Direct Numerical Simulation Model Research Articles

Tunable deformation design of porous Al2O3 based on the Direct FE2 method

Abstract The tunable deformation design of porous ceramics has raised many interests in many engineering and manufacturing fields, where its corresponding design methodologies still suffer from the lower efficiency and higher computational cost. To handle this problem, a novel optimization and design methodology based on the Direct FE2 method has been proposed in this study, and several numerical examples of the porous Al2O3 tunable deformation design has been performed by this novel methodology. Compared with the traditional methodologies, the proposed method is more convenient to conduct the tunable deformation design and improves the optimization efficiency. Based on this method, the distribution and assembly of the microscale RVE could be tailored along the space dimension to handle the sinusoidal deformation and variable Poisson’s ratio ceramic design at the macroscale. By comparing the simulation results with the Direct Numerical Simulation (DNS) model, the effectiveness and accuracy of this methodology is well validated. Meanwhile, the simulation results based on the proposed methodology found that the predictability of porous Al2O3 deformation could be enhanced by changing the micro structure parameters such as the elliptical hole angle and aspect ratio. This methodology holds great potential for applications in the design and optimization of porous ceramics with tailored deformation characteristics.

The 3D Elliptical Parcel-In-Cell (EPIC) method

We present the three-dimensional version of the Elliptical Parcel-In-Cell (EPIC) method for the simulation of fluid flows and analogous continuum systems. The method represents a flow using a space-filling set of ellipsoidal parcels, which move, rotate and deform in the flow field. Additionally, parcels may carry any number of attributes, such as vorticity, density, temperature, etc, which generally evolve in time on the moving parcels. An underlying grid is used for efficiency in computing the velocity field from the interpolated vorticity field, and in obtaining parcel attribute tendencies. Mixing is enabled by permitting parcels to split when excessively deformed, and by merging very small parcels with the nearest other parcel. Several tests are provided which illustrate the behaviour of the method and demonstrate its effectiveness in modelling complex, buoyancy-driven turbulent fluid flows. The results are compared with a large eddy simulation (LES) and a direct numerical simulation (DNS) model.

Direct numerical simulation of an unsteady wall-bounded turbulent flow configuration for the assessment of large-eddy simulation models

A new benchmark case for the evaluation of direct numerical simulation (DNS) and large-eddy simulation (LES) models and methods is presented in this study. The known Taylor–Green vortex is modified by replacing the periodic boundary conditions in one direction with a no-slip boundary. A passive scalar is added and transported from the wall into the fluid. The addition of walls allows for the study of transient-instationary flows in a simple geometry with clean boundary and initial conditions, which is a key requirement for the assessment of LES modeling strategies. The added scalar mimics heat transfer through the wall. The case features reasonable computational cost for highly-resolved LES and DNS calculations. Simulations of the wall-bounded Taylor–Green vortex are easy to setup and do not require additional modeling. The proposed modification of the case is compared to the default Taylor–Green vortex and the difference in flow-physics is discussed. A detailed convergence study with four meshes, each of them refined by a factor of 2, has been conducted. The results reveal that converged second-order statistics can be obtained up to a dimensionless time of t/t_0 = 20. Beyond that, due to the unsteady chaotic nature of the flow, some uncertainties remain. The results show that the case features challenging (near-wall) flow dynamics, which cannot be covered using the default Taylor–Green vortex and hence, justify the proposed case as a useful benchmark.

Efficient direct numerical simulation of gas absorption in falling films using a combined high-throughput/high-performance approach

Direct Numerical Simulation (DNS) of liquid–gas mass transfer processes in falling film can model the transfer effect enhancement accurately, but requires huge computational effort. To improve the computational efficiency, we propose a hybrid parallel strategy combining high-throughput computing on the top level and high-performance unit simulations with different interface capture strategies on the bottom level. We investigate the CO2 absorption in methanol with different concentrations of Al2O3 nanoparticles using the proposed computation strategy to demonstrate its performance and assess the intensification mass transfer effect. Moreover, the Structural Similarity Index Measure (SSIM) is utilized in the case of oxygen absorption in water film to compare local gas concentration profiles obtained by the proposed approach, those obtained by the reduced modeling approach and the experimental data generated by a planar laser induced luminescence method under similar conditions. The results show that DNS model matches better the experimental data with high computational accuracy and efficiency.

Generalizability of reservoir computing for flux-driven two-dimensional convection.

We explore the generalization properties of an echo state network applied as a reduced-order model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain with constant height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-Bénard case, thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input of the echo state network is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.

Large eddy simulation of a turbulent supercritical hydrothermal flame with a novel direct moment closure model

A novel direct moment closure (DMC) model has been developed in the context of large eddy simulation (LES) and applied to simulate a supercritical flame. To evaluate the performance of the model, three-dimensional direct numerical simulation (DNS) of a supercritical hydrothermal non-premixed jet flame is conducted. The characteristics of the ignition and propagation of the supercritical hydrothermal flame are analyzed, and then the a-priori analysis of the DMC model is carried out based on the DNS model data. It is found that the prediction of reaction rate can be remarkably improved by the DMC model compared with the laminar chemistry closure (LCC) model. In the a-posteriori study, LES of the turbulent supercritical hydrothermal flame with the DMC and LCC models have been performed and compared with the DNS data respectively. It turns out that the LES-DMC model can successfully reproduce the complex behaviors of the turbulent supercritical hydrothermal flame, and the predicted mean and rms values of velocities, temperature, and species are more accurate than those of the LES-LCC model.

Sandwich meta-panel based on grooved corrugation for low-frequency sound absorption

In this work, a novel sandwich meta-panel (SMP) with grooved corrugations is proposed to efficiently attenuate low-frequency sound waves under deep subwavelength thickness (e.g., at 133 Hz). Most innovatively, SMP possesses tremendous mechanical characteristics (e.g., high bending stiffness) simultaneously, stemming from its corrugation core configuration. A theoretical prediction for sound absorption with an explicit expression of effective length is built, as well as a direct numerical simulation model. The theoretical and numerical results coincide well with each other, and demonstrate the SMPs' great capacity of manipulating low-frequency sound waves. Further, the SMPs can be tuned flexibly through altering perforation diameter, channel length and folding number, and multiple diverse unit cells can be coupled to get wide high-absorption bands (e.g., from 203 Hz to 249 Hz). The SMPs pave a new way for coiled-up space metastructures to engineering applications, with simple layout and perspicuous designing guidance.

Dendrite-resolved, full-melt-pool phase-field simulations to reveal non-steady-state effects and to test an approximate model

We study the epitaxial, columnar growth of (multiply oriented) dendrites/cells for a spot melt in a polycrystalline Al–Cu substrate using two-dimensional, phase-field, direct numerical simulations (DNS) at the full-melt-pool scale. Our main objective is to compare the expensive DNS model to a much cheaper but approximate “line” model in which a single-crystal phase-field simulation is confined to a narrow rectangular geometry. To perform this comparison, we develop algorithms that automatically extract quantities of interest (QoIs) from both DNS and line models. These QoIs allow us to quantitatively assess the assumptions in the line model and help us analyze its discrepancy with the DNS model. We consider four sets of heat source parameters, mimicking welding and additive manufacturing conditions, that create a combination shallow and deep melt pools. Our largest DNS simulation used 16K × 14K grid points in space. Our main findings can be summarized as follows. Under AM conditions, the QoIs of line models are in excellent agreement with the full DNS results for both shallow and deep melt pools. Under welding conditions, the primary spacing of the DNS model is smaller than the prediction of line model. We identify a geometric crowding effect that accounts for the discrepancies between the DNS and line models. We propose two potential mechanisms that determine the response of the microstructure to geometric crowding.

Using Direct Numerical Simulation of Pore-Level Events to Improve Pore-Network Models for Prediction of Residual Trapping of CO2

Direct numerical simulation and pore-network modeling are common approaches to study the physics of two-phase flow through natural rocks. For assessment of the long-term performance of geological sequestration of CO2, it is important to model the full drainage-imbibition cycle to provide an accurate estimate of the trapped CO2. While direct numerical simulation using pore geometry from micro-CT rock images accurately models two-phase flow physics, it is computationally prohibitive for large rock volumes. On the other hand, pore-network modeling on networks extracted from micro-CT rock images is computationally efficient but utilizes simplified physics in idealized geometric pore elements. This study uses the lattice-Boltzmann method for direct numerical simulation of CO2-brine flow in idealized pore elements to develop a new set of pore-level flow models for the pore-body filling and snap-off events in pore-network modeling of imbibition. Lattice-Boltzmann simulations are conducted on typical idealized pore-network configurations, and the interface evolution and local capillary pressure are evaluated to develop modified equations of local threshold capillary pressure of pore elements as a function of shape factor and other geometrical parameters. The modified equations are then incorporated into a quasi-static pore-network flow solver. The modified model is applied on extracted pore-network of sandstone samples, and saturation of residual trapped CO2 is computed for a drainage-imbibition cycle. The modified model yields different statistics of pore-level events compared with the original model; in particular, the occurrence of snap-off in pore-throats is reduced resulting in a more frontal displacement pattern along the main injection direction. Compared to the original model, the modified model is in closer agreement with the residual trapped CO2 obtained from core flow experiments and direct numerical simulation.

A two-scale computational continua multiscale analysis model for honeycomb sandwich plates

A two-scale computational continua (C 2) model is proposed for the multiscale analysis of honeycomb sandwich plates. In this model, the macroscopic problem is simulated by the third-order shear deformation theory (TSDT), while a single computational unit cell (CUC) with facesheets and honeycomb core is regarded as the microscopic problem and it is discretized by the 3D solid elements, so the proposed model is called as two-scale C 2-TSDT. In the numerical examples, the results of proposed C 2 model are compared with these of the direct numerical simulation (DNS) model and the homogenization model, and a good agreement is achieved.

Consideration of the interactions between the reaction zones in the new extended Eddy dissipation concept model

The latest Direct Numerical Simulation (DNS) modeling results in flameless combustion suggest interactions between the combustion reaction zones. The New Extended Eddy Dissipation Concept (NE-EDC) model, where model coefficients are calculated based on local Reynolds and Damköhler numbers, was proposed to improve the standard Eddy Dissipation Concept (EDC) model's accuracy when modeling flameless combustion, but this model does not include the interactions between the reaction zones.In this work, a revised version of the NE-EDC model is presented, called here Generalized NE-EDC model, where the chemical time scale is calculated in detail, considering the reaction rates of CH4, H2, O2, CO and CO2, making the interaction between the reaction zones more realistic (in the NE-EDC only a one-step CH4 global reaction mechanism is considered). A comparative study of four global reaction mechanisms is carried out to select the best mechanism for chemical time scale definition: the adjusted Jones & Lindstedt (JL1); the adjusted Westbrook & Dryer (WD1); the adjusted Westbrook & Dryer (WD2); and the one-step CH4 global mechanism (1-step).The four global reaction mechanisms, in combination with the NE-EDC model, are applied to the Delft lab-scale furnace and the modeling results are compared against those experimental measurements. The NE-EDC modeling results, in combination with WD2, present a slight improvement over the other global mechanisms in flameless modeling.

Mathematical Methodology and Metallurgical Application of Turbulence Modelling: A Review

This paper focusses on three main numerical methods, i.e., the Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), and Direct Numerical Simulation (DNS) methods. The formulation and variation of different RANS methods are evaluated. The advantage and disadvantage of RANS models to characterize turbulent flows are discussed. The progress of LES with different subgrid scale models is presented. Special attention is paid to the inflow boundary condition for LES modelling. Application and limitation of the DNS model are described. Different experimental techniques for model validation are given. The consistency between physical experimentation/modelling and industrial cases is discussed. An emphasis is placed on the model validation through physical experimentation. Subsequently, the application of a turbulence model for three specific flow problems commonly encountered in metallurgical process, i.e., bubble-induced turbulence, supersonic jet transport, and electromagnetic suppression of turbulence, is discussed. Some future perspectives for the simulation of turbulent flow are formulated.

Direct numerical simulation of a pulsatile flow in a stenotic channel using immersed boundary method

AbstractA three‐dimensional direct numerical simulation model coupled with the immersed boundary method has been developed to simulate a pulsatile flow in a planar channel with single and double one‐sided semicircular constrictions. For relevance to blood flow in large arteries, simulations have been performed at Reynolds numbers of 750 and 1000. Flow physics and resultant wall shear stress (WSS)‐based hemodynamic parameters are presented. The instantaneous vortex dynamics, mean flow characteristics, and turbulent energy spectra are evaluated for flow physics. Subsequently, three WSS‐based parameters, namely the time‐averaged WSS, oscillatory shear index, and relative residence time, are calculated over the stenotic wall and correlated with flow physics to identify the regions prone to atherosclerotic plaque progression. Results show that the double stenotic channel leads to high‐intensity and broadband turbulent characteristics downstream, promoting critical values of the WSS‐based parameters in the post‐stenotic areas. In addition, the inter‐space area between two stenoses displays multiple strong recirculations, making this area highly prone to atherosclerosis progression. The effect of stenosis degree on the WSS‐based parameters is studied up to 60% degree. As the degree of occlusion is increased, larger regions are involved with the nonphysiological ranges of the WSS‐based parameters.

Structural subgrid scale model based on wavelet filter for large eddy simulation of particle-laden turbulence

Coherent vortex structures in subgrid scale (SGS) motions are important for preferential concentration and collision of particles with small and intermediate Stokes number (Xiong et al., 2019). In this study, a new large eddy simulation (LES) strategy that combines wavelet filtered large eddy simulation with a differential filter SGS model is proposed. First, a wavelet filtered direct numerical simulation (WFDNS) enables good preservation of SGS structures due to the high compressibility and local fidelity of the wavelet filter. Second, a differential filter (DF) model, containing only a parameter related to the nominal filter width, is used to dynamically reconstruct unresolved eddies. The SGS model presented here is verified using direct numerical simulation (DNS) data for particle-laden homogenous isotropic turbulence. Compared to the classical spectral-filtered DNS (FDNS) model, the new SGS model enables to achieve better agreement with DNS results related to the dispersed-phase statistics, such as particle acceleration, particle-seen fluid kinetic energy, particle-seen Lagrangian integral time etc. Furthermore, obtained results also exhibit the advantages of a proposed model over the stochastic Langevin model in the prediction of particle dynamics, especially collision-related statistics such as radial distribution function, radial relative velocities, and particle collision rates. Moreover, the model also demonstrates good performance in application to particle-pair related statistics at different Reynolds numbers and different filter depths. This is attributed to the ability of this model to multispectrally enhance coherent vortex structures in SGS, which is promising to apply for recovering SGS effects in the LES of turbulent particle-laden flows.

Solids back-mixing in the transport zone of circulating fluidized bed boilers

This work investigates the back-mixing of solids in the transport zone of large-scale circulating fluidized bed (CFB) boilers, with the aims of identifying and evaluating the governing mechanisms and providing a mathematical description based on a solid theoretical background rather than on purely empirical correlations. In addition, transient Direct Numerical Simulation (DNS) modeling is used to identify the mechanism that drives migration of the solids from the dilute up-flow in the core region to the down-flow at the furnace walls. Previously published concentration and pressure profiles are collated and analyzed through modeling of the steady-state mass balance of the dispersed solids in the transport zone. The study shows that solids back-mixing at the furnace wall layers is limited (hence governed) by the core-to-wall layer mass transfer transport mechanism rather than by the lateral movement of solids within the core region. The latter is shown by the 3-dimensional (3D) mass balance model, and the transient DNS modeling indicates that this is due to a turbophoresis mechanism. We also show that the use of Pe-numbers to describe the lateral solids dispersion is not straightforward but rather depends on the unit scale, and that Pe-numbers < 26 are needed to yield the solids back-mixing rates measured in large-scale CFB boilers. Finally, we propose a mathematical expression for the core-to-wall layer mass transfer coefficient derived from a Sherwood number (Sh)-correlation fitted to measured values of the characteristic decay constant that result from the solids back-mixing. This expression shows better agreement with the large-scale measurements than do the expressions given in the literature.

Digital rock physics, chemistry, and biology: challenges and prospects of pore-scale modelling approach

Conventional and unconventional hydrocarbon rocks have complicated pore structures with heterogeneities distributed over various length scales (from nanometre to centimetre or even larger scales). Effective characterization of the properties of such rocks based on their digital twins is a challenging task. Digital rock physics (DRP) can be used to quantify the structural and morphological parameters of rocks directly and predict flow transport properties at the pore scale. Digital rock chemistry (DRC) or biology (DRB) applies when the changes in pore structures are due to interaction with solutes or microbial activities. Fluid–rock interactions or microbial activities complicate fluid flow by introducing new heterogeneities at the pore scale. DRP/DRC/DRB modelling approaches can achieve an understanding of spatiotemporal porosity/permeability relationships that develop at the pore scale during reactive flow or microbial activities. There has recently been a surge in publications on the modelling of pore-scale models. However, this approach has many challenges, from theoretical issues such as how best to combine rock properties at different resolutions to technical challenges such as performing simulations using pore-scale models that contain too many pores and throats. Multiscale pore modelling approaches are generally categorized using the number of scales represented, the minimum being a dual-scale pore model, in which both void and porous voxels (e.g., unresolved pores) are modelled simultaneously. Two common approaches that can be implemented to predict rocks' behaviour across different scales are direct numerical simulation (DNS) and pore network model (PNM). Multiscale PNMs received more attention because of their ability to model a wide pore size distribution at various scales, while multiscale DNS requires resource-demanding Navier-Stokes-Brinkman models in GB voxel space. An overview of the recent progress and challenges involved in modelling digital rock physics, chemistry, and biology of multiscale systems is presented here.

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.

(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].

The Terminal Velocity of Axisymmetric Cloud Drops and Raindrops Evaluated by the Immersed Boundary Method

AbstractThe terminal velocity of cloud drops and raindrops used in numerical model calculations can significantly affect weather predictions. Current formulations rely on laboratory experiments made in the 1940s and 1960s. Because these experiments were performed only at typical environmental conditions of 20°C and 1013 hPa, parameterizations have been introduced to deduce the terminal velocity aloft without rigorous evaluation. In this study, an incompressible two-phase flow direct numerical simulation model is used to calculate the free-falling motion of axisymmetric drops with diameters between 0.025 and 0.5 mm to study the terminal fall velocity. Simulated terminal fall velocities of free-falling drops at 20°C and 1013 hPa agree within 3.2% with the previous empirical parameterization (Beard formula), and 4.5% with existing laboratory data in the diameter range between 0.3 and 0.5 mm. The velocities converge to the analytic Hadamard–Rybczynski solution within 2% for small Reynolds numbers, demonstrating the robustness of our simulations. Simulations under various atmospheric conditions show that existing empirical parameterizations that account for the air density dependence of the terminal velocity have errors up to 11.8% under the conditions examined in this study. We propose a new empirical formula that describes the air density dependence of the terminal velocity. It is also shown that the falling speed of a small drop is not sensitive to shape oscillation, and the terminal velocity decreases by only less than 1.3% when the axis ratio increases by 12% with reduced surface tension. Internal circulation within falling drops is also presented and compared with previous studies.

Large eddy simulation of Rayleigh–Taylor mixing based on helicity model

This paper focuses on large eddy simulation of Rayleigh–Taylor instability (RTI) based on helicity model (HM) which is derived from our previous research. Based on the RTI problem, we obtain from a priori test and theoretical analysis that the suggested model can automatically distinguish laminar flow and turbulence. Comparing the numerical simulation results with direct numerical simulation (DNS) and traditional model in RTI problem, we could find that the suggested model overcomes some defects of the traditional model, such as the traditional model cannot predict transition accurately and the suggested model can predict the turbulence mixing width and mass fraction precisely. It provides a beneficial tool for the research of RTI.