Inverse design technique for cascades

A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided

Frictional Collisions Off Sharp Objects

This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement

Controllability of a viscoelastic plate using one boundary control in displacement or bending

In this paper we consider a viscoelastic plate (linear viscoelasticity of the Maxwell-Boltzmann type) and we compare its controllability properties with the (known) controllability of a purely elastic plate (the control acts on the boundary displacement or bending). By combining operator and moment methods, we prove that the viscoelastic plate inherits the controllability properties of the purely elastic plate

Modelling and solutions to the linear stability of a detonation wave in the kinetic frame

Artigo publicado num número especial da revista.The analysis of linear stability of a steady detonation wave is formulated for the first time at the kinetic level in the frame of the Boltzmann equation extended to reacting gases. Within this context and for a reversible reaction, the stability problem is carried out, in agreement with most classical papers on gas detonation, through a normal mode approach for the one-dimensional disturbances of the steady wave solution, and an acoustic radiation condition at the final equilibrium as closure condition. The proposed modelling leads to an initial value problem, constituted by the linearized reactive Euler equations in the perturbed shock frame with related Rankine-Hugoniot conditions, which can be solved by means of a proper numerical technique. An application is provided for an elementary bimolecular reaction.Centro de Matemática da Universidade do MinhoFundação para a Ciência e a Tecnologia (FCT)Italian INDAM-GNF

Variability of aerosol optical properties in the Western Mediterranean Basin

Aerosol light scattering, absorption and particulate matter (PM) concentrations were measured at Montseny, a regional background site in the Western Mediterranean Basin (WMB) which is part of the European Supersite for Atmospheric Aerosol Research (EUSAAR). Off line analyses of 24 h PM filters collected with Hi-Vol instruments were performed for the determination of the main chemical components of PM. Mean scattering and hemispheric backscattering coefficients (@ 635 nm) were 26.6±23.2 Mm<sup>−1</sup> and 4.3±2.7 Mm<sup>−1</sup>, respectively and the mean aerosol absorption coefficient (@ 637 nm) was 2.8±2.2 Mm<sup>−1</sup>. Mean values of Single Scattering Albedo (SSA) and Ångström exponent (<i>å</i>) (calculated from 450 nm to 635 nm) at MSY were 0.90±0.05 and 1.3±0.5 respectively. A clear relationship was observed between the PM<sub>1</sub>/PM<sub>10</sub> and PM<sub>2.5</sub>/PM<sub>10</sub> ratios as a function of the calculated Ångström exponents. Mass scattering cross sections (MSC) for fine mass and sulfate at 635 nm were 2.8±0.5 m<sup>2</sup> g<sup>−1</sup> and 11.8±2.2 m<sup>2</sup> g<sup>−1</sup>, respectively, while the mean aerosol absorption cross section (MAC) was 10.4±2.0 m<sup>2</sup> g<sup>−1</sup>. The variability in aerosol optical properties in the WMB were largely explained by the origin and ageing of air masses over the measurement site. The MAC values appear dependent of particles aging: similar to the expected absorption cross-section for fresh emissions under Atlantic Advection episodes and higher under aerosol pollution episodes. The analysis of the Ångström exponent as a function of the origin the air masses revealed that polluted winter anticyclonic conditions and summer recirculation scenarios typical of the WMB led to an increase of fine particles in the atmosphere (<i>å</i> = 1.5±0.1) while the aerosol optical properties under Atlantic Advection episodes and Saharan dust outbreaks were clearly dominated by coarser particles (<i>å</i> = 1.0±0.4). The sea breeze played an important role in transporting pollutants from the developed WMB coastlines towards inland rural areas, changing the optical properties of aerosols. Aerosol scattering and backscattering coefficients increased by around 40 % in the afternoon when the sea breeze was fully developed while the absorption coefficient increased by more than 100 % as a consequence of the increase in the equivalent black carbon concentration (EBC) observed at MSY under sea breeze circulation

A reactive BGK-type model: influence of elastic collisions and chemical interactions

A BGK‐type model for a reactive multicomponent gas undergoing chemical bimolecular reactions is here presented. The mathematical and physical consistency of the model is stated in detail. The relaxation process towards local Maxwellians, depending on mass and numerical densities of each species, as well as on common mean velocity and temperature, is investigated with respect to chemical equilibrium. Such a trend is numerically tested within the hydrogen‐air reaction mechanism

On the kinetic modelling of reactive waves in the hydrodynamic limit

The present study deals with the extension of the exact and approximate models of the Boltzmann equation to a gas mixture of four constituents undergoing a reversible bimolecular reaction, and its application to wave propagation problems. The paper intends to highlight how Boltzmann type models, on the basis of a shared kinetic framework, can be adopted as the starting point for a consistent derivation of the reactive hydrodynamic equations, at both the Euler and Navier Stokes limit. At this scope, a proper mathematical procedure is applied to obtain an approximate solution to the model equations, which is necessary in order to derive the closed system of the governing equations in the above said hydrodynamic limits. Resorting to this unified kinetic approach which is presented in detail, one can recognize how the dynamics of rather different wave problems well known in literature, as the steady detonation wave and its linear stability, the sound wave propagation and the light scattering phenomena, match a satisfactory description with care for the chemical mechanism at the microscopic scale. The knowledge of the chemical process at this level permits to evaluate the influence of the chemical reaction on the fundamental aspects of the reacting gas system, reinforcing the proposed kinetic approach. Accordingly, some propagation wave problems, recently studied by the authors in this context, are in turn here reviewed at the end of focusing how their formulation and solution depend on the proposed hydrodynamic closure procedure.Fundação para a Ciência e a Tecnologia (FCT

Climatology of aerosol optical properties and black carbon mass absorption cross section at a remote high-altitude site in the western Mediterranean Basin

Aerosol light scattering (&sigma;_sp), backscattering (&sigma;_bsp) and absorption (&sigma;_ap) were measured at Montsec (MSC; 42°3' N, 0°44' E, 1570 m a.s.l.), a remote high-altitude site in the western Mediterranean Basin. Mean (±SD) &sigma;_sp, &sigma;_bsp and &sigma;_ap were 18.9 ± 20.8, 2.6 ± 2.8 and 1.5 ± 1.4 Mm⁻¹, respectively at 635 nm during the period under study (June 2011–June 2013). Mean values of single-scattering albedo (SSA, 635 nm), the scattering Ångström exponent (SAE, 450–635 nm), backscatter-to-scatter ratio (<i>B</i> / <i>S</i>, 635 nm), asymmetry parameter (<i>g</i>, 635 nm), black carbon mass absorption cross section (MAC, 637 nm) and PM_2.5 mass scattering cross section (MSCS, 635 nm) were 0.92 ± 0.03, 1.56 ± 0.88, 0.16 ± 0.09, 0.53 ± 0.16, 10.9 ± 3.5 m² g⁻¹ and 2.5 ± 1.3 m² g⁻¹, respectively. The scattering measurements performed at MSC were in the medium/upper range of values reported by Andrews et al. (2011) for other mountaintop sites in Europe due to the frequent regional recirculation scenarios (SREG) and Saharan dust episodes (NAF) occurring mostly in spring/summer and causing the presence of polluted layers at the MSC altitude. However, the development of upslope winds and the possible presence of planetary boundary layer air at MSC altitude in summer may also have contributed to the high scattering observed. Under these summer conditions no clear diurnal cycles were observed for the measured extensive aerosol optical properties (&sigma;_sp, &sigma;_bsp and &sigma;_ap). Conversely, low &sigma;_sp and &sigma;_ap at MSC were measured during Atlantic advections (AA) and winter regional anticyclonic episodes (WREG) typically observed during the cold season in the western Mediterranean. Therefore, a season-dependent decrease in the magnitude of aerosol extensive properties was observed when MSC was in the free troposphere, with the highest free-troposphere vs. all-data difference observed in winter and the lowest in spring/summer. The location of MSC station allowed for a reliable characterization of aerosols as a function of the main synoptic meteorological patterns. The SAE was the lowest during NAF and showed an inverse correlation with the outbreak intensity, indicating a progressive shift toward larger particles. Moreover, the strength of NAF episodes in the region led to a slope of the scattering vs. absorption relationship among the lowest reported for other mountaintop sites worldwide, indicating that MSC was dominated by dust aerosols at high aerosol loading. As a consequence, SSA showed a nearly monotonic increase with increasing particle concentration and scattering. The SAE was the highest during SREG, indicating the presence of polluted layers dominated by smaller particles. Correspondingly, the asymmetry parameter was lower under SREG compared with NAF. The MAC and MSCS were significantly higher during NAF and SREG compared to AA and WREG, indicating an increase of absorption and scattering efficiencies associated with the summer polluted scenarios. The optical measurements performed at the MSC remote site were compared with those simultaneously performed at a regional background station in the western Mediterranean Basin located at around 700 m a.s.l. upstream of the MSC station