Statistical process control has been successfully used to monitor manufacturing processes for decades. Some key variables are usually monitored, and their values can give valuable indications if the ...process is out of control. Usually, engineering optimization is deterministic, which does not consider any type of randomness in model parameters. However, robust optimization assuming uncertainties has been recently developed for engineering applications. In this work, we propose an approach using the data usually obtained from the statistical process control to design a 3D periodic structure with a vibration attenuation band robust to manufacturing variability. A procedure using a statistical regression model is proposed, as well as a design of experiments approach, to correlate the random mechanical properties that are usually already measured for statistical process control purposes. Forty-five samples are produced with a 3D printer to characterize the process variability and used to design the metastructure optimally. The obtained statistical model is subsequently combined with a kernel smoother to generate spatially correlated mechanical proprieties. The resulting random field model is then used to predict the wave and vibration response of the designed periodic structure. Finally, a robust optimization approach is proposed to define a final shape for the metastructure that is robust against the inferred variability. The final design presents a robust full and complete attenuation band from 5.9 kHz to 7.5 kHz. The optimal design is then manufactured, and vibration response measurements are used to validate the proposed methodology. It is shown that the final structure presents a band gap from 5.7 kHz to 9.9 kHz, which is inside the simulated 95% confidence interval for the width of the band gap. Although the proposed approach is applied to the vibration response of a periodic 3D frame structure, it opens the way for further extended and generalized robust design approaches in different fields.
In this paper, the Eulerian stochastic fields (ESF) method in a LES framework is applied to a generic selective catalytic reduction (SCR) configuration in order to retrieve seamlessly the effect of ...turbulence–chemistry interaction on the NH3-conversion and AdBlue film formation. The ESF method is based on the transport equation of a joint scalar filtered density function. The injection of AdBlue and relevant spray dynamics are modeled by the Lagrange-particle description where a computational parcel represents a cluster of real AdBlue droplets. Owing to the low injection pressure, weak atomization of AdBlue leads to intense droplet wall-impingement and film formation on the SCR duct wall and/or on the mixer elements, if present. A 2-D thin film approach is adopted to model the film formation and dynamics in combination with multi-regimes droplet–wall interaction model. After verification tasks against the reference data for simple gas phase reactive cases, the verified ESF method is coupled with a one-equation based LES turbulence model together with the Lagrange particle-tracking which is combined with the 2-D thin film approach to simulate the AdBlue injection and the film formation in the generic SCR configuration. At first, the assessment of the adopted LES mesh is carried out in terms of the so-called LES quality of index to determine the optimal mesh resolution. Next, to ensure the convergence with respect to the number of required ESF and mesh resolution, SCR simulations are performed by using various (2, 4, 6, 8, 12 and 16) stochastic fields and also with refined mesh. Thereby, the sensitivity of the predictive capability of the numerical tool is evaluated for the production of NH3 and HNCO with and without ESFs. This clearly indicates the importance of an accurate description of the turbulence–chemistry interaction to retrieve reliably the conversion of NH3. Finally, the film dynamics especially the evolution of the film thickness described with six required ESF and without ESF is compared with experimental data from the generic SCR configurations. To further demonstrate the potential of suggested numerical approach, a detailed numerical analysis is provided in terms of spray-impingement dynamics, scalar uniformity index, droplet life time and characteristics of the droplets prone to form solid deposits in the monolith channel.
•A novel LES-based study of AdBlue injection & wall film evolution in a generic SCR.•Coupling with ESF approach to account for the turbulence–chemistry Interaction.•Consideration of multi-cycle AdBlue injection & temporal evolution for the first time.•Validation of liquid wall film dynamics with recently available experimental data.•Impact of operating parameters on uniformity index & likelihood of deposit formation.
Foundation soil is an important medium for vibration wave propagation in the running of metro train. The spatial variability of soil properties has an important influence on vibration response. The ...parameters of foundation soil are often determined. Based on the probability density evolution method (PDEM) and stochastic field theory, a coupling model of the metro train-track-shield tunnel-foundation soil is established. The stochastic field is expressed by the series of stochastic variables and deterministic space functions by the Karhunen-Loeve Expansion (KLE) method. The stochastic parameters of the cross-section of tunnel-foundation soil are specified to simulate the stochastic field of foundation soil. Based on PDEM, the environmental vibration caused by metro trains in shield tunnels is studied. The results of ground surface vibration displacement under different metro train speeds are analyzed, and the upper and lower limits and probability density information of ground surface vibration displacement are obtained. The results show that the probability density distribution of ground vibration displacement at each time is approximately normal due to the stochastic field of foundation soil. The peak and valley of the vibration displacement curve at the inverted arch of the tunnel are caused by the wheel distance of the metro train. The probability density distribution of velocity and acceleration is more sensitive to the stochastic field of velocity foundation soil and the change in metro train speed. The maximum Z vibration level results under different metro train speeds all meet the requirements of vibration allowable limits in the specification.
•A compressive sampling approach for wind data reconstruction and extrapolation.•L1-norm minimization is used in conjunction with an adaptive basis scheme.•Higher-dimensional problems are addressed ...by nuclear norm minimization.•The approach can be integrated with structural system analysis and design schemes.
A methodology based on compressive sampling is developed for incomplete wind time-histories reconstruction and extrapolation in a single spatial dimension, as well as for related stochastic field statistics estimation. This relies on l1-norm minimization in conjunction with an adaptive basis re-weighting scheme. Indicatively, the proposed methodology can be employed for monitoring of wind turbine systems, where the objective relates to either reconstructing incomplete time-histories measured at specific points along the height of a turbine tower, or to extrapolating to other locations in the vertical dimension where sensors and measurement records are not available. Further, the methodology can be used potentially for environmental hazard modeling within the context of performance-based design optimization of structural systems. Unfortunately, a straightforward implementation of the aforementioned approach to account for two spatial dimensions is hindered by significant, even prohibitive in some cases, computational cost. In this regard, to address computational challenges associated with higher-dimensional domains, a methodology based on low rank matrices and nuclear norm minimization is developed next for wind field extrapolation in two spatial dimensions. The efficacy of the proposed methodologies is demonstrated by considering various numerical examples. These refer to reconstruction of wind time-histories with missing data compatible with a joint wavenumber-frequency power spectral density, as well as to extrapolation to various locations in the spatial domain.
Cool flame has an important impact on the performance and emission of advanced low-temperature combustion (LTC) internal combustion engines (ICEs) in which the liquid fuel is injected earlier at a ...lower ambient temperature (Tam) than that in the conventional diesel combustion engines. However, the cool flame characteristics of spray combustion under ICEs conditions are not fully understood, e.g., the effect of cool flame on the spray ignition and flame stabilization is not well studied. In this paper, the so-called cool flame wave propagation (CFWP) in the Engine Combustion Networks Spray A flames at three ambient temperatures Tam (800 K, 900 K and 1000 K) is analyzed using the data from large eddy simulation with an improved Eulerian based transported probability density function sub-grid combustion model. A good agreement between the LES results and experimental data is obtained for the spray liquid penetration length, vapor fuel penetration length, mean pressure rise profile, and flame liftoff length. It is shown that CFWP in the spray ignition process promotes the ignition of the fuel-rich and cold reactant mixture, leading to the most reactive mixture shifting toward fuel-richer locations due to the spatial stratification of temperature and concentration, and turbulent mixing. As a result, the high temperature ignition (HTI) can be shortened compared to the ignition in the homogeneous mixture. At Tam = 800 K, the HTI kernels are consistently formed following the CFWP propagating toward the spray head region. However, as Tam increases, the spatial correlation between HTI kernels and CFWP fronts is weakened. On the other hand, the turbulent mixing (quantified using local scalar dissipation rate) contributes more to the formation of HTI kernels at higher Tam. The present results indicate that CFWP is more profound at lower Tam in the spray ignition process. Finally, it is found that cool flame propagates mainly into pre-reacted fuel-rich mixture in an ignition wave propagation mode from the spray upstream region toward downstream region, whereas the ignition assisted flame mode is found in the spray upstream region where the combustion heat release is negligible.
The paper describes the results of a comprehensive study of turbulent mixing, fuel spray dispersion and evaporation and combustion in a gas-turbine combustor geometry (the DLR Generic Single Sector ...Combustor) with the aid of Large Eddy Simulation (LES). An Eulerian description of the continuous phase is adopted and is coupled with a Lagrangian formulation of the dispersed phase. The sub-grid scale (sgs) probability density function approach in conjunction with the stochastic fields solution method is used to account for sgs turbulence-chemistry interactions. Stochastic models are used to represent the influence of sgs fluctuations on droplet dispersion and evaporation. Two different test cases are simulated involving reacting and non-reacting conditions. The simulations of the underlying flow field are satisfying in terms of mean statistics and the structure of the flame is captured accurately. Detailed spray simulations are also presented and compared with measurements where the fuel spray model is shown to reproduce the measured Sauter Mean Diameter (SMD) and the velocity of the droplets accurately.
The cold spot is one of the observed CMB anomalies proposed to be produced by various primary and secondary effects. In this work, we study the gravitational lensing of some of the candidates that ...could produce the cold spot, namely a huge void and a cosmic texture, on the various components of CMB random field. Our results demonstrated that the signal to noise ratio of gravitational lensing effect on the CMB temperature field is higher than that of on CMB polarization. We found that for a cylindrically symmetric void at z_Void=0.8 with σ=-1.0 a thousand minute observation would detect the gravitational lensing signal while for a cosmic texture at z_Texture=6.0 a longer observation is required. We expect the future high resolution surveys can put strong constraints on the amplitudes of the template of these models.
Large-eddy simulation (LES) of multiple-injection spray combustion under engine-like conditions is performed using a coupled model of an Eulerian stochastic field transported probability density ...function (ESF T-PDF) and a flamelet generated manifold (FGM). This coupled model allows the use of the T-PDF methods in modeling the interaction of turbulence and chemistry at affordable computational costs for engine applications. Simulation results are compared with the available experimental data for spray flames with multiple-injection and at a high level of exhaust gas recirculation (EGR) under conditions relevant to internal combustion engines. It is shown that the T-PDF/FGM LES model is capable of reproducing not only global combustion characteristics, such as the pressure rise and ignition delay time but also replicating the evolution of liftoff length and the spray flame structure.
The effects of pre-injection strategies are then investigated, by systematically varying the pre-injection duration and the dwell time between two injections, while keeping the total injected fuel mass constant. The LES results reveal different mechanisms by which a pre-injection can change the ignition delay time, the combustion mode and the emissions in spray flames, depending on the injection timing. It is shown that even an extremely short non-igniting pre-injection can substantially change the ignition and emissions characteristics of the main-injection. It is shown that the combustion mode of a single-injection can be altered by splitting the injection to pre- and main-injections. The current study also demonstrates that decreasing the dwell time, within the range that is examined here, at a given pre-injection, will potentially increase the soot oxidation rates while it does not significantly change the rate of soot formation.
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