Direct numerical simulation of turbulent wake behind a surface-mounted square cylinder

In this research, direct numerical simulation has been performed to study the turbulent wake behind a wall-mounted square cylinder with aspect ratio 4 and Reynolds number 12 000 (based on the free-stream velocity and obstacle side length) in a developing boundary layer. Owing to the relatively high Reynolds number and high aspect ratio of the cylinder tested, the wake is wide spread behind the cylinder and exhibits complex and energetic vortex motions. The lateral and tip vortex shedding patterns at different frequencies, coherent structures downstream of the obstacle, the production rate and distribution of turbulent kinetic energy, and the instantaneous pressure distribution in the wake region have been thoroughly investigated. In order to validate the numerical results, the first- and second-order flow statistics obtained from the simulations have been carefully compared against available wind-tunnel measurement data.     

Hairpin vortices in the largest scale of turbulent boundary layers

We have conducted direct numerical simulations of a turbulent boundary layer for the momentum-thickness-based Reynolds number ${\mathit{Re}}_{\theta }$ = 180–4600. To extract the largest-scale vortices, we coarse-grain the fluctuating velocity fields by using a Gaussian filter with the filter width comparable to the boundary layer thickness. Most of the largest-scale vortices identified by isosurfaces of the second invariant of the coarse-grained velocity gradient tensor are similar to coherent vortices observed in low-Reynolds-number regions, that is, hairpin vortices or quasi-streamwise vortices inclined to the wall. We also develop a percolation analysis to investigate the threshold-dependence of the isosurfaces and objectively identify the largest-scale hairpin vortices in terms of the coarse-grained vorticity, which leads to the quantitative evidence that they never disappear even in fully developed turbulent regions. Hence, we conclude that hairpin vortices exist in the largest-scale structures irrespective of the Reynolds number.     

Direct numerical simulation of a turbulent plane Couette-Poiseuille flow with zero-mean shear

Direct numerical simulations of a turbulent Couette-Poiseuille flow with zero-mean-shear at the moving wall (SL-flow) is performed to examine flow features compared to those for a turbulent pure Poiseuille flow (P-flow). Profiles of the streamwise mean velocity, indicator function and ratio of production to dissipation show that the logarithmic region is significantly elongated for the SL-flow compared to that for the P-flow at a similar Reynolds number. In addition, the magnitudes of the Reynolds stresses are found to be larger in both inner and outer layers for the SL-flow than those for the P-flow. The spanwise spectra of the production term in the turbulent kinetic energy equation are examined to provide a structural basis for explaining the statistical behaviors. In addition, because the growth of the energy-containing motions extends to the outer layer further for the SL-flow due to the presence of a positive mean shear throughout the entire wall layer, the self-similar behavior of the energy balance between the production and transport terms with respect to the self-similar wavenumber is found far from the wall. We also find the increase in the number of uniform momentum zones in the SL-flow, revealing the hierarchical distribution of the energy-containing eddies which are composed of multiple uniform momentum zones. These coherent motions lead to the elongation of the logarithmic region for the SL-flow. Finally, investigation of the turbulent energy transfer process in a spectral domain for the SL-flow demonstrates importance of outer layer very-long structures, and these structures attribute to the energy transport process in an entire flow field.     

Vortex collapse and turbulence

Recent calculations related to the self-induced collapse of large-scale vortex structures into fine scale, possibly singular, structures in the Euler and Navier–Stokes equations are described. The practical importance of these intense events is their possible role in turbulence through the effects of strong intermittency and how that will direct turbulence modelling. Despite a concerted international effort to simulate these events over a decade ago, their dynamical origin remains largely unknown. A new international collaboration designed to push our understanding of the Euler singularity problem is described. These events are closely related to one of the outstanding mathematical questions of our time: whether solutions of the three-dimensional incompressible Navier–Stokes equations, lying in a bounded domain with finite energy and no external forcing, remain regular for arbitrarily long times (www.claymath.org/Millennium_Prize_Problems).     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Identifying the radiating core of Lighthill’s source term

A decomposition of the Lighthill source term is effected which yields ten sub-terms comprising velocity, vorticity, dilatation and density fields. An analysis methodology is then developed, aimed at understanding the respective roles played by these sub-terms in the production of sound. By Direct Numerical Simulation of a temporal mixing-layer—chosen both for its simplicity and its amenability to analysis in wavenumber space—the radiating components of the different sub-terms are isolated and studied. Interesting identities are observed between specific events in the evolution of the flow and the various sub-terms of the source, and the essence of the sound production mechanism is found to comprise subtle imbalances which disrupt inherent space–time symmetries which exist between the various sub-terms.      

The variation in the maximum loading of a circular cylinder impacted by a 2D vortex with time of impact

Direct numerical simulation is used to study the loading of a rigid, circular cylinder impacted by a 2D vortex. The vortex travels within a stream of fluid characterized by Reynolds number of 150. Vortex impact occurs at twenty-five different times within one vortex shedding cycle. Substantial variation is observed in the maximum values of the drag and lift force coefficients. This variation is due to interaction between the impinging vortex and those attached to the cylinder. As the radius of the impinging vortex is increased from one to three times the cylinder’s diameter, the variation in maximum force coefficients with time of impact decreases. The variation decreases because the larger vortex alters the flow field and vortex shedding cycle prior to impacting the cylinder. For structures impacted by a vortex similar in size, significant under-prediction of the maximum loading may occur if variation in loading with vortex impact time is not considered.     

Direct numerical simulation of particle transport by hairpin vortices in a laminar boundary layer

The transport of solid particles by coherent wall structures is studied here. This phenomenon is present in numerous environmental and engineering flows. The flow above a wall-mounted hemisphere is used for generating hairpin vortices in a laminar boundary layer in a controlled way. By means of direct numerical simulation (DNS) of the fluid flow and simultaneous Lagrangian tracking of particles, the influence of hairpin vortices on solid particles released in the wake of the obstacle is analyzed.     

Direct numerical simulation of a turbulent Couette-Poiseuille flow,part 2: Large- and very-large-scale motions

A direct numerical simulation dataset of a fully developed turbulent Couette-Poiseuille flow is analyzed to investigate the spatial organization of streamwise velocity-fluctuating u-structures on large and very large scales. Instantaneous and statistical flow fields show that negative-u structures with a small scale on a stationary bottom wall grow throughout the centerline due to the continuous positive mean shear, and they penetrate to the opposite moving wall. The development of an initial vortical structure related to negative-u structures on the bottom wall into a large-scale hairpin vortex packet with new hairpin vortices, which are created upstream and close to the wall, is consistent with the auto-generation process in a Poiseuille flow (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). Although the initial vortical structure associated with positive-u structures on the top wall also grows toward the bottom wall, the spatial development of the structure is less coherent with weak strength due to the reduced mean shear near the top wall, resulting in less turbulent energy on the top wall. The continuous growth of the structures from a wall to the opposite wall explains the enhanced wall-normal transport of the streamwise turbulent kinetic energy near the centerline. Finally, an inspection of the time-evolving instantaneous fields and conditional averaged flow fields for the streamwise growth of a very long structure near the centerline exhibits that a streamwise concatenation of adjacent large-scale u-structures creates a very-large-scale structure near the channel centerline.     

Direct numerical simulation of flexible molecules and data-driven molecular conformation

The present work aims at performing a molecular dynamics modeling of suspensions composed of flexible linear molecules. Molecules are represented by a series of connected beads, whose dynamics is governed by three potentials: the extension potential affecting the elongation of segments connecting consecutive beads, the one governing the molecule bending and finally the Lennard-Jones describing the interaction of non-consecutive beads. A population of non-interacting molecules is simulated in elongation and shear flows for different flow and molecule parameters. The flow-induced conformation is analyzed in the different considered situations. Finally a model for predicting the evolution of the population conformation will be obtained by using deep-learning.     

Direct numerical simulation of particulate flows with a fictitious domain method

Our works on the fictitious domain method for the direct numerical simulation of particulate flows are reviewed, and particularly our recent progresses in the simulations of the motion of particles in Poiseuille flow at moderately high Reynolds numbers are reported. The method is briefly described, and its capability to simulate the motion of spherical and non-spherical particles in Newtonian, non-Newtonian and non-isothermal fluids is demonstrated. In addition, the applications of the fictitious domain method reported in the literature are also reviewed, and some comments on the features of the fictitious domain method and the immersed boundary method are given.     

Numerical simulation and control of horseshoe vortex around an appendage-body junction

The horseshoe vortex generated around the appendage-body junction of submarines strongly influences the non-uniformity of submarine wakes at the propeller discs. The flow characteristics around the appended submarine body are numerically simulated and analyzed, and a new method on the vortex control baffle is presented. Then, the influence of the vortex control baffle on the horseshoe vortex generated at the sail-body junction is numerically studied, and the flow phenomena caused by the vortex control baffle with different transverse positions is investigated further. Results show that the vortex control baffle can induce a kind of attached vortex in a rotational direction opposite to the horseshoe vortex; these two kinds of vortices undermine each other. Furthermore, when the transverse position of the vortex control baffle is close to the horseshoe vortex, the state of the horseshoe vortex is directly affected, and the flow structure becomes even more complex. We adapt the vortex control baffle for the horseshoe vortex generated at the stern foil-body junction. Results from the numerical simulation of the flow around the fully appended submarine model indicate that the effect of the vortex control baffle greatly improves the performance of the submarine wake. The circumferential non-uniformity of the axial, tangential, and radial velocity components are decreased markedly. The engineering applicability of the vortex control baffle has been well presented.     

Direct numerical simulation of stable and unstable turbulent thermal boundary layers

This paper presents direct numerical simulations (DNS) of stable and unstable turbulent thermal boundary layers. Since a buoyancy-affected boundary layer is often encountered in an urban environmental space where stable and unstable stratifications exist, exploring a buoyancy-affected boundary layer is very important to know the transport phenomena of the flow in an urban space. Although actual observation may qualitatively provide the characteristics of these flows, the relevant quantitative turbulent quantities are very difficult to measure. Thus, in order to quantitatively investigate a buoyancy-affected boundary layer in detail, we have here carried out for the first time time- and space-developing DNS of slightly stable and unstable turbulent thermal boundary layers. The DNS results show the quantitative turbulent statistics and structures of stable and unstable thermal boundary layers, in which the characteristic transport phenomena of thermally stratified boundary layers are demonstrated by indicating the budgets of turbulent shear stress and turbulent heat flux. Even though the input of buoyant force is not large, the influence of buoyancy is clearly revealed in both stable and unstable turbulent boundary layers. In particular, it is found that both stable and unstable thermal stratifications caused by the weak buoyant force remarkably alter the structure of near-wall turbulence.     

Direct numerical simulation of a particle-laden low Reynolds number turbulent round jet

Direct numerical simulation method is used for the investigating of particle-laden turbulent flows in a spatially evolution of low Reynolds number axisymmetric jet, and the Eulerian–Lagrangian point-particle approach is employed in the simulation. The simulation uses an explicit coupling scheme between particles and the fluid, which considers two-way coupling between the particle and the fluid. The DNS results are compared well with experimental data with equal Reynolds number (R_e = 1700). Our objects are: (i) to investigate the correlation between the particle number density and the fluctuating of fluid streamwise velocity; (ii) to examine whether the three-dimensional vortex structures in the particle-laden jet are the same as that in the free-air jet and how the particles modulate the thee-dimensional vortex structures and turbulence properties with different Stokes number particles; (iii) to discover the particle circumferential dispersion with different Stokes number particles. Our findings: (i) all the particles, regardless of their particle size, tend to preferentially accumulate in the region with large-than-mean fluid streamwise velocity; (ii) the small Stokes number particles take an important part in the modulation of three-dimensional vortex structures, but for the intermediate and larger sized particles, this modulation effect seems not so apparent; (iii) the particle circumferential dispersion is more effective for the smaller and intermediate sized particles, especially for the intermediate sized particles.     

The effects of acceleration in jets: kinematics of the near field vortices

Direct and large-eddy simulations (DNS/LES) of accelerating round jets are used to analyze the effects of acceleration on the kinematics of vortex rings in the near field of the jet (x/D < 12). The acceleration is obtained by increasing the nozzle jet velocity with time, in a previously established (steady) jet, and ends once the inlet jet velocity is equal to twice its initial value. Several acceleration rates (α = 0.02–0.6) and Reynolds numbers (Re _D = 500–20000) were simulated. Acceleration maps were used to make a detailed study of the kinematics of vortex rings in accelerating jets. One of the effects of the acceleration is to cause a number of new primary and secondary vortex merging events that are absent from steady jets. As the acceleration rate α increases, both the number of primary merging events between rings and the axial position where these take place decreases. The statistics for the speed of the starting ring that forms at the start of the acceleration phase for each simulation, agree well with the statistics for the “front” speed observed by Zhang and Johari (Phys Fluids 8:2185–2195, 1996). Acceleration maps and flow visualizations show that during the acceleration phase the near field coherent vortices become smaller and are formed at an higher frequency than in the steady jet, and their (mean) shedding frequency increases linearly with the acceleration rate. Finally, it was observed that the acceleration decreases the spreading rate of the jet, in agreement with previous experimental works.      

Direct numerical simulation of particle interaction with ejections in turbulent channel flows

Direct numerical simulations (DNS) of incompressible turbulent channel flows coupled with Lagrangian particle tracking are performed to study the characteristics of ejections that surround solid particles. The behavior of particles in dilute turbulent channel flows, without particle collisions and without feedback of particles on the carrier fluid, is studied using high Reynolds number DNS (Re = 12,500). The results show that particles moving away from the wall are surrounded by ejections, confirming previous studies on this issue. A threshold value separating ejections with only upward moving particles is established. When normalized by the square root of the Stokes number and the square of the friction velocity, the threshold profiles follow the same qualitative trends, for all the parameters tested in this study, in the range of the experiments. When compared to suspension thresholds proposed by other studies in the Shields diagram, our simulations predict a much larger value because of the measure used to characterize the fluid and the criterion chosen to decide whether particles are influenced by the surrounding fluid. However, for intermediate particle Reynolds numbers, the threshold proposed here is in fair agreement with the theoretical criterion proposed by Bagnold (1966) [Bagnold, R., 1966. Geological Survey Professional Paper, vol. 422-1]. Nevertheless, further studies will be conducted to understand the normalization of the threshold.     

Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers

Formation and evolution of secondary streamwise vortices in the compressible transitional boundary layers over a flat plate are studied using a direct numerical simulation method with high-order accuracy and highly effective non-reflecting characteristic boundary conditions. Generation and development processes of the secondary streamwise vortices in the complicated transitional boundary flow are clearly analyzed based on the of numerical results, and the effects on the formation of the ring-like vortex that is vital to the boundary layer transition are explored. A new mechanism forming the ring-like vortex through the mutual effect of the primary and secondary streamwise vortices is expressed.     

Direct numerical simulation of turbulent heat transfer in a square duct with transverse ribs mounted on one wall

Turbulent heat transfer in a ribbed square duct of three different blockage ratios are investigated using direct numerical simulation (DNS). The results of ribbed duct cases are compared with those of a heated smooth duct flow. It is observed that owing to the existence of the ribs and confinement of the duct, organized secondary flows appear as large streamwise-elongated vortices, which intensely interact with the rib elements and four sidewalls and have profound influences on the transport of momentum and thermal energy. This study also shows that the drag and heat transfer coefficients are highly sensitive to the rib height. It is observed that as the rib height increases, the impinging effect of the flow on the windward face of the rib strengthens, leading to enhanced rates of turbulent mixing and heat transfer. The influence of sidewalls and rib height on the turbulence structures associated with temperature fluctuations are analyzed based on multiple tools such as vortex swirling strengths, temporal auto-correlations, spatial two-point cross-correlations, joint probability density functions (JPDF) between the temperature and velocity fluctuations, statistical moments of different orders, and temperature spectra.     

Direct numerical simulation of turbulent heat transfer on the Reynolds analogy over irregular rough surfaces

The effect of rough surface topography on heat and momentum transfer is studied by direct numerical simulations of turbulent heat transfer over uniformly heated three-dimensional irregular rough surfaces, where the effective slope and skewness values are systematically varied while maintaining a fixed root-mean-square roughness. The friction Reynolds number is fixed at 450, and the temperature is treated as a passive scalar with a Prandtl number of unity. Both the skin friction coefficient and Stanton number are enhanced by the wall roughness. However, the Reynolds analogy factor for the rough surface is lower than that for the smooth surface. The semi-analytical expression for the Reynolds analogy factor suggests that the Reynolds analogy factor is related to the skin friction coefficient and the difference between the temperature and velocity roughness functions, and the Reynolds analogy factor for the present rough surfaces is found to be predicted solely based on the equivalent sand-grain roughness. This suggests that the relationship between the Reynolds analogy factor and the equivalent sand-grain roughness is not affected by the effective slope and skewness values. Analysis of the heat and momentum transfer mechanisms based on the spatial- and time-averaged equations suggests that two factors decrease the Reynolds analogy factor. One is the increased effective Prandtl number within the rough surface in which the momentum diffusivity due to the combined effects of turbulence and dispersion is larger than the corresponding thermal diffusivity. The other is the significant increase in the pressure drag force term above the mean roughness height.