Kinematic simulation for stably stratified and rotating turbulence

The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the rapid distortion theory (RDT) to a kinematic simulation (KS) of the Boussinesq equation with a Coriolis term.Scalings for one- and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.     

Identification,characterization and evolution of non-local quasi-Lagrangian structures in turbulence

The recent progress on non-local Lagrangian and quasi-Lagrangian structures in turbulence is reviewed. The quasi-Lagrangian structures, e.g., vortex surfaces in vis-cous flow, gas-liquid interfaces in multi-phase flow, and flame fronts in premixed combustion, can show essential Lagrangian following properties, but they are able to have topological changes in the temporal evolution. In addition, they can represent or influence the turbulent flow field. The challenges for the investigation of the non-local structures include their identification, characterization, and evolution. The improving understanding of the quasi-Lagrangian struc-tures is expected to be helpful to elucidate crucial dynamics and develop structure-based predictive models in turbulence.     

Direct numerical simulation of homogeneous stratified rotating turbulence

The effects of the Prandtl number on stratified rotating turbulence have been studied in homogeneous turbulence by using direct numerical simulations and a rapid distortion theory. Fluctuations under strong stable-density stratification can be theoretically divided into the WAVE and the potential vorticity (PV) modes. In low-Prandtl-number fluids, the WAVE mode deteriorates, while the PV mode remains. Imposing rotation on a low-Prandtl-number fluid makes turbulence two-dimensional as well as geostrophic; it is found from the instantaneous turbulent structure that the vortices merge to form a few vertically-elongated vortex columns. During the period toward two-dimensionalization, the vertical vortices become asymmetric in the sense of rotation. Communicated by S. Obi PACS 47.55.Hd     

A structural model for the vortex tubes of isotropic turbulence

A class of exact solutions of the Navier–Stokes equations is introduced to model the fine-scale, tubular structures of isotropic turbulence. The model vortices exhibit slow algebraic fall-off of the induced velocity, and accurately reproduce the velocity signatures observed in DNS and experiments. The proposed model has interesting implications for the theoretical analysis of turbulence, supporting the view that the inertial range energy scaling may have a link with the near-singular velocity field induced by vortex tubes produced by the roll-up of vortex sheets.      

Coherent structures in trailing-edge cooling and the challenge for turbulent heat transfer modelling

The present paper tests the capability of a standard Reynolds-Averaged Navier–Stokes (RANS) turbulence model for predicting the turbulent heat transfer in a generic trailing-edge situation with a cutback on the pressure side of the blade. The model investigated uses a gradient-diffusion assumption with a scalar turbulent-diffusivity and constant turbulent Prandtl number. High-fidelity Large-Eddy Simulations (LES) were performed for three blowing ratios to provide reliable target data and the mean velocity and eddy viscosity as input for the heat transfer model testing. Reasonably good agreement between the LES and recent experiments was achieved for mean flow and turbulence statistics. The LES yielded coherent structures which were analysed, in particular with respect to their effect on the turbulent heat transfer. For increasing blowing ratio, the LES replicated an also experimentally observed counter-intuitive decrease of the cooling effectiveness caused by the coherent structures becoming stronger. In contrast, the RANS turbulent heat transfer model failed in predicting this behaviour and yielded significantly too high cooling effectiveness. It is shown that the model cannot predict the strong upstream and wall-directed turbulent heat fluxes caused by large coherent structures, which were found to be responsible for the counter-intuitive decrease of the cooling effectiveness.     

A study of the energetic turbulence structures during stall delay

This study revealed the three-dimensional instantaneous topologies of the large-scale turbulence structures in the separated flow on the suction surface of wind turbine’s blade during stall delay. These structures are the major contributors to the first two POD (proper orthogonal decomposition) modes. The two kinds of instantaneous flow structures as major contributors to the first POD mode are: (1) extended regions of downwash flow with an upstream upward flow beside it and a compact vortex pair closer to the blade’s leading edge; (2) a large-scale clockwise vortex with strong induced flows. The two kinds of flow structures contributing significantly to the second POD mode are: (1) large counter-rotating vortices inducing strong upward velocities and a series of small vortices; (2) strong downwash flow coming from the leading-edge shear layer with a large and strong vortex on the left side and small vortices upstream. The statistical impacts of these large-scale and energetic structures on the turbulence have also been studied. It was observed that when these turbulence structures were removed from the flow, the peak values of some statistics were significantly reduced.     

A study on coherent structures and drag-reduction in the wall turbulence with polymer additives by TRPIV

An experimental measurement was performed using time-resolved particle image velocimetry (TRPIV) to investigate the spatial topological character of coherent structures in wall-bounded turbulence of polymer additive solution. The fully developed near-wall turbulent flow fields with and without polymer additives at the same Reynolds number were measured by TRPIV in a water channel. The comparisons of turbulent statistics confirm that due to viscoelastic structure of long-chain polymers, the wall-normal velocity fluctuation and Reynolds shear stress in the near-wall region are suppressed significantly. Furthermore, it is noted that such a behavior of polymers is closely related to the decease of the motion of the second and forth quadrants, i.e., the ejection and sweep events, in the near-wall region. The spatial topological mode of coherent structures during bursts has been extracted by the new mu-level criteria based on locally averaged velocity structure function. Although the general shapes of coherent structures are unchanged by polymer additives, the fluctuating velocity, velocity gradient, velocity strain rate and vorticity of coherent structures during burst events are suppressed in the polymer additive solution compared with that in water. The results show that due to the polymer additives the occurrence and intensity of coherent structures are suppressed, leading to drag reduction.     

Intense Reynolds-stress events in turbulent ducts

The aim of the present work is to investigate the role of intense Reynolds shear-stress events in the generation of the secondary flow in turbulent ducts. We consider the connected regions of flow where the product of the instantaneous fluctuations of two velocity components is higher than a threshold based on the long-time turbulence statistics, in the spirit of the three-dimensional quadrant analysis proposed by Lozano-Durán et al. (J. Fluid Mech., vol. 694, 2012, pp. 100–130). We examine both the geometrical properties of these structures and their contribution to the mean in-plane velocity components, and we perfom a comparison with turbulent channel flow at similar Reynolds number. The contribution to a certain mean quantity is defined as the ensemble average over the detected coherent structures, weighted with their own occupied volume fraction. In the core region of the duct, the contribution of intense events to the wall-normal component of the mean velocity is in very good agreement with that in the channel, despite the presence of the secondary flow in the former. Additionally, the shapes of the three-dimensional objects do not differ significantly in both flows. In the corner region of the duct, the proximity of the walls affects both the geometrical properties of the coherent structures and the contribution to the mean component of the vertical velocity. However, such contribution is less relevant than that of the complementary portion of the flow not included in such objects. Our results show that strong Reynolds shear-stress events are affected by the presence of a corner but, despite the important role of these structures in the dynamics of wall-bounded turbulent flows, their contribution to the secondary flow is relatively low, both in the core and in the corner.     

Kinematics and dynamics of small-scale vorticity and strain-rate structures in the transition from isotropic to shear turbulence

We applied a technique that defines and extracts “structures” from a DNS dataset of a turbulence variable in a way that allows concurrent quantitative and visual analysis. Local topological and statistical measures of enstrophy and strain-rate structures were compared with global statistics to determine the role of mean shear in the dynamical interactions between fluctuating vorticity and strain-rate during transition from isotropic to shear-dominated turbulence. We find that mean shear adjusts the alignment of fluctuating vorticity, fluctuating strain-rate in principal axes, and mean strain-rate in a way that (1) enhances both global and local alignments between vorticity and the second eigenvector of fluctuating strain-rate, (2) two-dimensionalizes fluctuating strain-rate, and (3) aligns the compressional components of fluctuating and mean strain-rate. Shear causes amalgamation of enstrophy and strain-rate structures, and suppresses the existence of strain-rate structures in low-vorticity regions between enstrophy structures. A primary effect of shear is to enhance “passive” strain-rate fluctuations, strain-rate kinematically induced by local vorticity concentrations with negligible enstrophy production, relative to “active,” or vorticity-generating strain-rate fluctuations. Enstrophy structures separate into “active” and “passive” based on the level of the second eigenvalue of fluctuating strain-rate. We embedded the structure-extraction algorithm into an interactive visualization-based analysis system from which the time evolution of a shear-induced hairpin enstrophy structure was visually and quantitatively analyzed. The structure originated in the initial isotropic state as a vortex sheet, evolved into a vortex tube during a transitional period, and developed into a well-defined horseshoe vortex in the shear-dominated asymptotic state.     

Low- and high-speed structures in the outer region of an adverse-pressure-gradient turbulent boundary layer

Large- and very large-scale structures in the form of elongated regions of low and high streamwise momentum have been studied in the outer region of a turbulent boundary layer subjected to a strong adverse pressure gradient. Large sets of streamwise–spanwise instantaneous velocity fields are acquired by particle image velocimetry at three wall-normal positions (0.2δ, 0.5δ, 0.8δ) at three different streamwise locations and at 0.1δ at the last streamwise location which allows us to study the wall-normal and streamwise variations of the structures. Subsequently, a pattern-recognition method and a classification scheme are employed in order to detect, classify and characterize the structures in an efficient and rigorous manner. Like in the case of zero-pressure-gradient turbulent boundary layers, long meandering streaky regions of low and high momentum are observed in the outer region of the present flow but they appear less frequently; especially in the lower part (at 0.1δ and 0.2δ) of the large-velocity-defect zone, i.e. near detachment. The dimensions of these large structures scale on boundary-layer thickness (δ) and are generally comparable to those previously reported for such structures in the overlap region of zero-pressure-gradient turbulent boundary layers. Interestingly, the adverse pressure gradient does not significantly affect the dimensions and arrangement of the large-scale structures in the upper part (at 0.5δ and 0.8δ) a segment of the outer region where the scaled Reynolds stresses also remain fairly self-similar.     

On the dynamics of rotating circular cable structures

The combined effect of gravity and a centrifugal field on the dynamics of a heavy cable with negligible bending stiffness is treated. The inextensible length of the cable is preassigned in such a way that the cross-sectional shape of the cable structure is circular if the contiguration rotates about its central axis with a constant speed and no external forces act. Under the additional influence of gravity, complicated nonlinear weight-excited vibrations occur.To understand the variety of vibrational phenomena. The dynamic system is studied by some experiments first. In order to explain the experimental results theoretically, the governing nonlinear boundary value problem is derived next. Subsequently, an appropriate variational formulation for application of a Rayleigh Ritz procedure is suggested. The resulting nonlinear ordinary differential equations approximately deseribe a part of the observed vibrational behaviour.Both the experiments and the calculations demonstrate that, for high speeds, nonlinear weight-excited vibrations about the circular reference configuration occur. On the other hand, for low velocitites, periodie and even chaos-like snap-through phenomena appear.     

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).     

Shock waves and turbulence in a hypersonic inlet

A numerical investigation for an axisymmetric hypersonic turbulent inlet flow field of a perfect gas is presented for a three-shock configuration consisting of a biconic and a cowl. An upwind parabolized Navier-Stokes solver based on Roe's scheme is used to compute an oncoming flow Mach numberM =8, temperatureT =216 K, and pressureP =5.5293×10³ N/m². In order to assess the flow quantities, the interaction between shock and turbulence, and the inlet efficiency, three different flow calculations — laminar, turbulent with incompressible and compressible two-equationk- turbulence models — have been performed in this work.Computational results show that turbulence is markedly enhanced across an oblique shock with step-like increases in turbulence kinetic energy and dissipation rate. This enhancement is at the expense of the mean kinetic energy of the flow. Therefore, the velocity behind the shock is smaller in turbulent flow and hence the shock becomes stronger. The entropy increase through a shock is caused not only by the amplification of random molecular motion, but also by the enhancement of the chaotic turbulent flow motion. However, only the compressiblek- turbulence model can properly predict a decrease in turbulence length scale across a shock. Our numerical simulation reveals that the incompressiblek- turbulence model exaggerates the interaction between shock and turbulence with turbulence kinetic energy and dissipation rate remaining high and almost undissipated far beyond the shock region. It is shown that proper modeling of turbulence is essential for a realistic prediction of hypersonic inlet flowfield. The performed study shows that the viscous effect is not restricted in the boundary layer but extends into the main flow behind a shock wave. The loss of the available energy in the inlet performance therefore needs to be determined from the shock-turbulence interaction. The present study predicts that the inlet efficiency becomes relatively lower when turbulence is taken into account.     

Large eddy simulation of flows after a bluff body: Coherent structures and mixing properties

This paper performs large eddy simulations (LES) to investigate coherent structures in the flows after the Sydney bluff-body burner, a circular bluff body with an orifice at its center. The simulations are validated by comparison to existing experimental data. The Q function method is used to visualize the instantaneous vortex structures. Three kinds of structures are found, a cylindrical shell structure in the outer shear layer, a ring structure and some hairpin-like structures in the inner shear layer. An eduction scheme is employed to investigate the coherent structures in this flow. Some large streaks constituted by counter-rotating vortices are found in the outer shear layer and some well-organized strong structures are found in the inner shear layer. Finally, the influences of coherent structures on scalar mixing are studied and it is shown that scalar in the recirculation region is transported outward by coherent structures.     

Apparent transition behavior of widely-used turbulence models

The Spalart–Allmaras and the Menter k–ω SST turbulence models are shown to have the undesirable characteristic that, for fully turbulent external flow computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart–Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a freestream turbulence level higher than the threshold or by making a simple change to one of the model constants. Near the area where turbulence initiates, the SST model exhibits sensitivity to numerical resolution, but its solutions are unique on a given grid. Inconsistent apparent transition behavior with grid refinement in this case does not stem from the presence of a degenerate fixed point. A nullcline analysis is used to visualize the local behavior of the model.