Current Direct Numerical Simulation Research Articles

Onset of shear-layer instability at the interface of parallel Couette flows

A non-planar or a bilateral mixing-layer is studied by means of a series of direct numerical simulations (DNSs). This mixing-layer forms at the interface of two co-current plane Couette flows of different Reynolds numbers. The current DNS study determined the conditions for the onset of shear-layer instability at the interface. The influence of different Reynolds number (of the co-current plane Couette flows) and their Reynolds number ratio on the mixing-layer is studied. A critical Reynolds number of about 500 (or more particularly one of the co-current plane Couette flows must be turbulent) and a Reynolds number ratio greater than 2 is required for the genesis of this bilateral shear-layer instability. Independent of the Reynolds number and the Reynolds number ratio, the temporal evolution of the shear-layer instability followed the same pattern. In addition, the oscillation frequency of the instability was found to increase with increasing Reynolds number and increasing Reynolds number ratio. Further, influence of instability on the local skin friction and the two-point correlation is elaborated on.

Spatiotemporal evolutions of forces and vortices of flow past ellipsoidal bubbles: Direct numerical simulation based on a Cartesian grid scheme

An in-depth investigation of two fixed non-spherical bubbles is an indispensable step toward revealing fundamental mechanisms in complex bubbly flows, where direct numerical simulation (DNS) is one of the most promising approaches to conduct such a task. However, accurately modeling force distribution and efficiently generating satisfactory mesh around a non-spherical bubble pair are challenging to current DNS methods. In this study, an effective non-body-fitted gas–liquid interface tracking scheme based on the Cartesian grid was developed to conduct three-dimensional DNS of two fixed ellipsoidal bubbles with frozen shape in an incompressible Newtonian fluid. The grid-independent analysis and analytical validation prove that our developed non-body-fitted gas–liquid interface tracking scheme is able to accurately retrieve all force components exerted on a bubble with less mesh generation and computational efforts than body-fitted counterparts. Using this non-body-fitted gas–liquid interface tracking scheme, spatiotemporal evolutions of forces and vortices around the two fixed ellipsoidal bubbles were directly simulated under various values of Reynolds numbers, separation distances, and the bubble’s ellipsoidicity. The analysis of drag force shows that the overall drag behaviors of ellipsoidal bubbles are quite similar to those of spherical bubbles though larger ellipsoidicity produces a higher drag coefficient. However, the sign of lift forces, i.e., either the two bubbles attract or repel each other, is highly dependent on ellipsoidicity. For the bubble pair with moderate ellipsoidicity, attractive force dominates at moderate-to-high Reynold numbers, while the two bubbles tend to repel at low Reynolds numbers. For the bubble pair with high ellipsoidicity, the two bubbles repel each other at all values of Reynolds numbers and separation distances. Characteristics of vortex developments, which are the reason behind these ellipsoidicity-dependent force behaviors, are presented and discussed. This study highlights the importance of the bubble’s shape in the interactions and associated vortex between two adjacent fixed ellipsoidal bubbles.

Reynolds number effects in rib-roughened turbulent channel flow

A study involving the direct numerical simulation (DNS) of turbulent rough channel flow at Reynolds number $$\hbox {Re}_{\tau }=180$$ is undertaken, to investigate the effects of Reynolds number variation on the various statistical quantities and the near-wall dynamical structures. The definition of Reynolds number predominantly considered in this study, $$\hbox {Re}_{\tau }$$, is based on the wall friction velocity $$u_{\tau }$$ and the half-height of the channel h. The channel walls are roughened by square ribs elongated along the span of the channel. The ribs are arranged at a constant pitch width and in a manner such that the crests face the ones on the opposite wall, i.e., the roughness on the channel is symmetric about the channel centerline. The results obtained from the current DNS are compared with those from two DNSs at a higher Reynolds number of 400, one of them with roughness height $$k^+$$ comparable to that in the current DNS and the other with a higher value of $$k^+$$. The mean streamline patterns are contrasting in the presence or absence of the secondary vortex; the effects on the location of a seemingly persistent saddle point are also observed. Variation of the skin friction coefficient over a pitch width has apparently lent support to the observations. A measure of the roughness function is presented. The near-wall structures in terms of the contours of the fluctuating velocity reveal finer scale structures at the higher Reynolds number, when the value of $$k^+$$ is also high.

On new scaling laws in a temporally evolving turbulent plane jet using Lie symmetry analysis and direct numerical simulation

A temporally evolving turbulent plane jet is studied both by direct numerical simulation (DNS) and Lie symmetry analysis. The DNS is based on a high-order scheme to solve the Navier–Stokes equations for an incompressible fluid. Computations were conducted at Reynolds number $\mathit{Re}_{0}=8000$, where $\mathit{Re}_{0}$ is defined based on the initial jet thickness, $\unicode[STIX]{x1D6FF}_{0.5}(0)$, and the initial centreline velocity, $\overline{U}_{1}(0)$. A symmetry approach, known as the Lie group, is used to find symmetry transformations, and, in turn, group invariant solutions, which are also denoted as scaling laws in turbulence. This approach, which has been extensively developed to create analytical solutions of differential equations, is presently applied to the mean momentum and two-point correlation equations in a temporally evolving turbulent plane jet. The symmetry analysis of these equations allows us to derive new invariant (self-similar) solutions for the mean flow and higher moments of the velocities in the jet flow. The current DNS validates the consequence of Lie symmetry analysis and therefore confirms the establishment of novel scaling laws in turbulence. It is shown that the classical scaling law for the mean velocity is a specific form of the current scaling (which has a more general form); however, the scaling for the second and higher moments (such as Reynolds stresses) has a completely different structure compared to the classical scaling. While the failure of the classical scaling for the second moments of the fluctuating velocities has been noted from the jet data for many years, the DNS results nicely match with the present self-similar relations derived from Lie symmetry analysis. Key ingredients for the present results, in particular for the scaling laws of the higher moments, are symmetries, which are of a purely statistical nature. i.e. these symmetries are admitted by the moment equations, however, they are not observed by the original Navier–Stokes equations.

Direct numerical simulation of a wall jet: flow physics

A direct numerical simulation (DNS) of a plane wall jet is performed at a Reynolds number of$Re_{j}=7500$. The streamwise length of the domain is long enough to achieve self-similarity for the mean flow and the Reynolds shear stress. This is the highest Reynolds number wall jet DNS for a large domain achieved to date. The high resolution simulation reveals the unsteady flow field in great detail and shows the transition process in the outer shear layer and inner boundary layer. Mean flow parameters of maximum velocity decay, wall shear stress, friction coefficient and jet spreading rate are consistent with several other studies reported in the literature. Mean flow, Reynolds normal and shear stress profiles are presented with various scalings, revealing the self-similar behaviour of the wall jet. The Reynolds normal stresses do not show complete similarity for the given Reynolds number and domain length. Previously published inner layer budgets based on LES are inaccurate and those that have been measured are only available in the outer layer. The current DNS provides fully balanced, explicitly calculated budgets for the turbulence kinetic energy, Reynolds normal stresses and Reynolds shear stress in both the inner and outer layers. The budgets are scaled with inner and outer variables. The inner-scaled budgets in the near wall region show great similarity with turbulent boundary layers. The only remarkable difference is for the turbulent diffusion in the wall-normal Reynolds stress and Reynolds shear stress budgets. The outer layer interacts with the inner layer through turbulent diffusion and the excess energy from the wall-normal direction is transferred to the spanwise direction.

Assessment of Algebraic Flame Surface Density Closures in the Context of Large Eddy Simulations of Head-On Quenching of Turbulent Premixed Flames

ABSTRACTThe applicability of algebraic large eddy simulation (LES) closures of flame surface density (FSD) for head-on quenching of premixed turbulent flames by an isothermal inert wall has been assessed using 3D direct numerical simulations (DNS) data for different values of root-mean-square turbulent velocity fluctuation, Damköhler and Karlovitz numbers. An algebraic FSD closure, which has been reported to perform relatively satisfactorily among several available models, has been considered for this analysis alongside a model, which has recently been used for LES of flame-wall interaction. The applicability of previously proposed near-wall damping factors for flame surface wrinkling and consumption rate in the context of Reynolds Averaged Navier Stokes (RANS) simulations has also been assessed for LES based on the current a-priori DNS analysis. It has been found that existing models considered for this analysis do not predict the near-wall behavior of the FSD accurately for all cases considered here. Furthermore, the widely used expression (where and are the unburned gas density and the laminar burning velocity, respectively) has been found to overpredict the combined reaction rate and molecular diffusion term in the near-wall region but the agreement between these terms gets better away from the wall. However, does not sufficiently capture the local behavior of the density-weighted surface filtered displacement speed so the correlation coefficient between and the combined reaction rate and molecular diffusion term remains much smaller than unity. It has been found that the damping factors proposed for RANS are not suitable for LES, and they severely damp the near-wall magnitudes of FSD and the combined reaction rate and molecular diffusion term and lead to significant under-predictions. Based on this a-priori analyses new near-wall modifications to the generalized FSD and the combined reaction and molecular diffusion term have been proposed in the context of LES, which have been found to capture both qualitative and quantitative trends obtained from DNS data.

Cloud Droplet Collisions in Turbulent Environment: Collision Statistics and Parameterization

Abstract The purpose of this paper is to quantify the influence of turbulence in collision statistics by separately studying the impacts of computational domain sizes, eddy dissipation rates (EDRs), and droplet sizes and eventually to develop an accurate parameterization of collision kernels. Direct numerical simulations (DNS) were performed with a relatively wide range of EDRs and Taylor microscale Reynolds numbers . EDR measures the turbulence intensity levels. DNS model studies have simulated homogeneous turbulence in a small domain in the cloud’s adiabatic core. Clouds clearly have much larger scales than current DNS can simulate. For this reason, it is emphasized that obtained from current DNS is fundamentally only a measure of the computational domain size for a given EDR and cannot completely describe the physical properties of cloud turbulence. Results show that the collision statistics are independent of the domain sizes and hence of the computational for droplet sizes no bigger than 25 μm as long as the droplet separation distance, which is on the order of the Kolmogorov scale in real clouds, is resolved. Instead, they are found to be highly correlated with EDRs and droplet sizes, and this correlation is used to formulate an improved parameterization scheme. The new scheme well represents the turbulent geometric collision kernel with a relative uncertainty of 14%. A comparison between different parameterizations is made, and the formulas proposed here are shown to improve the fit to the collision statistics.

Direct numerical simulation of a fully developed turbulent square duct flow up to [formula omitted

Various fundamental studies based on a turbulent duct flow have gained popularity including heat transfer, magnetohydrodynamics as well as particle-laden transportation. An accurate prediction on the turbulent flow field is critical for these researches. However, the database of the mean flow and turbulence statistics is fairly insufficient due to the enormous cost of numerical simulation at high Reynolds number. This paper aims at providing available information by conducting several Direct Numerical Simulations (DNS) on turbulent duct flows at Reτ=300,600,900and1200. A quantitative comparison between current and previous DNS results was performed where a good agreement was achieved at Reτ=300. However, further comparisons of the present results with the previous DNS results at Reτ=600 obtained with much coarser meshes revealed some discrepancies which can be explained by the insufficient mesh resolution. At last, the mean flow and turbulent statistics at higher Reτ was presented and the effect of Reτ on the mean flow and flow dynamics was discussed.

Statistical Flow Properties in the Turbulent Wake of a Tapered Flat Plate Placed Normal to the Free-stream

Reynolds-averaged statistical flow properties in the turbulent near-wake of a tapered flat plate placed normal to the free-stream were analysed by means of direct numerical simulation (DNS). A taper ratio of 20 was considered in the present study while the Reynolds numbers based on the uniform inflow velocity and the width of the plate at the wide and narrow ends were 1000 and 250, respectively. The tapering gave rise to cellular vortex shedding with randomly occurring vortex dislocations which prohibited a distinction between coherent and incoherent fluctuations. In the current DNS, it was observed that the magnitude of the Reynolds stresses and the production and dissipation rates of fluctuating kinetic energy are much lower than in the wake of a uniform normal flat plate. This reduced magnitude is perhaps due to the fact that the present tapered plate produces a highly incoherent wake, which may result in the reduction of the coherent velocity fluctuations and their overall contribution to the Reynolds-averaged data. In addition to the primary shear-stress term, a secondary shear-stress component was found to co-exist in the present case. The appearance of this secondary shear-stress term, together with the inherent spanwise inhomogeneity and the existence of a distinct secondary flow, was found to drive the fluctuations towards isotropy. In addition, the present DNS surprisingly revealed the appearance of Kelvin-Helmholtz instabilities towards the higher local Reynolds numbers, i.e. beyond 920.

Numerical Investigations of Passive Scalar Transport in Turbulent Taylor-Couette Flows: Large Eddy Simulation Versus Direct Numerical Simulations

The highly turbulent flow occurring inside (electro)chemical reactors requires accurate simulation of scalar mixing if computational fluid dynamics (CFD) methods are to be used with confidence in design. This has motivated the present paper, which describes the implementation of a passive scalar transport equation into a hybrid spectral/finite-element code. Direct numerical simulations (DNS) and large eddy simulation (LES) were performed to study the effects of gravitational and centrifugal potentials on the stability of incom-pressible Taylor-Couette flow. The flow is confined between two concentric cylinders with an inner rotating cylinder while the outer one is at rest. The Navier-Stokes equations with the uncoupled convection–diffusion–reaction (CDR) equation are solved using a code named spectral/finite element large eddy simulations (SFELES) which is based on spectral development in one direction combined with a finite element discretization in the remaining directions. The performance of the LES code is validated with published DNS data for channel flow. Velocity and scalar statistics showed good agreement between the current LES predictions and DNS data. Special attention was given to the flow field, in the vicinity of Reynolds number of 68.2 with radii ratio of 0.5. The effect of Sc on the concentration peak is pointed out while the magnitude of heat transfer shows a dependence of the Prandtl number with an exponent of 0.375.

Turbulent transport of passive scalar behind line sources in an unstably stratified open channel flow

This study employs a direct numerical simulation (DNS) technique to study the flow, turbulence structure, and passive scalar plume transport behind line sources in an unstably stratified open channel flow. The scalar transport behaviors for five emission heights ( z s = 0, 0.25 H, 0.5 H, 0.75 H, and H, where H is the channel height) at a Reynolds number of 3000, a Prandtl number and a Schmidt number of 0.72, and a Richardson number of −0.2 are investigated. The vertically meandering mean plume heights and dispersion coefficients calculated by the current DNS model agree well with laboratory results and field measurements in literature. It is found that the plume meandering is due to the movement of the positive and negative vertical turbulent scalar fluxes above and below the mean plume heights, respectively. These findings help explaining the plume meandering mechanism in the unstably stratified atmospheric boundary layer.

Stokes Mechanism of Drag Reduction

The mechanism of drag reduction due to spanwise wall oscillation in a turbulent boundary layer is considered. Published measurements and simulation data are analyzed in light of Stokes’ second problem. A kinematic vorticity reorientation hypothesis of drag reduction is first developed. It is shown that spanwise oscillation seeds the near-wall region with oblique and skewed Stokes vorticity waves. They are attached to the wall and gradually align to the freestream direction away from it. The resulting Stokes layer has an attenuated nature compared to its laminar counterpart. The attenuation factor increases in the buffer and viscous sublayer as the wall is approached. The mean velocity profile at the condition of maximum drag reduction is similar to that due to polymer. The final mean state of maximum drag reduction due to turbulence suppression appears to be universal in nature. Finally, it is shown that the proposed kinematic drag reduction hypothesis describes the measurements significantly better than what current direct numerical simulation does.

Turbulent Plane Couette Flow and Scalar Transport at Low Reynolds Number

Abstract The turbulence structure and passive scalar (heat) transport in plane Couette flow at Reynolds number equal to 3000 (based on the relative speed and distance between the walls) are studied using direct numerical simulation (DNS). The numerical model is a three-dimensional trilinear Galerkin finite element code. It is found that the structures of the mean velocity and temperature in plane Couette flow are similar to those in forced channel flow, but the empirical coefficients are different. The total (turbulent and viscous) shear stress and total (turbulent and conductive) heat flux are constant throughout the channel. The locations of maximum root-mean-square streamwise velocity and temperature fluctuations are close to the walls, while the location of maximum root-mean-square spanwise and vertical velocity fluctuations are at the channel center. The correlation coefficients between velocities and temperature are fairly constant in the center core of the channel. In particular, the streamwise velocity is highly correlated with temperature (correlation coefficient ≈−0.9). At the channel center, the turbulence production is unable to counterbalance the dissipation, in which the diffusion terms (both turbulent and viscous) bring turbulent kinetic energy from the near-wall regions toward the channel center. The snapshots of the DNS database help explain the nature of the correlation coefficients. The elongated wall streaks for both streamwise velocity and temperature in the viscous sublayer are well simulated. Moreover, the current DNS shows organized large-scale eddies (secondary rotations) perpendicular to the direction of mean flow at the channel center.

A Preliminary Study of the Burgers Equation with Symbolic Computation

A novel approach based on recursive symbolic computation is introduced for the approximate analytic solution of the Burgers equation. Once obtained, appropriate numerical values can be inserted into the symbolic solution to explore parametric variations. The solution is valid for both inviscid and viscous cases, covering the range of Reynolds number from 500 to infinity, whereas current direct numerical simulation (DNS) methods are limited to Reynolds numbers no greater than 4000. What further distinguishes the symbolic approach from numerical and traditional analytic techniques is the ability to reveal and examine direct nonlinear interactions between waves, including the interplay between inertia and viscosity. Thus, preliminary efforts suggest that symbolic computation may be quite effective in unveiling the “anatomy” of the myriad interactions that underlie turbulent behavior. However, due to the tendency of nonlinear symbolic operations to produce combinatorial explosion, future efforts will require the development of improved filtering processes to select and eliminate computations leading to negligible high order terms. Indeed, the initial symbolic computations present the character of turbulence as a problem in combinatorics. At present, results are limited in time evolution, but reveal the beginnings of the well-known “saw tooth” waveform that occurs in the inviscid case (i.e., Re=∞). Future efforts will explore more fully developed 1-D flows and investigate the potential to extend symbolic computations to 2-D and 3-D. Potential applications include the development of improved subgrid scale (SGS) parameterizations for large eddy simulation (LES) models, and studies that complement DNS in exploring fundamental aspects of turbulent flow behavior.