Direct Numerical Modeling Research Articles

Optical properties of silicon nanopillars with a built-in vertical p-n-junction

Resonance reflection of light from the ordered arrays of silicon nanopillars (Si NP) was investigated. The height of Si NP was 450 nm. The effect of Si NP oxidation in concentrated nitric acid on the position of resonances in reflection spectra was studied. A weak influence of the additional polymeric coating on the characteristics of reflection from the structures was proven. It is established on the basis of the results of experimental investigation and direct numerical modeling by means of three-dimensional finite difference time domain algorithm (3D FDTD) that the dependence of the resonant wavelength for Si NP on the diameter of Si NP is a linear function with nonzero displacement depending on the pitch. Keywords: silicon nanopillars, structural colors, all-dielectric nanophotonics.

Using 2D/3D convolutional neural networks and direct numerical modeling for ranscranial ultrasound problems

Using 2D/3D convolutional neural networks and direct numerical modeling for ranscranial ultrasound problems

SIMULATION OF AERODYNAMIC INSTABILITY OF BUILDING STRUCTURES ON THE EXAMPLE OF A BRIDGE SECTION. PART 2: SOLUTION OF THE PROBLEM IN A COUPLED AEROELASTIC FORMULATION AND COMPARISON WITH ENGINEERING ESTIMATES

In this paper, we study aerodynamic instability using the example of a two-dimensional problem of flow around a simplified section of a flexible suspension bridge (on the Tacoma River, USA). A direct dynamic coupled calculation was performed to determine the critical speed of manifestation of aerodynamic instability. The results obtained were compared with the results of engineering estimates presented in [40]. This example shows that to solve such problems it is possible to use the lighter des turbulence model instead of the les turbulence model and, therefore, a coarser mesh. In contrast to existing engineering techniques, direct numerical modeling of the interaction between the structure and the air flow allows one to take into account the reverse effect of the structure on the flow, as well as the mutual influence of several types ofaerodynamic instability.

Evolution of Coal Permeability under Constant Effective Stresses: Direct Measurements and Numerical Modeling

Evolution of Coal Permeability under Constant Effective Stresses: Direct Measurements and Numerical Modeling

Моделирование теплопроводности разреженных газов стохастическим методом

One of the main successes of the kinetic theory of gases is the explicit calculation of the transport coefficients of rarefied gases. However, the greatest problems arise when calculating the thermal conductivity coefficient, especially for polyatomic gases. Also, when using different potentials, it is necessary to systematically calculate the so-called Ω-integrals, which in itself is a rather difficult task. For this reason, direct numerical molecular modeling of the processes of transfer of rarefied gases, in particular, the calculation of their transfer coefficients, is also relevant. A well-known method for such modeling is the molecular dynamics method. Unfortunately, until now this method is not available for modeling the processes of rarefied gas transfer. Under nor-mal conditions, the simulation cell should contain tens or even hundreds of millions of molecules during calculations. At the same time, the numerical implementation of the molecular dynamics method is accompanied by a systematic appearance of errors, which is the reason for the appearance of dynamic chaos. With this simulation, the true phase trajectories of the system under consideration cannot be obtained. Therefore, naturally, the idea of developing a method for modeling transport processes arises, in which phase trajectories are not calculated based on Newton's laws, but are simulated, and then are used to calculate any observables. In our works, we developed a method of stochastic molecular modeling (STM) of rarefied gas transfer processes, where this idea was implemented. The efficiency of the SMM method was demonstrated by calculating the coefficients of self-diffusion, diffusion, and viscosity of both monoatomic gases and polyatomic gases. At the same time, the possibility of modeling the most complex transfer process – the energy transfer process – has not yet been considered. This work aims to simulate the thermal conductivity coefficient by the SMM method. Both monoatomic (Ar, Kr, Ne, Xe) and polyatomic gases (CH4, O2) were considered.

Estimation of Relative Transport Properties in Porous Transport Layers Using Pore-Scale and Pore-Network Simulations

Improvements in imaging techniques have enabled the reconstruction of complex porous media which can be analyzed by computer simulations. The two most popular methods for numerical analysis of transport in porous media are direct numerical simulation (DNS) and pore network modeling (PNM). This work aims at assessing the suitability of these techniques to study dry and wet transport properties of porous transport layers for fuel cells and electrolyzers by comparing numerical predictions to experimental data for mercury intrusion, and transport properties. The microstructures of different materials are obtained using micro X-ray computed tomography and characterized by measuring mercury intrusion porosimetry (MIP) curves, dry permeability and diffusivity. Their results are compared to numerically predicted MIP, and dry and wet permeability and diffusivity. Results show that DNS is capable of accurately predicting intrusion, and transport properties without using any fitting parameters. Accurate predictions could be achieved with a PNM when the inscribed diameter method was used for pore size distribution, and the equivalent diameter was used to estimate pore transport properties. While DNS provides more accurate results without necessitating any calibration, a properly constructed PNM is shown to provide relatively good estimations of transport properties at a reduced computational expense.

Transformation of envelope solitons on a bottom step

In this paper, we study the transformation of surface envelope solitons traveling over a bottom step in water of a finite depth. Using the transformation coefficients earlier derived in the linear approximation, we find the parameters of transmitted pulses and subsequent evolution of the pulses in the course of propagation. Relying on the weakly nonlinear theory, the analytic formulas are derived which describe the maximum attainable wave amplitude in the neighborhood of the step and in the far zone. Solitary waves may be greatly amplified (within the weakly nonlinear theory formally, even without a limit) when propagating from relatively shallow water to the deeper domain due to the constructive interference between the newly emerging envelope solitons and the residual quasi-linear waves. The theoretical results are in good agreement with the data of direct numerical modeling of soliton transformation. In particular, more than double wave amplification is demonstrated in the performed simulations.

Strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction using hierarchical decomposition

The key to the design of advanced micro electro–mechanical devices is an accurate evaluation of the circuit-integrated piezoelectric oscillator that accounts for its complicated configuration. Here, the direct numerical modeling of this oscillator leads to a general formulation as a structure–piezoelectric–circuit interaction. Hence, this study developed a strongly coupled partitioned iterative method for the structure–piezoelectric–circuit interaction. The proposed method was constructed using hierarchical decomposition, the partitioned iterative method for two coupled fields, and loop union. That is, the whole system of the coupled multiphysics is hierarchically decomposed into coupled two-field subsystems, partitioned iterative algorithms for two coupled fields are applied to these subsystems, and the coupling algorithms for these subsystems are reduced to a single coupling algorithm. In the proposed method, three distinct direct piezoelectric, inverse piezoelectric, and circuit solvers are strongly coupled with each other. The inverse piezoelectric solver uses shell finite elements to analyze the response of the thin oscillator efficiently, while the direct piezoelectric solver uses solid finite elements to accurately describe the three-dimensional distribution of the electric potential in the piezoelectric continuum. The proposed method can accurately analyze coupling phenomena in the RC circuit, piezoelectric shunt damping, and piezoelectric energy harvesting.

(Invited) Multi-Scale Analysis of Transport in Dry and Partially-Saturated Porous Media

Improvements in imaging techniques, such as micro- and nano-computer tomography (CT) and focus ion beam scanning electron microscopy (FIB-SEM), have enabled the reconstruction of complex porous media that can then be analyzed by computer simulation to estimate effective transport properties, e.g., ref. [1, 2]. Experimental setups have also been developed to measure dry and partially-saturated gas diffusivity and permeability of gas diffusion layers (GDLs) and catalyst layer (CLs), e.g., ref. [3, 4]. Based on the available literature, a comparison between micro-scale simulation results and experimental data must be performed to assess the accuracy of direct numerical simulation CT image analysis for dry and partially-saturated transport property estimation. In the later case, the validity of computational methods to predict water intrusion, such as full morphology/morphological image opening [1] and watershed segmentation [5], should also be assessed by comparing mercury intrusion experiments to numerical predictions, and by direct comparison of numerical results to CT images. Finally, these transport properties should be integrated into complete fuel cell models where volume-averaging techniques are used to properly estimate channel-porous media interactions. Such interactions however are seldom studied in literature.The proposed contribution aims at first studying the validity of two popular methods for numerical estimation of effective transport properties from three-dimensional reconstructed porous media, i.e., direct numerical simulation (DNS) and pore network modeling (PNM). Two fuel cell gas diffusion media and an electrolyzer porous transport layer are analyzed by CT and characterized by measuring mercury intrusion porosimetry (MIP), and dry permeability and diffusivity. A comparison of numerical and experimental results shows that DNS tools in OpenFCST [6] are capable of accurately predicting intrusion, and transport properties without using any fitting parameters. Accurate predictions are also achieved with the PNM implementation in OpenPNM [7] when the inscribed diameter method is used to estimate the pore size distribution, and the equivalent diameter is used to estimate pore transport properties. These tools open an avenue for computational design of porous materials.Effective transport properties must be integrated into volume-averaged fuel cell models where porous media-channel interactions are of paramount importance. These interactions however, as well as the method used for volume averaging fuel cell equations, are seldom studied in detail. Therefore, the second contribution of the talk aims at analyzing channel-porous media interactions by developing a compressible volume-averaged channel-porous media model in OpenFCST, and validating it with respect to permeability and diffusion bridge experiments in the literature. Comparison of numerical and experimental results show that, depending on the volume-averaging methodology used, experimentally obtained transport properties do not correspond to the input parameters needed in volume-averaged models. Finally, the numerical model is used to estimate flow by-pass in serpentine and inter-digitated channels, as well as compressibility effects [8].

Numerical optimization of evaporative cooling in artificial gas diffusion layers

The utilization of evaporative cooling in the gas diffusion layers (GDLs) of fuel cells or electrolyzers can effectively dissipate the heat produced by high power density operation, thus leading to economically more competitive electrochemical cells. The highly porous GDLs offer a large surface area, allowing to cope with larger heat fluxes and leading to larger evaporation rates. The understanding of the best GDL structure and cell operating conditions for optimized cooling is difficult to determine, given the complexity of the multi-physical processes involved. A direct pore-level numerical modeling framework was developed to analyze the heat and mass transport phenomena occurring within GDLs with integrated evaporative cooling. A three-dimensional model was developed that solves the Navier-Stokes equations, species transport and energy conservation equations in the gas domain, and energy conservation equations in the stagnant fluid phase and solid phase. Evaporation at the liquid-vapor interface was modeled using kinetic theory. The GDL geometry was approximated by an artificial lattice so as to enable the analysis of the effect of a systematic change in the geometry on the transport and evaporation characteristics. A parametric study indicated that increasing the GDL’s porosity from 0.8 to 0.9 and the operating temperature from 60°C to 80°C led to an increase of the evaporation rate of 19.9% and 197%, respectively. Changing the thermophysical properties of the carrier gas (air to hydrogen) enhanced the evaporation rate, and therefore the cooling of the GDL, by a factor 2.7. The decrease of the amount of vapor in the carrier gas at the water-gas interface impacted positively the evaporative cooling in the GDL.

A methodology for coupling DNS and discretised population balance for modelling turbulent precipitation

In this paper, we present a methodology for simulating nanoparticle formation in a turbulent flow by coupling Direct Numerical Simulation (DNS) and population balance modelling. The population balance equation (PBE) is solved via a discretisation method employing a composite grid that provides sufficient detail over the wide range of particle sizes reached during the precipitation process. The coupled DNS/PBE approach captures accurately the strong interaction between the dynamics of turbulent mixing and particle formation processes. It also allows the calculation of the particle size distribution (PSD) of the product and enables an investigation on how it is controlled by turbulent mixing. Finally, it provides the statistics of kinetic processes and their timescales so that further analysis can be performed. The methodology is applied to the simulation of experiments of hydrodynamics and nanoparticle precipitation in a T-mixer (Schwertfirm et al., Int. J. of Heat and Fluid Flow 28, pp. 1429–1442; Schwarzer et al., Chem. Eng. Sci. 61, pp. 167–181), and the agreement with the experimental results is very good.

Development of High-Power Millimeter-Wave Surface-Wave Generators Based on Relativistic Ribbon Electron Beams

We analyze theoretically millimeter-wave surface-wave generators based on relativistic ribbon electron beams within the framework of the averaged quasioptical model, as well as using direct numerical modeling by the Particle-in-Cell method. The regime of excitation of π modes and the regime of the backward-wave oscillator based on a surface wave are studied. The possibility to achieve generation of pulsed radiation at a frequency of 75 GHz with a power of up to 100 MW on the basis of the SINUKI acceleration (IAP RAS) is demonstrated. Experiments have been performed to test experimentally the formation of a relativistic ribbon electron beam with a particle energy of 600 keV, a current of up to 1 kA, and a width of up to 2 cm, which will be used to feed the developed generator.

DEVELOPMENT OF RIGOROUS METHODS IN FLUID MECHANICS AND THEORY OF WATER WAVES

The thesis consists of five chapters where the following problems are considered - the transformation of long linear waves in an ocean with a variable depth; long wave scattering in a canal with a rapidly varying cross-section; long linear surface waves on stationary currents in a canal of constant depth and variable width; and a resonant interaction of a solitary wave with external pulse-type perturbations within the framework of forced Korteweg-de Vries equation. Chapter 1 reviews the history of these problems, and notes previous literature and research in this area. In Chapter 2, the transformation of long linear waves in an ocean of a variable depth is studied. The transformation coeffcients are considered as functions of frequency and the total depth drop for three typical models of bottom profile variation: piecewise linear, piecewise quadratic and hyperbolic tangent profiles. The results obtained for all these profiles are analysed and compared from the physical point of view. In Chapter 3, long wave scattering in a canal with a rapidly varying cross-section is studied. The scattering coeffcients are calculated for all possible incident wave orientations (background current downstream and upstream with respect to the background flow); and current types subcritical, transcritical, and supercritical. It is shown that when the over-reflection or over-transmission occurs, negative energy waves can appear in the flow. A spontaneous wave generation can happen in a transcritical accelerating flow, resembling a spontaneous wave generation on the horizon of an evaporating black hole due to the Hawking effect in astrophysics. In Chapter 4, long wave transformation is studied in the canal with abrupt variation of width and depth. Again, all possible wave orientation with respect to the background current is considered, and all types of a current is studied (subcritical, transcritical, and supercritical). The transformation coefficients are calculated and analysed as functions of wave frequency, Froud number, and depth drop. In Chapter 5, we revise the solutions of the forced Korteweg{de Vries equation for the resonant interaction of a solitary wave with the various external pulse-type perturbations. In contrast to the previous studies, we consider an arbitrary relationship between the width of a solitary wave and external forcing. In many cases, exact solutions of the forced Korteweg{de Vries equation can be obtained for the specific forcings of arbitrary amplitude. The theoretical outcomes obtained by asymptotic method are in good agreement with the results of direct numerical modelling within the framework of forced Korteweg-de Vries equation. In Conclusion, we summarise the results obtained within the various models and equations; discuss the future applications and innovation of the results; and suggest further perspectives for the future research.

Analytical and Numerical Solution of the Equation for the Probability Density Function of the Particle Velocity in a Turbulent Flow

A study has been made of the random motion of inertial particles in a homogeneous isotropic turbulent gas flow. Fluctuations of the gas velocity along the particle path were modeled by the Gaussian random process with a finite time of degeneracy of the autocorrelation function. A closed equation has been obtained for the probability density function of the particle velocity, for which two methods of numerical solution have been proposed: using the finite-difference scheme and using one based on direct numerical modeling of an empirical probability density function. The empirical probability density function was obtained as a result of the averaging of random particle paths, which are a solution of a system of ordinary stochastic differential equations. The results of numerical calculation have been compared with the analytical solution describing the dynamics of the probability density function of the particle-velocity distribution.

Particle Velocity Fluctuations in Viscous Gas with Random Velocity as the Sum of Two Correlated Color Noises

The article focuses on methods for studying the phenomenon of two-phase turbulent flows. The turbulence effect on the movement of solid particles in a viscous gas is under study. Dynamics of particles movement in a gas is written in the Stokes approximation, which allows us to suppose the dynamic relaxation time to be a constant value.The random gas velocity is modeled by the sum of two correlated random noises. It is shown that this approach makes it possible to model noise of any structural complexity. The paper describes two research methods based on fundamentally different Euler and Lagrange approaches to the description of a continuous medium. The first approach uses a well-known generalization of the spectral analysis technique for random processes, a popular method for studying turbulence. The second approach implementation is based on the modern generalizations of the theory of numerical algorithms for solving stochastic ordinary differential equations. The spectral method is used to obtain analytical expressions of correlation functions and variance of random processes describing the velocity of gas and solid particles. The qualitative difference between the correlation of fluctuations of modulated random velocities and the behavior of correlations in the case of a single-component gas velocity composition is analyzed. A method of direct numerical simulation for studied processes based on the numerical solution of a stochastic ordinary differential equations system is proposed and analyzed in detail. An array of statistical data obtained as a result of direct numerical modeling is collected and processed. Analytical results are compared qualitatively with numerical results. The influence of input parameters on the character of turbulent flow is studied. The dynamic relaxation time has a significant effect on the complexity of the autocorrelation function of the particle velocity and the response function of particles to gas velocity fluctuations. It is shown that the obtained functions tend to the known results of the standard theory. The considered methods for describing two-phase turbulent flows hold promise for further research.

Peridynamic modeling and simulation of thermo-mechanical de-icing process with modified ice failure criterion

De-icing technology has become an increasingly important subject in numerous applications in recent years. However, the direct numerical modeling and simulation the physical process of thermo-mechanical deicing is limited. This work is focusing on developing a numerical model and tool to direct simulate the de-icing process in the framework of the coupled thermo-mechanical peridynamics theory. Here, we adopted the fully coupled thermo-mechanical bond-based peridynamics (TM-BB-PD) method for modeling and simulation of de-icing. Within the framework of TM-BB-PD, the ice constitutive model is established by considering the influence of the temperature difference between two material points, and a modified failure criteria is proposed, which takes into account temperature effect to predict the damage of quasi-brittle ice material. Moreover, thermal boundary condition is used to simulate the thermal load in the de-icing process. By comparing with the experimental results and the previous reported finite element modeling, our numerical model shows good agreement with the previous predictions. Based on the numerical results, we find that the developed method can not only predict crack initiation and propagation in the ice, but also predict the temperature distribution and heat conduction during the de-icing process. Furthermore, the influence of the temperature for the ice crack growth pattern is discussed accordingly. In conclusion, the coupled thermal-mechanical peridynamics formulation with modified failure criterion is capable of providing a modeling tool for engineering applications of de-icing technology.

A Multiscale Approach to Terahertz Electric Field Estimation in Corneal Tissues

Computational dosimetry is the main approach to electric field estimation for radiation-safety regulation and treatment design when no measurements of fields within the body are possible. At high frequencies such as THz, the electromagnetic fields are absorbed at the body surface (exposed skin or the cornea of the eyes). New safety studies require not only the estimation of the average electric field intensity within the superficial tissue, but also the possible localization or concentration of electric fields due to inhomogenities in the microstructure of the tissue such as cellular membranes, which can be of importance in microthermal or nonthermal effects on cells. A direct numerical modeling with all fine structure suffers from the problem of dimensions: the source is at the scale of the whole tissue, whereas fine electric field distributions are required at the cell scale of several micrometers. In this article, a multiscale approach is formulated to efficiently estimate the induced field distributions at tissue and cellular scales. Estimation of the electric fields in the corneal tissue is then solved and discussed with numerical results. It is seen that mild localizations at the microscale are possible.

Fibre kinematics in dilute non-Newtonian fibre suspensions during confined and lubricated squeeze flow: Direct numerical simulation and analytical modelling

The properties of short fibre-reinforced polymer composites depend on the distribution and the orientation of fibres which drastically changes during the forming of composites. During this stage, these materials behave as fibre suspensions and usually flow in confined geometries. To analyse their flow-induced fibrous microstructures, we previously conducted 3D real-time in situ observations of the compression of non-Newtonian dilute fibre suspensions using fast X-ray microtomography [T. Laurencin et al., Compos Sci Technol134 (2016)]. Here, we successfully simulated these experiments with a multi-domain Finite Element code and compared them with the predictions of Jeffery's model. Often, the Jeffery's equations agree with the experimental and numerical data. However, for fibres closed to compression platens, important deviations were observed with faster simulated and experimental fibre rotation. Adopting the dumbbell approach and revisiting the recent work of Perez et al. [J non-Newtonian Fluid Mech233 (2016)], an extension of the Jeffery's model is proposed to account both for the non-Newtonian rheology of the suspending fluid and confinement effects. Despite its simplicity, the new model allows a good description of simulation and experimental results.

Numerical Modeling of the Behavior of a Destructive Rain Flood on a Mountain River

The objective of this study was to provide the most accurate presentation of the behavior of a disastrous rain flood, which had resulted in destruction of a dam, casualties, and significant material damage. The problems set were solved by methods of numerical modeling in the two-dimensional setting applying the STREAM 2D CUDA software package. To calculate the rain flood, a catchment model of the Durso River was developed on a triangular non-uniform mesh, adapted to the river channel and the main inflows. To ensure direct numerical modeling of the dam’s destruction, a model was developed, which included the water area of the reservoir, the dam, composed of non-homogeneous earth material, and a downstream section of the river from the dam to the river mouth. The main results of the study were: the hydrograph of the water discharge of the rain flood, calculated by the actual precipitation data; a description of the washout of the earth dam composed of non-homogeneous materials, resulting from water spill over the dam crest, and a desctiption of the downstream spread of the breach wave.

The effects of interplay between the rotation and shoaling for a solitary wave on variable topography

AbstractThis paper presents specific features of solitary wave dynamics within the framework of the Ostrovsky equation with variable coefficients in relation to surface and internal waves in a rotating ocean with a variable bottom topography. For solitary waves moving toward the beach, the terminal decay caused by the rotation effect can be suppressed by the shoaling effect. Two basic examples of a bottom profile are analyzed in detail and supported by direct numerical modeling. One of them is a constant‐slope bottom and the other is a specific bottom profile providing a constant amplitude solitary wave. Estimates with real oceanic parameters show that the predicted effects of stable soliton dynamics in a coastal zone can occur, in particular, for internal waves.