Numerical simulation of pulsed planar evaporation into background gas based on direct Monte Carlo simulation and solution of the BGK model kinetic equation

A numerical study of the planar gas expansion under pulsed evaporation into the background gas is carried out. The chosen conditions are typical for nanosecond laser deposition of thin films and nanostructure synthesis, with the saturated gas pressure at the surface of 5.4 MPa and the background pressure of 50 and 500 Pa. The problem is solved based on the direct simulation Monte Carlo method and direct numerical solution of the BGK model kinetic equation. A generally good agreement was obtained for all computed macroscopic quantities, with the exception of the higher density peak in the compressed layer and a wider shock front in the background gas for the BGK model.

Stochastic Analysis of Predator–Prey Models under Combined Gaussian and Poisson White Noise via Stochastic Averaging Method

In the present paper, the statistical responses of two-special prey–predator type ecosystem models excited by combined Gaussian and Poisson white noise are investigated by generalizing the stochastic averaging method. First, we unify the deterministic models for the two cases where preys are abundant and the predator population is large, respectively. Then, under some natural assumptions of small perturbations and system parameters, the stochastic models are introduced. The stochastic averaging method is generalized to compute the statistical responses described by stationary probability density functions (PDFs) and moments for population densities in the ecosystems using a perturbation technique. Based on these statistical responses, the effects of ecosystem parameters and the noise parameters on the stationary PDFs and moments are discussed. Additionally, we also calculate the Gaussian approximate solution to illustrate the effectiveness of the perturbation results. The results show that the larger the mean arrival rate, the smaller the difference between the perturbation solution and Gaussian approximation solution. In addition, direct Monte Carlo simulation is performed to validate the above results.

On the Development of a Module for the Modification of Computational Meshes by the dsmcInitialise Utility

The research, the results of which are presented in this article, is devoted to the development of a software module with a graphical user interface that provides a modification of the computational mesh based on the dsmcInitialise utility, which is used at the preprocessing stage of numerical modeling of continuum mechanics problems using the OpenFOAM software environment. The paper describes the existing graphical shells for working with OpenFOAM with an indication of their shortcomings, formulates the relevance of the work, and defines the goals and objectives of the study. The article presents the features of the direct Monte Carlo simulation method, a description of the dsmcInitialise utility integrated into OpenFOAM and designed for such modeling, as well as a description of the corresponding dictionary file with parameters. The article includes diagrams of the structure and logic of the application, describes the technology stack used. The results of the application of the program on the example of one of the training problem of OpenFOAM are presented. The final conclusions are formulated, as well as the provisions that determine the scientific novelty of the research, and its intended practical value is determined. A link to the repository with the source code of the presented software module is provided.

Robust Dynamic Optimization of a Dual-rotor System Based on Polynomial Chaos Expansion

A novel methodology of robust dynamic optimization of a dual-rotor system based on polynomial chaos expansion (PCE) is developed in this paper. The dual-rotor system model was built by the Timoshenko theory and the finite element method. Instead of the direct Monte Carlo simulation (MCS), the PCE of the present dual-rotor system under support stiffness uncertainty is generated to facilitate a rapid analysis of stochastic responses and yield desirable results in significantly less number of functional evaluations. The PCE is explored as a basis for robust optimization, focusing on the problem of minimizing the unbalance response at operating conditions while minimizing its sensitivity to uncertainty in the support stiffness. This strategy avoids the use of MCS in order to effectively increase the efficiency of the optimization and significantly reduce the computing cost and time spending. The robust dynamic optimization attempts to both optimize the mean performance and minimizes the variance of the performance simultaneously. The multi-objective optimization results show that vibration response can be decreased and is significantly less sensitive to the variation of design parameters compared with initial design case by matching of unbalance amplitude and phase angle differences. Implementation of the proposed robust dynamic optimization in the present dual-rotor system illustrates its potential for further complicated applications.

A HYBRID MONTE-CARLO-DETERMINISTIC METHOD FOR AP1000 EX-CORE DETECTOR RESPONSE SIMULATION

The ex-core detector-response calculation is a typical deep-penetration problem, which is challenging for the Monte Carlo method. The response of the ex-core detector is an important parameter for the safe operation of the nuclear power plants. Meanwhile, evaluation of the ex-core detector response during each step of fuel-loading is used to guide the fuel-loading sequence. The response can also be used to reconstruct core-power distribution for online monitoring of long-term power. The detector used for the ex-core response is the source-range detector which is sensitive to thermal neutrons. For a Monte Carlo shielding calculation of the above detector response, the thermal flux under 0.625eV is needed, which is too small to be tallied by traditional Monte Carlo simulations. In practice, the tally results are close to zero in the detector region under direct Monte Carlo calculation. Even if the number of particles is increased to a significant amount, the statistical variance is still very large. The high variance along with a significant calculation time leads to a small Figure Of Merit (FOM). In order to solve this problem and to improve the tally efficiency of the ex-core detector response, a hybrid Monte-Carlo-deterministic method is employed in this study, and an in-house hybrid Monte-Carlo-deterministic particle transport code, NECP-MCX, is developed in this paper. The method takes the space-energy-dependent adjoint fluxes to generate importance parameters for the mesh-based weight window in the Monte Carlo calculation. Simultaneously, the mesh-based source biasing is performed with the consistent importance parameters to make the starting weight of neutrons matching with the survival weight of the weight windows. As the mesh used in the hybrid Monte-Carlo-deterministic method is superimposed, the mesh of the weight window will not be affected by the complex geometry model. The adjoint flux is obtained by the efficient SN method with the multi-group cross-section data. The whole toolset is convenient to use with single set of the modelling data for both Monte Carlo and deterministic simulations. Compared with the direct Monte Carlo simulation, the hybrid Monte-Carlo-deterministic method has a higher efficiency for a typical deep-penetration problem such as the AP1000 ex-core detector-response simulation.

Uncertainty analysis of mechanical behavior of natural fiber composites

The natural origin of the fibers combined with random production flaws results in significant uncertainties in the properties of natural fiber reinforced composites. A probabilistic assessment can help to characterize the uncertainties and evaluate the reliability of natural fiber composites, enabling their use in engineering designs. Toward this end, this study aims to quantify the uncertainties in the tensile strength and frequency response of a unidirectional flax/epoxy composite due to the variability of various input parameters, including the fiber material properties and manufacturing flaws. Based on the available data in the literature, the non-deterministic input variables were divided into normal and uniform variables using a statistical test. A computationally efficient response surface approach based on the polynomial chaos expansion was adopted to conduct the uncertainty analysis with multi-type uncertain variables. Moreover, the results were validated by the direct Monte Carlo simulation to demonstrate the accuracy and efficiency of the surrogate model.

Subset Simulation for Structural Reliability Analysis of Pipeline Corrosion Defects

One of the leading threats to the integrity of oil and gas transmission pipeline systems is metal-loss corrosion. This threat is commonly managed by evaluating measurements obtained with in-line inspection tools, which locate and size individual metal-loss defects in order to plan maintenance and repair activities. Both deterministic and probabilistic methods are used in the pipeline industry to evaluate the severity of these defects. Probabilistic evaluations typically utilize structural reliability, which is an approach to designing and assessing structures that focuses on the calculation and prediction of the probability that a structure may fail. In the structural reliability approach, the probability of failure is obtained from a multidimensional integral. The solution to this integral is typically estimated numerically using Direct Monte Carlo (DMC) simulation as DMC is relatively simple and robust. The downside is that DMC requires a significant amount of computational effort to estimate small probabilities. The objective of this paper is to explore the use of a more efficient approach, called Subset Simulation (SS), to estimate the probability of burst failure for a pipeline metal-loss defect. We present comparisons between the probability of failure estimates generated for a sample defect by Direct Monte Carlo simulation and Subset Simulation for differing numbers of simulations. These cases illustrate the decreased computational effort required by Subset Simulation to produce stable probability of failure estimates, particularly for small probabilities. For defects with a burst probability in the range of 10−4 to 10−7, SS is shown to reduce the computational effort (time or cost) by 10 to 1,000 times. By significantly reducing the computational effort required to obtain stable estimates of small failure probabilities, this methodology reduces one of the major barriers to the use of reliability methods for system-wide pipeline reliability assessment.

Random dynamic analysis of vertical train–bridge systems under small probability by surrogate model and subset simulation with splitting

The response of the train–bridge system has an obvious random behavior. A high traffic density and a long maintenance period of a track will result in a substantial increase in the number of trains running on a bridge, and there is small likelihood that the maximum responses of the train and bridge happen in the total maintenance period of the track. Firstly, the coupling model of train–bridge systems is reviewed. Then, an ensemble method is presented, which can estimate the small probabilities of a dynamic system with stochastic excitations. The main idea of the ensemble method is to use the NARX (nonlinear autoregressive with exogenous input) model to replace the physical model and apply subset simulation with splitting to obtain the extreme distribution. Finally, the efficiency of the suggested method is compared with the direct Monte Carlo simulation method, and the probability exceedance of train responses under the vertical track irregularity is discussed. The results show that when the small probability of train responses under vertical track irregularity is estimated, the ensemble method can reduce both the calculation time of a single sample and the required number of samples.

Uncertainty Quantification of Mode Shape Variation Utilizing Multi-Level Multi-Response Gaussian Process

Mode shape information plays the essential role in deciding the spatial pattern of vibratory response of a structure. The uncertainty quantification of mode shape, i.e., predicting mode shape variation when the structure is subjected to uncertainty, can provide guidance for robust design and control. Nevertheless, computational efficiency is a challenging issue. Direct Monte Carlo simulation is unlikely to be feasible especially for a complex structure with a large number of degrees-of-freedom. In this research, we develop a new probabilistic framework built upon the Gaussian process meta-modeling architecture to analyze mode shape variation. To expedite the generation of input data set for meta-model establishment, a multi-level strategy is adopted which can blend a large amount of low-fidelity data acquired from order-reduced analysis with a small amount of high-fidelity data produced by high-dimensional full finite element analysis. To take advantage of the intrinsic relation of spatial distribution of mode shape, a multi-response strategy is incorporated to predict mode shape variation at different locations simultaneously. These yield a multi-level, multi-response Gaussian process that can efficiently and accurately quantify the effect of structural uncertainty to mode shape variation. Comprehensive case studies are carried out for demonstration and validation.