Underlying Flow Structure Research Articles

High-resolution light-field particle imaging velocimetry with color-and-depth encoded illumination

Three-dimensional and three-components (3D-3C) measurement of flow velocity vector is important for the investigation of mechanism underlying flow structure. Light-field particle imaging velocimetry (LF-PIV) is a newly emerged technique for flow velocity measurement. However, LF-PIV suffers low axial resolution, prohibiting it for high fidelity imaging. To overcome this limitation, we proposed to employ color-depth-encoded illumination in light-field PIV (Code LF-PIV) to refine the particle's axial location with the color-depth information of the illumination beam. Code LF-PIV is the first system that integrates the snapshot acquisition of light-field acquisition and the high resolution capability of color coded illumination. Compared to conventional light-field PIV, Code LF-PIV can achieve much higher axial resolution due to the new illumination strategy. Compared to traditional coded illumination PIV, such as Rainbow PIV, Code LF-PIV has higher flexibility for variant imaging applications because of the elimination of customized diffractive optical element. We demonstrated the superiority of our system by imaging fixed particle, randomly distributed cavities inside crystal cube, and the square lid-driven cavity flow, where our Code LF system has increased the axial resolution by a factor of 23 when compared to the conventional LF system, and has achieved a comparable axial resolution as the depth super-resolved Rainbow PIV. Comprehensive evaluation of the imaging results demonstrated that Code LF-PIV combines the advantages of the high resolution of color-depth coded method with the convenient volumetric imaging of light-field camera, making Code LF-PIV a useful technique for high-resolution and large-scale flow measurement.

Water surface response to turbulent flow over a backward-facing step

The water surface response to subcritical turbulent flow over a backward-facing step (BFS) is studied via high-resolution large-eddy simulation (LES). The LES method is validated first using data of previously reported experiments. The LES-predicted water surface is decomposed into different types of gravity waves as well as turbulence-driven forced waves. Analysis of the LES data reveals the interplay between low-frequency large-scale turbulence structures, which are the result of flow separation from the step and reattachment behind the step, and the dynamics of the water surface. The water surface deformation is mainly the result of freely propagating gravity waves and forced waves, owing to turbulence in the form of rollers and/or hairpin vortices. Gravity waves with zero group velocity define the characteristic spatial and temporal scales of the surface deformations at higher frequencies, while large eddies determine their low-frequency modulation. These deformations are mainly confined in lateral bands that propagate downstream following the advection of the near-surface streamwise vortices (rollers) that are shed from the step. Steeper surface waves are observed in regions of negative perturbation velocity gradient and down-welling, downstream of the larger rollers, and are associated with thin isolated regions of high vorticity near the surface. The investigation of such a complex flow has shown that the decomposition of the water surface fluctuations into its different physical components may be used to identify the dynamics of the underlying flow structure.

Transpiration cooling of high pressure turbine vane with optimized porosity distribution

The additive manufacturing allows to fabricate porous structures with elevated mechanical strength, which enable designers to apply transpiration cooling to gas turbine blades. However, most transpiration cooling investigations are carried out using the flat plate geometry. To understand transpiration cooling of a turbine blade better, it is necessary to conduct the investigations using real turbine blade geometry. The current study focuses on the numerical investigation and optimization of a transpiration cooled C3X vane. The C3X vane is designed with multiple porous zones whose porosities are in a range from 0.2 to 0.7. The Darcy-Brinkman-Forchheimer equation and the local thermal equilibrium model are used to simulate the flow and heat transfer in the porous zones. A surrogate-based optimization framework incorporating the Kriging method and the genetic algorithm is built to optimize the transpiration cooling performance. The numerical approach is carefully validated with the available experimental data, and then the optimization method is validated with the numerical results. The optimal designs under injection ratios of 1.2% and 2.0% are obtained, and the underlying flow structure and heat transfer physics are revealed. The results show that for an optimal transpiration cooled turbine vane design, large porosity should be applied first to the leading edge and the pressure side just downstream of the leading edge. The coolant issuing from the leading edge and the upstream pressure side convects downstream, forming an effective transpiration cooling film. The transpiration cooling film adheres well to the pressure surface, while it decays quickly on the suction surface. The temperature non-uniformity of the coolant in the plenum and the suction side endwall vortices can lead to the non-uniform surface temperature distribution along the vane height.

Possibility results for graph clustering: A novel consistency axiom

Kleinberg introduced three natural clustering properties, or axioms, and showed they cannot be simultaneously satisfied by any clustering algorithm. We present a new clustering property, Monotonic Consistency, which avoids the well-known problematic behaviour of Kleinberg’s Consistency axiom, and the impossibility result. Namely, we describe a clustering algorithm, Morse Clustering, inspired by Morse Theory in Differential Topology, which satisfies Kleinberg’s original axioms with Consistency replaced by Monotonic Consistency. Morse clustering uncovers the underlying flow structure on a set or graph and returns a partition into trees representing basins of attraction of critical vertices. We also generalise Kleinberg’s axiomatic approach to sparse graphs, showing an impossibility result for Consistency, and a possibility result for Monotonic Consistency and Morse clustering.

Reconstruction of the 3D hydrodynamics in a baffled stirred tank using Proper Orthogonal Decomposition

In this work, the unsteady turbulent flow in a four-baffled stirred tank equipped with a Rushton turbine is computed with ANSYS FLUENT® using the sliding mesh technique. The POD algorithm is applied first to each mesh zone (fixed and rotating) and, in a novel and original way, to the full 3D CFD data without distinguishing between the stationary and rotating zones. The resulting modes cannot be regarded as spatial modes revealing the underlying flow structure. The POD results showed that 99.9% of the system variance is recovered with the first three modes. The reconstruction of the velocity field from these modes reveals the trailing vortices plus the mean flow. The accuracy of the POD reconstructed flow fields is quantified. The present work is the first evidence of a POD reconstruction of the unsteady turbulent flow performed over the entire 3D domain in a baffled stirred tank.

Nonlinear interaction underlying flow structure transition of inclined oil–water two-phase countercurrent flow

Nonlinear interaction underlying flow structure transition of inclined oil–water two-phase countercurrent flow

Effect of inertial migration of particles on flow transitions of a suspension Taylor-Couette flow

Uniformly distributed particles in inertial flows migrate across the streamlines to form nonuniform distributions in the flow cross sections. Here, an experimental study of the influence of inertial migration of particles on flow transitions of a suspension in Taylor-Couette geometry is presented. It is shown that, relative to uniform concentration, the particle distribution following inertial migration either stabilizes or destabilizes the flow depending on the underlying flow structure and flow Reynolds number.

3D SPH Simulation of Dynamic Water Surface and Its Interaction with Underlying Flow Structure for Turbulent Open Channel Flows Over Rough Beds

In this study, a fully 3D numerical model based on the Smoothed Particle Hydrodynamics (SPH) approach has been developed to simulate turbulent open channel flows over a fixed rough bed. The model focuses on the study of dynamic free surface behavior as well as its interaction with underlying flow structures near the rough bed. The model is improved from the open source code SPHysics ( http://www.sphysics.org ) by adding more advanced turbulence and rough bed treatment schemes. A modified sub-particle-scale (SPS) eddy viscosity model is proposed to reflect the turbulence transfer mechanisms and a modified drag force equation is included into the momentum equations to account for the existence of roughness elements on the bed as well as on the sidewalls. The computed results of various free surface patterns have been compared with the laboratory measurements of the fluctuating water surface elevations in the streamwise and spanwise directions of a rectangular open-channel flow under a range of flow conditions. The comparison has demonstrated that the proposed 3D SPH model can simulate well the complex free surface flows over a fixed rough bed.

The Hidden Flow Structure and Metric Space of Network Embedding Algorithms Based on Random Walks

Network embedding which encodes all vertices in a network as a set of numerical vectors in accordance with it’s local and global structures, has drawn widespread attention. Network embedding not only learns significant features of a network, such as the clustering and linking prediction but also learns the latent vector representation of the nodes which provides theoretical support for a variety of applications, such as visualization, link prediction, node classification, and recommendation. As the latest progress of the research, several algorithms based on random walks have been devised. Although those algorithms have drawn much attention for their high scores in learning efficiency and accuracy, there is still a lack of theoretical explanation, and the transparency of those algorithms has been doubted. Here, we propose an approach based on the open-flow network model to reveal the underlying flow structure and its hidden metric space of different random walk strategies on networks. We show that the essence of embedding based on random walks is the latent metric structure defined on the open-flow network. This not only deepens our understanding of random- walk-based embedding algorithms but also helps in finding new potential applications in network embedding.

Numerical investigation of the bowed stator effects in a transonic fan at low Reynolds number

The performance of fan stage in a small turbofan engines is significantly affected at high-altitude low Reynolds number. In order to examine the effect of low Reynolds number on the fan stage, 3D numerical simulation method was employed to analyse the performance variations and the underlying flow structure in the fan stage. For the sake of decreasing the influence of low Reynolds number, the different bowed stator airfoils were redesigned and the effect of the modified design was evaluated.

Optimal perturbations in time-dependent variable-density Kelvin–Helmholtz billows

We analyse the influence of the specific features of time-dependent variable-density Kelvin–Helmholtz (VDKH) roll-ups on the development of three-dimensional secondary instabilities. Due to inertial (high Froude number) baroclinic sources of spanwise vorticity at high Atwood number (up to 0.5 here), temporally evolving mixing layers exhibit a layered structure associated with a strain field radically different from their homogeneous counterpart. We use a direct-adjoint non-modal linear approach to determine the fastest growing perturbations over a single period of the time-evolving two-dimensional base flow during a given time interval $[t_{0},T]$. When perturbations are seeded at the initial time of the primary KH mode growth, i.e. $t_{0}=0$, it is found that additional mechanisms of energy growth are onset around a bifurcation time $t_{b}$, a little before the saturation of the primary two-dimensional instability. The evolution of optimal perturbations is thus observed to develop in two distinct stages. Whatever the Atwood number, the first period $[t_{0},t_{b}]$ is characterised by a unique route for optimal energy growth resulting from a combination of the Orr and lift-up transient mechanisms. In the second period $[t_{b},T]$, the growing influence of mass inhomogeneities raises the energy gain over the whole range of spanwise wavenumbers. As the Atwood number increases, the short spanwise wavelength perturbations tend to benefit more from the onset of variable-density effects than large wavelength ones. The extra energy gain due to increasing Atwood numbers relies on contributions from spanwise baroclinic sources. The resulting vorticity field is structured into two elongated dipoles localised along the braid on either side of the saddle point. In return they yield two longitudinal velocity streaks of opposite sign which account for most of the energy growth. This transition towards three-dimensional motions is in marked contrast with the classic streamwise rib vortices, so far accepted as the paradigm for the transition of free shear flows, either homogeneous or not. It is argued that the emergence of these longitudinal velocity streaks is generic of the transition in variable-density shear flows. Among them, the light round jet is known to display striking side ejections as a result of the loss of axisymmetry. The present analysis helps to renew the question of the underlying flow structure behind side jets, otherwise based on radial induction between pairs of counter-rotating longitudinal vortices (Monkewitz & Pfizenmaier, Phys. Fluids A, vol. 3 (5), 1991, pp. 1356–1361). Instead, it is more likely that side ejections would result from the convergence of the longitudinal velocity streaks near the braid saddle point. When the injection time is delayed so as to suppress the initial stage of energy growth, a new class of perturbations arises at low wavenumber with energy gains far larger than those observed so far. They correspond to the two-dimensional Kelvin–Helmholtz secondary instability of the baroclinically enhanced vorticity braid discovered by Reinaud et al. (Phys. Fluids, vol. 12 (10), pp. 2489–2505), leading potentially to another route to turbulence through a two-dimensional fractal cascade.

Spatial and Temporal Variability of the Concentration Field from Localized Releases in a Regular Building Array

Spatial and temporal fluctuations in the concentration field from an ensemble of continuous point-source releases in a regular building array are analyzed from data generated by direct numerical simulations. The release is of a passive scalar under conditions of neutral stability. Results are related to the underlying flow structure by contrasting data for an imposed wind direction of $$0{^{\circ }}$$ and $$45{^{\circ }}$$ relative to the buildings. Furthermore, the effects of distance from the source and vicinity to the plume centreline on the spatial and temporal variability are documented. The general picture that emerges is that this particular geometry splits the flow domain into segments (e.g., “streets” and “intersections”) in each of which the air is, to a first approximation, well mixed. Notable exceptions to this general rule include regions close to the source, near the plume edge, and in unobstructed channels to which the flow is aligned. In the oblique ( $$45{^{\circ }})$$ case the strongly three-dimensional nature of the flow enhances mixing of a scalar within the canopy leading to reduced temporal and spatial concentration fluctuations within the plume core. These fluctuations are in general larger for the parallel flow ( $$0{^{\circ }})$$ case, especially so in the long unobstructed channels. Due to the more complex flow structure in the canyon-type streets behind buildings, fluctuations are lower than in the open channels, though still substantially larger than for oblique flow. These results are relevant to the formulation of simple models for dispersion in urban areas and to the quantification of the uncertainties in their predictions.

Shock wave–boundary layer interactions in rectangular inlets: three-dimensional separation topology and critical points

AbstractThe interaction between two separated flow regions was studied for the fundamental problem of a shock wave–boundary layer interaction (SBLI) within a rectangular inlet. One motivation is that the inlet of an engine on a supersonic aircraft may contain separation zones on the sidewalls and the bottom wall; if one region separates first it can alter the flow on the other wall and lead to engine unstart. In our work an oblique shock wave was generated by a wedge suspended from the upper wall of a Mach 2.75 wind tunnel. Stereo particle image velocimetry (PIV) measurements were recorded in 25 planes that include all three possible orthogonal orientations. The lateral velocity and vorticity measurements help to explain the underlying flow structure and these quantities were not measured previously for this problem. It is concluded that the sidewall and bottom wall separation zones interact due to an underlying flow structure that is similar to the two types of 3-D separation patterns previously described by Tobak & Peake (Annu. Rev. Fluid Mech., vol. 14, 1982, pp. 61–85). Separation first occurs at an upstream location where the shock interacts with the sidewall. Lateral velocities direct flow toward the centreline to cause separation on the bottom wall. This causes significant curvature of the shock wave, so that even the region near the tunnel centreline cannot be explained by conventional 2-D concepts. A number of critical points (saddle points, nodes, focus points) were identified. Results are consistent with the general ideas of Burton & Babinsky (J. Fluid Mech., vol. 707, 2012, pp. 287–306) and help to provide details of how the sidewalls redistribute the adverse pressure gradient in space.

Flow structure and near-field dispersion in arrays of building-like obstacles

Dispersion in the near-field region of localised releases in urban areas is difficult to predict because of the strong influence of individual buildings. Effects include upstream dispersion, trapping of material into building wakes and enhanced concentration fluctuations. As a result, concentration patterns are highly variable in time and mean profiles in the near field are strongly non-Gaussian. These aspects of near-field dispersion are documented by analysing data from direct numerical simulations in arrays of building-like obstacles and are related to the underlying flow structure. The mean flow structure around the buildings is found to exert a strong influence over the dispersion of material in the near field. Diverging streamlines around buildings enhance lateral dispersion. Entrainment of material into building wakes in the very near field gives rise to secondary sources, which then affect the subsequent dispersion pattern. High levels of concentration fluctuations are also found in this very near field; the fluctuation intensity is of order 2 to 5.

Image-based streamline generation and rendering

Seeding streamlines in 3D flow fields without considering their projections in screen space can produce visually cluttered rendering results. Streamlines will overlap or intersect with each other in the output image, which makes it difficult for the user to perceive the underlying flow structure. This paper presents a method to control the seeding and generation of streamlines in image space to avoid visual cluttering and allow a more flexible exploration of flow fields. In our algorithm, 2D images with depth maps generated by a variety of visualization techniques can be used as input from which seeds are placed and streamlines are generated. The density and rendering styles of streamlines can be flexibly controlled based on various criteria to improve visual clarity. With our image space approach, it is straightforward to implement the level of detail rendering, depth peeling, and stylized rendering of streamlines to allow for more effective visualization of 3D flow fields.

Image-Based Streamline Generation and Rendering

Seeding streamlines in 3D flow fields without considering their projections in screen space can produce visually cluttered rendering results. Streamlines will overlap or intersect with each other in the output image, which makes it difficult for the user to perceive the underlying flow structure. This paper presents a method to control the seeding and generation of streamlines in image space to avoid visual cluttering and allow a more flexible exploration of flow fields. In our algorithm, 2D images with depth maps generated by a variety of visualization techniques can be used as input from which seeds are placed and streamlines are generated. The density and rendering styles of streamlines can be flexibly controlled based on various criteria to improve visual clarity. With our image space approach, it is straightforward to implement the level of detail rendering, depth peeling, and stylized rendering of streamlines to allow for more effective visualization of 3D flow fields.

A theoretical and experimental investigation of tri-helical gravure roll coating

Tri-helical, gravure roll coating, operated in reverse mode, is investigated via a complementary experimental and theoretical approach. Flow visualisation reveals the underlying flow structure within the roll-to-web transfer region and highlights when loss of stability, that is a propensity to streaking, occurs. The latter is found to be influenced in turn by the depth of the tri-helical grooves and the capillary number. Experiments show that as the web-to-roll speed ratio is increased, so too is fluid pick-out from the grooves, although the coated film thickness may decrease. Extensive data are provided for coated film thickness, pick-out and meniscus location as a function of speed ratio, for different operating parameters. A key feature of the present investigation is the formulation of a novel complementary mathematical model for the process. The base flow within the grooves is modelled as a Poisson equation in conjunction with simplified approximations for the attendant free-surface boundary conditions. The resultant equation set is written in terms of finite Fourier sine transforms and unique solutions obtained by varying the flux until a consistent pressure distribution throughout the coating bead is obtained. Results from the model are found to be in generally good agreement with their experimental counter-parts, and are seen to predict and capture all the major features of the process over the operating range explored.

U.S. National Laboratory Research Supporting Low Wind Speed Technology

Harvesting wind energy from sites with lower annual average wind speeds at costs comparable to what can now be achieved in higher wind sites is an international challenge. It requires pushing the technology to optimize the use of materials and machinery and tuning the structure to withstand the loads unique to the lower wind speed sites. The U.S. Department of Energy’s laboratories— The National Renewable Energy Laboratory NREL and Sandia National Laboratories—are engaged in both basic science and applied research to overcome current technology limitations and enhance the individual components necessary to achieve costeffective low wind speed turbines. Technology improvements are necessary in three principal areas to minimize the cost of electricity production at lower wind speed sites.

Transient streamlines: texture synthesis for in vivo flow visualisation.

Magnetic resonance (MR) imaging is a versatile technique for providing detailed information on blood vessel morphology and function. With its ability to acquire multi-dimensional cine flow data, MR is also an important tool for providing insight into blood flow patterns in vivo. The purpose of this paper is to describe the application of texture synthesis for flow visualisation. Two related issues are addressed, one is the removal of image noise from the acquired velocity data to ensure a correct representation of the underlying flow structure, and the other is the formation of transient streamlines through flow texture synthesis. The process of noise removal is achieved by using a convex projection algorithm based on the principle of mass conservation, whereas transient streamlines are formed via an iterative orientated pattern formation and enhancement procedure. The method described provides realistic visualisation of the flow patterns and avoids distortions caused by integration errors associated with conventional streamline tracking techniques. Effectiveness of the method applied to MR flow data acquired in healthy volunteers and patients is demonstrated.

Role of the lithosphere in mantle convection

Plate geometry and kinematics generally reflect the mechanical properties of the solid lithosphere rather than those of the fluid mantle underneath, and plate formation and subduction account for most of the heat transport from the Earth's interior. Correspondingly, mantle convection models must incorporate a stiff but mobile boundary layer, like the lithosphere, before they can reproduce the main features of mantle convection. A relatively easy way to accomplish this in numerical models is to combine a temperature‐dependent viscosity with an imposed, piecewise constant surface velocity boundary condition. It is shown how surface heat flux, topography, gravity, and geoid (but not plate velocities or stresses) can then be derived. Numerical models confirm that a lithosphere has a first‐order effect on the underlying flow structure. For internally heated models, approx‐imating the case of whole mantle convection, the calculated surface signatures are in first‐order agreement with observations, a level of empirical success which hitherto has not been approached by models of mantle convection. Companion papers exploit the observations more fully to constrain the main features of mantle convection.