Two-step simulation of slat noise

The flow field and the acoustic field of a high-lift configuration consisting of a slat and a main wing are numerically investigated by a hybrid method. In a first step, the unsteady flow field is computed via a large-eddy simulation (LES) and in a second step, the acoustic field is determined by solving the acoustic perturbation equations (APE). The mean flow field is compared to experimental findings followed by an investigation of the turbulent structures which are visualized by λ₂ contours. The analysis of the acoustic field shows that at the main wing trailing edge acoustic pressure fluctuations of approximately 5 kHz are generated. Correlations between the noise sources and the acoustic pressure identify the slat-gap region to be responsible for the mixture of broadband and tonal noise between 1 and 3 kHz. The decay of the pressure spectrum is found to be approximately f⁻² which is in agreement with the literature.     

Lateral migration of particles suspended in viscoelastic fluids in a microchannel flow

In this work, we investigated the lateral migration of microparticles suspended in two different viscoelastic fluids with or without the second normal stress difference. For the viscoelastic fluid without the second normal stress difference, competing forces existed between microfluidic inertia and the first normal stress difference (N ₁), which resulted in a synergetic effect of particle focusing. For the fluid with the second normal stress difference (N ₂), particles were greatly affected by a N ₂-induced secondary flow, and the competition among the inertia, N ₁, and N ₂ determined the lateral migration trajectories of the particles. The obtained results were delineated with the blockage ratio, which showed good agreement with the results of a recent numerical study (Villone et al. in J Non Newton Fluid Mech 195:1–8, 2013). The present study also examined the possibility of particle separation in a size-dependent manner using the N ₂-induced secondary flow in microchannel flow.     

Analysis, design, and performance limitations of optimal filtering in the presence of an additional input with known frequency

In this paper, the inputs are considered to be of two types. The first type of input, as in standard H₂ optimal filtering, is a zero mean wide sense stationary white noise, while the second type is a linear combination of sinusoidal signals each of which has an unknown amplitude and phase but known frequency. The generalized H₂ optimal filtering problem seeks to find a linear stable filter that estimates a desired output such that the H₂ norm of the transfer matrix from the white noise input to the estimation error is minimized subject to the constraint that the mean of the error converges to zero for all initial conditions of the given system and filter and for all possible external sinusoidal signals. The analysis, design, and performance limitations of generalized H₂ optimal filters are presented here.     

Bifurcations and buffet of transonic flow past flattened surfaces

Turbulent transonic flow past flattened aerodynamic surfaces is investigated numerically using the RANS equations. The study is focused on: (★) a buffet onset caused by instability of the shock wave/boundary layer interaction, (★★) instability of the entire flow structure and related flow bifurcations.For a symmetric airfoil at zero angle of attack, computations reveal both bifurcations and buffet in a range of the freestream Mach number M_∞. At nonzero angles of attack, α=±1°, there are two ranges of M_∞ in which the buffet onset takes place. For a Whitcomb type airfoil, computations demonstrate instability of the flow structure only at negative α. Axisymmetric flow past axisymmetric bodies is also considered, and instability of the flow structure at certain freestream Mach numbers is shown.     

A contribution to the computation of transonic supersonic flows over blunt bodies

Stationary inviscid transonic supersonic flowfield around sphrese, ellipsoids and hemisphere-cylinders are calculated. The freestream Mach numbers considered are between $\text{M}{}_{\mathrm{\infty }}\text{= 1.02}$ and $\text{M}{}_{\mathrm{\infty }}\text{= 1.1}$. A special coordinate system is created which is adjusted to the subsonic stagnation point region for transonic freestream Mach numbers. The integration of the governing equations is carried out by means of a time-dependent finite-difference procedure. All the calculations discussed were stable and converged uniquely to the asymptotic stationary state. The influence of an artificial dissipation term added to the finite-difference scheme is studied. It is further shown, that in all cases the limiting characteristics come from the front part of the bodies. The results include bow shocks, sonic lines, characteristics, lines of constant pressure, density and Mach numbers. A comparison is made between such flow quantities which are calculable by analytical functions and the predicted ones. The quality of the results is checked by considering the conservation of the total enthalpy. For some examples the present solutions are compared with other theories and experimental data.     

Quantitative structure–retention relationship modelling of esters on stationary phases of different polarity

The semi-empirical electrotopological index, I_SET, used for QSRR models, was developed and optimized to describe the chromatographic retention of saturated esters on the five different stationary phases (SE-30, OV-7, DC-710, OV-225 and XE-60). The simple linear regressions between the retention indices and the proposed index were of good statistical quality, high internal stability and good predictive ability for external groups, especially for the stationary phase with low polarity, showing that the specific molecular interactions occur on highly polar phases. For the esters, the interactions between the molecules and the stationary phase are slowly increased relative to hydrocarbons due to the charge redistribution that occurs in the presence of the heteroatom. These facts were included in the calculation of I_SET through a small increase in the SET_i values for heteroatoms and the carbon atoms attached to them. The increase in the SET_i values originates from the dipole moment of the whole molecule and an equivalent local dipole moment related to the net charges of the atoms belonging to the functional group and the carbon atoms attached to them. The polarity of the stationary phases, indicated by the retention polarity (P_R) given by Tarján, is reflected in the intercept of the equations obtained for each stationary phase. Thus, a single combined QSRR model was generated with a satisfactory predictive quality, including a parameter that represents the polarity retention of all stationary phases studied.     

A comparative study on particle�Cfluid interactions in micro and nanofluids of aluminium oxide

Stable dispersions of micro and nanosized Al₂O₃ particles in ethylene glycol are prepared with the aid of sonication. The temperature dependant acoustic properties such as ultrasonic velocity, adiabatic compressibility, attenuation and acoustic impedance are studied and reported in this paper. In microfluids the particle–fluid interaction is observed to decrease with increase of concentration of particles whereas in nanofluids it is observed to increase up to the critical concentration (0.6 Wt%) and above which the particle–particle interaction dominates due to agglomeration of particles. A range of concentration with significant particle–fluid interaction is identified for effective nanofluid applications.     

High-throughput electrokinetic bioparticle focusing based on a travelling-wave dielectrophoretic field

This study presents a sheathless and portable microfluidic chip that is capable of high-throughput focusing bioparticles based on 3D travelling-wave dielectrophoresis (twDEP). High-throughput focusing is achieved by sustaining a centralized twDEP field normal to the continuous through-flow direction. Two twDEP electrode arrays are formed from upper and lower walls of the microchannel and extend to its center, which induce twDEP forces to provide the lateral displacements in two directions for focusing the bioparticles. Bioparticles can be focused to the center of the microchannel effectively by twDEP conveyance when the characteristic time due to twDEP conveying in the y direction is shorter than the residence time of the particles within twDEP electrode array. Red blood cells can be effectively focused into a narrow particle stream (~10 μm) below a critical flow rate of 10 μl/min (linear flow velocity ~5 mm/s), when under a voltage of 14 V_p–p at a frequency of 500 kHz is applied. Approximately 90% focusing efficiency for red blood cells can be achieved within two 6-mm-long electrode arrays when the flow rate is below 12 μl/min. Blood cells and Candida cells were also focused and sorted successfully based on their different twDEP mobilities. Compared to conventional 3D-paired DEP focusing, velocity is enhanced nearly four folds of magnitude. 3D twDEP provides the lateral displacements of particles and long residence time for migrating particles in a high-speed continuous flow, which breaks through the limitation of many electrokinetic cell manipulation techniques.     

An equivalence between rational H2 and Hankel-norm approximations

Let H(z) be a given function in H₂ A classical problem in engineering analysis is to find a rational function G (z) ε H₂ degree M say, which is closest to H(z) in 2-norm. This problem is typically approached using the cost function |H(z) − G(z)|₂, in which G(z) is allowed to vary over the set of Mth-order rational functions in H₂ and for which stationary points are sought. We show that each stationary point of degree M of this functional coincides with a weighted Hankel-norm approximant to H(z). The weighting function derives from the outer factor of the error function H(z) − G(z) stationary point of the rational H₂ approximation problem.     

Min–max Kalman filtering

The problem of H_∞-optimal state estimation of linear continuous-time systems that are measured with an additive white noise is addressed. The relevant cost function is the expected value of the standard H_∞ performance index, with respect to the measurement noise statistics. The solution is obtained by applying the matrix version of the maximum principle to the solution of the min–max problem in which the estimator tries to minimize the mean square estimation error and the exogenous disturbance tries to maximize it while being penalized for its energy. The solution is given in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated Kalman filter is recovered. In the stationary case, where all the signals are stationary, an upper-bound on the solutions of the coupled Riccati equations is obtained via a solution of coupled linear matrix inequalities. The resulting filter then guarantees a bound on the estimation error covariance matrix. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the position.     

A numerical model-assisted experimental design study of inertia-based particle focusing in stepped microchannels

Focusing methods based on fluid inertia have been demonstrated to be able to concentrate particles with a high precision and predictability offering great potential for practical application as manipulation of bodily fluids as blood for clinical diagnostics. However, to perform focusing to one single position at the center location of a channel with high focusing quality on the one hand and low pressure losses and shear stresses on the other hand still is a challenge in microchannel design. Three different stepped microchannels are analyzed via bright-field microscopy to investigate the impact of various geometric parameters on the focusing behavior of spherical particles. Reynolds numbers within a range of \( 8 \le Re \le 75\) are measured to evaluate the impact of flow conditions on the focusing characteristics. The microchannels show the ability to focus particles to a single stream with a maximum focusing efficiency of 97.1\(\%\) and purity of 99.1\(\%\). The focusing strongly depends on the channel geometry, that is, step length, step height, and settling length. A semiempirical model is developed to predict force-induced focusing ability at maximum shear stresses that are reduced significantly compared to previous systems. This model is demonstrated to be in very good agreement with experimental results and therefore can be utilized for future device design. Finally, guidelines for the design of stepped single-stream focusing devices at low pressure losses and low maximum shear stresses are derived based on experimental, numerical, and semiempirical data.     

Quantitative characterization of the focusing process and dynamic behavior of differently sized microparticles in a spiral microchannel

In this paper, a spiral microchannel was fabricated to systematically investigate particle dynamics. The focusing process or migration behavior of different-sized particles in the outlet region was presented. Specifically, for focused microparticles, quantitative characterization and analysis of how particles migrate towards the equilibrium positions with the increase in flow rate (De = 0.31–3.36) were performed. For unfocused microparticles, the particle migration behavior and the particle-free region’s formation process were characterized over a wide range of flow rates (De = 0.31–4.58), and the emergence of double particle-free regions was observed at De ≥ 3.36. These results provide insights into the design and operation of high-throughput particle/cell filtration and separation. Furthermore, using the location markers pre-fabricated along with the microchannel structures, the focusing or migration dynamics of different-sized particles along the spiral microchannel was systematically explored. The particle migration length effects on focusing degree and particle-free region width were analyzed. These analyses may be valuable for the optimization of microchannel structures. In addition, this device was successfully used to efficiently filter rare particles from a large-volume sample and separate particles of two different sizes according to their focusing states.     

Inertial particle focusing dynamics in a trapezoidal straight microchannel: application to particle filtration

Inertial microfluidics has emerged recently as a promising tool for high-throughput manipulation of particles and cells for a wide range of flow cytometric tasks including cell separation/filtration, cell counting, and mechanical phenotyping. Inertial focusing is profoundly reliant on the cross-sectional shape of channel and its impacts on not only the shear field but also the wall-effect lift force near the wall region. In this study, particle focusing dynamics inside trapezoidal straight microchannels was first studied systematically for a broad range of channel Re number (20 < Re < 800). The altered axial velocity profile and consequently new shear force arrangement led to a cross-lateral movement of equilibration toward the longer side wall when the rectangular straight channel was changed to a trapezoid; however, the lateral focusing started to move backward toward the middle and the shorter side wall, depending on particle clogging ratio, channel aspect ratio, and slope of slanted wall, as the channel Reynolds number further increased (Re > 50). Remarkably, an almost complete transition of major focusing from the longer side wall to the shorter side wall was found for large-sized particles of clogging ratio K ~ 0.9 (K = a/H_min) when Re increased noticeably to ~ 650. Finally, based on our findings, a trapezoidal straight channel along with a bifurcation was designed and applied for continuous filtration of a broad range of particle size (0.3 < K < 1) exiting through the longer wall outlet with ~ 99% efficiency (Re < 100).     

Time evolution of a system of two valued interacting elements : a microscopic interpretation of birth and death equations

We consider here one of the simplest possible systems with N interacting particles. It has the following features : (i) the state variable of each particle takes the values σ_i(= ?1 ; (ii) the interaction is chosen in such a way to preserve the symmetry of the distribution function p(σ₁, σ₂, [tdot], σ _N ; t) with respect to the σ _i and (iii) the evolution of the system is defined in a stochastic way by the transition probabilities of each particle as depending on the state of all other particles. The master equation of this Markov process is shown to be the equation of a general birth and death process in one dimension. More precisely, the birth and death process is : linear if the particles are independent ; quadratic if there is a binary interaction ; or cubic if there is a third-order interaction. We develop the reduced distribution equations hierarchy (which is the analogue of the BBGKY hierarchy) and we study under what conditions this hierarchy closes. Then we show that for specific systems there is a conserved quantity (in the mean) and we discuss for what kind of intercation there is respectively an H-theorem and a postulate of equal a priori probabilities at equilibrium. It appears in particular that this postulate should not be true in the strong form in which it is usually stated.     

Analysis of mixed motion in deterministic ratchets via experiment and particle simulation

Deterministic lateral displacement (DLD) ratchets are microfluidic devices, which are used for size-based sorting of cells or DNA. Based on their size, particles are showing different kinds of motion, leading to their fractionation. In earlier studies, so-called zigzag and displacement motions are observed, and in recent study by our group (Kulrattanarak et al., Meas Sci Technol, 2010a; J Colloid Interface Sci, 2010b), we have shown that also mixed motion occurs, which is an irregular alternation of zigzag and displacement motion. We have shown that the mixed motion is due to asymmetry of the flow lane distribution, induced by the symmetry breaking of the oblique primitive lattice cell (Kulrattanarak et al. 2010b). In this study, we investigate mixed motion in depth by numerical and experimental analysis. Via 3D simulations, we have computed explicit particle trajectories in DLD, and are able to show that there are two critical length scales determining the type of motion. The first length scale d _f,1 is the first flow lane width, which determines the transition between zigzag motion and mixed motion. The other length scale, d _f,c , determines the transition between mixed motion and displacement motion. Based on our experimental and numerical results we have been able to correlate the migration angle of particles showing mixed motion to the particle size, relative to the two critical length scales d _f,1 and d _f,c .     

Non-full-rank causal approximations of full-rank multivariate stationary processes with rational spectrum

Let Y = (Y_n)_{n ε ζ} be a q-variate wide-sense stationary process with full-rank rational spectral density. We characterize the q-variate stationary processes , causally subordinated to Y, whose spectral densities have rank p < q almost everywhere, and for which is minimum.     

Model reduction of discrete Markovian jump systems with time‐weighted H2 performance

This paper is concerned with the optimal time‐weighted H₂ model reduction problem for discrete Markovian jump linear systems (MJLSs). The purpose is to find a mean square stable MJLS of lower order such that the time‐weighted H₂ norm of the corresponding error system is minimized for a given mean square stable discrete MJLSs. The notation of time‐weighted H₂ norm of discrete MJLS is defined for the first time, and then a computational formula of this norm is given, which requires the solution of two sets of recursive discrete Markovian jump Lyapunov‐type linear matrix equations. Based on the time‐weighted H₂ norm formula, we propose a gradient flow method to solve the optimal time‐weighted H₂ model reduction problem. A necessary condition for minimality is derived, which generalizes the standard result for systems when Markov jumps and the time‐weighting term do not appear. Finally, numerical examples are used to illustrate the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal time-weighted H 2 model reduction for Markovian jump systems

This article addresses the optimal time-weighted H ₂ model reduction problem for Markovian jump linear systems. That is, for a given mean square stable Markovian jump system, our aim is to find a mean square stable jump system of lower order such that the time-weighted H ₂ norm of the corresponding error system is minimised. The time-weighted H ₂ norm of the system is first defined, and then a computational method is constructed. The computation requires the solution of two sets of recursive Lyapunov-type linear matrix equations associated with the Markovian jump system. To solve the optimal time-weighted H ₂ model reduction problem, we propose a gradient flow method for its solution. A necessary condition for minimality is derived, and a computational procedure is provided to obtain the minimising reduced-order model. The necessary condition generalises the standard result for systems when Markov jumps and the time-weighting term do not appear. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed approach.     

Numerical simulation of cloud droplet formation in a tank

Using the computational fluid dynamics (CFD) code FLUENT 6 together with the fine particle model (FPM), numerical simulations of droplet dynamics in a 12.4 m³ cloud tank were conducted. The coupled fields of water vapor, temperature, flow velocity, particle number concentration, and particle mass concentration inside the cloud tank were computed.The system responses to changes of the wall's temperature and mass fraction of water vapor, respectively, were investigated. Typical times for mixing the cloud tank's contents are in the range of some tens of seconds. The maximum volume-averaged deviations from the mean of temperature and mass fraction of water vapor are around 5% of the respective parameter changes applied to the wall.Time-dependent simulations were performed in order to study the growth of ammonium-sulfate particles in humid air at around room temperature. Supersaturation up to (S_w–1)=8.2×10⁻³ was achieved by the expansion of the gas. The particles were activated and grew rapidly to a maximum diameter of 5.2×10⁻⁶ m after critical supersaturation was reached. After S_w fell again below the equilibrium value, the particles shrank quickly and deactivated roughly 60 s after activation.The spatial inhomogeneities of temperature and water-vapor concentration cause volume-averaged deviations of the particle number N and diameter d_g of up to 2.3% and 36%, respectively.     

Flow-rate-insensitive deterministic particle sorting using a combination of travelling and standing surface acoustic waves

Manipulation of cells by acoustic forces in a continuous flow offers a means to sort on the basis of physical properties in a contactless, label-free and biocompatible manner. Many acoustic sorting systems rely on either standing waves or travelling waves alone and require specific exposure times to the acoustic field, fine-tuned by manipulating the bulk flow rate. In this work, we demonstrate a flow-rate-insensitive device for continuous particle sorting by employing a pressure field that utilises both travelling and standing acoustic wave components, whose non-uniform spatial distribution arises from the attenuation of a leaky surface acoustic wave. We show that in parts of the pressure field in which the travelling wave component dominates, particles migrate across multiple wavelengths. In doing so, they drift into areas of standing wave dominance, whereby particles are confined within their respective nodal positions. It is demonstrated that this final confinement location is dependent on the particle size and independent of the force field exposure time and thus the flow rate, permitting the continuous separation of 5.1-, 6.1- and 7.0-µm particles. Omitting the need to precisely control the bulk flow rate potentially enables sorting in systems in which flow is not driven by external pumps.