature, and pH) on the conversion rate. The results indicated that the reaction was second order overall and first order with respect to both permanganate and MC-LR. The second-order rate constant ranged from 0.66 to 1.35 M/s at temperatures from 10 to 30 degrees C, and the activation energy was 24.44 kJ/mol. The rates of MMPB production can be accelerated through increasing reaction temperature and oxidant concentration, and sufficient periodate is necessary for the formation of MMPB. The initial reaction rate under alkaline and neutral conditions is higher than that under acidic conditions, but the former decreases faster than the latter except under weakly acidic conditions. These results provided new insight concerning selection of the permanganate-periodate concentration, pH, and temperature needed for the oxidation of MCs with a high and stable yield of MMPB.

Studies on the adsorption equilibrium and kinetics of pentachlorophenol on suspended particulate matter of Donghu Lake water

In this paper, the adsorption equilibrium and kinetic behaviors of pentachlorophenol (PCP) on suspended particulate matter (SPM) in Donghu Lake water were investigated. The Langmuir and Freundlich adsorption models were applied to describe the equilibrium isotherms and their constants were evaluated. The results indicated that the adsorption of PCP on Donghu Lake SPM followed the Freundlich isotherm. Furthermore, the first order Lagergren rate equation and the pseudo-second order rate equation were used to describe the kinetic behaviors of PCP adsorption on Donghu Lake SPM, the rate constants were determined, and the kinetic process of the adsorption of PCP on Donghu Lake SPM followed the second order kinetic model.

Partial and total replacement of fishmeal with poultry by-product meal in diets for gibel carp, Carassius auratus gibelio Bloch

Triplicate groups of gibel carp Carassius auratus gibelio Bloch (initial body weight: 4.89 g) were fed for 8 weeks at 24.8-30.8 degrees C with nine isonitrogenous and isoenergetic diets. The control diet (F1) used white fishmeal (FM) as the sole protein source. In the other eight diets (F2-F9), 40.5-100% of FM protein was substituted by poultry by-product meal (PBM) at 8.5% increments. The specific growth rate (SGR), feed efficiency ratio, protein efficiency ratio, protein retention efficiency and energy retention rate for fish fed PBM diets (F2-F9) were all higher, but not always significantly, than those for fish fed F1. All apparent digestibility coefficients for fish fed PBM diets were lower than those for fish fed F1. Fish fed F1 had a significantly higher hepatosomatic index value than fish fed PBM diets (P < 0.05). No significant (P > 0.05) effect of diet was found in whole-body moisture and fat content. Whole-body protein and energy content for fish fed PBM diets were slightly higher than that for fish fed F1. The optimal replacement level of FM by PBM was estimated by second-order polynomial regression to be 66.5% in protein.