Gradient Flow Field Research Articles

Consistent Video Saliency Using Local Gradient Flow Optimization and Global Refinement.

We present a novel spatiotemporal saliency detection method to estimate salient regions in videos based on the gradient flow field and energy optimization. The proposed gradient flow field incorporates two distinctive features: 1) intra-frame boundary information and 2) inter-frame motion information together for indicating the salient regions. Based on the effective utilization of both intra-frame and inter-frame information in the gradient flow field, our algorithm is robust enough to estimate the object and background in complex scenes with various motion patterns and appearances. Then, we introduce local as well as global contrast saliency measures using the foreground and background information estimated from the gradient flow field. These enhanced contrast saliency cues uniformly highlight an entire object. We further propose a new energy function to encourage the spatiotemporal consistency of the output saliency maps, which is seldom explored in previous video saliency methods. The experimental results show that the proposed algorithm outperforms state-of-the-art video saliency detection methods.

Three-dimensional analysis and enhancement of continuous magnetic separation of particles in microfluidics

In continuous magnetic separation process, particles can be deflected and separated from the direction of laminar flow by means of magnetic force depending on their magnetic susceptibility and size as well as the flow rate. To analyze and control dynamic behavior of these particles flowing in microchannels, a three-dimensional numerical model was proposed and solved for obtaining the particle trajectories under the action of a gradient magnetic field and flow field. The magnetic force distribution and particle trajectories obtained were firstly verified by analytical and experimental results. Then, a detailed analysis for the enhancement of the continuous magnetic separation efficiency by optimizing the flow parameters and microchannel configurations was carried out. The results show that the separation efficiency can be greatly improved by controlling the flow rate ratio of the two fluid streams and introducing a broadened segment in the T-shaped microchannel. And it has been demonstrated to be effective through the sorting of 2-μm and 5-μm non-magnetic particles suspended in a dilute ferrofluid by a permanent magnet. The results reported could be encouraging for the design and optimization of efficient microfluidic separation systems.

Stability of Dissipation Elements: A Case Study in Combustion

AbstractRecently, dissipation elements have been gaining popularity as a mechanism for measurement of fundamental properties of turbulent flow, such as turbulence length scales and zonal partitioning. Dissipation elements segment a domain according to the source and destination of streamlines in the gradient flow field of a scalar function f : → ℝ. They have traditionally been computed by numerically integrating streamlines from the center of each voxel in the positive and negative gradient directions, and grouping those voxels whose streamlines terminate at the same extremal pair. We show that the same structures map well to combinatorial topology concepts developed recently in the visualization community. Namely, dissipation elements correspond to sets of cells of the Morse‐Smale complex. The topology‐based formulation enables a more exploratory analysis of the nature of dissipation elements, in particular, in understanding their stability with respect to small scale variations. We present two examples from combustion science that raise significant questions about the role of small scale perturbation and indeed the definition of dissipation elements themselves.

Numerical research and optimization of convective heat transfer for multi-segment amplifiers

Optimized convective heat transfer is applied to accelerate the thermal recovery of a large aperture multi-segment amplifier. The paper proposes a novel project of changing the structural parameters of the inlet jet to the Nd:glass slab in the multi-segment amplifier at the same flow rate. The convective heat transfer coefficient depends on the diameter of the inlet jet, as well as on the number of inlet jets. The simulation calculations indicate that at the same flow rate, different numbers of inlet jet lead to different temperature gradient contours and flow field distributions on the Nd:glass slab surface in the multi-segment amplifier. In addition, the convective heat transfer coefficient increases with the decrease of inlet diameter. This work analyzes the path of the coolant air over the slab surface to lessen the eddy and to achieve better convective heat transfer, as well as to determine the optimized number of inlet jets (5) and the optimized diameter (5mm).

Quantitative assessment of flow and electric fields for electrophoretic focusing at a converging channel entrance with interfacial electrode

The electric field and flow field gradients near an electrified converging channel are amenable to separating and focusing specific classes of electrokinetic material, but the detailed local electric field and flow dynamics in this region have not been thoroughly investigated. Finite elemental analysis was used to develop a model of a buffer reservoir connected to a smaller channel to simulate the electrophoretic and flow velocities (which correspond directly to the respective electric and flow fields) at a converging entrance. A detailed PTV (Particle Tracking Velocimetry) study using charged fluorescent microspheres was performed to assess the model validity both in the absence and presence of an applied electric field. The predicted flow velocity gradient from the model agreed with the PTV data when no electric field was present. Once the additional forces that act on the large particles required for tracing (dielectrophoresis) were included, the model accurately described the velocity of the charged particles in electric fields.

A transparent cell-culture microchamber with a variably controlled concentration gradient generator and flow field rectifier

Real-time observation of cell growth provides essential information for studies such as cell migration and chemotaxis. A conventional cell incubation device is usually too clumsy for these applications. Here we report a transparent microfluidic device that has an integrated heater and a concentration gradient generator. A piece of indium tin oxide (ITO) coated glass was ablated by our newly developed visible laser-induced backside wet etching (LIBWE) so that transparent heater strips were prepared on the glass substrate. A polymethylmethacrylate (PMMA) microfluidic chamber with flow field rectifiers and a reagent effusion hole was fabricated by a CO(2) laser and then assembled with the ITO heater so that the chamber temperature can be controlled for cell culturing. A variable chemical gradient was generated inside the chamber by combining the lateral medium flow and the flow from the effusion hole. Successful culturing was performed inside the device. Continuous long-term (>10 days) observation on cell growth was achieved. In this work the flow field, medium replacement, and chemical gradient in the microchamber are elaborated.

High‐order ENO and WENO schemes for unstructured grids

AbstractThis work describes the implementation and analysis of high‐order accurate schemes applied to high‐speed flows on unstructured grids. The class of essentially non‐oscillatory schemes (ENO), that includes weighted ENO schemes (WENO), is discussed in the paper with regard to the implementation of third‐ and fourth‐order accurate methods. The entire reconstruction process of ENO and WENO schemes is described with emphasis on the stencil selection algorithms. The stencils can be composed by control volumes with any number of edges, e.g. triangles, quadrilaterals and hybrid meshes. In the paper, ENO and WENO schemes are implemented for the solution of the dimensionless, 2‐D Euler equations in a cell centred finite volume context. High‐order flux integration is achieved using Gaussian quadratures. An approximate Riemann solver is used to evaluate the fluxes on the interfaces of the control volumes and a TVD Runge–Kutta scheme provides the time integration of the equations. Such a coupling of all these numerical tools, together with the high‐order interpolation of primitive variables provided by ENO and WENO schemes, leads to the desired order of accuracy expected in the solutions. An adaptive mesh refinement technique provides better resolution in regions with strong flowfield gradients. Results for high‐speed flow simulations are presented with the objective of assessing the implemented capability. Copyright © 2007 John Wiley & Sons, Ltd.

Level set method for numerical simulation of a cavitation bubble, its growth, collapse and rebound near a rigid wall

A level set method of non-uniform grids is used to simulate the whole evolution of a cavitation bubble, including its growth, collapse and rebound near a rigid wall. Single-phase Navier–Stokes equation in the liquid region is solved by MAC projection algorithm combined with second-order ENO scheme for the advection terms. The moving interface is captured by the level set function, and the interface velocity is resolved by “one-side” velocity extension from the liquid region to the bubble region, complementing the second-order weighted least squares method across the interface and projection inside bubble. The use of non-uniform grid overcomes the difficulty caused by the large computational domain and very small bubble size. The computation is very stable without suffering from large flow-field gradients, and the results are in good agreements with other studies. The bubble interface kinematics, dynamics and its effect on the wall are highlighted, which shows that the code can effectively capture the “shock wave”-like pressure and velocity at jet impact, toroidal bubble, and complicated pressure structure with peak, plateau and valley in the later stage of bubble oscillating.

Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones

A new technology, hydraulic/partitioning tracer tomography (HPTT), is proposed to survey spatial distributions of hydraulic properties and dense nonaqueous phase liquids (DNAPLs) in the subsurface. HPTT is nothing more than a set of multiple hydraulic/partitioning tracer tests and synthesis of all the tests to map the spatial distributions. It involves injection of water at one borehole in a source zone to create a steady state forced gradient flow field, then release of conservative/partitioning tracers at the same borehole, and monitoring heads and tracer breakthroughs at the others. The same operation is repeated using different boreholes for the water and the tracer injections. To analyze the head and tracer data obtained from the proposed tomographic survey, a joint stochastic estimator was developed. Numerical experiments were then conducted to evaluate the effectiveness of HPTT as well as the stochastic estimator. Results show that prior knowledge of hydraulic heterogeneity is critical for mapping the distribution of DNAPLs. In addition, the results suggest that the proposed HPTT in conjunction with the stochastic estimator is potentially a viable tool for high‐resolution characterization of subsurface heterogeneity and contamination.

A topological approach to simplification of three-dimensional scalar functions

This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.

Modified Shear-Stress Transport Turbulence Model for Supersonic Flows

The shear-stress transport turbulence model of Menter was derived to predict an accurate separated flow in the adverse pressure gradient flowfield, but it has sometimes failed to analyze these regions due to the strong shock/boundary-layer interaction. The modification of the shear-stress transport turbulence model adopted the shear strain rate instead of the vorticity as a limitation of the shear stress. The modified shear-stress transport turbulence model was applied to simulate supersonic compression corner flows including strong shock/boundarylayer interactions, and its performance in predicting the wall pressure distribution and the skin-friction coefficient was evaluated. The pressure distributions on the wall surface predicted by the modified shear-stress transport turbulence model showed an agreement with the experimental data in a transonic axisymmetric bump flow with the weak shock/boundary-layer interaction. In the cases of the 20- and 24-deg compression corner flows with strong shock/boundary-layer interactions, the modified shear-stress transport turbulence model yielded a more accurate prediction of the shock location and the wall pressure distribution and it also produced the more reasonable mean velocity profiles and skin-friction coefficient distribution in the redevelopment region as compared to the shear-stress transport turbulence model.

Higher Order Conditions for Weak Shocks: Modified Prandtl Relation

The classical equations for the jumps in the state variables across a planar shock wave in an inviscid flow - which can be solved by starting with the Prandtl relation for the jump in the normal velocity - have been applied locally in gas dynamics to a tangent plane of a curved shock. This tangent plane approximation has been validated for real fluids using matched asymptotics with a small parameter ϵ ≔ δ/l, where δ is the effective shock thickness and l is a typical radius of curvature of the shock; ϵ is of order 1/Re where Re is the Reynolds number based on l. The leading order inner solution in the scale δ yields the classical shock structure resolving the discontinuities across the shock in the larger scale l, while the O(ϵ) corrections to the classical shock conditions account for the shock structure, shock curvature and the flow field gradients behind and ahead of the shock. We prove that there is an analog (correction) of the classical Prandtl relation that shows that the first order correction to the tangent plane approximation is O(ϵ/Δ), where Δ denotes the scaled shock strength. Hence, the correction to the Prandtl relation is of paramount importance in the analysis of weak shocks.

Stretching of Polyelectrolyte Coils and Globules in an Elongational Flow

Scaling theory describing the stretching of a weakly charged polyelectrolyte molecule by elongational shear flow is developed. This stretching transition occurs as a first-order dynamic phase transition at a certain critical value of the flow-field gradient. The dependence of this critical gradient on the degree of chain ionization and on the solvent strength with respect to the interaction of uncharged monomers is analyzed. The stretching transition in neutral and polyelectrolyte globules is considered. It is shown that for a polyelectrolyte immersed in a salt-added solution two critical values of the flow-field gradient exist : the lower critical point corresponds to the stretching of the chain on the scale of superblobs of the size equal to Debye screening length, and the upper critical point corresponds to the complete stretching of the chain on the scale of monomer units.

Unstructured adaptive remeshing finite element method for dusty shock flow

The passage of planar shocks in a dusty gas was investigated to note effects due to particle loading and initial shock Mach number. Two-phase flow equations have been added to a conservative, monotonic flow solver to allow study of compressible particle and droplet flows, which are of importance for shock propagation in two-phase flows and spray propulsion systems. The formulation developed herein employed a conservative Eulerian treatment for the gas and particle phases. The computations were performed using the finite element method-flux corrected transport (FEM-FCT) scheme, which has shown excellent predictive capability of various compressible flows which include both strong and weak shocks. The flux limiting technique was modified to provide monotonic particle velocity fields to increase the scheme's computational stability. Adaptive unstructured methodology based on adapting to high gradients of both the fluid and particle densities was used in conjunction with the conservative shock-capturing scheme to adequately resolve strong flowfield gradients. The shock attenuation of this scheme was then compared with previous experimental and numerical results and was found to yield robust predictions. Various interphase coupling terms were also considered to note their effect on the shock attenuation.

Grid-independent upwind scheme for multidimensional flow

Recent advances in the development of a grid-independent finite volume scheme for the Euler equations of gas dynamics are described. In the proposed method, flowfield gradient data are reconstructed locally (on a triangle) using five elementary planar waves, and an upwind numerical flux function for grid-oblique waves is developed to model the effect of the passage of these waves on the data in a cell. Numerical examples for several two-dimensional test problems are included. These results show high wave resolution and nearly monotone strong-wave transitions.

On the natural variability of trace-metal content of particulate matter in a deep aquifer

A multilayer sampler (MLS) has been used in a deep phreatic aquifer to collect particulate matter transported by a natural gradient flow field. The trace-metal content (Fe, Mn, Cu, Zn, Ag) associated to the carbonate, organic and oxide fractions of the particulate matter has been characterized by Eulerian variability at a microscale level (< 1 m). The observed variability in metal content reflects the chemical heterogeneity of groundwater in contact with the particles, which is the result of the scale of variability of recharging water into the groundwater reservoir. These findings should be taken into consideration in the application of thermodynamic models for the understanding of natural systems.

Solution-adaptive grid procedure for the parabolized Navier-Stokes equations

A solution-adapt ive grid procedure based on an error equidistribution principle is developed and applied to a three-dimensional parabolized Navier-Stokes solver. The scheme redistributes grid points line by line in both crossflow directions, with grid point motion controlled by forces analogous to tensional and torsional spring forces. The tensional force is proportional to the error measure or a weighting function related to the error measure. The torsional force is used to control grid skewness relative to the upstream and cross-stream coordinate lines. Weighting functions are selected by first normalizing flowfield gradients and/or curvature of a number of dependent variables and then selecting the largest at each point. The hypersonic flow over a right-circular cone at three different yaw angles is studied to demonstrate the performance of the solution-adaptive grid procedure. Pitot pressure profiles and surface pressure computed using the solution-adaptive algorithm are compared with experimental results as well as with numerical results obtained using a fixed grid. Pitot pressure predictions using the adaptive grid algorithm show better agreement with experiment than those obtained using a fixed grid.

Vorticity produced by shock wave diffraction

Numerical simulations with a monotonicity preserving flow solver have been performed to study shock diffraction phenomena and shock wave generated vorticity. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme, which has been shown to have an excellent predictive capability for various compressible flows with both strong and weak shocks. Adaptive unstructured methodology based on adapting to high density and entropy gradients was used in conjunction with a conservative shock-capturing scheme to adequately resolve storng and weak flowfield gradients. The chief interest was therefore, a topic of vortices (original paper:the formation of vorticity) arising from shock wave propagation over a sharp corner and the high accuracy and resolution of the interacting compressible wave features. Numerical simulations were compared with previous experimental results and exhibited remarkably good agreement in terms of compressible wave propagation, as well as vorticity development and transport. The computations also allowed insight to the fundamental fluid dynamics, spencifically shock diffraction, vortex convection and shock-vortex interactions.

Solution-adaptive grid procedure for high-speed parabolic flow solvers

A solution-adaptive grid procedure based bn an error equidistribution scheme is developed and applied to a parabolized Navier-Stokes solver. An improved method of selecting weighting functions is introduced that involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point. The scheme redistributes grid points line by line with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions. Torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability. A grid-fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum. Results for several problems are presented to demonstrate the improvements obtainable with the solution-adaptive grid procedure.

Tracing the influx of sewage from a leaky sewer into a very thin and fast-flowing aquifer

Water parcels of different chemical composition were detected in a 1 m thick and up to 17 m/d fast-flowing groundwater system using a multi-layer sampler based on the dialysis cell technique. The parcels result from the infiltration of sewage effluents and also probably due to the leaching of sewage sludge from the agricultural land surface. Samples obtained at depth intervals as small as 3 cm in a natural gradient flow field revealed relative high concentrations and variable vertical profiles of Na +, NO 3 −, HCO 3 −, SO 4 2− and DOC 9 m downstream of the infiltration pipe. A pump used to obtain water samples during a 2 year period, in the same research field, proved to be an inadequate sampling technique to trace the movement of sewage effluent.