Two-dimensional Velocity Field Research Articles

Identifying the body force from partial observations of a two-dimensional incompressible velocity field

Identifying the body force from partial observations of a two-dimensional incompressible velocity field

Reconstruction and prediction of the rotor wake flow field in hovering state

A clear understanding of the flow structure and evolution of the rotor wake flow field is one of the key problems to be solved in the development of rotor aerodynamics. The tip vortices are the primary structure of the rotor wake flow field. A theoretical model of the vortex ring was established to verify the feasibility of flow field reconstruction. Particle image velocimetry (PIV) is used to measure the two-dimensional velocity field in the rotor wake. Because of the wandering motion of tip vortices, a new conditional average algorithm is proposed to deal with the flow field. On this basis, it is proposed that the plane interval of the rotor wake flow field reconstructed by interpolation should be less than 20 deg. The vortex core radius is obtained by the analysis method based on the circulation. A Back Propagation (BP) neural network was established to predict the axial and radial positions of the tip vortices and the radius of the vortex core. The inputs are the vortex ages measured by the experiment, and the outputs are the position and radius of the vortex core under any vortex ages. The predicted values were in good agreement with the experimental results. The study provides further analytical methods and new insights for the characteristics and evolution of tip vortices.

Transient Tire Slip Losses Using the Brush Theory

ABSTRACT Tire slip losses have been shown to have a significant impact on vehicle performance in terms of energy efficiency, thus requiring accurate studies. In this paper, the transient dissipation mechanisms connected to the presence of micro-sliding phenomena occurring at the tire–road interface are investigated analytically. The influence of a two-dimensional velocity field inside the contact patch is also considered in light of the new brush theory recently developed by the authors. Theoretical results align with findings already known from literature but suggest that the camber and turn spins contribute differently to the slip losses and should be regarded as separate entities when the camber angle is sufficiently large. The present work shows that an additional amount of power which relates to the initial sliding conditions is generated or lost during the unsteady-state maneuvers. A simple example is presented to illustrate the discrepancy between the microscopic and macroscopic approaches during a transient maneuver.

Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows

We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in processes, and apparatuses of chemical technology. To describe the steady shear flows of an incompressible fluid, the system of Navier–Stokes equations in the Boussinesq approximation is redefined, so the construction of exact and numerical solutions to the equations of hydrodynamics is a very difficult and urgent task. A non-trivial exact solution is constructed in the Lin-Sidorov-Aristov class. For this class of exact solutions, the hydrodynamic fields (velocity field, pressure field, temperature field, and solute concentration field) were considered as linear forms in the x and y coordinates. The coefficients of linear forms depend on the third coordinate z. Thus, when considering a shear flow, the two-dimensional velocity field depends on three coordinates. It is worth noting that the solvability condition given in the article imposes a condition (relation) only between the velocity gradients. A theorem on the uniqueness of the exact solution in the Lin–Sidorov–Aristov class is formulated. The remaining coefficients of linear forms for hydrodynamic fields have functional arbitrariness. To illustrate the exact solution of the overdetermined system of Oberbeck–Boussinesq equations, a boundary value problem was solved to describe the complex convection of a vertical swirling fluid without its preliminary rotation. It was shown that the velocity field is highly stratified. Complex countercurrents are recorded in the fluid.

Reliability assessment and performance improvement of long-span roof structure subjected to coupled wind-snow multi-hazard

Sensitivity to wind and snow loads has been the focus of reliability analysis and safety design of long-span roof structures in cold regions. In this study, the reliability assessment and performance improvement of a long-span roof structure subjected to coupled wind-snow multi-hazard are addressed. To this end, the average wind pressure coefficients of roof surface are first derived from wind tunnel tests, and the two-dimensional wind velocity field simulation is carried out by using the refined spectral representation scheme based on joint wavenumber-frequency power spectrum and stochastic harmonic function. The snow pressure coefficients of structural roof considering wind-induced snow drift effects are obtained by conducting computational fluid dynamics simulation. Then the global reliability of the structure subjected to coupled wind-snow multi-hazard with 100-yr return period is assessed using the probability density evolution method (PDEM). To improve structural performance, a control scheme of distributed tuned mass dampers (d-TMDs) is designed according to the structural dynamics of their deployment positions. Numerical results show that the fluctuating wind is a critical factor resulting in deformation failure of the long-span roof structure, and the proposed control scheme has sound effectiveness and robustness to mitigate the fluctuating wind effect and thus improve the structural performance.

The investigation of the correction factor for ultrasonic flow meters

The aim of this work is to combine analytical and computational techniques in investigation of correction factor for ultrasonic flow meters to improve their accuracy.Exploring velocity profiles that do not have axial symmetry we applied reconstruction of two-dimensional velocity field based on the inverse Abel’s transform.For velocity profiles that do not have rotational symmetry around the axis of the pipeline, the value of the correction factor will depend on the angle of measuring plane orientation relative to the diametrical plane of the flow meter. The calculation of the actual average flow velocity in the cross section of the meter was obtained from a specific mathematical dependencies describing velocity distribution by integration technique.This study allows us to conclude that even under conditions of distorted non-symmetric flows it is possible to determine the performance of ultrasonic flowmeters with sufficient accuracy using both methods of theoretical research and computational hydrodynamics.

Tracking motion of thermal turbulent structures at the water surface in compound channel flows using block matching algorithm

In this research a novel approach is used to track the motion of the coherent structures at the water surface of a compound channel flow with vegetated floodplain. Thermal sequences images in conjunction with a block matching algorithm (BM) approach is utilized to track the motion of turbulent structures by extracting a 2-D velocity field at the water surface. A laboratory flume was used and a compound channel of half cross-section was installed along the flume length. To mimic the vegetation elements, three diameters of wooden rigid, emergent cylindrical rods that located in staggered form were used. A thermal camera was vertically installed at section where a fully turbulent flow was achieved. Injected hot water was released from a water tank at the main channel-floodplain's edge at a small distance from upstream location of the thermal camera. A thorough assessment is performed to evaluate the performance of using the new approach. Where a Fast Fourier transform (FFT) is utilised to extract the energy of the eddies through arbitrary selected points between the cylinders wake and showed that the FFT successive peaks have different slopes. The exponent was deduced and showed different magnitudes from the Kolmogorov exponent (-5/3). The power law (-5/3) was found in the region where the fully turbulent flow is still developing, whereas the other exponents were found near to the cylinders where the velocity fluctuations are decreased in strength. Furthermore, the two-dimensional velocity field was extracted and analysed according to the BM approach and its coherent motion profiles are presented and discussed for all the experiments. The results showed a good estimation of tracking the motion of the coherent turbulent flows at the wake of the cylinders. The present results showed that the new proposed approach is primarily useful for providing visualisation of the coherent turbulent flows motion and can be extended for a wide range of turbulent flows as an easy and reliable technique.

Volumetric measurement of a Newtonian fluid flow through three-dimensional porous media using Lagrangian particle tracking (Shake-the-Box) technique

This work experimentally investigates the pressure-driven flow of a pure Newtonian fluid through three-dimensional (3D) porous media models. The porous media model consists of square arrays of rods that also could be interpreted as a periodic tandem rod arrangement. We employed a time-resolved three-dimensional particle tracking velocimetry (3D Shake-the-Box) technique for a range of Reynolds numbers 111 ≤ R e ≤ 890 to observe flow structures and vortex formation between the rods in porous media structures with different porosities of ε = 0.7 , 0.8 , and 0.9 , which corresponds to the spacing ratio of L D = 1.75 , 2 , and 3, where L is the distance between the centers of the rods, and D is the diameter of the rods. For all the examined cases, we further analyzed the effect of the Reynolds number and the spacing ratio on the instantaneous and averaged patterns of velocity, vorticity, and the other flow parameters after obtaining the two-dimensional velocity fields using the bin-averaging method. We observed both symmetrical and asymmetrical patterns of structure and recirculation regions between the rods depending on the Reynolds number and spacing ratio. Increasing the Reynolds number reduced the symmetrical patterns of flow structures with respect to the centerline of the gap region, while the spacing ratio was randomly affecting the symmetry degree. Vortex shedding was considerable for the two examined high Reynolds numbers of Re = 444 and Re = 890 behind the upstream rod as the porosity increased. The backward movement of the reattachment point has been observed by increasing the Reynolds number.

Investigation on the influence of spur dikes on the weighted usable area for the two native species in a city-crossing river

Spur dikes, mainly for regulating water flow and protecting river banks in the past, were found recently to have the ability to increase the fish physical habitat and improve aquatic system. However, the effect of spur dikes on aquatic system was generally ignored previously, and the studies on the influence of spur dikes on improving specific native fish physical habitat are still rare. This study reports a numerical investigation for the effects of spur dikes on the physical habitat and the minimum ecological flow in the Jinjiang River. Three spur dikes are placed along the inner bend in the study reach and two fish species of the Pelteobagrus fulvidraco and carps are selected as the target species. Two-dimensional water depth and velocity field are simulated in different discharges and the results are used to predict the corresponding weight use area (WUA). The differences of WUA before and after the building of spur dikes for the two selected fish species show that spur dikes have a significant effect on the physical habitats. And the minimum ecological flows from the instream flow increment approach are different for the two objective fish species and are also considerably impacted by spur dikes.

Regime transitions in stratified shear flows: the link between horizontal and inclined ducts

We present the analytical solution for the two-dimensional velocity and density fields within an approximation for laminar stratified inclined duct (SID) flows where diffusion dominates over inertia in the along-channel momentum equation but is negligible in the density transport equation. We refer to this approximation as the hydrostatic/gravitational/viscous in momentum and advective in density (HGV-A) approximation due to the leading balances in the governing equations. The analytical solution is valid for laminar flows in a two-layer configuration in the limit of long ducts. The non-dimensional volume flux within the HGV-A approximation is given by $Fr^* ={{Re}}_g/(AK)$ , which is a control parameter with ${{Re}}_g$ the gravitational Reynolds number, $A$ the aspect ratio of the duct and $K$ a geometrical parameter that depends on the tilt of the duct and is obtained from the analytical solution. This analytical solution was validated against results from laboratory experiments, and allows us to gain new insight into the dynamics and properties of SID flows. Most importantly, constant values of $Fr^*$ describe, in both horizontal and inclined ducts, the transitions between increasingly turbulent flow regimes: from laminar flow, to interfacial waves, to intermittent turbulence and sustained turbulence.

Fringe Reconstruction Technology of Two-Dimensional Shock Wave Velocity Field Based on Total Variation Regularization Constraints

Fringe Reconstruction Technology of Two-Dimensional Shock Wave Velocity Field Based on Total Variation Regularization Constraints

Observation and Measurement of Two-Dimensional Velocity Fields Induced by Laser-Induced Cloud Cavitation via Particle Image Velocimetry

Observation and Measurement of Two-Dimensional Velocity Fields Induced by Laser-Induced Cloud Cavitation via Particle Image Velocimetry

Subgrid Variational Optimized Optical Flow Estimation Algorithm for Image Velocimetry

The variational optical flow model is used in this work to investigate a subgrid-scale optimization approach for modeling complex fluid flows in image sequences and estimating their two-dimensional velocity fields. To solve the problem of lack of sub-grid small-scale structure information in variational optical flow estimation, we combine the motion laws of incompressible fluids. Introducing the idea of large eddy simulation, the instantaneous motion can be decomposed into large-scale motion and a small-scale turbulence in the data term. The Smagorinsky model is used to model and solve the small-scale turbulence. The improved subgrid scale Horn-Schunck (SGS-HS) optical flow algorithm provides better results in velocity field estimation of turbulent image sequences than the traditional Farneback dense optical flow algorithm. To make the SGS-HS algorithm equally competent for the open channel flow measurement task, a velocity gradient constraint is chosen for the canonical term of the model, which is used to improve the accuracy of the SGS-HS algorithm in velocimetric experiments in the case of the relatively uniform flow direction of the open channel flow field. The experimental results show that our algorithm has better performance in open channel velocimetry compared with the conventional algorithm.

Unsteady Mass Transfer in Bubble Wakes Analyzed by Lagrangian Coherent Structures in a Flat-Bed Reactor

To increase the yield and selectivity in reactive bubbly flows, the gas-liquid interactions have to be understood in depth. In the current fundamental study, flow and concentration data of the wakes of two-dimensional bubbles in an organic solvent are obtained experimentally in a flat-bed reactor. The unsteady mass transport phenomena in these turbulent wakes of two freely rising, two-dimensional bubbles with bubble Reynolds numbers Re=949 and Re=388 are evaluated by analyzing Lagrangian Coherent Structures (LCS). To reveal how LCS govern the transport of dissolved gas in bubble wakes, and therefore affect gas-liquid reactions, LCS in two-dimensional velocity fields are computed and compared with concentration fields of dissolved gas. The analysis of backward Finite Time Lyapunov Exponent (bFTLE) fields reveals coherent fluid dynamic structures for both bubble Reynolds numbers studied. In the higher bubble Reynolds number case, two types of coherent structures are found, which hinder the mixing of the dissolved gas and the liquid bulk. Repelling LCS are found to enclose parcels transported into the vortices, and indicate thus, which fluid parcels can possibly take part in chemical reactions. Due to higher mixing, unveiled by details from the LCS and FTLE analyses, and therefore increased contact area between dissolved gas and fresh liquid, higher yields of reaction products are suggested for the lower bubble Reynolds number case in this two-dimensional study. This is contradicting the rule of thumb that mixing increases for higher bubble Reynolds numbers.

Acoustic measurement of velocity filed using improved radial basic function neural network

In coal-fired boilers, the aerodynamic field directly affects the combustion conditions of the boiler and safety of the furnace. In this work, a new method based on acoustic tomography (AT) is proposed to measure the velocity field by using radial basis function neural network (RBFNN). First, we establish the proposed RBFNN model to reconstruct the velocity field and study the influence of various parameters including the number and arrangement of sensors, the shape parameters and the number of center points in RBF, and the hyper parameters in the neural network to improve the reconstruction performance. Second, a novel improved RBFNN acoustic algorithm is used to reconstruct different two-dimensional velocity fields based on numerical simulations. The reconstruction results obtained using the proposed algorithms have higher accuracy, better real-time performance, and noise immunity as compared with other classical acoustic algorithms. Third, the physical experiments are conducted in lab to further assess the proposed algorithm. The results exhibit that the proposed RBFNN acoustic method provided satisfactory consistency as compared to the traditional measurement approaches. This proves the effectiveness of the proposed acoustic method in practical velocity field measurement.

Experimental and analytical study on inclined turbulent fire in still air. Part 2. Round fire

This paper reports an experimental and analytical study on non-vertical round turbulent jet fire. A series of propane jet fire tests are performed under different initial flame angles (θ0) and initial fuel velocities. The two-dimensional velocity and temperature fields of the flame are measured, and the flame geometry is determined from video images. Experimental results show that the flame entrainment is enhanced as θ0 decreases. The flame deflection-induced buoyancy flow plays an essential role in the local flame structure and turbulence. A model of round fire combined with a kinetic energy equation is established, in which the flame entrainment coefficient is analytically correlated with the buoyancy and streamline curvature. Model calculations reproduce the flame entrainment and flame trajectory, consistent with the experimental indications. Under the same burner area and heat release rate, the entrainment coefficient of round fire is greater than that of line fire, closely associated with the difference in integral buoyancy triggered by different burner geometries. The results of this paper may help understand the flame motion and predict the flame radiation of turbulent jet fires.

Estimation of spray flow characteristics using ensemble Kalman filter

Spray flows are widely used in several industrial applications, such as combustion engines. Accurate measurement of spray flow characteristics requires sophisticated equipment and techniques. In recent years, the discrete droplet method (DDM), which analyses droplet scattering, has become a mature technique and has been applied to various analyses. We propose an estimation system based on particle image velocimetry (PIV) measurements and an ensemble Kalman filter, together with DDM, to efficiently investigate spray flow characteristics. The proposed method performs data assimilation on the velocity distribution in a two-dimensional cross-section obtained by PIV to estimate the characteristics of the spray flow in three dimensions. In this study, the system was constructed so that droplet particle is ensembled during data assimilation to estimate the droplet diameter distribution indirectly. The proposed method can be used to estimate the spray velocity and droplet size distribution. The numerical solution obtained using DDM was used as a criterion for assimilation and validated by conducting twin experiments. The results showed that, in terms of spray velocity, the estimation error for the velocity component parallel to the main flow was 2% and that for the velocity component perpendicular to the main flow was around 10%. Finally, the velocity and particle size distributions of the spray stream and the three-dimensional droplet distribution were estimated by assimilating the velocity distributions measured by PIV. This technique predicts the spray angle and droplet size distribution from the two-dimensional velocity field of the PIV only and is expected to contribute to the development of injectors and atomizers.

Investigation of aluminum dust cloud dispersion characteristics in an explosion hazard testing device using laser-based particle and flow diagnostics

Monitoring the dust cloud dispersion process inside testing equipment like the MIKE3 minimum ignition energy device is useful for assessing the ignitability characteristics of different dust materials. However, it is difficult to comprehensively capture the relevant micro-scale particle properties and macro-scale flow behavior of a dust cloud dispersion using a single measurement method. Thus, the objective of this work is to combine two complementary laser diagnostic techniques to obtain quantitative particle and flow properties from dust clouds in the MIKE3 glass tube. For this experiment, thirty repeated runs for each method were conducted using small (15-mg) aluminum powder samples. No ignition electrodes are included in the test geometry to establish a baseline flow configuration for the glass tube, although measurements are still made at the characteristic time delay and location of ignition tests. The first technique, digital in-line holography (DIH) is used for three-dimensional micro-scale particle diagnostics, yielding particle number (n = 78 ± 20), size (D̅ = 18.9 ± 0.6 µm), and three-component velocity (v̅x = 0.05 ± 0.05 m/s, v̅y = 0.60 ± 0.09 m/s, v̅z = − 0.07 ± 0.16 m/s) measurements. The second laser diagnostic technique, particle image velocimetry (PIV), is used for macro-scale flow diagnostics, yielding two-dimensional flow velocity and vorticity vector field measurements. Particle sizes are observed to follow a lognormal distribution (μ = 2.89, σ = 0.31), and a discrepancy between in-situ and ex-situ sizing results is identified for particle sizes larger than ~55 µm. Two-dimensional particle velocities follow a Weibull distribution (θ = 0.86, β = 2.12), and reasonable agreement is found between the DIH and PIV velocity measurements.

Blood Flow Quantification with High-Frame-Rate, Contrast-Enhanced Ultrasound Velocimetry in Stented Aortoiliac Arteries: In Vivo Feasibility.

Local flow patterns influence stent patency, while blood flow quantification in stents is challenging. The aim of this study was to investigate the feasibility of 2-D blood flow quantification using high-frame-rate, contrast-enhanced ultrasound (HFR-CEUS) and particle image velocimetry (PIV), or echoPIV, in patients with aortoiliac stents. HFR-CEUS measurements were performed at 129 locations in 62 patients. Two-dimensional blood flow velocity fields were obtained using echoPIV. Visual inspection was performed by five observers to evaluate feasibility. The contrast-to-background ratio and average vector correlation were calculated and compared between stented and native vessel segments. Flow quantification with echoPIV was feasible in 128 of 129 locations (99%), with optimal quantification in 40 of 129 locations (31%). Partial quantification was achieved in 88 of 129 locations (68%), where one or multiple limiting issues occurred (not related to the stent) including loss of correlation during systole (57/129), short vessel segments (20/129), loss of contrast during diastole (20/129) and shadow regions (20/129). The contrast-to-background ratio and vector correlation were lower downstream in the imaged blood vessel, independent of the location of the stent. In conclusion, echoPIV was feasible in stents placed in the aortoiliac region, and the stents did not adversely affect flow tracking.

Sensitivity of modeled tracer motion in tidal areas to numerics and to non-Hamiltonian perturbations

This study focuses on the motion of passive tracers induced by the joint action of tidal and residual currents in shallow seas with an irregular bottom topography. Interest in this problem has rapidly increased in recent years, because of the detection of large-scale pollution of marine waters by plastics. Early simplified models considered advection of tracers by a two-dimensional depth-averaged velocity field that is solenoidal, thereby resulting in a system that is Hamiltonian and nonintegrable. Here, two new aspects are considered. First, the sensitivity of solutions to three different numerical schemes is investigated. To quantify the behavior of orbits, both the largest Lyapunov exponent and the K-coefficient of the zero-one test for chaos were calculated. It turns out that a new scheme, which extends a known symplectic scheme to systems that also contain non-Hamiltonian terms, performs best. The second aspect concerns the fact that a depth-averaged velocity field is actually divergent, thereby rendering the model of tracer motion to be non-Hamiltonian. It is demonstrated that the divergent velocity components, no matter how small, cause the appearance of attractors in the system and thus they have a strong impact on the fate of tracers. Interpretation of the numerical results is given by deriving and analyzing approximate analytical solutions of the system.