Tomographic Particle Image Velocimetry Research Articles

Shedding-scheme transition of hemisphere near wake dependent on Reynolds number

The shedding-scheme transition of hemispherical wake is investigated with time-resolved tomographic particle image velocimetry. Experiments are carried out with Reynolds numbers based on the hemisphere radius R in the range of Rer=924–2315, crossing the critical value of Rer≈2000. The variation of the hemispherical wake across the critical Reynolds number is carefully studied, and a detailed mechanism of the shedding-scheme transition is explored. A singular-shedding pattern of hairpin vortices at a low Rer is replaced by a pairing-shedding pattern at a moderate Rer, and finally, a less ordered wake and an unstable shedding pattern are observed at Rer > 2000. The onset of the pairing-shedding pattern is due to a streamwise modulation caused by the varicose modes, which is related to the Kelvin–Helmholtz (K–H) instability. Consequently, the pseudo-periodicity induced by the K–H instability is observed in the wake. When Rer > 2000, the stronger sinuous modulation intensifies interactions among the hairpin vortices, leading to frequent absorption and annihilation of those coherent structures, which further makes the dominant frequency of main hairpin vortices halved downstream.

Experimental Study On Anastomotic Hemodynamics Using Tomographic Particle Image Velocimetry

Fluid mechanics is an important factor to the failure of the graft anastomosis surgery. In order to better understand the mechanism of restenosis and graft failure of the anastomosis from the perspective of fluid mechanics, an end-toside silicone anastomosis model with 45° anastomotic angle was used for research. The anastomosis model was connected to a continuous flow loop. where the flow rate can be adjusted during the experiment to simulate several conditions. The tomographic particle image velocimetry (TPIV) was applied to obtain the internal three-dimensional and three-component (3D-3C) flow field. The hemodynamics inside the anastomosis model was quantitatively analyzed based on the averaged 3D-3C flow field. The results present that there are phenomena such as recirculation, spiral flow, flow stagnation, and large vortex structures inside the anastomotic flow field. The oscillation of the recirculation zone size and flow stagnation point indicate the fluid stimulation to the endothelial cells. Also, the double spiral vortex structure could cause high local shear stress, which in turn cause trauma to the red blood cells and lead to local coagulation. Besides, thanks to the 3D-3C flow field, the wall shear stress (WSS) on the entire model wall was obtained, which enables us to predict the mechanical influence to the intimal hyperplasia. The local low WSS was found near the graft toe and recirculation regions, while the local high WSS was found on the host vessel bottom where the jet directly impinges. The abnormal flow phenomena can explain the high-risk regions in the anastomosis, where the stenosis and intimal hyperplasia are prone to appear. The 3D-3C flow field based on the in vitro experiment can strengthen the understanding of the anastomotic restenosis pathology and provide further reference for the surgery improvement.

Experimental Study On Anastomotic Hemodynamics Using Tomographic Particle Image Velocimetry

Fluid mechanics is an important factor to the failure of the graft anastomosis surgery. In order to better understand the mechanism of restenosis and graft failure of the anastomosis from the perspective of fluid mechanics, an end-toside silicone anastomosis model with 45° anastomotic angle was used for research. The anastomosis model was connected to a continuous flow loop. where the flow rate can be adjusted during the experiment to simulate several conditions. The tomographic particle image velocimetry (TPIV) was applied to obtain the internal three-dimensional and three-component (3D-3C) flow field. The hemodynamics inside the anastomosis model was quantitatively analyzed based on the averaged 3D-3C flow field. The results present that there are phenomena such as recirculation, spiral flow, flow stagnation, and large vortex structures inside the anastomotic flow field. The oscillation of the recirculation zone size and flow stagnation point indicate the fluid stimulation to the endothelial cells. Also, the double spiral vortex structure could cause high local shear stress, which in turn cause trauma to the red blood cells and lead to local coagulation. Besides, thanks to the 3D-3C flow field, the wall shear stress (WSS) on the entire model wall was obtained, which enables us to predict the mechanical influence to the intimal hyperplasia. The local low WSS was found near the graft toe and recirculation regions, while the local high WSS was found on the host vessel bottom where the jet directly impinges. The abnormal flow phenomena can explain the high-risk regions in the anastomosis, where the stenosis and intimal hyperplasia are prone to appear. The 3D-3C flow field based on the in vitro experiment can strengthen the understanding of the anastomotic restenosis pathology and provide further reference for the surgery improvement.

Experimental Study On Bubble Pairs And Induced Flow Fields Using Tomographic Particle Image Velocimetry

Gas-liquid two-phase flows, such as bubbly flows, are widely used across various engineering and military applications due to their distinctive fluid dynamics. This study utilizes advanced imaging techniques, including shadowgraphy and laser-induced fluorescence tomographic particle image velocimetry (LIF-TPIV), to provide a quantitative analysis of bubble motions and the resulting flow fields. We systematically investigate the effects of orifice distances (s) set at 10, 15, 20, and 25 mm to assess the impact of spacing on bubble behavior and interactions. Our findings indicate that at orifice distances of 20 mm or less, the proximity of bubbles facilitates interactions, promoting dynamic bubble behaviors. In contrast, at distances greater than 25 mm, interactions become markedly weaker, leading to increased separation between bubbles during their free oscillation stages. This weak interaction directly influences the characteristics of bubble-induced flow fields. As orifice spacing increases, there is a noticeable decrease in the velocity of the flow field between bubbles, particularly noticeable at spacings of 20 mm and above. At these larger spacings, a low-velocity zone develops between the bubbles at higher heights, which, according to Bernoulli's principle, corresponds to a high-pressure area. This high pressure contributes to a reduction in bubble volume with increasing orifice spacing. Furthermore, the intensity of wake vortices between two bubbles is observed to be highest at the smallest spacing of 10 mm, closely resembling the flow structure characteristic of a single rising bubble. For spacings of 15 and 20 mm, the induced flow fields of the bubbles continue to interact significantly. However, at a spacing of 25 mm, the flow fields appear to function independently, suggesting a threshold beyond which bubble interactions stop to significantly affect their surrounding fluid environments. These findings are helpful for comprehending the two-phase flow dynamics, particularly in multi-orifices bubbly flow.

Experimental Study On Bubble Pairs And Induced Flow Fields Using Tomographic Particle Image Velocimetry

Gas-liquid two-phase flows, such as bubbly flows, are widely used across various engineering and military applications due to their distinctive fluid dynamics. This study utilizes advanced imaging techniques, including shadowgraphy and laser-induced fluorescence tomographic particle image velocimetry (LIF-TPIV), to provide a quantitative analysis of bubble motions and the resulting flow fields. We systematically investigate the effects of orifice distances (s) set at 10, 15, 20, and 25 mm to assess the impact of spacing on bubble behavior and interactions. Our findings indicate that at orifice distances of 20 mm or less, the proximity of bubbles facilitates interactions, promoting dynamic bubble behaviors. In contrast, at distances greater than 25 mm, interactions become markedly weaker, leading to increased separation between bubbles during their free oscillation stages. This weak interaction directly influences the characteristics of bubble-induced flow fields. As orifice spacing increases, there is a noticeable decrease in the velocity of the flow field between bubbles, particularly noticeable at spacings of 20 mm and above. At these larger spacings, a low-velocity zone develops between the bubbles at higher heights, which, according to Bernoulli's principle, corresponds to a high-pressure area. This high pressure contributes to a reduction in bubble volume with increasing orifice spacing. Furthermore, the intensity of wake vortices between two bubbles is observed to be highest at the smallest spacing of 10 mm, closely resembling the flow structure characteristic of a single rising bubble. For spacings of 15 and 20 mm, the induced flow fields of the bubbles continue to interact significantly. However, at a spacing of 25 mm, the flow fields appear to function independently, suggesting a threshold beyond which bubble interactions stop to significantly affect their surrounding fluid environments. These findings are helpful for comprehending the two-phase flow dynamics, particularly in multi-orifices bubbly flow.

Analysis of coherent structures over interacting barchan dunes based on tomographic particle image velocimetry

The influence of barchan dune interaction upon unsteady flow separation and wake dynamics around the fixed-bed downstream barchan dune (DBD) model are experimentally investigated at a Reynolds number of 2640 based on the tomographic particle image velocimetry (PIV) system. The time-averaged statistics including the mean velocities, recirculation area, vortex spatial topology, Reynolds stress, and turbulent kinetic energy were used to characterize the flow field and large-scale anisotropy. It was found that arch-shaped vortex “chains” with strong spanwise coherence shedding from isolated barchan crestline populate the whole wake region, while elongated rod-shaped vortex structures with strong streamwise coherence induced by the up-downwash flow around the DBD were found to fill the whole measurement range, which is closely related to “sheltering” effect on the incoming flow acting at DBD due to the presence of upstream barchan dune (UBD). Additionally, in order to study the complex dynamic features of these predominated vortex structure transformations, time-resolved planar particle image velocimetry was applied. This technique allows for providing complementary insights into the temporal behavior of the unsteady coherent flow structures populating the wake field in different experimental configurations. It was found that the basic unsteady flapping motion, vortex roll-up, and complex vortex interactions including vortex pairing, merging, and breaking up can all be analyzed by dividing into certain scales with ease in a combination wavelet and Lagrangian framework.

Reconstruction of particle distribution for tomographic particle image velocimetry based on unsupervised learning method

The development of deep learning has inspired some new methods to solve the 3D reconstruction problem for Tomographic Particle Image Velocimetry (Tomo-PIV). However, the supervised learning method requires a large number of data with ground truth as training information, which is very difficult to gather from experiments. Although synthetic datasets can be used as alternatives, they are still not exactly the same with the real-world experimental data. In this paper, an Unsupervised Reconstruction Technique based on U-net (UnRTU) is proposed to reconstruct volume particle distribution explicitly. Instead of using ground truth data, a projection function is used as an unsupervised loss function for network training to reconstruct particle distribution. The UnRTU was compared with some traditional algebraic reconstruction algorithms and supervised learning method using synthetic data under different particle density and noise level. The results indicate that UnRTU outperforms these traditional approaches in both reconstruction quality and noise robustness, and is comparable to the supervised learning methods AI-PR. For experimental tests, particles dispersed in cured epoxy resin are moved by an electric rail with a certain speed to obtain the ground truth data of particle velocity. Compared with other algorithms, the reconstructed particle distribution by UnRTU has the best reconstruction fidelity. And the accuracy of the 3D velocity field estimated by UnRTU is 12.9% higher than that from the traditional MLOS-MART algorithm. It demonstrates significant potential and advantages for UnRTU in 3D reconstruction of particle distribution. Finally, UnRTU was successfully applied to the high-speed planar cascade airflow field, demonstrating its applicability for measuring complex fluid flow fields at higher particle density.

Assessment of Multi-Physical Fields Reconstruction Approaches in Three-Dimensional Supersonic Flow with Shocks

The paper evaluates the application of several multi-physical fields reconstruction approaches based on the Tomographic Particle Image Velocimetry (PIV) in three-dimensional supersonic flows with shock waves, including the pressure, temperature, and density. The MacCormack method and the Flux Vector Splitting method with outstanding performance in two-dimensional supersonic flow are extended into three-dimensional forms. The conventional Poisson method is also considered because of its widespread application and high accuracy in subsonic and transonic flow. All of these approaches are established by the conservative Navier-Stokes equations and solved by the time-marching iteration process, combined with the perfect gas law and adiabatic flow assumption. The performances are evaluated by numerical velocimetry data. To simulate the typical three-dimensional features, the cases of uniform freestream at Mach 0.78 and 3 past a cone with a 20° half-angle are selected to obtain a sufficient spanwise velocity component. The results confirm the feasibility of the PIV-based reconstruction methods in the conical flow field. The conventional Poisson method performs well only in the subsonic case while the Flux Vector Splitting method has a better performance in supersonic flow, including higher accuracy, stability, and efficiency, with a low-level root-mean-square error of 0.449% and local maximum relative error of 1%.

Investigating three-dimensional vortex evolution in centrifugal pump under rotating stall conditions using tomographic particle image velocimetry

A rotating stall in centrifugal pumps commonly occurs under off-design operations, which is a detrimental phenomenon leading to flow instabilities, pressure fluctuations, and reduced performance. A time-resolved non-intrusive three-dimensional (3D) flow visualization method is developed for investigating complex vortex structures in centrifugal pumps based on Omega vortex identification and tomographic particle image velocimetry (tomo-PIV). A special-made centrifugal pump prototype was developed with acrylic glass allowing for optical access. This method enables both qualitative and quantitative analysis of high spatiotemporal resolution on flow behaviors and dynamics under various stall conditions. The ultra-high sampling frequency realized over 40 time-consecutive observations per revolution under 0.2 Qd, 0.4 Qd, 0.6 Qd, and 0.8 Qd. It captures the instantaneous evolution of vortex structures that undergoes a growth–breakup transition within 7–9 ms. The rotating stall mechanism is revealed experimentally from the evolution of the vortex structure. Our analysis shows the tomo-PIV's additional velocity component aids in understanding the 3D characteristics of the stall. A substantial region of reverse flow in the z-axis direction is observed under 0.2 Qd. Vortex structures are more prone to blockage at the impeller inlet, exacerbating the stall phenomenon. As the flow rate increases, the velocity distributions across different layers exhibit a laminar characteristic with a more uniform profile. The vortex structures extend radially and migrate toward the outlet. The evolutions of the stall vortex, wake vortex, and inlet vortex share the same dominant frequency components (4.75fn and 5.25fn), but the flow rate affects the proportion of different frequency components.

Wake effect on bubble–particle collision: An experimental study using 4D particle tracking velocimetry

The analysis of particle–bubble collisions in turbulent flow is a fundamental problem of high technological relevance, e.g., for the separation of valuable mineral particles by froth flotation. This relevance contrasts with an apparent lack of experimental data and understanding of this collision process. To this end, a periodic bubble chain was used to study the collision of millimeter-sized bubbles with polystyrene particles. The collision process between these entities was measured using 4D particle tracking velocimetry (PTV). By analyzing the collision data as a function of the polar angle along the bubble surface, we show that the collision took place not only at the leading edge but also at the trailing edge of the bubble. To understand the underlying mechanisms of the trailing edge collision, the flow field around a rising bubble chain was measured with Tomographic Particle Image Velocimetry (TPIV). The vortex formed in the bubble wake led to a velocity in the direction of the bubble surface that enabled trailing edge collisions. This effect is amplified by an increase in the turbulent kinetic energy and dissipation rate in the bubble wake. Overall, the investigation reveals different collision mechanisms and advances our understanding of the role of the wake in the bubble–particle collision.

Experimental study on hemodynamics of an end-to-side anastomosis

A three-dimensional and three-component velocity measurement on the flow field in a 45° end-to-side anastomosis model is conducted to investigate the hemodynamics, which is an important factor to the intimal hyperplasia formation and graft failure after surgery. Thanks to the advanced volumetric measurement technology of tomographic particle image velocimetry, the recirculation zone, low-speed region, and the spiral flow structures can be visualized. As a result, the flow field of three cases with the local maximum velocity of 0.15, 0.8, and 1.4 m/s are visible and the inlet velocity profile tends to be skewed as the flow rate increases. The mean vorticity contours indicate that the positive vortex center rotates 6.47°, 50.23°, and 90.4° and the negative vortex center rotates 20.44°, 15.73°, and 68.47°, respectively, in three cases. The instantaneous vortex structures identified by the λci criterion demonstrate two large-scale vortex structures in the distal section. The two vortices have the tendency to intertwine while one of them decays earlier. The wall shear stress (WSS) distributions on the entire model with the local maximum of 0.8, 5.8, and 13.8 Pa in three cases have been quantitatively achieved. The abnormal WSS and WSS gradient can help localize risk areas and understand the intimal hyperplasia formation. A detailed illustration of hemodynamics inside the 45° end-to-side anastomosis model has been provided, which demonstrates more comprehensive large-scale flow structures and abnormal WSS regions. Combined with the information of flow structures and WSS distribution, the understanding of the hemodynamics in the anastomosis can be strengthened.

Three-dimensional particle image velocimetry measurement through three-dimensional U-Net neural network

This paper proposes a light field (LF) three-dimensional (3D) particle image velocimetry (PIV) method based on a digital refocused algorithm and 3D U-Net neural network for 3D three-component (3D-3C) velocity measurement. A digital refocused algorithm is used to generate a stack of LF-refocused images of tracer particles for establishing the 3D U-Net. The 3D U-Net is then used for the 3D particle field reconstruction. Based on a pair of 3D particle fields, the 3D-3C velocity field is obtained through a 3D cross correlation algorithm. Numerical simulations and experiments are conducted to analyze the accuracy and efficiency of the proposed method. The simulation results show that the elongation along the depth direction and the efficiency of the 3D particle field reconstruction are improved by the 3D U-Net. The 3D U-Net also provides a better correlation coefficient. The experimental results show that the reconstruction time of the proposed method is ∼220 s which is 10 times faster than the LF tomographic PIV. This further demonstrates that the proposed method improves the reconstruction efficiency without affecting the accuracy of velocity measurement.

A polynomial model with line-of-sight constraints for Lagrangian particle tracking under interface refraction

This paper introduces an improvement of the ‘shake-the-box (STB)’ (Schanz, Gesemann, and Schröder, Exp. Fluids 57.5, 2016) technique using the polynomial calibration model and the line-of-sight constraints (LOSC) to overcome the refractive interface issues in Lagrangian particle tracking (LPT) measurement. The method (named LOSC-LPT) draws inspiration from the two-plane polynomial camera calibration in tomographic particle image velocimetry (Worth, Nickels, Thesis, 2010) and the STB-based open-source Lagrangian particle tracking (OpenLPT) framework (Tan, Salibindla, Masuk, and Ni, Exp. Fluids 61.2, 2019). The LOSC-LPT introduces polynomial mapping functions into STB calibration in conditions involving gas–solid–liquid interfaces at container walls exhibiting large refractive index variations, which facilitates the realization of particle stereo matching, three-dimensional (3D) triangulation, iterative particle reconstruction, and further refinement of 3D particle position by shaking the LOS. Performance evaluation based on synthetic noise-free images with a particle image density of 0.05 particle per pixel in the presence of refractive interfaces demonstrates that LOSC-LPT can detect a higher number of particles and exhibits lower position uncertainty in the reconstructed particles, resulting in higher accuracy and robustness than that achieved with OpenLPT. In the application to an elliptical jet flow in an octagonal tank with refractive interfaces, the use of polynomial mapping results in smaller errors (mean calibration error <0.1 px) and thus more long trajectories identified by LOSC-LPT (13 000) compared with OpenLPT (4500) which uses the pinhole Tsai model (mean calibration error >1.0 px). Moreover, 3D flow-field reconstructions demonstrate that the LOSC-LPT framework can recover a more accurate 3D Eulerian flow field and capture more complete coherent structures in the flow, and thus holds great potential for widespread application in 3D experimental fluid measurements.

Tip effects on three-dimensional flow structures over low-aspect-ratio plates: mechanisms of spanwise fluid transport

Three-dimensional flows over low-aspect-ratio rectangular flat plates ( ${A{\kern-4pt}R} = 1.00$ – $1.50$ ) are investigated using tomographic and planar particle image velocimetry techniques. The chord-based Reynolds number is $5400$ , and the angle of attack is fixed at $6^\circ$ . This study reveals for the first time the interplay between spanwise fluid transport and downwash, both originating from the tip effects. Spanwise fluid transport promotes the formation and subsequent coherent development of leading-edge vortices, whereas downwash stabilizes the flow. Specifically, two mechanisms related to spanwise fluid transport are revealed. First, the spanwise fluid transport enhances the intensity of the reversed flow, promoting the shear layer roll-up and vortex shedding. Second, the near-wall spanwise flow interacts with the shed C-shape vortices, thereby strengthening the vortex heads. In particular, through these interactions, spanwise fluid transport can sustain the coherence of the C-shape vortices until the vortex heads split in a regular fashion. Consequently, the C-shape vortices are transformed into novel Þ-shape vortices for the plates of ${A{\kern-4pt}R} \leq 1.25$ , which supplements the previously discovered transformation from C-shape to M-shape vortices for larger ${A{\kern-4pt}R}$ plates. Downstream of this novel vortex-splitting transformation, two fundamental processes contribute to the formation of hairpin vortices. The above comprehensive understanding of complete vortex evolution routine provides valuable insights into the tip effects on the formation of three-dimensional flows over low- ${A{\kern-4pt}R}$ plates.

Generation of nearly homogeneous isotropic turbulence using a novel oscillating grid system

The creation and control of homogeneous isotropic turbulence in laboratory settings is of practical significance. In this paper, we propose a novel design for a turbulence generation apparatus driven by two pairs of oscillating grids, with the object of striking a balance between the stochastics of momentum injection and the flexibility of control of turbulent kinematic energy (TKE). To validate the performance of this system, tomographic particle image velocimetry measurements are conducted. Based on Reynolds decomposition, we characterize the secondary flow pattern and examine the impact of the mean velocity on the TKE transport. Analysis of one- and two-point statistics indicates that the generated turbulence exhibits reasonable approximations of homogeneity and isotropy. The TKE and the dissipation rate are linearly proportional to the grid oscillation frequency, with the Taylor-scale Reynolds number Reλ ranging from 47 to 154, suggesting a convenient control of turbulence with low-to-moderate intensity.

Maximizing wind farm power output with the helix approach: Experimental validation and wake analysis using tomographic particle image velocimetry

AbstractWind farm control can play a key role in reducing the negative impact of wakes on wind turbine power production. The helix approach is a recent innovation in the field of wind farm control, which employs individual blade pitch control to induce a helical velocity profile in a wind turbine wake. This forced meandering of the wake has turned out to be very effective for the recovery of the wake, increasing the power output of downstream turbines by a significant amount. This paper presents a wind tunnel study with two scaled wind turbine models of which the upstream turbine is operated with the helix approach. We used tomographic particle image velocimetry to study the dynamic behavior of the wake under the influence of the helix excitation. The measured flow fields confirm the wake recovery capabilities of the helix approach compared with normal operation. Additional emphasis is put on the effect of the helix approach on the breakdown of blade tip vortices, a process that plays an important role in re‐energizing the wake. Measurements indicate that the breakdown of tip vortices and the resulting destabilization of the wake are enhanced significantly with the helix approach. Finally, turbine measurements show that the helix approach was able to increase the combined power for this particular two‐turbine setup by as much as 15%.

Experiments of Lift-Bending Response on a Slender UAV Wing Structure with Control Surface under Extreme Flow Turbulence

The aeroelastic response of lightweight low-speed aircrafts with slender wings under extreme flow turbulence intensity is not well understood. Experiments on a commercial unmanned aerial vehicle (UAV) with a 3 m wingspan and aspect ratio of 13.6 were performed in a large open-return wind tunnel with extreme flow turbulence intensity of ≈10%. The wing bending displacement and the flow beneath the wing were measured by using laser-displacement sensors and tomographic particle image velocimetry (PIV) techniques, respectively. The unsteady lift produced by the wing was also measured by using a high-capacity load cell at an angle of attack of two degrees for three freestream velocities of 13.4 m/s, 17.9 m/s, and 26.8 m/s, representing the UAV’s stall speed, a speed approximately equal to the cruise speed, and a speed considerably higher than the cruise speed, respectively. It was found that a high flow turbulence intensity with large integral length scales relative to the wing chord plays a dominant role in the large unsteady lift and wing displacements measured. The power spectral density (PSD) of the wing structural vibration shows that flow shedding from the wing and the integral length scales have a significant impact on the overall power inherent in the bending vibration of the wing. Computations of the vorticity isosurfaces in the flow measurement volume surrounding the aileron reveal a striking observation: an aileron deflection of 10° becomes less effective in producing additional spanwise vorticity, which is proportional to circulation and lift at 26.8 m/s since the freestream already has elevated levels of vorticity. A paradigm shift in design is suggested for light aircraft structures with slender wings operating in highly turbulent flow, which is to employ multiple control surfaces in order to respond to this flow and mitigate large bending or torsion displacements and the probability of structural failure.

TPIV Experimental Investigation of Film Coolant-to-Mainstream Interaction From Shaped Cooling Holes With Various Inlet Geometries

Abstract In this investigation, multiple sets of time-averaged tomographic particle imaging velocimetry measurements are completed for laid-back, fan-shaped film cooling holes with “racetrack” shaped inlets. Traditional 10-10-10, laid-back, fan-shaped holes are inclined 30 deg to the mainstream flow on a flat plate. The inlet cross section varies from round to two elongated racetrack shapes. The cross-sectional area and the outlet-to-inlet area ratio for all the geometries are held constant. The flat plate is installed in a low-speed wind tunnel with a mainstream turbulence intensity of 8% and an average velocity of 21.6 m/s. The blowing ratios of the film jets range from 0.6 to 1.5 and the density ratio is 1. The Reynolds number of the cooling jet varies from 2600 to 8400. The characteristics of the resulting flowfield are coupled with the detailed film cooling effectiveness distributions. It can be noted from the results that the counter-rotating vortex pair generated by the 2:1 inlet is the closest to the surface and weakest in strength, likely caused by the minimum peak jet momentum of the three. The Reynolds stresses downstream of the 2:1 and 4:1 inlets are significantly lower than those downstream of the shaped hole with a round inlet. An inverse relation between volumetric turbulence accumulation (TA), and surface effectiveness (η), can be correlated for the blowing ratios considered. The turbulence accumulation term can thus be used to evaluate the performance of a film cooling hole design with flowfield data.

Four-dimensional variational data assimilation of a turbulent jet for super-temporal-resolution reconstruction

The super-temporal-resolution (STR) reconstruction of turbulent flows is an important data augmentation application for increasing the data reach in measurement techniques and understanding turbulence dynamics. This paper proposes a data assimilation (DA) strategy based on weak-constraint four-dimensional variation to conduct an STR reconstruction in a turbulent jet beyond the Nyquist limit from given low-sampling-rate observations. Highly resolved large-eddy simulation (LES) data are used to produce synthetic measurements, which are used as observations and for validation. A segregated assimilation procedure is realised to assimilate the initial condition, inflow boundary condition and model error separately. Different types of observational data are tested. The first type is down-sampled LES data containing many small-scale turbulence structures with or without synthetic noise. The DA results show that the temporal variation of the small-scale structures is well recovered even with noise in the observations. The spectra are resolved to a frequency approximately one order of magnitude higher than what can be captured within the Nyquist limit. The second type of observation is low-sampling-rate tomographic particle image velocimetry (tomo-PIV) data with or without the injection of small-scale structures. The modulation between the large-scale structures contained in the tomo-PIV fields and the small scales injected from the observations is improved. The resultant small scales in the STR reconstruction have the characteristics of authentic turbulence to a considerable extent. Additionally, DA yields much smaller errors in the prediction of particle positions when compared with the Wiener filter, demonstrating the great potential for Lagrangian particle tracking in measurement techniques.

Exploring multi-stability in three-dimensional viscoelastic flow around a free stagnation point

Fluid elements passing near a stagnation point experience finite strain rates over long persistence times, and thus accumulate large strains. By the numerical optimization of a microfluidic 6-arm cross-slot geometry, recent works have harnessed this flow type as a tool for performing uniaxial and biaxial extensional rheometry (Haward et al., 2023 [5,6]). Here we use the microfluidic ‘Optimized-shape Uniaxial and Biaxial Extensional Rheometer’ (OUBER) geometry to probe an elastic flow instability which is sensitive to the alignment of the extensional flow. A three-dimensional symmetry-breaking instability occurring for flow of a dilute polymer solution in the OUBER geometry is studied experimentally by leveraging tomographic particle image velocimetry. Above a critical Weissenberg number, flow in uniaxial extension undergoes a supercritical pitchfork bifurcation to a multi-stable state. However, for biaxial extension (which is simply the kinematic inverse of uniaxial extension) the instability is strongly suppressed. In uniaxial extension, the multiple stable states align in an apparently random orientation as flow joining from four neighbouring inlet channels passes to one of the two opposing outlets; thus forming a mirrored asymmetry about the stagnation point. We relate the suppression of the instability in biaxial extension to the kinematic history of flow under the context of breaking the time-reversibility assumption.