Effect of wave frequency on the nonlinear interaction between Görtler vortices and three-dimensional Tollmien-Schlichting waves

The nonlinear interaction between Görtler vortices (GV) and three-dimensional Tollmien-Schlichting (TS) waves nonlinear interaction is studied with a spatial, nonparallel model based on the Parabolized Stability Equations (PSE). In this investigation the effect of TS wave frequency on the nonlinear interaction is studied. As verified in previous investigations using the same numerical model, the relative amplitudes and growth rates are the dominant parameters in GV/TS wave interaction. In this sense, the wave frequency influence is important in defining the streamwise distance traveled by the disturbances in the unstable region of the stability diagram and in defining the amplification rates that they go through.

An experimental/numerical study of the turbulent boundary layer development along a surface with a sudden change in roughness

A theory for the description of turbulent boundary layer flows over surfaces with a sudden change in roughness is considered. The theory resorts to the concept of displacement in origin to specify a wall function boundary condition for a kappa-epsilon model. An approximate algebraic expression for the displacement in origin is obtained from the experimental data by using the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963). This expression is subsequently included in the near wall logarithmic velocity profile, which is then adopted as a boundary condition for a kappa-epsilon modelling of the external flow. The results are compared with the lower atmospheric observations made by Bradley(Q. J. Roy. Meteo. Soc., vol. 94, pp. 361-379, 1968) as well as with velocity profiles extracted from a set of wind tunnel experiments carried out by Avelino et al.( 7th ENCIT, 1998). The measurements are found to be in good agreement with the theoretical computations. The skin-friction coefficient was calculated according to the chart method of Perry and Joubert(J.F.M., vol. 17, pp. 193-122, 1963) and to a balance of the integral momentum equation. In particular, the growth of the internal boundary layer thickness obtained from the numerical simulation is compared with predictions of the experimental data calculated by two methods, the "knee" point method and the "merge" point method.

On the numerical simulation of machining processes

Numerical simulation of machining processes can be traced back to the early seventies when finite element models for continuous chip formation were proposed. The advent of fast computers and development of new techniques to model large plastic deformations have favoured machining simulation. Relevant aspects of finite element simulation of machining processes are discussed in this paper, such as solution methods, material models, thermo-mechanical coupling, friction models, chip separation and breakage strategies and meshing/re-meshing strategies.

Numerical study of Petrov-Galerkin formulations for the shallow water wave equations

The behavior of Petrov-Galerkin formulations for shallow water wave equations is evaluated numerically considering typical one-dimensional propagation problems. The formulations considered here use stabilizing operators to improve classical Galerkin approaches. Their advantages and disadvantages are pointed out according to the intrinsic time scale (free parameter) which has a particular importance in this kind of problem. The influence of the Courant number and the performance of the formulation in dealing with spurious oscillations are adressed.

Numerical study on mixed convection in a horizontal flow past a square porous cavity using UNIFAES scheme

Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained.

On the numerical integration of rigid body nonlinear dynamics in presence of parameters singularities

One of the main complexities in the simulation of the nonlinear dynamics of rigid bodies consists in describing properly the finite rotations that they may undergo. It is well known that, to avoid singularities in the representation of the SO(3) rotation group, at least four parameters must be used. However, it is computationally expensive to use a four-parameters representation since, as only three of the parameters are independent, one needs to introduce constraint equations in the model, leading to differential-algebraic equations instead of ordinary differential ones. Three-parameter representations are numerically more efficient. Therefore, the objective of this paper is to evaluate numerically the influence of the parametrization and its singularities on the simulation of the dynamics of a rigid body. This is done through the analysis of a heavy top with a fixed point, using two three-parameter systems, Euler's angles and rotation vector. Theoretical results were used to guide the numerical simulation and to assure that all possible cases were analyzed. The two parametrizations were compared using several integrators. The results show that Euler's angles lead to faster integration compared to the rotation vector. An Euler's angles singular case, where representation approaches a theoretical singular point, was analyzed in detail. It is shown that on the contrary of what may be expected, 1) the numerical integration is very efficient, even more than for any other case, and 2) in spite of the uncertainty on the Euler's angles themselves, the body motion is well represented.

Numerical and experimental investigation of thermal louvers for space applications

Thermal louvers, using movable or rotating shutters over a radiating surface, have gained a wide acceptance as highly efficient devices for controlling the temperature of a spacecraft. This paper presents a detailed analysis of the performance of a rectangular thermal louver with movable blades. The radiative capacity of the louver, determined by its effective emittance, is calculated for different values of the blades opening angle. Experimental results obtained with a prototype of a spacecraft thermal louver show good agreement with the theoretical values.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Numerical Simulation of the Cavitation in the Hydrodynamic Lubrication of Journal Bearings: a Parallel Algorithm

In this paper we present an algorithm for the numerical simulation of the cavitation in the hydrodynamic lubrication of journal bearings. Despite the fact that this physical process is usually modelled as a free boundary problem, we adopted the equivalent variational inequality formulation. We propose a two-level iterative algorithm, where the outer iteration is associated to the penalty method, used to transform the variational inequality into a variational equation, and the inner iteration is associated to the conjugate gradient method, used to solve the linear system generated by applying the finite element method to the variational equation. This inner part was implemented using the element by element strategy, which is easily parallelized. We analyse the behavior of two physical parameters and discuss some numerical results. Also, we analyse some results related to the performance of a parallel implementation of the algorithm.

Numerical study of wedge supported oblique shock wave-oblique detonation wave transitions

The results of a numerical study of premixed Hydrogen-air flows ignition by an oblique shock wave (OSW) stabilized by a wedge are presented, in situations when initial and boundary conditions are such that transition between the initial OSW and an oblique detonation wave (ODW) is observed. More precisely, the objectives of the paper are: (i) to identify the different possible structures of the transition region that exist between the initial OSW and the resulting ODW and (ii) to evidence the effect on the ODW of an abrupt decrease of the wedge angle in such a way that the final part of the wedge surface becomes parallel to the initial flow. For such a geometrical configuration and for the initial and boundary conditions considered, the overdriven detonation supported by the initial wedge angle is found to relax towards a Chapman-Jouguet detonation in the region where the wedge surface is parallel to the initial flow. Computations are performed using an adaptive, unstructured grid, finite volume computer code previously developed for the sake of the computations of high speed, compressible flows of reactive gas mixtures. Physico-chemical properties are functions of the local mixture composition, temperature and pressure, and they are computed using the CHEMKIN-II subroutines.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.

Infestation maps and spatial stability of main weed species in maize culture

A study on the spatial distribution of the major weeds in maize was carried out in 2007 and 2008 in a field located in Golegã (Ribatejo region, Portugal). The geo-referenced sampling focused on 150 points of a 10 x 10 m mesh covering an area of 1.5 ha, before herbicide application and before harvest. In the first year, 40 species (21 botanical families) were identified at seedling stage and only 22 during the last observation. The difference in species richness can be attributed to maize monoculture favouring reduction in species number. Three of the most representative species were selected for the spatial distribution analysis: Solanum nigrum, Chenopodium album and Echinochloa crus-galli. The three species showed an aggregated spatial pattern and spatial stability over both years, although the herbicide effect is evident in the distribution of some of them in the space. These results could be taken into account when planning site-specific treatments in maize.

Laser cladding with scanning optics

Scanning optics create different types of phenomena and limitation to cladding process compared to cladding with static optics. This work concentrates on identifying and explaining the special features of laser cladding with scanning optics. Scanner optics changes cladding process energy input mechanics. Laser energy is introduced into the process through a relatively small laser spot which moves rapidly back and forth, distributing the energy to a relatively large area. The moving laser spot was noticed to cause dynamic movement in the melt pool. Due to different energy input mechanism scanner optic can make cladding process unstable if parameter selection is not done carefully. Especially laser beam intensity and scanning frequency have significant role in the process stability. The laser beam scanning frequency determines how long the laser beam affects with specific place local specific energy input. It was determined that if the scanning frequency in too low, under 40 Hz, scanned beam can start to vaporize material. The intensity in turn determines on how large package this energy is brought and if the intensity of the laser beam was too high, over 191 kW/cm2, laser beam started to vaporize material. If there was vapor formation noticed in the melt pool, the process starts to resample more laser alloying due to deep penetration of laser beam in to the substrate. Scanner optics enables more flexibility to the process than static optics. The numerical adjustment of scanning amplitude enables clad bead width adjustment. In turn scanner power modulation (where laser power is adjusted according to where the scanner is pointing) enables modification of clad bead cross-section geometry when laser power can be adjusted locally and thus affect how much laser beam melts material in each sector. Power modulation is also an important factor in terms of process stability. When a linear scanner is used, oscillating the scanning mirror causes a dwell time in scanning amplitude border area, where the scanning mirror changes the direction of movement. This can cause excessive energy input to this area which in turn can cause vaporization and process instability. This process instability can be avoided by decreasing energy in this region by power modulation. Powder feeding parameters have a significant role in terms of process stability. It was determined that with certain powder feeding parameter combinations powder cloud behavior became unstable, due to the vaporizing powder material in powder cloud. Mainly this was noticed, when either or both the scanning frequency or powder feeding gas flow was low or steep powder feeding angle was used. When powder material vaporization occurred, it created vapor flow, which prevented powder material to reach the melt pool and thus dilution increased. Also powder material vaporization was noticed to produce emission of light at wavelength range of visible light. This emission intensity was noticed to be correlated with the amount of vaporization in the powder cloud.

Modal testing and numerical modeling of the dynamic properties of layered sheet-steel structure

Recently, due to the increasing total construction and transportation cost and difficulties associated with handling massive structural components or assemblies, there has been increasing financial pressure to reduce structural weight. Furthermore, advances in material technology coupled with continuing advances in design tools and techniques have encouraged engineers to vary and combine materials, offering new opportunities to reduce the weight of mechanical structures. These new lower mass systems, however, are more susceptible to inherent imbalances, a weakness that can result in higher shock and harmonic resonances which leads to poor structural dynamic performances. The objective of this thesis is the modeling of layered sheet steel elements, to accurately predict dynamic performance. During the development of the layered sheet steel model, the numerical modeling approach, the Finite Element Analysis and the Experimental Modal Analysis are applied in building a modal model of the layered sheet steel elements. Furthermore, in view of getting a better understanding of the dynamic behavior of layered sheet steel, several binding methods have been studied to understand and demonstrate how a binding method affects the dynamic behavior of layered sheet steel elements when compared to single homogeneous steel plate. Based on the developed layered sheet steel model, the dynamic behavior of a lightweight wheel structure to be used as the structure for the stator of an outer rotor Direct-Drive Permanent Magnet Synchronous Generator designed for high-power wind turbines is studied.

Effect of sigma factor S (sigmaS) on the stability of penicillin-binding protein 3 (PBP3) of Escherichia colt K12

The stability of penicillin-binding protein 3 (PBP3), a cell septum synthesizing protein, was analyzed at different incubation temperatures in three Escherichia coli K12 strains carrying a PBP3-overproducing plasmid. The stability of PBP3 was significantly reduced in stationary phase cells shifted to 42°C for 4 h, compared to samples incubated at 28 or 37°C. The half-life of PBP3 in the C600 strain was 60 min at 42°C, while samples incubated at 28 or 37°C had PBP3 half-lives greater than 4 h. Analysis of the PBP3 content in mutants deficient in rpoS (coding for the stationary phase sigma factor, sigmaS) and rpoH (coding for the heat shock sigma factor, sigma32) genes after shift to 42°C showed that stability of the protein was controlled by sigmaS but not by sigma32. These results suggest that control of the PBP3 levels in E. coli K12 is through a post-transcriptional mechanism regulated by the stationary phase regulon. We demonstrated that stability of PBP3 in E. coli K12 involves degradation of the protein. Moreover, we observed that incubation of cells at 42°C significantly reduces the stability of PBP3 in early stationary phase cells in a process controlled by sigmaS.