Direct Numerical Simulation Data Research Articles

Turbulent scalar fluxes in H2-air premixed flames at low and high Karlovitz numbers

The statistical behaviour and closure of sub-grid scalar fluxes in the context of turbulent premixed combustion have been assessed based on an a priori analysis of a detailed chemistry Direct Numerical Simulation (DNS) database consisting of three hydrogen-air flames spanning the corrugated flamelets (CF), thin reaction zones (TRZ) and broken reaction zones (BRZ) regimes of premixed turbulent combustion. The sub-grid scalar fluxes have been extracted by explicit filtering of DNS data. It has been found that the conventional gradient hypothesis model is not appropriate for the closure of sub-grid scalar flux for any scalar in the context of a multispecies system. However, the predictions of the conventional gradient hypothesis exhibit a greater level of qualitative agreement with DNS data for the flame representing the BRZ regime. The aforementioned behaviour has been analysed in terms of the properties of the invariants of the anisotropy tensor in the Lumley triangle. The flames in the CF and TRZ regimes are characterised by a pronounced two-dimensional anisotropy due to strong heat release whereas a three-dimensional and more isotropic behaviour is observed for the flame located in the BRZ regime. Two sub-grid scalar flux models which are capable of predicting counter-gradient transport have been considered for a priori DNS assessment of multispecies systems and have been analysed in terms of both qualitative and quantitative agreements. By combining the latter two sub-grid scalar flux closures, a new modelling strategy is suggested where one model is responsible for properly predicting the conditional mean accurately and the other model is responsible for the correlations between model and unclosed term. Detailed physical explanations for the observed behaviour and an assessment of existing modelling assumptions have been provided. Finally, the classical Bray–Moss–Libby theory for the scalar flux closure has been extended to address multispecies transport in the context of large eddy simulations.

Remote visual analysis of large turbulence databases at multiple scales

The remote analysis and visualization of raw large turbulence datasets is challenging. Current accurate direct numerical simulations (DNS) of turbulent flows generate datasets with billions of points per time-step and several thousand time-steps per simulation. Until recently, the analysis and visualization of such datasets was restricted to scientists with access to large supercomputers. The public Johns Hopkins Turbulence database simplifies access to multi-terabyte turbulence datasets and facilitates the computation of statistics and extraction of features through the use of commodity hardware. We present a framework designed around wavelet-based compression for high-speed visualization of large datasets and methods supporting multi-resolution analysis of turbulence. By integrating common technologies, this framework enables remote access to tools available on supercomputers and over 230 terabytes of DNS data over the Web. The database toolset is expanded by providing access to exploratory data analysis tools, such as wavelet decomposition capabilities and coherent feature extraction.

Large-scale clustering of coherent fine-scale eddies in a turbulent mixing layer

Clustering of coherent fine-scale eddies in a turbulent mixing layer has been analyzed by using direct numerical simulation (DNS) data at Reλ ≃ 250. The coherent fine-scale eddies are defined based on the second invariant of the velocity gradient tensor and the vorticity vector. The clustering is evaluated by the number density of coherent fine-scale eddies, and the large-scale structures are extracted by low-pass filtered velocity fields. Conditional averaging shows that the large-scale enstrophy increases with the number density, whereas the large-scale strain rate stays around the average in the high number density region. The alignments of the vorticity vector and the eigenvectors of the large-scale strain rate tensor are conditioned by the number density or the strain rate magnitude. The eigenvectors and the vorticity vector indicate strong preferential alignments under the intense large-scale strain rate condition. On the other hand, those alignments become weak in the high number density regions. The inter-scale energy transfer between grid and subgrid scales is significantly correlated with the magnitude of the large-scale strain rate while there is no apparent correlation with the number density.

Evaluating the modulated gradient model in large eddy simulation of channel flow with OpenFOAM

ABSTRACT Recently, a new family of subgrid-scale (SGS) models, termed as gradient-based models, has been introduced to calculate the SGS stresses in large eddy simulation (LES). In the present work, the modulated gradient model (MGM) was implemented in the OpenFOAM package, and the pimpleFoam solver was improved to be adopted with non-eddy viscosity models. The MGM is a new, nonlinear model that uses the local equilibrium hypothesis to assess the SGS kinetic energy and the velocity gradient tensor to calculate the relative weight of the different components of the SGS stress tensor. To evaluate the accuracy of the MGM along with the modified pimpleFoam solver, a turbulent channel flow was simulated at the three different frictional Reynolds numbers of 180, 395 and 590. Furthermore, the results were compared with direct numerical simulation data, as well as the numerical results obtained by the established SGS models such as the dynamic Smagorinsky model (DSM). A suitable accuracy for the first- and second-order turbulence parameters was reported. Moreover, it was demonstrated that MGM is computationally efficient compared to the DSM in treating channel flow.

Extended integral wall-model for large-eddy simulations of compressible wall-bounded turbulent flows

Wall-modeling is required to make large-eddy simulations of high-Reynolds number wall-bounded turbulent flows feasible in terms of computational cost. Here, an extension of the integral wall-model for large-eddy simulations (iWMLESs) for incompressible flows developed by Yang et al. [“Integral wall model for large eddy simulations of wall-bounded turbulent flows,” Phys. Fluids 27(2), 025112 (2015)] to compressible and isothermal flows is proposed and assessed. The iWMLES approach is analogous to the von Kármán-Pohlhausen integral method for laminar flows: the velocity profile is parameterized, and unknown coefficients are determined by matching boundary conditions obeying the integral boundary layer momentum equation. It allows non-equilibrium effects such as pressure gradient and convection to be included at a computing cost similar to analytical wall-models. To take into account density variations and temperature gradients, the temperature profile is also parameterized and the integral compressible boundary layer energy equation is considered. Parameterized profiles are based on the usual logarithmic wall functions with corrective terms to extend their range of validity. Instead of solving a set of differential equations as wall-models based on the thin boundary layer equation approach, a simple linear system is solved. The proposed wall-model is implemented in a finite-volume cell-centered structured grid solver and assessed on adiabatic and isothermal plane channel flows at several friction Reynolds and Mach numbers. For low Mach number cases, mean profiles, wall fluxes, and turbulent fluctuations are in agreement with those of Direct Numerical Simulation (DNS). For supersonic flows, the results are in good agreement with the DNS data, especially the mean velocity quantities and the wall friction, while standard analytical wall-models show their limits.

Analyzing the spectral energy cascade in turbulent channel flow

An analysis of the spectral turbulent kinetic energy budget in a fully developed turbulent plane channel flow is performed. Direct numerical simulation data are evaluated at friction Reynolds numbers Reτ of 180 and 1000. The analysis is focused on the influence of the Reynolds number on the spectral cascade of energy and the corresponding energy cascade in physical space in the presence of inhomogeneity and anisotropy. The turbulent kinetic energy distribution is compared for both Reynolds numbers, and the relevant characteristics of the energy transfer process in a wall-bounded turbulent flow are described. Differences in energy cascade are noted between the Reynolds number at both low and high wavenumbers. The results of the analysis are further assessed with a comparison to an earlier study of spectral energy transfer at Reτ = 180.

Evaluation of Interfacial Heat Transfer Models for Flashing Flow with Two-Fluid CFD

The complexity of flashing flows is increased vastly by the interphase heat transfer as well as its coupling with mass and momentum transfers. A reliable heat transfer coefficient is the key in the modelling of such kinds of flows with the two-fluid model. An extensive literature survey on computational modelling of flashing flows has been given in previous work. The present work is aimed at giving a brief review on available theories and correlations for the estimation of interphase heat transfer coefficient, and evaluating them quantitatively based on computational fluid dynamics simulations of bubble growth in superheated liquid. The comparison of predictions for bubble growth rate obtained by using different correlations with the experimental as well as direct numerical simulation data reveals that the performance of the correlations is dependent on the Jakob number and Reynolds number. No generally applicable correlations are available. Both conduction and convection are important in cases of bubble rising and translating in stagnant liquid at high Jakob numbers. The correlations combining the analytical solution for heat diffusion and the theoretical relation for potential flow give the best agreement.

Towards simulating natural transition in hypersonic boundary layers via random inflow disturbances

A random forcing approach was implemented into a high-order accurate finite-difference code in order to investigate ‘natural’ laminar–turbulent transition in hypersonic boundary layers. In hypersonic transition wind-tunnel experiments, transition is caused ‘naturally’, by free-stream disturbances even when so-called quiet tunnels are employed such as the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The nature and composition of the free-stream disturbance environment in high-speed transition experiments is difficult to assess and therefore largely unknown. Consequently, in the direct numerical simulations (DNS) presented here, the free-stream disturbance environment is simply modelled by random pressure (acoustic) disturbances with a broad spectrum of frequencies and a wide range of azimuthal wavenumbers. Results of a high-resolution DNS for a flared cone at Mach 6, using the random forcing approach, are presented and compared to a fundamental breakdown simulation using a ‘controlled’ disturbance input (with a specified frequency and azimuthal wavenumber). The DNS results with random forcing clearly exhibit the ‘primary’ and ‘secondary’ streak pattern, which has previously been observed in our ‘controlled’ breakdown simulations and the experiments in the BAM6QT. In particular, the spanwise spacing of the ‘primary’ streaks for the random forcing case is identical to the spacing obtained from the ‘controlled’ fundamental breakdown simulation. A comparison of the wall pressure disturbance signals between the random forcing DNS and experimental data shows remarkable agreement. The random forcing approach seems to be a promising strategy to investigate nonlinear breakdown in hypersonic boundary layers without introducing any bias towards a distinct nonlinear breakdown mechanism and/or the selection of specific frequencies or wavenumbers that is required in the ‘controlled’ breakdown simulations.

Numerical study of an airfoil with riblets installed based on large eddy simulation

The implicit large eddy simulation method is applied in a riblet drag reduction study of a low-speed airfoil. The numerical method is tested by a channel flow with streamwise riblets installed on one side. The mean velocity profile, root mean square of velocity and Reynolds shear stress match well with reference direct numerical simulation data. Next, numerical investigation is conducted on an airfoil called Eppler E374 at free stream Mach number 0.2, angle of attack 3° and Reynolds number 2.0 × 105. The simulated flow around the airfoil without or with a numerical trip is in good agreement with the experimental data. When isosceles triangle riblets are installed on the airfoil along the streamwise direction, the lift coefficient is increased, and the friction drag is decreased. The pressure distribution on the airfoil is slightly changed, corresponding to the increased pressure drag. The Reynolds stresses are greatly reduced by the riblets at locations of strong pressure gradient. The result of the power spectrum density of pressure shows that the high-frequency fluctuations are suppressed when the riblet film is installed on the airfoil, and the vortex structures in the boundary layer are also reduced.

Re-understanding the law-of-the-wall for wall-bounded turbulence based on in-depth investigation of DNS data

Based on direct numerical simulation (DNS) data of the straight ducts, namely square and rectangular annular ducts, detailed analyses were conducted for the mean streamwise velocity, relevant velocity scales, and turbulence statistics. It is concluded that turbulent boundary layers (TBL) should be broadly classified into three types (Type-A, -B, and -C) in terms of their distribution patterns of the time-averaged local wall-shear stress ( $$\tau _\mathrm{w} )$$ or the mean local frictional velocity ( $$u_\tau )$$ . With reference to the Type-A TBL analysis by von Karman in developing the law-of-the-wall using the time-averaged local frictional velocity ( $$u_\tau )$$ as scale, the current study extended the approach to the Type-B TBL and obtained the analytical expressions for streamwise velocity in the inner-layer using ensemble-averaged frictional velocity ( $$\bar{{u}}_\tau )$$ as scale. These analytical formulae were formed by introducing the general damping and enhancing functions. Further, the research applied a near-wall DNS-guided integration to the governing equations of Type-B TBL and quantitatively proved the correctness and accuracy of the inner-layer analytical expressions for this type.

An inverse problem to assess the two-component unsteady wall shear rate

The instantaneous two-dimensional wall shear rate is assessed through an inverse problem using mass transfer data from a three-segment electrodiffusion probe. The method is validated numerically in complex flow conditions involving (i) high amplitude periodic fluctuations on both wall shear rate magnitude and direction and (ii) direct numerical simulation (DNS) data from a turbulent three-dimensional channel flow. The approach is shown to outperform every other post-treatments available for mass transfer sensors, especially regarding its versatility and application range. The impact of the three-segment probe gap size is also examined numerically.

Analysis of red blood cell partitioning at bifurcations in simulated microvascular networks

Partitioning of red blood cells (RBCs) at vascular bifurcations has been studied over many decades using in vivo, in vitro, and theoretical models. These studies have shown that RBCs usually do not distribute to the daughter vessels with the same proportion as the blood flow. Such disproportionality occurs, whereby the cell distribution fractions are either higher or lower than the flow fractions and have been referred to as classical partitioning and reverse partitioning, respectively. The current work presents a study of RBC partitioning based on, for the first time, a direct numerical simulation (DNS) of a flowing cell suspension through modeled vascular networks that are comprised of multiple bifurcations and have topological similarity to microvasculature in vivo. The flow of deformable RBCs at physiological hematocrits is considered through the networks, and the 3D dynamics of each individual cell are accurately resolved. The focus is on the detailed analysis of the partitioning, based on the DNS data, as it develops naturally in successive bifurcations, and the underlying mechanisms. We find that while the time-averaged partitioning at a bifurcation manifests in one of two ways, namely, the classical or reverse partitioning, the time-dependent behavior can cycle between these two types. We identify and analyze four different cellular-scale mechanisms underlying the time-dependent partitioning. These mechanisms arise, in general, either due to an asymmetry in the RBC distribution in the feeding vessels caused by the events at an upstream bifurcation or due to a temporary increase in cell concentration near capillary bifurcations. Using the DNS results, we show that a positive skewness in the hematocrit profile in the feeding vessel is associated with the classical partitioning, while a negative skewness is associated with the reverse one. We then present a detailed analysis of the two components of disproportionate partitioning as identified in prior studies, namely, plasma skimming and cell screening. The plasma skimming component is shown to under-predict the disproportionality, leaving the cell screening component to make up for the difference. The crossing of the separation surface by the cells is observed to be a dominant mechanism underlying the cell screening, which is shown to mitigate extreme heterogeneity in RBC distribution across the networks.

Direct numerical simulation of turbulent heat transfer in a T-junction

In this paper we report on a direct numerical simulation (DNS) of turbulent heat transfer in a T-junction. In particular, we study the interaction between two liquid streams, a hot horizontal cross-flow and a cold vertical liquid jet coming from above, in a T-junction of rectangular cross-section. We discuss in detail the instantaneous flow structures and present results for the first- and second-order statistics of the flow quantities, and for the budget of the turbulent kinetic energy. Further, we present results of the power spectral density of the velocity and temperature signals at selected locations of the flow field. Our analysis elucidates the properties of the important features of the flow such as the large recirculation bubble and the secondary separation zones that are formed in the vicinity of the entry of the jet. According to our simulations, thermal mixing is mainly driven by the shear layer between the two streams and, to a lesser extent, by the shear layer between the incoming jet and the large recirculation bubble. Thermal mixing is further enhanced by turbulence generation in the regions of adverse pressure gradients downstream of the large recirculation bubble. Within the framework of our study, we have also conducted a wall-resolved large-eddy simulation (LES) of the flow of interest so as to assess its predictive capacity. Overall, the LES predictions agree satisfactorily with our DNS data; the most noticeable discrepancy is that the LES produces mildly diffused profiles for the second-order statistics in the regions of intense turbulence production.

A modified Parametric Forcing Approach for modelling of roughness

Surface roughness in turbulent channel flow is effectively modelled using a modified version of the Parametric Forcing Approach introduced by Busse and Sandham (2012). In this modified approach, the model functions are determined based on the surface geometry and two model constants, whose value can be fine tuned. In addition to a quadratic forcing term, accounting for the effect of form drag due to roughness, a linear forcing term, analogous to the Darcy term in the context of porous media, is employed in order to represent the viscous drag. Comparison of the results with full-geometry resolved Direct Numerical Simulation (DNS) data for the case of dense roughness (frontal solidity ≅0.4) shows a satisfactory prediction of mean velocity profile, and hence the friction factor, by the model. The model is found to be able to reproduce the trends of friction factor with morphological properties of surface such as skewness of the surface height probability density function and coefficient of variation of the peak heights.

Flow and heat transfer in cross-stream type T-junctions: A computational study

The present computational study is concerned with the thermal mixing of flow-crossing streams in a T-shaped junction, focussing primarily on a configuration subjected to temperature-dependent fluid property conditions. The reference experimental investigation is conducted by Hirota et al. (2010). Preliminary, a quasi two-dimensional configuration with constant fluid properties, for which the reference DNS (Direct Numerical Simulation) database is made available by Hattori et al. (2014), is simulated. The presently applied computational model is based on a VLES (Very Large Eddy Simulation) formulation of Chang et al. (2014). The residual turbulence is modeled employing the appropriately modified RANS-based (Reynolds-Averaged Navier–Stokes) elliptic-relaxation eddy-viscosity model of Hanjalić et al. (2004). In addition to the VLES, both flow configurations are computed applying the background RANS model representing the constituent of the present VLES method. Whereas the eddy viscosity model describes fully-modeled turbulence in the RANS framework, it relates to the unresolved sub-scale turbulence within the VLES methodology. Unlike the RANS method, the VLES method is capable of capturing the spectral dynamics of turbulence to an extent complying with the underlying grid resolution. The latter model feature contributes decisively to an appropriately intensified turbulence activity in the separated shear layer regions and, consequently, to an enhanced mixing process. The results obtained with the present VLES model follow closely the reference DNS data in the Hattori et al. (2014) case with respect to velocity and temperature fields as well as the fields of associated turbulent quantities in all characteristic regions of the flow domain: main and branch streams’ merging zone, flow-reversal and post-reattachment regions. In the more complex Hirota et al. (2010) configuration, the flow field is captured reasonably well, while the computationally obtained thermal fields suggest a somewhat more intensive mixing relative to the reference experiment.

A-priori analysis of an alternative wrinkling factor definition for flame surface density based Large Eddy Simulation modelling of turbulent premixed combustion

ABSTRACTThis paper discusses an alternative definition of the wrinkling factor and the resolved component of flame surface density (FSD) in the context of Large Eddy Simulations (LES) modelling of turbulent premixed combustion. The performances of conventional and an alternative definition of wrinkling factor are compared by employing a-priori analysis using explicitly filtered direct numerical simulation (DNS) data of statistically planar turbulent premixed, flames. It is demonstrated that the alternative definition of wrinkling factor can be used as well as the conventional definition to model the sub-grid scale flame wrinkling. The conventional definition of the wrinkling factor and resolved FSD might be more satisfactory from a theoretical point of view but the alternative definition has the advantage that the resolved FSD is no longer an unclosed expression and artificial flame thickening can be avoided without referring to an implicit counter-gradient transport closure.

Analysis of uncertainties and convergence of the statistical quantities in turbulent wall-bounded flows by means of a physically based criterion

The present paper provides an analysis of the statistical uncertainties associated with direct numerical simulation (DNS) results and experimental data for turbulent channel and pipe flows, showing a new physically based quantification of these errors, to improve the determination of the statistical deviations between DNSs and experiments. The analysis is carried out using a recently proposed criterion by Thompson et al. [“A methodology to evaluate statistical errors in DNS data of plane channel flows,” Comput. Fluids 130, 1–7 (2016)] for fully turbulent plane channel flows, where the mean velocity error is estimated by considering the Reynolds stress tensor, and using the balance of the mean force equation. It also presents how the residual error evolves in time for a DNS of a plane channel flow, and the influence of the Reynolds number on its convergence rate. The root mean square of the residual error is shown in order to capture a single quantitative value of the error associated with the dimensionless averaging time. The evolution in time of the error norm is compared with the final error provided by DNS data of similar Reynolds numbers available in the literature. A direct consequence of this approach is that it was possible to compare different numerical results and experimental data, providing an improved understanding of the convergence of the statistical quantities in turbulent wall-bounded flows.

Effects of Lewis number on the statistics of the invariants of the velocity gradient tensor and local flow topologies in turbulent premixed flames.

The behaviours of the three invariants of the velocity gradient tensor and the resultant local flow topologies in turbulent premixed flames have been analysed using three-dimensional direct numerical simulation data for different values of the characteristic Lewis number ranging from 0.34 to 1.2. The results have been analysed to reveal the statistical behaviours of the invariants and the flow topologies conditional upon the reaction progress variable. The behaviours of the invariants have been explained in terms of the relative strengths of the thermal and mass diffusions, embodied by the influence of the Lewis number on turbulent premixed combustion. Similarly, the behaviours of the flow topologies have been explained in terms not only of the Lewis number but also of the likelihood of the occurrence of individual flow topologies in the different flame regions. Furthermore, the sensitivity of the joint probability density function of the second and third invariants and the joint probability density functions of the mean and Gaussian curvatures to the variation in Lewis number have similarly been examined. Finally, the dependences of the scalar--turbulence interaction term on augmented heat release and of the vortex-stretching term on flame-induced turbulence have been explained in terms of the Lewis number, flow topology and reaction progress variable.

Assessment of SGS closure for isochoric combustion of hydrogen-air mixture

Direct numerical simulation (DNS) data of freely propagating turbulent premixed flame of stoichiometric hydrogen air mixture inside a closed vessel is analysed to study a sub-grid combustion closure based on unstrained flamelet approach. This modeling framework needs closures for the sub-grid scale (SGS) reaction rate and scalar dissipation rate. The results show that the closure models for these two SGS quantities work quite well. The dissipation rate closure involves a scale dependent parameter, βc, which is related to the flame curvature induced effects. The reactivity of reactant mixture increases with time in isochoric combustion because the mixture temperature and pressure increase with time. This also influences the parameter βc and thus the dynamic evaluation of this parameter is investigated using the DNS data.

Determination of wall shear stress from mean velocity and Reynolds shear stress profiles

A method for determining the wall shear stress under arbitrary streamwise pressure gradients and wall roughness conditions using Reynolds shear stress and mean velocity profile data is presented. Data from very near the wall are not required. The method is tested with experimental and direct numerical simulation data.