Direct Numerical Simulation Data Research Articles

Closure Relations for Fluxes of Flame Surface Density and Scalar Dissipation Rate in Turbulent Premixed Flames

In this study, closure relations for total and turbulent convection fluxes of flame surface density and scalar dissipation rate were developed (i) by placing the focus of consideration on the flow velocity conditioned to the instantaneous flame within the mean flame brush and (ii) by considering the limiting behavior of this velocity at the leading and trailing edges of the flame brush. The model was tested against direct numerical simulation (DNS) data obtained from three statistically stationary, one-dimensional, planar, premixed turbulent flames associated with the flamelet regime of turbulent burning. While turbulent fluxes of flame surface density and scalar dissipation rate, obtained in the DNSs, showed the countergradient behavior, the model predicted the total fluxes reasonably well without using any tuning parameter. The model predictions were also compared with results computed using an alternative closure relation for the flame-conditioned velocity.

GPU-based, parallel-line, omni-directional integration of measured pressure gradient field to obtain the 3D pressure distribution

The introduction of 3D time-resolved velocity measurement techniques enables calculation of the instantaneous pressure distribution by spatially integrating the material acceleration. This paper introduces an efficient method for 3D integration of the acceleration, which does not require prescribed Dirichlet boundary condition on one of the surfaces, minimizes the propagation of errors in acceleration, and can be easily utilized in flows with complex boundaries. This parallel-line, omni-directional integration procedure (Omni3D) calculates the pressure at every point by integration from all directions, while avoiding regions with large acceleration errors. To reduce the computational costs, the calculations are performed by a GPU-based algorithm, which determines the 3D pressure field from tomographic PIV data in 1 min. The accuracy of Omni3D is compared to that of several techniques, including procedures based on solving the Pressure Poisson Equation (PPE) with different Dirichlet boundary conditions. The error analysis is based on Direct Numerical Simulation (DNS) data for isotropic turbulence, synthetic 3D PIV images for turbulent channel flow generated from DNS data, and experimental data. It examines the effects of spatial resolution, propagation, and avoidance of embedded local errors, boundary conditions, method for calculating the velocity, as well as viscous and sub-grid stresses on the calculated pressures. For acceleration fields with low errors and properly specified boundary conditions, Omni3D and PPE give similar results. However, Omni3D is more effective in suppressing the effects of acceleration errors. Sample experimental results including instantaneous plot of pressure, pressure statistics, and pressure–velocity correlations based on tomographic PIV data are also provided.

A quantitative study of track initialization of the four-frame best estimate algorithm for three-dimensional Lagrangian particle tracking

We introduce a method to improve three-dimensional particle tracking velocimetry (3D-PTV) algorithms. 3D-PTV is an experimental method used to measure the Lagrangian trajectories of individual particles over time. The trajectories are constructed by linking the particle positions from a sequence of images. Different 3D-PTV algorithms have been proposed in the literature, ranging from simply taking the nearest neighbor in the next frame to using multiframe schemes. This work focuses on the initialization of the four-frame best estimate (4BE) method introduced by Ouellette et al (2006 Exp. Fluids 40 301–13). Previously, tracking algorithms have been initialized by using the particle’s nearest neighbor(s) in the next frame or by using a velocity guess to predict the particle’s location in the next frame. We propose a more robust initialization, coupled with 4BE, that performs better than existing methods in the literature, in the sense of yielding a higher number of correct tracks. The performance of the proposed initialization method is compared to the 4BE method that uses nearest neighbor initialization by applying both methods on direct numerical simulation data from the Johns Hopkins turbulence databases. We show that the modified initialization greatly improves tracking in two canonical cases, homogeneous isotropic turbulence and turbulent channel flow (inhomogenous and anisotropic), greatly increasing the percentage of correct tracks found even under challenging seeding/particle displacement conditions.

A hybrid point-particle force model that combines physical and data-driven approaches

This study improves upon the physics-based pairwise interaction extended point-particle (PIEP) model. The PIEP model leverages our physical understanding to predict fluid mediated interactions between solid particles [1,2]. By considering the relative location of neighboring particles, the PIEP model is able to provide better predictions than existing drag models. While the current physical PIEP model is a powerful tool, its assumptions lead to increased error in flows with higher particle volume fractions. To reduce this error, a regression algorithm makes direct use of the results of direct numerical simulations (DNS) of an array of monodisperse solid particles subjected to uniform ambient flow at varying Reynolds numbers. The resulting statistical model and the physical PIEP model are superimposed to construct a hybrid, physics-based data-driven PIEP model. It must be noted that the performance of a pure data-driven approach without the model-form provided by the physical PIEP model is substantially inferior. The hybrid model's predictive capabilities are analyzed using additional DNS data that was not part of training the data-driven model. In every case tested, the hybrid models resulting from the regression were capable of (1) improving upon the physical PIEP model's prediction and (2) recovering underlying relevant physics from the DNS data. As the particle volume fraction increases, the physical PIEP model loses the ability to approximate the forces experienced by the particles, but the statistical model continues to produce accurate approximations.

Numerical simulation of forced and mixed convection turbulent liquid sodium flow over a vertical backward facing step with a four parameter turbulence model

Liquid metals are promising fluids for engineering applications since they have interesting physical properties such as high thermal conductivity and low kinematic viscosity with respect to the values of common operating fluids, i.e. air and water. This implies low Prandtl number values and therefore the similarity assumption between velocity and temperature fields does not hold. In the present work we solve a four parameter turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward facing step. On the wall behind the step a uniform heat flux is applied in order to study both forced and mixed convection flow regimes. This model for turbulent heat transfer, taking into account different boundary conditions, is analyzed and compared with the Kays correlation and Direct Numerical Simulation data. Profiles of velocity, turbulent kinetic energy, turbulent heat flux, temperature and its squared fluctuations are provided for two simulated Richardson number values, namely 0 and 0.338. Obtained results show a reasonable agreement with reference Direct Numerical Simulation values.

On identification of self-similar characteristics using the Tensor Train decomposition method with application to channel turbulence flow

A study on the application of the Tensor Train decomposition method to 3D direct numerical simulation data of channel turbulence flow is presented. The approach is validated with respect to compression rate and storage requirement. In tests with synthetic data, it is found that grid-aligned self-similar patterns are well captured, and also the application to non grid-aligned self-similarity yields satisfying results. It is observed that the shape of the input Tensor significantly affects the compression rate. Applied to data of channel turbulent flow, the Tensor Train format allows for surprisingly high compression rates whilst ensuring low relative errors.

Inhomogeneity and anisotropy in Eulerian–Eulerian near-wall modelling

This paper tackles the issue of image vorticity in turbulent Eulerian–Eulerian simulations. A pressure-velocity model to account for the no permeability constraint on the fluid- and particle-phase wall normal stress components is proposed. The pressure-velocity model is derived with in a Reynolds-Averaged Two-Fluid model (RA-TFM) framework and is implemented within the open-source CFD toolbox OpenFOAM. We demonstrate that this approach is capable of accounting for the strong near-wall inhomogeneity, a flow feature that hitherto has been neglected in Eulerian–Eulerian modelling. Simulation predictions are validated against benchmark Direct Numerical Simulation data and show a promising step forward in near-wall modelling in Eulerian–Eulerian simulations. The predictions reveal that the approach proposed herein can lead to a satisfactory agreement across all turbulence statistics paving the way for the correct prediction of more complex mechanisms. Finally, the source code of the recently developed solver ratfmFoam and supplementary material used in this work is made available online.

On the non-equilibrium models for subfilter scalar variance in large eddy simulation of turbulent mixing and combustion

This paper presents an analysis of the discretization errors in the non-equilibrium models for the subfilter variance of the mixture fraction, a key quantity to model in large eddy simulation (LES) of turbulent mixing and combustion. Two discretely distinct formulations of the non-equilibrium models that solve the transport equations to obtain the subfilter variance, i.e., the second moment transport equation (STE) and the variance transport equation (VTE), are analyzed. By deriving discrete equations for the evolution of subfilter variance by the two formulations, it is seen that the difference originates primarily from the product rule of differentiation applied to the scalar convection term, which does not hold discretely. LES of scalar mixing in a planar jet is performed to illustrate the outcome of the analysis. Results show that the discrete product rule error is significant and of the same order as the production and dissipation terms on average. A priori analysis using direct numerical simulation (DNS) data for scalar mixing in homogeneous isotropic turbulence is also performed. From the analysis, it is seen that the VTE model under-predicts the subfilter variance, whereas the STE model over-predicts it substantially with sharp oscillations.

Direct numerical simulation of turbulence over systematically varied irregular rough surfaces

Lattice Boltzmann direct numerical simulation of turbulent open-channel flows over randomly distributed hemispheres at $Re_{\unicode[STIX]{x1D70F}}=600$ is carried out to reveal the influence of roughness parameters related to a probability density function of rough-surface elevation on turbulence by analysing the spatial and Reynolds- (double-) averaged Navier–Stokes equation. This study specifically concentrates on the influence of the root-mean-square roughness and the skewness, and profiles of turbulence statistics are compared by introducing an effective wall-normal distance defined as a wall-normal integrated plane porosity. The effective distance can completely collapse the total shear stress outside the roughness sublayer, and thus the similarity of the streamwise mean velocity is clearer by introducing the effective distance. In order to examine the influence of the root-mean-square roughness and the skewness on dynamical effects that contribute to an increase in the skin friction coefficient, the triple-integrated double-averaged Navier–Stokes equation is analysed. The main contributors to the skin friction coefficient are found to be turbulence and drag force. The turbulence contribution increases with the root-mean-square roughness and/or the skewness. The drag force contribution, on the other hand, increases in particular with the root-mean-square roughness whereas an increase in the skewness does not increase the drag force contribution because it does not necessarily increase the surface area of the roughness elements. The contribution of the mean velocity dispersion induced by spatial inhomogeneity of the rough surfaces substantially increases with the root-mean-square roughness. A linear correlation is confirmed between the root-mean-square roughness and the equivalent roughness while the equivalent roughness monotonically increases with the skewness. A new correlation function based on the root-mean-square roughness and the skewness is developed with the available experimental and direct numerical simulation data, and it is confirmed that the developed correlation reasonably predicts the equivalent roughness of various types of real rough surfaces.

Numerical Investigation of Roughness Effects on Transition on Spherical Capsules

To address the hitherto unknown mechanism of boundary-layer transition on blunt reentry capsules, the role of roughness-induced disturbance growth on a spherical-section forebody is assessed via optimal transient growth theory and direct numerical simulations (DNS). Optimal transient-growth studies have been performed for the blunt capsule experiments at Mach 5.9 in the Hypersonic Ludwieg tube at the Technische Universität Braunschweig (HLB), which included measurements behind a patch of controlled, distributed micron-sized surface roughness. Transient-growth results for the HLB capsule indicate similar trends as the corresponding numerical data for a Mach 6 experiment in the Actively Controlled Expansion (ACE) facility of the Texas A&M University (TAMU) at a lower Reynolds number. Both configurations indicate a similar dependence on surface temperature ratio and, more important, rather low values of maximum energy gain. DNS are performed for the conditions of the HLB experiment to understand the generation of stationary disturbances by the roughness patch and the accompanying evolution of unsteady perturbations. However, no evidence of either modal or nonmodal disturbance growth in the wake of the roughness patch is found in the DNS data; thus, the physical mechanism underlying the observed onset of transition still remains unknown.

Assessment of a transport equation for mean reaction rate using DNS data obtained from highly unsteady premixed turbulent flames

Recently, a transport equation for the mean rate of product creation in a premixed turbulent flame was derived and a joint closure relation for dominant terms in that equation was developed and validated against Direct Numerical Simulation (DNS) data obtained from weakly turbulent flames. Present communication reports results of further DNS tests of this newly introduced approach, performed using recent data computed under substantially different turbulent conditions. In particular, the ability of the approach to predict significant oscillations of the turbulent burning velocity with time is shown under conditions associated with not only the flamelet but also the thin-reaction-zone regimes of premixed turbulent burning. While such oscillations are documented in the present and other DNS studies, capabilities of other models of premixed turbulent combustion to reproduce this challenging phenomenon have not yet been demonstrated in the literature.

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the Fukagata-Iwamoto-Kasagi (FIK) identity (FUKAGATA, K., IWAMOTO, K., and KASAGI, N. Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Physics of Fluids, 14(11), L73–L76 (2002)) and the Renard-Deck (RD) identity (DECK, S., RENARD, N., LARAUFIE, R., and WEISS, P. E. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650. Journal of Fluid Mechanics, 743, 202–248 (2014)). The direct numerical simulation (DNS) data provided by Lee and Moser (LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics, 774, 395–415 (2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers. The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

A modification of the k-kL-ω turbulence model for simulation of short and long separation bubbles

The prediction of separation bubbles is highly important due to the controlling effects that they have on the airfoils performance. In the present study, a two-dimensional numerical simulation of the incompressible transitional flow around the NACA 0012 and Eppler 387 airfoils is studied. In order to examine the capability of the turbulence models for predicting the separation bubbles, several modified versions of the three-equation k-kL-ω turbulence model presented in previous research studies and the original four-equation SST k-ω turbulence model are compared with the experimental and Direct Numerical Simulation (DNS) data. A new modification based on the previous modified versions of the k-kL-ω model is also proposed. The Reynolds number based on the airfoil chord length is between 3 × 104 and 1.3 × 105. Simulation of the flow-field is performed by the solution of the Reynolds-averaged Navier–Stokes equations using a pressure-velocity coupling algorithm so-called RK-SIMPLER. An explicit method of second-order accuracy in time and space is used to integrate the momentum conservation equations. The results from this study indicate that the new proposed modification presents the better prediction for the separation bubbles than the previous versions, especially in the long separation bubbles. An excellent result is also obtained for the lift coefficients.

Autoignition and flame propagation in non-premixed MILD combustion

Direct Numerical Simulation (DNS) data of Moderate or Intense Low-oxygen Dilution (MILD) combustion are analysed to gather insights on autoignition and flame propagation in MILD combustion. Unlike in conventional combustion, the chemical reactions occur over a large portion of the computational domain. The presence of ignition and flame propagation and their coexistence are studied through spatial and statistical analyses of the convective, diffusive and chemical effects in the species transport equations. Autoignition is observed in regions with lean mixtures because of their low ignition delay times and these events propagate into richer mixtures either as a flame or ignition. This is found to be highly dependent on the mixture fraction length scale, ℓZ, and autoignition is favoured when ℓZ is small.

Reduced-order modeling of fully turbulent buoyancy-driven flows using the Green's function method

A One-Dimensional (1D) Reduced-Order Model (ROM) has been developed for a 3D Rayleigh-B\'enard convection system in the turbulent regime with Rayleigh number $\mathrm{Ra}=10^6$. The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's Function (GRF) method, which involves applying many localized, weak forcings to the system one at a time and calculating the responses using long-time averaged Direct Numerical Simulations (DNS), the system's Linear Response Function (LRF) has been computed. Another matrix, called the Eddy Flux Matrix (EFM), that relates changes in the divergence of vertical eddy heat fluxes to changes in the state vector, has also been calculated. Using various tests, it is shown that the LRF and EFM can accurately predict the time-mean responses of temperature and eddy heat flux to external forcings, and that the LRF can well predict the forcing needed to change the mean flow in a specified way (inverse problem). The non-normality of the LRF is discussed and its eigen/singular vectors are compared with the leading Proper Orthogonal Decomposition (POD) modes of the DNS data. Furthermore, it is shown that if the LRF and EFM are simply scaled by the square-root of Rayleigh number, they perform equally well for flows at other $\mathrm{Ra}$, at least in the investigated range of $ 5 \times 10^5 \le \mathrm{Ra} \le 1.25 \times 10^6$. The GRF method can be applied to develop 1D or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with better analyzing and controlling the nonlinear system.

Analysis of heat transfer of supercritical water by direct numerical simulation of heated upward pipe flows

Direct numerical simulation (DNS) was performed to investigate the turbulent heat transfer of supercritical water in an upward pipe with and without buoyancy. The heat transfer deterioration mechanisms were comprehensively studied by analyzing the effects of large thermophysical property variations, flow acceleration and buoyancy. It is shown that the large property variations near the wall severely impair the heat transfer in supercritical water especially for forced convection. The flow acceleration induced by thermal expansion shows an obvious suppression on turbulence but does not affect the heat transfer significantly due to the quick developing of thermal boundary layer. A small buoyancy first impairs the heat transfer and then improves the heat transfer due to the turbulence attenuation and recovery. With buoyancy increasing, the turbulence recovery gets earlier and stronger, and the wall temperature is significantly reduced due to the large buoyancy production of turbulent kinetic energy (TKE) in supercritical water flows. The instantaneous vortical structures based on Q criterion also clearly show the process of turbulence attenuation and recovery. In addition, the simulation using two eddy-viscosity turbulent models is compared to DNS data. The results show that the failed prediction of wall temperature and Nusselt number by those turbulent models is possibly due to the bad results of TKE, production of TKE and turbulent Prandtl number (Prt).

On the minimum ignition energy and its transition in the localised forced ignition of turbulent homogeneous mixtures

The minimum energy requirements for ensuring (i) just successful ignition and (ii) successful self-sustained flame propagation without the assistance of an external energy source following a successful ignition event have been analysed for the forced ignition of a homogeneous stoichiometric methane–air mixture under a wide range of turbulence intensities using three-dimensional Direct Numerical Simulation (DNS) data. It has been found that the minimum energy needed for successful ignition is also sufficient to ensure self-sustained flame propagation for small turbulence intensities. However, for large turbulence intensities, the minimum energy for ensuring self-sustained flame propagation can be considerably greater than the minimum energy needed just to successfully ignite the mixture. At low turbulence intensities, the thermal runaway has been obtained for the minimum ignition energy after the end of the energy deposition indicating an autoignition. For larger energy inputs and turbulence intensity, the thermal runaway was obtained during the energy deposition period. It has been found that the minimum energy requirements for ignition and self-sustained flame propagation increase with increasing turbulence intensity but a transition in this behaviour has been observed. There is a critical turbulence intensity such that the increase in the energy demand is significantly more rapid above the critical value than that for turbulence intensities smaller than the critical value. This has been found to be qualitatively consistent with previous experimental findings. The stochastic nature of the ignition event has been demonstrated by considering different realisations of statistically similar turbulent flow fields. The conditions giving rise to a successful ignition have been identified by a detailed analysis of the energy budget. A scaling analysis has been performed for the critical condition for ensuring self-sustained flame propagation and the insights gained from this analysis have been utilised to explain the physical mechanisms behind the transition of the minimum ignition energy.

Three-dimensional nonadiabatic electron- optical gyrotron systems with inhomogeneous current density

The results of a numerical study of the effect of threedimensional perturbations of the space charge density distribution in a nonadiabatic electron-optic systems of gyrotrons are presented. Data of direct numerical simulation using the 3-D program CST Studio Suite are described.

Machine learning methods for turbulence modeling in subsonic flows around airfoils

In recent years, the data-driven turbulence model has attracted widespread concern in fluid mechanics. The existing approaches modify or supplement the original turbulence model by machine learning based on the experimental/numerical data, in order to augment the capability of the present turbulence models. Different from the previous researches, this paper directly reconstructs a mapping function between the turbulent eddy viscosity and the mean flow variables by neural networks and completely replaces the original partial differential equation model. On the other hand, compared with the machine learning models for the low Reynolds (Re) number flows based on direct numerical simulation data, high Reynolds number flows around airfoils present the apparent scaling effects and strong anisotropy, which induce large challenges in accuracy and generalization capability for the machine learning algorithm. We mainly concentrate on the high Reynolds number turbulent flows around the airfoils and take the results calculated by the computational fluid dynamics solver with the Spallart-Allmaras (SA) model as training data to construct a high-dimensional data-driven network model based on machine learning. The radial basis function neural network and the auxiliary optimization methods are adopted, and the individual models are built separately for the flow fields of the near-wall region, wake region, and far-field region. The training data in this paper is extracted from only three subsonic flow fields of NACA0012 airfoil. The data-driven turbulence model can be applied to various airfoils and flow states, and the predicted eddy viscosity, lift/drag coefficients, and skin friction distributions are all in good agreement with the results of the original SA model. This research demonstrates the promising prospect of machine learning methods in future studies about turbulence modeling.

Effects of Rotation on Turbulence Production

Direct numerical simulations (DNS) of non-rotating and rotating turbulent channel flow were conducted. The data base obtained from these DNS simulations was used to investigate the prominent coherent structures involved in the turbulence generation cycle. Predictions from three theoretical models concerning the formation and evolution of sublayer streaks, three-dimensional hairpin vortices and propagating plane waves were validated using visualizations from the present DNS data. Quadrant analysis was used to determine a phase shift between the fluctuating streamwise and wall-normal velocities as a characteristic of turbulence production in the suction region at a low rotation number.