Algorithm For Direct Numerical Simulation Research Articles

Development and application of turbulent heat flux model for lead-bismuth eutectic based on deep learning

Existing turbulent heat flux (THF) closure models in Reynolds-averaged Navier–Stokes simulation of scalar transport are insufficient on accuracy for fluids with a low Prandtl number (Pr), such as lead–bismuth eutectic (LBE), especially under complex operating conditions like in heat exchangers of nuclear reactors. This paper aims to propose a THF model suitable for such conditions. Firstly, we established a high-fidelity database of forced convection flow past two tandem cylinders under a Reynolds number (Re) of 1 × 105 and various low Pr conditions by hybrid large eddy simulation and direct numerical simulation algorithm. Based on the database, a deep learning architecture was then built and trained to predict dimensionless THF. Finally, a posteriori test proved that the proposed THF model helps to improve the prediction performance for temperature fields and also performs well when extrapolated to cases of LBE past the tube bundles, especially under the case with large Peclet numbers.

Direct numerical simulation of particle pore-scale transport through three-dimensional porous media with arbitrarily polyhedral mesh

A new direct numerical simulation algorithm is developed for particle pore-scale transport through the porous media with arbitrarily polyhedral mesh. In the algorithm, the Navier-Stokes Equation is used to describe the continuous phase motion in the Eulerian framework; Newton's Second Law is used to describe the particle dynamics in the Lagrangian framework; Discrete element method is used to describe the particle-particle interactions and particle-wall interactions; RIGID is used to detect the contact state between particles with arbitrarily shaped pore walls. To suppress the spurious force oscillations (SFO) and improve the numerical accuracy of the evaluation of fluid-particle interaction, a novel consistent fictitious domain method (CFDM) in the arbitrarily collocated polyhedral mesh is developed. Numerical results of six test cases show that CFDM is accurate and second order in space, and no obvious SFO is found. Finally, the new direct numerical simulation algorithm is used to simulate the particle transport through three-dimensional porous media reconstructed from micro-CT scans from a real rock. The numerical results of a serial of tests with different particle sizes reveal several distinct microscopic flow mechanisms and the corresponding macroscopic characteristics. The change of channel resistance leads to the formation of particle motion paths in succession; Along a certain motion path, the particle moving velocity can be different at different sites; With the increase of particle size, the particle average retention time and particle average transit time increase; Particle velocity presents lognormal distribution, which becomes wider with the increase of particle size. The newly developed algorithm can be adopted as a direct numerical simulation tool to simulate particle motion in arbitrarily complex pore space.

A fast algorithm for Direct Numerical Simulation of turbulent convection with immersed boundaries

A parallel algorithm is presented for the Direct Numerical Simulation of convection flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids.The method presented includes a triperiodic Poisson solver employed irrespective of the actual boundary shape and a second order accuracy for the computational domain, including the near wall regions, when walls are defined as immersed boundaries.The numerical solution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for laminar and turbulent pipe flow, and for the case of flow around an array of heated cylindrical rods arranged in a triangular lattice. The formal accuracy of the method is demonstrated in laminar flow conditions, and DNS results in turbulent conditions are compared to available literature data, thus confirming the favorable qualities of the method.

Modifications to the SIMPLE algorithm with the MDCD approach for incompressible flow simulation

PurposeThe purpose of the paper is to propose some modifications to the SIMPLE (semi-implicit method for pressure-linked equations) algorithm. These modifications can ensure the numerical robustness and optimize computational efficiency. They remarkably promote the ability of the SIMPLE algorithm for incompressible DNS (direct numerical simulation) of multiscale problems, such as transitional flows and turbulent flows, by improving the properties of dispersion and dissipation.Design/methodology/approachThe MDCD (minimized dispersion and controllable dissipation) scheme and MMIM (modified momentum interpolation method) are introduced. Six typical test cases are used to validate the modified algorithm, including the linear convective flow, lid-driven cavity flow, laminar boundary layer, Taylor vortex and DHIT (decaying homogenous isotropic turbulence). Particularly, a highly unsteady DNS of separated-flow transition in turbomachinery is precisely predicted by the modified algorithm.FindingsThe numerical examples show the distinct superiority of the modified algorithm in both internal flows and external flows. The advantages of the MDCD scheme and MMIM make the SIMPLE algorithm a promising method for DNS.Originality/valueSome effective modifications to the SIMPLE algorithm are addressed. It is the first attempt to introduce the MDCD approach into the SIMPLE-type algorithms. The new algorithm is especially suitable for the incompressible DNS of convection-dominated flows.

Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations

Kinetic equations are widely used in many branches of science to describe the evolution of random wave spectra. To examine the validity of these equations, we study numerically the long-term evolution of water wave spectra without wind input using three different models. The first model is the classical kinetic (Hasselmann) equation (KE). The second model is the generalised kinetic equation (gKE), derived employing the same statistical closure as the KE but without the assumption of quasistationarity. The third model, which we refer to as the DNS-ZE, is a direct numerical simulation algorithm based on the Zakharov integrodifferential equation, which plays the role of the primitive equation for a weakly nonlinear wave field. It does not employ any statistical assumptions. We perform a comparison of the spectral evolution of the same initial distributions without forcing, with/without a statistical closure and with/without the quasistationarity assumption. For the initial conditions, we choose two narrow-banded spectra with the same frequency distribution and different degrees of directionality. The short-term evolution ($O(10^{2})$ wave periods) of both spectra has been previously thoroughly studied experimentally and numerically using a variety of approaches. Our DNS-ZE results are validated both with existing short-term DNS by other methods and with available laboratory observations of higher-order moment (kurtosis) evolution. All three models demonstrate very close evolution of integral characteristics of the spectra, approaching with time the theoretical asymptotes of the self-similar stage of evolution. Both kinetic equations give almost identical spectral evolution, unless the spectrum is initially too narrow in angle. However, there are major differences between the DNS-ZE and gKE/KE predictions. First, the rate of angular broadening of initially narrow angular distributions is much larger for the gKE and KE than for the DNS-ZE, although the angular width does appear to tend to the same universal value at large times. Second, the shapes of the frequency spectra differ substantially (even when the nonlinearity is decreased), the DNS-ZE spectra being wider than the KE/gKE ones and having much lower spectral peaks. Third, the maximal rates of change of the spectra obtained with the DNS-ZE scale as the fourth power of nonlinearity, which corresponds to the dynamical time scale of evolution, rather than the sixth power of nonlinearity typical of the kinetic time scale exhibited by the KE. The gKE predictions fall in between. While the long-term DNS show excellent agreement with the KE predictions for integral characteristics of evolving wave spectra, the striking systematic discrepancies for a number of specific spectral characteristics call for revision of the fundamentals of the wave kinetic description.

A weighted multiple-relaxation-time lattice Boltzmann method for multiphase flows and its application to partial coalescence cascades

We present a lattice Boltzmann method (LBM) with a weighted multiple-relaxation-time (WMRT) collision model and an adaptive mesh refinement (AMR) algorithm for direct numerical simulation of two-phase flows in three dimensions. The proposed WMRT model enhances the numerical stability of the LBM for immiscible fluids at high density ratios, particularly on the D3Q27 lattice. The effectiveness and efficiency of the proposed WMRT–LBM–AMR is validated through simulations of (a) buoyancy-driven motion and deformation of a gas bubble rising in a viscous liquid; (b) the bag-breakup mechanism of a falling drop; (c) crown splashing of a droplet on a wet surface; and (d) the partial coalescence mechanism of a liquid drop at a liquid–liquid interface. The numerical simulations agree well with available experimental data and theoretical approximations where applicable.

A fast algorithm for Direct Numerical Simulation of natural convection flows in arbitrarily-shaped periodic domains

A parallel algorithm is presented for the Direct Numerical Simulation of buoyancy- induced flows in open or partially confined periodic domains, containing immersed cylindrical bodies of arbitrary cross-section. The governing equations are discretized by means of the Finite Volume method on Cartesian grids. A semi-implicit scheme is employed for the diffusive terms, which are treated implicitly on the periodic plane and explicitly along the homogeneous direction, while all convective terms are explicit, via the second-order Adams-Bashfort scheme. The contemporary solution of velocity and pressure fields is achieved by means of a projection method. The numerical resolution of the set of linear equations resulting from discretization is carried out by means of efficient and highly parallel direct solvers. Verification and validation of the numerical procedure is reported in the paper, for the case of flow around an array of heated cylindrical rods arranged in a square lattice. Grid independence is assessed in laminar flow conditions, and DNS results in turbulent conditions are presented for two different grids and compared to available literature data, thus confirming the favorable qualities of the method.

Computational simulation for analysis and synthesis of impact resilient structure

Impact resilient structures are of great interest in many engineering applications varying from civil, land vehicle, aircraft and space structures, to mention a few examples. To design such structure, one has to resort fundamental principles and take into account progress in analytical and computational approaches as well as in material science and technology. With such perspectives, this work looks at a generic beam and plate structure subject to impact loading and carry out analysis and numerical simulation. The first objective of the work is to develop a computational algorithm to analyze flat plate as a generic structure subjected to impact loading for numerical simulation and parametric study. The analysis will be based on dynamic response analysis. Consideration is given to the elastic-plastic region. The second objective is to utilize the computational algorithm for direct numerical simulation, and as a parallel scheme, commercial off-the shelf numerical code is utilized for parametric study, optimization and synthesis. Through such analysis and numerical simulation, effort is devoted to arrive at an optimum configuration in terms of loading, structural dimensions, material properties and composite lay-up, among others. Results will be discussed in view of practical applications.

Computational Simulation for Static and Dynamic Load of Rectangular Plate in Elastic Region for Analysis of Impact Resilient Structure

Impact resilient structures are of great interest in many engineering applications varying from civil, land vehicle, aircraft and space structures, to mention a few examples. To design such structure, one has to resort fundamental principles and take into account progress in analytical and computational approaches as well as in material science and technology. With such perspective, the first objective of this work is to develop a computational algorithm to analyze flat plate as a generic structure subjected to impact loading for numerical simulation and parametric study without considering the surface impact effect. The analysis is carried out from first principles for static and dynamic analysis; the latter is based on dynamic response analysis in the elastic region. The second objective is to utilize the computational algorithm for direct numerical simulation, and as a parallel scheme, commercial off-the shelf numerical code is utilized for parametric study, optimization and synthesis. Through such analysis and numerical simulation, effort is devoted to arrive at optimum configuration in terms of loading, structural dimensions, and material properties, among others. The codes developed are validated for generic cases. Further simulations are carried out using commercial codes for some sample applications to explore impact resilient structural characteristics in the elastic region.

Spectral stability of traveling water waves: Eigenvalue collision, singularities, and direct numerical simulation

In a recent paper (Nicholls (2009) [1]) the author conjectured upon the connection between the onset of dynamic spectral instability of periodic traveling water waves, and singularities present in Taylor series representations of spectral data for the linearized water wave equations. More specifically, he proposed that the onset of instability is always coincident with encountering the smallest singularity in these Taylor series. In this paper we study this connection via a new Direct Numerical Simulation algorithm derived from the surface formulation of the water wave problem due to Zakharov (1968) [5] and Craig & Sulem (1993) [6]. We find compelling evidence that the conjecture is true in the case of deep (as compared to Benjamin & Feir’s (1967) [7] critical depth h ≈ 1.363 ) water, but false for shallow depths as it significantly underpredicts the onset of instability. The utility of the singularity identification strategy advocated in [1], while somewhat lessened in the shallow water case, is nonetheless upheld due to its ability to reliably identify a lower bound of stability and its extremely favorable computational complexity.

A spurious evolution of turbulence originated from round-off error in pseudo-spectral simulation

We report a slowly-developing, spurious numerical solution in pseudo-spectral direct numerical simulation (DNS) of incompressible fluid turbulence. When the effect of machine round-off on the divergence-free condition is not carefully controlled, a problem can develop slowly (over about 50 large-eddy turnover times) and eventually leads to an unphysical flow field. The problem was found with a previously published, highly-compact algorithm for pseudo-spectral DNS and therefore it is important to document the contamination of this numerical artifact on simulated turbulence structure and statistics. This is a striking example since the problem is not easily noticeable due to its very long development time, and it does not lead to numerical instability but rather a different flow state. A theory is developed to explain the unphysical evolution and predicts the exponential growth of round-off error induced velocity divergence. The theory shows that any correlation of the large-scale forcing with the velocity field at the beginning of the time step could lead to amplification of the velocity divergence. For this reason, the problem is quite reproducible. Several simple remedies are tested and shown to correct the problem. It is shown that all revised algorithms are identical theoretically to the original algorithm, with the only difference in the level of control for the divergence-free condition of the simulated flow field. A general recommendation is that the pressure projection operation should be performed at the end of each time step to ensure that the divergence-free condition is not contaminated by machine round-off.

Algorithm for direct numerical simulation of emulsion flow through a granular material

A multipole-accelerated 3D boundary-integral algorithm capable of modelling an emulsion flow through a granular material by direct multiparticle-multidrop simulations in a periodic box is developed and tested. The particles form a random arrangement at high volume fraction rigidly held in space (including the case of an equilibrium packing in mechanical contact). Deformable drops (with non-deformed diameter comparable with the particle size) squeeze between the particles under a specified average pressure gradient. The algorithm includes recent boundary-integral desingularization tools especially important for drop–solid and drop–drop interactions, the Hebeker representation for solid particle contributions, and unstructured surface triangulations with fixed topology. Multipole acceleration, with two levels of mesh node decomposition (entire drop/solid surfaces and “patches”), is a significant improvement over schemes used in previous, purely multidrop simulations; it remains efficient at very high resolutions ( 10 4 – 10 5 triangular elements per surface) and has no lower limitation on the number of particles or drops. Such resolutions are necessary in the problem to alleviate lubrication difficulties, especially for near-critical squeezing conditions, as well as using ∼ 10 4 time steps and an iterative solution at each step, both for contrast and matching viscosities. Examples are shown for squeezing of 25–40 drops through an array of 9–14 solids, with the total volume fraction of 70% for particles and drops. The flow rates for the drop and continuous phases are calculated. Extensive convergence testing with respect to program parameters (triangulation, multipole truncation, etc.) is made.

Mol solution for transient turbulent flow in a heated pipe

A computational fluid dynamics (CFD) code, based on direct numerical simulation (DNS) and method of lines (MOL) approach previously developed for the prediction of transient turbulent, incompressible, confined non-isothermal flows with constant wall temperature was applied to the prediction of turbulent flow and temperature fields in flows dominated by forced convection in circular tubes with strong heating. The code was parallelized in order to meet the high grid resolutions required by DNS of turbulent flows. Predictive accuracy of the code was assessed by validating its steady state predictions against measurements and numerical results available in the literature. Favorable comparisons obtained reveal that the code provides an efficient algorithm for DNS of non-isothermal turbulent flows.

A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows

A non-dissipative, robust, implicit algorithm is proposed for direct numerical and large-eddy simulation of compressible turbulent flows. The algorithm addresses the problems caused by low Mach numbers and under-resolved high Reynolds numbers. It colocates variables in space to allow easy extension to unstructured grids, and discretely conserves mass, momentum and total energy. The Navier–Stokes equations are non-dimensionalized using an incompressible scaling for pressure, and the energy equation is used to obtain an expression for the velocity divergence. A pressure-correction approach is used to solve the resulting equations, such that the discrete divergence is constrained by the energy equation. As a result, the discrete equations analytically reduce to the incompressible equations at very low Mach number, i.e., the algorithm overcomes the acoustic time-scale limit without preconditioning or solution of an implicit system of equations. The algorithm discretely conserves kinetic energy in the incompressible inviscid limit, and is robust for inviscid compressible turbulence on the convective time-scale. These properties make it well-suited for DNS/LES of compressible turbulent flows. Results are shown for acoustic propagation, the incompressible Taylor problem, periodic shock tube problem, and isotropic turbulence.

Instability-wave propagation in boundary-layer flows at subsonic through hypersonic Mach numbers

Direct numerical simulations (DNS) form an important ingredient to physics-based prediction of laminar-turbulent transition in boundary-layer flows, particularly in applications where it is desirable or even essential to model the various stages of transition process in an integrated manner. This paper addresses two building-block issues towards such capability: application to instability-wave propagation in boundary layers over curvilinear surfaces and robust outflow boundary conditions across the speed regime. In particular, detailed comparisons of linear and nonlinear development of instability waves in a range of boundary-layer flows are used to cross-validate a high-order direct numerical simulation algorithm against the approximate but computationally more efficient technique of parabolized stability equations (PSE). Three separate flow configurations are investigated in this study: (i) development of a Tollmien-Schlichting (TS) instability wave over a two-dimensional (2D), symmetric, low-speed airfoil, (ii) both first and second-mode development in a self-similar, flat plate boundary layer at Mach 4.5, and (iii) amplification of first and second modes of Rayleigh instability and a stationary Gortler vortex in the hypersonic, axisymmetric boundary layer over a flared cone. The satisfactory agreement between the DNS and PSE predictions for both amplitudes and mode shapes of the instability waves confirms the overall efficacy of the DNS algorithm, while underscoring the accuracy of predictions based on the PSE approximation.

A zonal grid algorithm for DNS of turbulent boundary layers

A zonal grid algorithm for direct numerical simulation (DNS) of incompressible turbulent flows within a Finite-Volume framework is presented. The algorithm uses fully coupled embedded grids and a conservative treatment of the grid-interface variables. A family of conservative prolongation operators is tested in a 2D vortex dipole and a 3D turbulent boundary layer flow. These tests show that both, first- and second-order interpolation conserves the overall second-order spatial accuracy of the scheme. The first-order conservative interpolation has a smaller damping effect on the solution but the second-order conservative interpolation has better spectral properties. The application of this algorithm in boundary layer flow separating and reattaching due to the presence of a streamwise pressure gradient reveals the power and usefulness of the presented algorithm. This simulation has been made possible by the zonal grid algorithm by reducing the required number of grid points from about 500 × 10 6 to 130 × 10 6 grid cells.

A DNS algorithm using B-spline collocation method for compressible turbulent channel flow

Abstract Direct numerical simulation (DNS) offers useful information about the understanding and modeling of turbulent flow. However, few DNSs of wall-bounded compressible turbulent flows have been performed. The objective of this paper is to construct a DNS algorithm which can simulate the compressible turbulent flow between the adiabatic and isothermal walls accurately and efficiently. Since this flow is the simplest turbulent flow with adiabatic and isothermal walls, it is ideal for the modeling of compressible turbulent flow near the adiabatic and isothermal walls. The present DNS algorithm for wall-bounded compressible turbulent flow is based on the B-spline collocation method in the wall-normal direction. In addition, the skew-symmetric form for convection term is used in the DNS algorithm to maintain numerical stability. The validity of the DNS algorithm is confirmed by comparing our results with those of an existing DNS of the compressible turbulent flow between isothermal walls [J. Fluid Mech. 305 (1995) 159]. The applicability and usefulness of the DNS algorithm are demonstrated by the stable computation of the DNS of compressible turbulent flow between adiabatic and isothermal walls.

DNS Algorithm for Wall Turbulence of Compressible Flow with B-Spline Method.

The direct numerical simulation (DNS) offers useful information about the understanding and modeling of turbulent flow. Few direct numerical simulations of wall-bounded compressible turbulent flows have been performed however. The objective of our study is to construct the DNS algorithm which can simulate the compressible turbulent flow between adiabatic and isothermal walls. The flow is selected since it is the simplest turbulent flow with an adiabatic wall, and therefore it is ideal for the modeling of compressible turbulent flow near the adiabatic wall. From the applicability and efficiency, we construct the new DNS algorithm based on the B-spline collocation method in the wall-normal direction. The validity and efficiency of the DNS algorithm are confirmed by comparing our results with those of an existing DNS in the compressible turbulent flow between isothermal walls. Then the DNS of compressible turbulent flow between the adiabatic and isothermal walls exhibits the applicability and usefulness of the algorithm.

Effective conductivity of loaded granular materials by numerical simulation

Thermal (or electrical) conduction through a stationary, random close packed granular material is studied by numerical simulation. The particles are smooth uniform spheres with either point contact...

Turbulent flow in a channel with permeable walls. Direct numerical simulation and results of three-parameter model

Steady turbulent viscous incompressible fluid flow in a plane channel is calculated for the case of uniform blowing and suction through opposite walls. There are no experimental data for flows of this type. The flows were calculated by two methods: a direct numerical simulation method and using a three-parameter turbulence model. Direct numerical simulation was carried out using the same (apart from the boundary conditions) algorithm for numerical solution of the Navier-Stokes equations as that used earlier for calculating flows in pipes and channels with impermeable walls. In the second group of calculations the version of the model published in 1978 was used. The results obtained by the two methods are in good agreement. The difference is within the spread of the experimental data used for determining the parameters of the model. The agreement obtained makes it possible to assert that the turbulence direct numerical simulation algorithm developed can be used for the analysis of flows with quite different boundary conditions, including cases where there are no corresponding experimental data.