Full Velocity Gradient Tensor Research Articles

Measurements Of The Energy Dissipation Rate In Homogeneous Turbulence Using Dense 3D Lagrangian Particle Tracking And FlowFit

We present measurements of the full velocity gradient tensor and all volumetric dissipation rate elements based on dense fields of fluid particle trajectories in homogeneous turbulence at Re_λ~270 and ~370 in a Kármán flow between two counter-rotating disks with impellers. Applying the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) algorithm, we are able to instantaneously track up to 80.000 particles in a volume of 40 x 40 x 15 mm³. The mean interparticle distance is lower than 7 Kolmogorov lengths for the Re_λ ~270 case. A data assimilation scheme (FlowFit) with continuity and Navier-Stokes- constraints is used to interpolate the scattered velocity and acceleration data by a continuous 3D B-Spline representation, enabling to recover (locally) the smallest flow scales. In the presentation, we show Lagrangian velocity and acceleration statistics, as well as the Eulerian counterparts on velocity gradients and pressure fields. We compute the energy dissipation rate directly by making use of quadruples of particle trajectories in close proximity (r < 3η) and compare it to indirect approaches using second-order velocity- and velocityacceleration structure functions in the inertial subrange.

Characteristics of a Single Sensor Fiber-Coupled Three-Dimensional Particle Image Velocimetry for Reacting Flow-Fields

Abstract Tomographic particle image velocimetry (Tomo-PIV) has become a standard tool for capturing a three-dimensional (3D) velocity fields in nonreacting flows. However, the diagnostic approach can become costly and challenging to implement when extended to applications which require high-speed cameras. This limitation has led to the use of fiber wound bundles to allow for multiple views to be captured on a single camera sensor. Additionally, employing this diagnostic approach on reacting flow-fields becomes more complex as the introduction of the flame causes additional luminosity and optical distortion which impacts the particle field reconstruction. This work seeks to validate and determine the limitations when utilizing a single sensor fiber-coupled approach for capturing Tomo-PIV data on a reacting flow-field. A premixed propane (C3H8) and air Bunsen burner flame is utilized to examine if the single sensor approach can meet the parameters for acceptable reconstruction based on previous research. The resulting velocity fields are then compared to a traditional PIV measurement to assess the deviation of the single sensor approach from a standard velocimetry measurement approach. It is demonstrated that there is strong agreement between the velocity and vorticity for the average flow-fields; however, when comparing the Reynolds shear stresses, a significant deviation is revealed. The deviation is attributed to strong velocity fluctuations occurring within the instantaneous Tomo-PIV data, which creates a significant divergence between the measurement techniques on an instantaneous basis. This demonstrates that while the approach can obtain reliable velocity and vorticity statistics, there are significant limitations in calculating second-order turbulence statistics. Thus, revealing that there is a tradeoff between the ability to extract the full velocity gradient tensor and the extent of the turbulence-related analysis which can be reliably performed.

Dual-plane stereo-astigmatism: a novel method to determine the full velocity gradient tensor in planar domain

A novel approach, which utilizes astigmatism-based depth codification and discrete dual-plane illumination, is developed to provide information on the full velocity-gradient tensor in pair of planar domains by means of stereoscopic particle image velocimetry (stereo-PIV). The technique is accordingly referred to as dual-plane stereo-astigmatism (DPSA). In contrast to conventional stereo-PIV, DPSA provides the determination of the desired out-of-plane gradient. The principle of the DPSA approach relies on the joint recording of two, consecutive, planar measurement domains and the subsequent allocation of particles based on their particle image shapes. For the identification of particles, a correlation-based particle identification approach (CPI), which addresses non-overlapping particles, is introduced. With regard to dense particle fields, a method for the iterative particle reconstruction (IPR) is adapted for DPSA. For displacement analysis, a modified PIV evaluation strategy is introduced, which utilizes derived information of particle locations. The DPSA approach is tested experimentally and synthetically by applying it to spray-induced flow measurement and synthetic images generated from DNS data of a turbulent boundary flow. Separate planar velocity fields are obtained by means of PIV and PTV evaluation. A performance analysis is carried out to assess the influence of noise, particle density and particle image size on the procedure of particle identification and allocation. The CPI technique provides adequate results for low to medium particle densities and further features a high robustness regarding particle identification with respect to background noise, optical aberrations and non-uniform particle images. The adapted IPR method, on the other hand, shows viable results for particle densities of up to 0.1 ppp.

Pressure evaluation of spray-induced flow in the framework of a statistical approach based on URANS and ensemble averaging

Using a statistical approach based on the unsteady Reynolds-averaged Navier–Stokes equations (URANS) and ensemble averaging, pressure evaluation of spray-induced flow is conducted by means of stereo-particle image velocimetry. The method allows the determination of the full velocity gradient tensor in order to characterize the governing equations. The spray-induced flow of a two-hole gasoline direct injection (GDI) research sample is investigated at 100 bar injection pressure, 1 bar ambient gas pressure, 25 °C fuel and ambient gas temperature. Low- and high-pressure regions are observed representing entrainment, displacement and recirculation flow. In reference to the ambient pressure, the mean pressure field indicates small pressure differences in the order of 0.1 mbar. For the assessment of pressure evaluation, a comparative measurement with a pressure sensor is carried out, which shows good agreement of the temporal pressure course in the intermediate spray region. The propagation of instantaneous velocity uncertainties to the pressure field indicates low pressure uncertainties for an ensemble average of 50 measurement samples. As a result of scale analysis, the pressure gradient is mainly described by the local acceleration, whereas the contribution of convective acceleration and Reynolds stresses focuses in the spray proximity. The analysis shows negligible effects of viscosity and gravity. The spray-induced flow is regarded as incompressible in case of low mass and heat transfer. The observations justify a simplification of the governing equations minimizing measurement and computational expense.

Numerical and experimental investigation of a wire-net compact heat exchanger performance for high-temperature applications

The objective of this paper is to have a detailed numerical investigation of the microchannel performance of a complex wire-net compact heat exchanger and investigate its collector performance experimentally for a micro combined heat and power system. Localised turbulence can enhance heat exchanger performance. Besides, this will increase the pressure losses also. In microchannels, shifting the Reynolds critical to smaller Reynolds number using perturbators will control the pressure losses and enhance the microchannel thermal efficiency. In this paper, we consider microchannels with wire-net perturbators. The wire-net micro heat exchanger is assembled as a stack of counterflow flow passages with optimised thickness separated by thin foils. A metallic wire-net mesh is inserted in the flow passages to provide the required stiffness and enhance the microchannel efficiency.A parametric study was conducted on various heat exchanger parameters to optimise the heat exchanger size, thermal effectiveness and pressure losses for a micro-CHP system. Besides, a detailed investigation of the wire-net flow physics was made using a higher order Reynolds stress turbulence model to obtain the full velocity gradient tensor. This could detail the effect of anisotropic flow physics in the isotropic wire-net microchannels. Lambda 2 criterion was implemented to investigate the flow mixing of the centrally convected non-disturbed mass flow. Furthermore, the analysis of the turbulence production terms provided a deeper insight into flow attachment and detachment near the wire-net intersections. The heat exchanger was experimentally tested, and it was found that the collector pressure losses are not sufficiently low as compared to the microchannel pressure losses. The microchannel conjugate heat transfer thermal effectiveness is in good agreement with the overall experimental efficiency.

Quad-plane stereoscopic PIV for fine-scale structure measurements in turbulence

The fine-scale structure in turbulence is investigated by quad-plane stereoscopic particle image velocimetry (QPSPIV). The quad-plane consists of two each of different polarizations and wavelengths, and it provides three velocity components at four independent parallel planes. Measurements have been undertaken in the developed region of a turbulent round jet with a spatial resolution sufficient to capture the small-scale structures. The advantage of the QPSPIV is presented in terms of the spectral response in the evaluation of the out-of-plane velocity gradient. The full velocity gradient tensor is computed with a fourth-order finite difference scheme in the out-of-plane direction as well as the in-plane directions. The turbulence quantities, such as the vorticity components, the energy dissipation rate and the second and third invariants of the velocity gradient tensor, are computed according to their faithful definitions. The coherent fine-scale eddies are extracted from the present QPSPIV data. The probability density functions of the diameter and the maximum azimuthal velocity of the extracted eddies exhibit their peak at approximately $$8\eta $$ and $$1.5u_k$$ , respectively, where $$\eta $$ and $$u_k$$ are the Kolmogorov length and velocity. These values agree well with the data in the literature. The phase-averaged distributions of turbulence quantities around the coherent fine-scale eddy indicate an apparent elliptic feature around the axis. Furthermore, the state of the strain rate exerting the eddy is quantified from the phase-averaged distributions of eigenvalues of the strain rate tensor and the alignment of the corresponding eigenvectors against the axis. The present study gives a solid experimental support of the coherent fine-scale structures in turbulence, and the technique can be applied to various flow fields and to the higher Reynolds number condition.

Breakup of Finite-Size Colloidal Aggregates in Turbulent Flow Investigated by Three-Dimensional (3D) Particle Tracking Velocimetry.

Aggregates grown in mild shear flow are released, one at a time, into homogeneous isotropic turbulence, where their motion and intermittent breakup is recorded by three-dimensional particle tracking velocimetry (3D-PTV). The aggregates have an open structure with a fractal dimension of ∼2.2, and their size is 1.4 ± 0.4 mm, which is large, compared to the Kolmogorov length scale (η = 0.15 mm). 3D-PTV of flow tracers allows for the simultaneous measurement of aggregate trajectories and the full velocity gradient tensor along their pathlines, which enables us to access the Lagrangian stress history of individual breakup events. From this data, we found no consistent pattern that relates breakup to the local flow properties at the point of breakup. Also, the correlation between the aggregate size and both shear stress and normal stress at the location of breakage is found to be weaker, when compared with the correlation between size and drag stress. The analysis suggests that the aggregates are mostly broken due to the accumulation of the drag stress over a time lag on the order of the Kolmogorov time scale. This finding is explained by the fact that the aggregates are large, which gives their motion inertia and increases the time for stress propagation inside the aggregate. Furthermore, it is found that the scaling of the largest fragment and the accumulated stress at breakup follows an earlier established power law, i.e., dfrag ∼ σ(-0.6) obtained from laminar nozzle experiments. This indicates that, despite the large size and the different type of hydrodynamic stress, the microscopic mechanism causing breakup is consistent over a wide range of aggregate size and stress magnitude.

Comparison of vortex identification criteria for planar velocity fields in wall turbulence

This study derives and compares vortex identification methods for detecting vortices in planar velocity fields. Two-dimensional (2D) forms of the commonly used Δ, Q, λci, and λ2 criteria are derived in detail based on the 2D counterpart of the full velocity gradient tensor. These four criteria are compared mathematically and experimentally in the case of using zero thresholds. The results show that while all methods are capable of extracting strong vortices, their efficiencies in identifying weaker vortices are not necessarily the same. The Δ and λci criteria impose the least requirements on the identified structures and extract the most number of vortices, and the λ2 criterion is the most restrictive one and tends to discard the weakest vortices. However, non-zero thresholds are generally necessary for applying vortex identification criteria in real turbulent flows, and normalizing the vortex indicators with their root mean squares is needed to enable the selection of universal threshold for vortices residing at different wall-normal positions in wall turbulence. The introduction of threshold makes the four vortex identification criteria equally efficacious, and equivalent thresholds are proposed to facilitate quantitative comparison of results based on different criteria in wall turbulence.

The kinematics of the reduced velocity gradient tensor in a fully developed turbulent free shear flow

AbstractThis paper examines the kinematic behaviour of the reduced velocity gradient tensor (VGT),$\tilde{\unicode[STIX]{x1D608}}_{ij}$, which is defined as a$2\times 2$block, from a single interrogation plane, of the full VGT$\unicode[STIX]{x1D608}_{ij}=\partial u_{i}/\partial x_{j}$. Direct numerical simulation data from the fully developed turbulent region of a nominally two-dimensional mixing layer are used in order to examine the extent to which information on the full VGT can be derived from the reduced VGT. It is shown that the reduced VGT is able to reveal significantly more information about regions of the flow in which strain rate is dominant over rotation. It is thus possible to use the assumptions of homogeneity and isotropy to place bounds on the first two statistical moments (and their covariance) of the eigenvalues of the reduced strain-rate tensor (the symmetric part of the reduced VGT) which in turn relate to the turbulent strain rates. These bounds are shown to be dependent upon the kurtosis of$\partial u_{1}/\partial x_{1}$and another variable defined from the constituents of the reduced VGT. The kurtosis is observed to be minimised on the centreline of the mixing layer and thus tighter bounds are possible at the centre of the mixing layer than at the periphery. Nevertheless, these bounds are observed to hold for the entirety of the mixing layer, despite departures from local isotropy. The interrogation plane from which the reduced VGT is formed is observed not to affect the joint probability density functions (p.d.f.s) between the strain-rate eigenvalues and the reduced strain-rate eigenvalues despite the fact that this shear flow has a significant mean shear in the cross-stream direction. Further, it is found that the projection of the eigenframe of the strain-rate tensor onto the interrogation plane of the reduced VGT is also independent of the plane that is chosen, validating the approach of bounding the full VGT using the assumption of local isotropy.

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

AbstractWe present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate from experimental results agree well with numerical findings. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (jPDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery’s equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the jPDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

A combined scanning PTV/LIF technique to simultaneously measure the full velocity gradient tensor and the 3D density field

We present a newly developed combined scanning particle tracking velocimetry (SPTV) and scanning laser-induced fluorescence (SLIF) technique. The new method allows for the first time to measure the full velocity gradient tensor and the three-dimensional density field simultaneously in a refractive index matched environment. The data thus obtained will be valuable in investigating the interaction between turbulence, i.e. the dynamics of vorticity and strain, and the density field. In this study, we describe the implementation of the measurement system in detail. As a showcase, the new technique is applied to a gravity current flow and the measured data are validated by imposing various checks. Further results are presented that illustrate the capability of the SPTV/SLIF technique in the investigation of interface dynamics.

Statistics of vertical vorticity, divergence, and strain in a developed submesoscale turbulence field

AbstractA detailed view of upper ocean vorticity, divergence, and strain statistics was obtained by a two‐vessel survey in the North Atlantic Mode Water region in winter 2012. Synchronous Acoustic Doppler Current Profiler sampling provided the first in situ estimates of the full velocity gradient tensor at O(1 km) scale without the usual mix of spatial and temporal aliasing. The observed vorticity distribution in the mixed layer was markedly asymmetric (skewness 2.5), with sparse strands of strong cyclonic vorticity embedded in a weak, predominantly anticyclonic background. Skewness of the vorticity distribution decreased linearly with depth, disappearing completely in the pycnocline. Statistics of divergence and strain rate generally followed the normal and χ distributions, respectively. These observations confirm a high‐resolution numerical model prediction for the structure of the active submesoscale turbulence field in this area.