Two-component Velocity Field Research Articles

Dual-camera off-axis holographic particle tracking velocimetry: Development and application to air-blast swirl spray measurement

Quantifying the droplet field near the atomizer exit poses a challenge due to its three-dimensional (3D), multiscale and turbulent characteristics. An optical measurement method named dual-camera high-resolution holographic particle tracking velocimetry (DCHR-HPTV) is proposed. This method enables the extraction of near-field spatial Sauter mean diameter (SMD) distribution and three-dimensional two-component (3D-2C) velocity field, from off-axis hologram pairs with a frame interval of 6 μs, recorded using two synchronized industrial cameras and pulsed lasers. The system achieves a resolution of 9344 × 7000 pixels with an individual pixel size (dpix) of 3.2 μm. The droplet size measurement range is from 10 μm to above 500 μm with an absolute error within 3 μm. The velocity measurement range is adjustable and is set to be 0 to 38.4 m/s in this study, with errors of 0.23 m/s and 0.15 m/s for horizontal and axial components, respectively. The method is applied to investigate a spray region of 29 mm × 20 mm with a depth of 35 mm (equivalent to 20.3 cm3) at the exit of an air-blast atomizer. The spatial distribution of circumferentially integrated SMD along radial and axial directions is obtained. Statistical analysis is performed on both spatial and quantity distributions of droplet 3D-2C velocities. Concurrently acquired droplet size and velocity in the central toroidal recirculation zone (CTRZ) indicate that both the increasing air pressure and enlarged size range lead to a weakened droplet backflow motion. This method, distinguished by its large field of view and high resolution for particle velocimetry, is suited for dynamic analysis of near-nozzle droplet fields and can be employed in various testing scenarios involving 3D motion of micron-sized particles within multiscale flow fields.

Solar horizontal flow evaluation using neural network and numerical simulations with snapshot data

Abstract We suggest a method that evaluates the horizontal velocity in the solar photosphere with easily observable values using a combination of neural network and radiative magnetohydrodynamics simulations. All three-component velocities of thermal convection on the solar surface have important roles in generating waves in the upper atmosphere. However, the velocity perpendicular to the line of sight (LoS) is difficult to observe. To deal with this problem, the local correlation tracking (LCT) method, which employs the difference between two images, has been widely used, but this method has several disadvantages. We develop a method that evaluates the horizontal velocity from a snapshot of the intensity and the LoS velocity with a neural network. We use data from numerical simulations for training the neural network. While two consecutive intensity images are required for LCT, our network needs just one intensity image at only a specific moment for input. From these input arrays, our network outputs a same-size array of a two-component velocity field. With only the intensity data, the network achieves a high correlation coefficient between the simulated and evaluated velocities of 0.83. In addition, the network performance can be improved when we add LoS velocity for input, enabling us to achieve a correlation coefficient of 0.90. Our method is also applied to observed data.

Event-based imaging velocimetry applied to a cylinder wake flow in air

Event-based vision is a new upcoming field within the field of computer vision. Unlike conventional frame-based imaging, event-based vision (or dynamic vision sensing) asynchronously records binary signals of contrast changes at the pixel level with microsecond resolution. Event-based imaging of small particles illuminated by a laser or other continuous light source generates streaks of events in a space-time domain. From this data the particles’ position in both space and time can be inferred. The present work explores the possibilities of harnessing the potentials of event- based vision for fluid flow measurement with focus on two-dimensional, two-component velocity field estimation at particle image densities corresponding to that of conventional PIV. Three different motion detection schemes are implemented. Measurements of a cylinder wake flow demonstrate that EBIV provides time resolved velocity data that is suitable for the retrieval of flow statistics as well as spectral and modal analysis. The present work is an extension of the recently published Exp. Fluids article by the authors on event-based imaging velocimetry and provides further details on current limitations related to event-based imaging.

Colour-Doppler echocardiography flow field velocity reconstruction using a streamfunction-vorticity formulation.

We introduce a new method (Doppler Velocity Reconstruction or DoVeR), for reconstructing two-component velocity fields from colour Doppler scans. DoVeR employs the streamfunction-vorticity equation, which satisfies mass conservation while accurately approximating the flow rate of rotation. We validated DoVeR using artificial colour Doppler images generated from computational fluid dynamics models of left ventricle (LV) flow. We compare DoVeR against the conventional intraventricular vector flow mapping (iVFM1D) and reformulated iVFM (iVFM2D). LV model error analysis showed that DoVeR is more robust to noise and probe placement, with noise RMS errors (nRMSE) between 3.81% and 6.67%, while the iVFM methods delivered 4.16-24.17% for iVFM1D and 4.06-400.21% for iVFM2D. We test the DoVeR and iVFM methods using in vivo mouse LV ultrasound scans. DoVeR yielded more haemodynamically accurate reconstructions, suggesting that it can provide a more reliable approach for robust quantification of cardiac flow.

Time-resolved reconstruction of turbulent flows using linear stochastic estimation and sequential data assimilation

The present work concentrates on the reconstruction of the time-resolved turbulent flows from probe signals and low sampling rate flow fields using linear stochastic estimation (LSE) and sequential data assimilation (DA). The separated and reattached flow over a blunt plate is used as the benchmark configuration. Experimental data are acquired with a microphone array (34 probes) installed on the plate surface to capture the pressure fluctuation at a sampling rate 1000 Hz, and with planar particle image velocimetry (PIV) measuring the two-dimensional two-component (2D2C) velocity fields synchronized with the microphones at 1 Hz. LSE is conducted first to estimate the raw temporal sequence of the flow field from PIV and microphone data. This temporal sequence then serves as the observations for the DA process based on continuous adjoint formulation for the flow field correction and pressure determination. The LSE results show that an appropriate size of proper orthogonal decomposition (POD) database should be evaluated considering the combined error induced by the truncation of the mapping function M, the size of the POD database, and the scaling of the model coefficient for the compensation of M truncation. Subsequently, the LSE reconstructions using the POD database of size Nt = 100 are employed as the observations in the DA process. The mean flow field is recovered quite well, while the normal Reynolds stress also has a significant improvement compared to large-eddy simulation. The temporal variation of the LSE reconstruction is significantly improved, and the resultant fluctuating pressure coefficient distribution agrees reasonably well with the microphone measurement.

Tuft deflection velocimetry: a simple method to extract quantitative flow field information

A novel method capable of assessing flow fields in a quick and relatively simple manner is introduced. In an extension to the classical qualitative flow visualization by means of cotton or polymeric tufts, digital data processing is used to extract the orientation of these tufts. This information can be related to physical quantities, in particular to time- and space-dependent velocity signals. The capability of this method is demonstrated in two test scenarios. First, it is applied to gain information on the unsteady near-wall flow along a turbulent separation bubble. Second, the two-component velocity field in the wake of a generic car model is measured, allowing for a quantification of the recirculation zone dimensions. Validation measurements with conventional techniques, e.g., particle image velocimetry, unsteady pressure measurements and hot wire anemometry, are conducted throughout the study. These generally suggest that the novel approach provides a quick and reasonably good quantitative overview of the flow configurations. However, the measurement error may be substantial in flow regions of low velocity or dominated by high-frequency oscillations.Graphic abstract

Instantaneous pressure determination from unsteady velocity fields using adjoint-based sequential data assimilation

A sequential data assimilation (DA) method is developed for pressure determination of turbulent velocity fields measured by particle image velocimetry (PIV), based on the unsteady adjoint formulation. A forcing term F, which is optimized using the adjoint system, is added to the primary Navier–Stokes (N–S) equations to drive the assimilated flow toward the observations at each time step. Compared with the conventional unsteady adjoint method, which requires the forward integration of the primary system and the backward integration of the adjoint system, the present approach integrates the primary-adjoint system all the way forward, discarding the requirement of data storage at every time step, being less computationally resource-consuming, and saving space. The pressure determination method of integration from eight paths [J. O. Dabiri et al., “An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements,” J. Exp. Biol. 217, 331 (2014)] is also evaluated for comparison. Using synthetic PIV data of a turbulent jet as the observational data, the present DA method is able to determine the instantaneous pressure field precisely using the three-dimensional velocity fields, regardless of the observational noise. For the two-dimensional three-component (3C) or two-component (2C) velocity fields, which are not sufficient for pressure determination by the integration method due to the lack of off-plane derivatives, the present DA method is able to reproduce pressure fields whose statistics agree reasonably well with those of the referential results. The 3C and 2C velocity fields yield quite similar results, indicating the possibility of pressure determination from only planar-PIV measurements in turbulent flows. The tomography PIV measurements are also used as observational data, and a clear pressure pattern is obtained with the present DA method.

Experimental Study of the Convective Motions by the PIV Technique within an Evaporating Liquid Layer into the Gas Flow

We present the experimental study of convection in a horizontal liquid layer (ethanol, 3-mm deep), evaporating from a localized surface (10 × 10 mm2) into the gas flow (air). Visualization and measurements of the two-component velocity field in the liquid layer has been carried out with the Particle Image Velocimetry (PIV) technique. In our experiments we consider a novel configuration in which the gas-liquid interface is maintained in the flat position in the confined square area and the volatile liquid evaporates from the planar surface into the gas flowing along the surface. We also consider the effect of the gas velocity (0.0138–0.138 m/s) and the gas and the liquid temperature (20 °C - 50 °C) on the convective flow structure within the liquid layer. It is shown that the gas velocity and both, the gas and the liquid temperatures induce significant changes in the convective flow structure. We give the first experimental proof of the phenomenon that the motion of the gas-liquid interface goes along the counter-current direction to the gas flow as theoretically predicted. The analysis of the experimental data shows that the influence of the gas flow velocity on the Marangoni convection at the maximum temperature (50 °C) is significantly reduced owing to the growth of the diffusion resistance for the gas flow under a strong evaporation from the interface. As a result, it leads to the low surface temperature gradient, which decreases thermocapillary stresses and the circulation velocity of the first (thermocapillary) vortex within the fluid layer. Further, we observe that the disappearance of the second convective vortex circulating in the same direction with the gas flow. The governing factor, determining the structure of convective flows within the liquid is the thermocapillary effect due to the intensive evaporation provided that the cooling and the temperature distribution are uniform on the gas-liquid interface.

Flowfield Characteristics of a Supersonic Jet Impinging on an Inclined Surface

The study of the flowfield and noise characteristics of supersonic impinging jets is important as these configurations can be found in many engineering applications, such as short takeoff and landing vehicles, hot surface cooling mechanisms, cold gas dynamic spray processes, and turbomachinery systems. This study experimentally investigates the flowfield characteristics of supersonic jets impinging on an inclined surface with nozzle-to-plate distances of and ( is the jet hydraulic diameter) and nozzle pressure ratios () of 3.7 and 5.9. The two-dimensional two-component velocity fields were acquired in the central plane of the test nozzle and along the 45° inclined impingement surface by using a planar particle image velocimetry (PIV) technique. The flow characteristics of supersonic impinging jets, such as mean velocity and turbulent kinetic energy, were computed from the acquired PIV velocity vector fields, and the statistical profiles were compared to study the effects of the impingement surface and on the flow characteristics. The obtained statistical results have shown the presence of shock cells near the nozzle outlet, oblique plate shocks near the impingement, and tail shocks along the inclined surface. In addition, spatial two-point cross-correlations of turbulent velocity were computed using the PIV velocity vectors to study the sizes, shapes, and orientation of turbulent flow structures in the impinging jets. Finally, a proper orthogonal decomposition analysis was performed on the collections of velocity snapshots extracting the coherent flow structures of a supersonic jet impinging on an inclined surface.

Identification of dominant structures and their flow dynamics in the turbulent two-phase flow using POD technique

The Proper orthogonal decomposition (POD) method has seen increasingly used in the last two decades and has a lot of applications for the comparison of experimental and numerically simulated data. The POD technique is often used to extract information about coherent structures dominating the flow. The two-dimensional and two-component instantaneous velocity fields of both liquid and gas phases of a slug flow were obtained by Particle image velocimetry (PIV) combined with Laser induced fluorescence (LIF). POD was applied to the velocity fields of both phases separately to identify the coherent flow structures. We focused on POD eigenmodes and their corresponding energy contents of both liquid and gas phases. The sum of first few eigenmodes that contain maximum turbulent kinetic energy of the flow represents the coherent structures. In the case of liquid phase the first eigenmode contained 42% of the total energy, while in the gas phase the decaying energy distribution was flat. The POD results showed that the coefficient of mode 1 for the liquid phase oscillated between positive and negative values and had the highest amplitude. For the visualization of coherent motion different linear combinations of eigenmodes for liquid and gas phases were used. The phenomena of turbulent bursting events associated with Q2 events (low momentum fluid moving away from the wall) and Q4 events (high momentum flow moving towards the wall) were also discussed to assess its contribution in turbulence production

Three-dimensional reconstruction of cardiac flows based on multi-planar velocity fields

Measurement of the three-dimensional flow field inside the cardiac chambers has proven to be a challenging task. This is mainly due to the fact that generalized full-volume velocimetry techniques cannot be easily implemented to the heart chambers. In addition, the rapid pace of the events in the heart does not allow for accurate real-time flow measurements in 3D using imaging modalities such as magnetic resonance imaging, which neglects the transient variations of the flow due to averaging of the flow over multiple heartbeats. In order to overcome these current limitations, we introduce a multi-planar velocity reconstruction approach that can characterize 3D incompressible flows based on the reconstruction of 2D velocity fields. Here, two-dimensional, two-component velocity fields acquired on multiple perpendicular planes are reconstructed into a 3D velocity field through Kriging interpolation and by imposing the incompressibility constraint. Subsequently, the scattered experimental data are projected into a divergence-free vector field space using a fractional step approach. We validate the method in exemplary 3D flows, including the Hill’s spherical vortex and a numerically simulated flow downstream of a 3D orifice. During the process of validation, different signal-to-noise ratios are introduced to the flow field, and the method’s performance is assessed accordingly. The results show that as the signal-to-noise ratio decreases, the corrected velocity field significantly improves. The method is also applied to the experimental flow inside a mock model of the heart’s right ventricle. Taking advantage of the periodicity of the flow, multiple 2D velocity fields in multiple perpendicular planes at different locations of the mock model are measured while being phase-locked for the 3D reconstruction. The results suggest the metamorphosis of the original transvalvular vortex, which forms downstream of the inlet valve during the early filling phase of the right ventricular model, into a streamline single-leg vortex extending toward the outlet.

Induction magnetic stability with a two-component velocity field

A generalization of the stability results of the induction magnetic field in a simple one space dimensional model for a protoplanetary disc, given in Rüdiger and Shalybkov (2004) and Straughan (2013), is proposed.The model studied in Rüdiger and Shalybkov (2004) and Straughan (2013) arises from the induction equation for the magnetic field in the presence of a sheared one-component velocity flow with Hall and ion-slip effects. Because of applications in some geophysical problems, here we consider a more general two-component velocity field that generalizes the case studied in Straughan (2013) and also includes elliptic (in particular uniform circular motions a=−b) and hyperbolic orbits.We study linear instability and nonlinear stability of the induction magnetic field by means of the classical spectral and energy methods.

Determination of the phase-resolved body force produced by a dielectric barrier discharge plasma actuator

Dielectric barrier discharge (DBD) plasma actuators are a promissing tool for active flow control applications. In order to determine the time-resolved body force induced by a DBD plasma actuator, which was driven by a 9.5 kHz sinusoidal signal, the flow has to be captured with a high spatial and temporal resolution. For this purpose we applied a laser Doppler velocity profile sensor for the measurements of the two-component velocity field and Lagrangian acceleration. A temporal and spatial resolution of 7.3 µs and 40 µm was achieved. We present the time-resolved local flow behaviours induced by the DBD actuator. Based on these measurement data the time-resolved body force generated by the plasma actuator was derived. Experiments revealed a defined dependence of the force direction on the phase angle of the ac operating voltage. This result is a contribution to the controversy on the temporal behaviour of the body force of plasma actuators.

Microfluidic characterization of cilia-driven fluid flow using optical coherence tomography-based particle tracking velocimetry

Motile cilia are cellular organelles that generate directional fluid flow across various epithelial surfaces including the embryonic node and respiratory mucosa. The proper functioning of cilia is necessary for normal embryo development and, for the respiratory system, the clearance of mucus and potentially harmful particulate matter. Here we show that optical coherence tomography (OCT) is well-suited for quantitatively characterizing the microfluidic-scale flow generated by motile cilia. Our imaging focuses on the ciliated epithelium of Xenopus tropicalis embryos, a genetically manipulable and experimentally tractable animal model of human disease. We show qualitative flow profile characterization using OCT-based particle pathline imaging. We show quantitative, two-dimensional, two-component flow velocity field characterization using OCT-based particle tracking velocimetry. Quantitative imaging and phenotyping of cilia-driven fluid flow using OCT will enable more detailed research in ciliary biology and in respiratory medicine.

Energy Deposition Applied to a Transverse Jet in a Supersonic Crossflow

An experimental investigation of a sonic underexpanded jet injected normally into a Mach 2.25 crossflow is reported. The jet exit geometry was circular and was operated at a jet-to-crossflow momentum flux ratio of 1.7. The unperturbed flowfield was analyzed with schlieren imaging, particle image velocimetry velocity data, surface oil flow visualizations, and pressure-sensitive paint measurements. As a means of excitation to the flowfield, an energy pulse from a Q-switched neodymium-doped-yttrium-aluminum-garnet laser was focused in the center of the jet exit at three different vertical locations. The focused laser pulse resulted in the induced optical breakdown of air, creating a plasma to perturb the flowfield. The perturbed resulting flowfield was analyzed with schlieren photography and particle image velocimetry. Analysis of phase-averaged schlieren images suggested that the resulting blast wave from the laser pulse disrupted the structure of the barrel shock and Mach disk. The two-component velocity field data revealed that the excitation pulse also caused a perturbation to the jet-shear layer and induced the formation of vortices that convect downstream.

A Study of Cycle-to-Cycle Variations and the Influence of Charge Motion Control on In-Cylinder Flow in an IC Engine

An experimental study is performed to investigate the cycle-to-cycle variations and the influence of charge motion control on in-cylinder flow measurement inside an internal combustion engine assembly. Molecular tagging velocimetry (MTV) is used to obtain the multiple point measurement of the instantaneous velocity field. MTV is a molecular counterpart of particle-based techniques, and it eliminates the use of seed particles. A two-component velocity field is obtained at various crank angle degrees for tumble and swirl measurement planes inside an optical engine assembly (1500 rpm and 2500 rpm engine speeds). Effects of charge motion control are studied considering different cases of: (i) charge motion control valve (CMCV) deactivated and (ii) CMCV activated. Both the measurement planes are used in each case to study the cycle-to-cycle variability inside an engine cylinder. Probability density functions of the normalized circulation are calculated from the instantaneous planar velocity to quantify the cycle-to-cycle variations of in-cylinder flows. In addition, the turbulent kinetic energy of flow is calculated and compared with the results of the probability density function. Different geometries of CMCV produce different effects on the in-cylinder flow field. It is found that the charge motion control used in this study has a profound effect on cycle-to-cycle variations during the intake and early compression; however, its influence reduces during the late compression. Therefore, it can be assumed that CMCV enhances the fuel-air mixing more than the flame speed.

Study on the characteristics of turbulent drag-reducing channel flow by particle image velocimetry combining with proper orthogonal decomposition analysis

Turbulent drag reduction of 30 ppm cetyltrimethyl ammonium chloride (CTAC) solution flow in a channel was investigated with particle image velocimetry (PIV) combining with proper orthogonal decomposition (POD). Measurements were made at inlet fluid temperature of 304 K and at Reynolds number 2.5×104 (based on the channel height, bulk velocity, and solvent viscosity) for both water and CTAC solution flows with 70.0% drag reduction rate. The two-component velocity fields in the streamwise-wall normal plane were recorded by PIV. In order to study the characteristics of turbulent drag-reducing channel flow, POD was performed to identify the near-wall coherent structures based on PIV-measured data. POD is a powerful low-dimensional analysis tool that can be used to identify coherent structures embedded in the turbulent shear flow. We mainly studied a comparison between the first dominant POD eigenmodes of water and drag-reducing CTAC solution flows. Coherent structures were seen as the sum of several eigenmodes that possess a dominant energy of the flow, say 90%. It was obtained that the amount of eigenmodes required for capturing the coherent structures was 233 and 195 for water and CTAC solution flows, respectively, which means the decrease in the complexity in CTAC solution flow. Based on the analysis of POD eigenmodes of water and CTAC solution flows, we captured the processes that can reflect the ejection motion of low-speed fluid from the wall and sweep motion of high-speed fluid toward the wall associating with turbulent bursting events. The results showed that CTAC additives can inhibit the turbulent bursting processes (both strength and occurrence frequency), resulting in a great decrease in turbulent contribution to frictional drag and drag reduction, which is sufficient to understand deeply the mechanism of turbulent drag reduction.

On turbulent entrainment and dissipation in dilute polymer solutions

We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions (25 and 50 wppm polyethylene oxide). The flow is forced by a planar grid that oscillates vertically with stroke S and frequency f in a square container of initially still fluid. Two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved particle image velocimetry. After the forcing is initiated, a turbulent layer develops that is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/nonturbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid until the fluid in the whole container is in turbulent motion. From the comparison of the experiments in clear water and polymer solutions we conclude: (i) Polymer additives modify the large scale shape of the TNTI. (ii) Both, in water and in the polymer solution the mean depth of the turbulent layer, H(t), follows the theoretical prediction for Newtonian fluids H(t)∝Kt, where K∝S2f is the “grid action.” (iii) We find a larger grid action for dilute polymer solutions than for water. As a consequence, the turbulent kinetic energy of the flow increases and the rate of energy input becomes higher. (iv) The entrainment rate β=ve/vrms (where ve=dH/dt is the interface propagation velocity and vrms is the root mean square of the vertical velocity) is lower for polymers (βp≈0.7) than for water (βw≈0.8). The measured values for β are in good agreement with similarity arguments, from which we estimate that in our experiment about 28% of the input energy is dissipated by polymers.

Three-dimensional two-component velocity measurement of the flow field induced by the Vorticella picta microorganism using a confocal microparticle image velocimetry technique

Understanding the biological feeding strategy and characteristics of a microorganism as an actuator requires the detailed and quantitative measurement of flow velocity and flow rate induced by the microorganism. Although some velocimetry methods have been applied to examine the flow, the measured dimensions were limited to at most two-dimensional two-component measurements. Here we have developed a method to measure three-dimensional two-component flow velocity fields generated by the microorganism Vorticella picta using a piezoscanner and a confocal microscope. We obtained the two-component velocities of the flow field in a two-dimensional plane denoted as the XY plane, with an observation area of 455x341 mum(2) and the resolution of 9.09 mum per each velocity vector by a confocal microparticle image velocimetry technique. The measurement of the flow field at each height took 37.5 ms, and it was repeated in 16 planes with a 2.50 mum separation in the Z direction. We reconstructed the three-dimensional two-component flow velocity field. From the reconstructed data, the flow velocity field [u((x,y,z)),v((x,y,z))] in an arbitrary plane can be visualized. The flow rates through YZ and ZX planes were also calculated. During feeding, we examined a suction flow to the mouth of the Vorticella picta and measured it to be to 300 pls.

Control of the Shear Layer Above a Supersonic Cavity Using Energy Deposition

An experimental study was conducted to investigate the effectiveness of pulsed energy deposition as a means of active flow control for the shear layer above a supersonic cavity in the open configuration. The excitation pulse was generated with a Q-switched Nd:YAG laser and was applied as a spanwise oriented line along the leading edge of a cavity. The study was conducted at a freestream Mach number of 1.4 and for a cavity length-to-depth ratio of 5.29. The flowfield was analyzed over a range of delay times from the excitation laser pulse using schlieren photography and particle image velocimetry. Analysis of phase-averaged schlieren images suggested the formation and growth of a coherent large-scale structure (consisting of two adjoining vortices) in the wake of the generated disturbance. This result was confirmed through two-component velocity field data obtained from particle image velocimetry measurements. The velocity information was also used to determine the instantaneous convective velocity and define characteristic scales for the large-scale structure.