Velocity Fluctuations Research Articles

Subsea pipeline inspection gauges fluctuating friction control under time-varying disturbance

To suppress friction fluctuations during the operation of a pipeline inspection gauge (PIG) and to avoid speed deviations, which may lead to poor detection accuracy and jamming, an adaptive backstepping controller with improved unscented Kalman filter (UKF) was proposed in this paper. Firstly, the friction model was derived, and based on this, the nonlinear dynamic model of PIG was established. Then, an adaptive backstepping controller was designed to estimate the dynamic parameters of the system and stabilize the operating velocity of the PIG by controlling the friction, and adaptive noise based UKF was applied to obtain more accurate feedback estimated signals to deal with the time-varying disturbances in the environment. An active control PIG prototype and a pipeline experimental platform was built, and experiments were conducted under various conditions. Under all conditions, compared to the uncontrolled system, the proposed control strategy can reduce the fluctuation range of friction values by more than 59%, reduce the velocity fluctuation range by more than 88%, and maintain the velocity control error within 4%. Compared to the other controllers, the proposed controller demonstrated better performance in terms of control precision and robustness, verifying the effectiveness and reliability of the proposed controller.

Turbulent pipe flow with spherical particles: Drag as a function of particle size and volume fraction

Suspensions of finite-size solid particles in a turbulent pipe flow are found in many industrial and technical flows. Due to the ample parameter space consisting of particle size, concentration, density and Reynolds number, a complete picture of the particle–fluid interaction is still lacking. Pressure drop predictions are often made using viscosity models only considering the bulk solid volume fraction. For the case of turbulent pipe flow laden with neutrally buoyant spherical particles, we investigate the pressure drop and overall drag (friction factor), fluid velocity and particle distribution in the pipe. We use a combination of experimental (MRV) and numerical (DNS) techniques and a continuum flow model. We find that the particle size and the bulk flow rate influence the mean fluid velocity, velocity fluctuations and the particle distribution in the pipe for low flow rates. However, the effects of the added solid particles diminish as the flow rate increases. We created a master curve for drag change compared to single-phase flow for the particle-laden cases. This curve can be used to achieve more accurate friction factor predictions than the traditional modified viscosity approach that does not account for particle size.

Evaluation of the prediction capability of mesoscale CFD models on velocity fluctuations in liquid-solid flows

Mesoscale CFD models are of great importance in multiphase flow studies due to their acceptable computational cost and great numerical fidelity. However, the evaluations of mesoscale models on velocity fluctuation predictions are still limited. An evaluation of the predictive capability of current CFD models on velocity fluctuations in liquid-solid flows is presented. Numerical simulations are carried out with both the Eulerian-Eulerian Two-Fluid Model (TFM) and the Eulerian-Lagrangian Discrete Phase Model (DPM), and compared with the available experimental data. Together with the proper models in both phases, the TFM satisfactorily predicts two-phase velocity fluctuations. A diffusion-based coupling method is implemented to mitigate the grid dependency problem in the DPM. The diffusion-based coupling method greatly improves the predictive fidelity of the particle volume fraction for DPM. However, it overpredicts velocity fluctuations for both phases. Further research is required to enhance the fidelity of velocity fluctuation prediction in fluid-particle flow simulation models.

The velocity studies in the pure viscoelastic liquid core in displacement flow with interfacial instabilities

The velocity profiles in the core of a pure viscoelastic liquid displacing a Newtonian oil in a 500 µm microchannel were measured with micro-particle image velocimetry (µPIV) to investigate the onset of elastic turbulence. During displacement, a film of the displaced phase remains on the channel wall while interfacial instabilities develop upstream of the displacing core. Two displacing phase flow rates were investigated at 0.1 ml/min and 0.2 ml/min, corresponding to elastic Mach numbers, Ma, of 0.43 and 0.86 respectively. It was found that the velocity profiles in the streamwise and wall-normal directions are almost symmetric with respect to the centre of the core phase, apart from the case at high Ma and at the position of maximum interface deformation. Velocity fluctuations are present for the 0.2 ml/min while they are almost zero for the 0.1 ml/min, indicating the presence of elastic turbulence at large flow rate. Similarly, the calculated turbulence strengths at different directions (which make up the turbulent kinetic energy) and the Reynolds stresses have significant values at 0.2 ml/min but are almost zero at the low flow rate. In both flow rates, a circulation pattern is formed below the interfacial instability.

Transient Friction Analysis of Pressure Waves Propagating in Power-Law Non-Newtonian Fluids

Modulated pressure waves propagating in the drilling fluids inside the drill string are a reliable real-time communication technology that transmit data from downhole to the surface during oil and gas drilling. In the analysis of pressure waves’ propagation characteristics, the modeling of transient friction in non-Newtonian fluids remains a great challenge. This paper establishes a numerical model for transient pipe flow of power-law non-Newtonian fluids by using the weighted residual collocation method. Then, the Newton–Raphson method is applied to solve the nonlinear equations. The numerical method is validated by using the theoretical solution of Newtonian fluids and is proven to converge reliably with larger time steps. Finally, the influencing factors of the wall shear stress are analyzed using this numerical method. For shear-thinning fluids, the friction loss of periodic flow decreases with the increase in flow rate, which is opposite to the variation law of friction with the flow rate for stable pipe flow. Keeping the amplitude of pressure pulsation unchanged, an increase in frequency leads to a decrease in velocity fluctuations; therefore, the friction loss decreases with the increase in frequency.

Lifting of Transversely Forced Turbulent Nonpremixed Coaxial Jet Flames

The lifting behavior of turbulent nonpremixed coaxial jet flames was investigated experimentally as a function of the center jet Reynolds number, annular-to-center jet velocity ratio, acoustic frequency, and acoustic amplitude, all with and without transverse acoustic disturbances acting on the flames situated at a pressure antinode. Global lifting regimes were mapped and consisted of attached flames, periodically lifted flames, and permanently lifted flames. With one exception, all flames were attached in the absence of acoustics and lifted only because of the applied acoustic excitation. The exception occurred at the highest Reynolds number and velocity ratio, where the flames were unconditionally lifted in all cases. Between these two extremes, a range of lifting regimes was observed. Lower applied frequencies and smaller amplitudes were found to generally promote attachment to the burner. Flow visualizations using high-speed Schlieren and OH* chemiluminescence imaging revealed a lateral spreading effect near the jet exit. The lateral spreading was hypothesized to be caused by an axially oriented counterflow collision between the downstream flowing jets and presumed local upstream portion of the acoustic velocity fluctuations. Physical mechanisms were hypothesized based on this observation, which appear to consistently explain most of the observed behavior.

Impact of H[formula omitted]-enrichment on the response of a partially premixed CH[formula omitted]–air flame to velocity and equivalence ratio fluctuations

The dynamics of hydrogen-enriched partially premixed methane–air flames are investigated, focusing on the frequency response to velocity and equivalence ratio fluctuations. Large-eddy simulations (LES) with conjugate heat transfer are performed on the partially premixed PRECCINSTA combustor for various methane–hydrogen mixtures, maintaining a constant thermal power and global equivalence ratio of 10 kW and 0.8, respectively. To reduce the computational cost of the LES, a three-step global mechanism is calibrated for each hydrogen-enriched partially premixed flame. The accuracy of the LES is assessed against experimental data, showing a good agreement with the mean velocity field and shape of the swirl-stabilized flame. The multiple-input–single-output structure for the flame transfer function is applied to separate the individual contributions of velocity and equivalence ratio fluctuations to the overall heat release rate oscillation in the partially premixed flames. System identification with broadband forcing is used to compute the various flame transfer functions. Hydrogen enrichment significantly influences the flame response to equivalence ratio fluctuations, explained by the respective impact on the response of the heat of reaction, the flame speed, and the flame surface area to equivalence ratio fluctuations. The interaction between velocity and equivalence ratio fluctuations is further characterized by the mixing transfer function, which describes the equivalence ratio fluctuations reaching the flame. The higher mass diffusivity of hydrogen results in lower equivalence ratio fluctuations reaching the flame as the frequency increases, attenuating the pronounced effect of hydrogen on the flame sensitivity to equivalence ratio fluctuations. This study contributes to the understanding of the impact of hydrogen enrichment on the thermoacoustic response of partially premixed flames.

Characteristics of the jet shear layer of a round elevated jet in crossflow

The present research aims at an experimental study to investigate the effect of velocity ratio (R) on the evolution of elevated round jet issued from a stack having an aspect ratio (AR) of 9.0 in a uniform crossflow at a Reynolds number of 2000. The experiments are conducted in a low-speed, recirculating water tunnel. Laser Doppler Velocimetry (LDV) is employed to characterize the water tunnel. Particle Image Velocimetry (PIV) is used to measure the flow field, and the dye visualization technique is utilized to capture the accompanying instantaneous flow structures. Depending on the velocity ratio (R = 0.16 - 1.5), distinct jet shear layer (JSL) structures are observed in the symmetric plane (XY), confirmed by both the flow visualization and PIV data. These structures include clockwise vortices, anticlockwise vortices, swing-induced mushroom vortices, and jet-like vortices. For R<0.5, entrainment of a substantial amount of jet fluid into the stack-wake region (downwash) has been observed. At R=0.5, the streak image captured in the wall parallel plane reveals the ring-like vortices that appear to wrap around the jet core while upright vortices are detected downstream on the lee side of the jet. Additionally, variations in average velocity and turbulent fluctuations in the near field, contingent on different velocity ratios, are discussed.

Interactions between polymer molecules and hydrodynamic responses in multi-ion induced charge electroosmosis

Induced charge electroosmosis (ICEO) can assist lab-on-a-chip devices and macromolecular separation involving interface, multi-ion species, and solution properties. To supplement the mechanistic insights into the ICEO phenomenon in complex electrochemical scenarios, we numerically address electrokinetic ion transport–fluid flow coupling regulated by multi-ion species and polymer macromolecular rheology around a polarized cylinder. The physics of the ICEO are analysed from multiple perspectives, including the azimuthal velocity, flow type, energy distribution, interfacial ion transport, and electroelastic instability. The main findings are as follows: (1) Deviations under neutral pH conditions (multi-ion species) cause flow field asymmetry and alter the input energy distribution (PE) in the tight double layer. Polymers greatly modify the interfacial force features in ion-enriched regions, as identified by the first stress difference (N1). (2) The kinetic energy vs. viscosity ratio (β) represents the nonlinear enhancement curve Ek=0.011*exp(β/0.64)-0.0138 due to the weakened effective viscosity Rvis. In addition, shear thinning notably lifts the charge density and salt concentration at the cylinder surface, which boosts the PE. (3) Quadrupolar vortex modes impact the positive correlation between β and the ion current (Jtotal) at different pH levels, resulting in less ion current dependence for small β. A low enhancement efficiency occurs at 10-4 ≤ α (molecular anisotropy) ≤ 0.1, whereas a high efficiency exists at α > 0.1. Electroelastic instabilities are confirmed by the spatiotemporal evolution of the velocity fluctuation, with a broadband structural power-law decline in the power spectral density. These results allow microdevice mixing manipulation and disclose non-Newtonian barrier of electrokinetic dynamics.

Experimental and numerical simulation research on the transport process of bubble clusters in aeration system

Improving gas-liquid mass transfer efficiency in aeration systems contributes to energy savings, cost reduction, and enhanced efficiency in wastewater treatment. However, due to the complex nonlinear interactions among bubbles in turbulence, understanding the transport mechanisms of non-uniform bubble clusters in turbulence remains unclear. This study employs a combined approach of experimental research and numerical simulations to investigate the shape, diameter distribution, trajectory, and velocity of bubbles under different aeration port sizes and flow rates. The diameter distribution of bubble clusters exhibits a bimodal distribution. Bubble trajectories during ascent mainly exhibit two types of motion patterns: “Z” shaped and linear. Increasing aeration port size and flow rate both lead to an increase in the maximum bubble diameter. Higher initial flow rates and smaller port sizes induce greater lateral velocity fluctuations in bubbles. The proposed numerical simulation method serves as a reference for simulating the transport of non-uniform bubble clusters.

Thermal-hydraulic investigation of liquid metal cross flow different arrangements of tube bundles under pulsating

The topic of this paper is to couple the passive and active approaches to enhance the heat transfer performance in the inline tube bundle heat exchanger. Firstly, the k-kl-ω turbulence model and Kays turbulent Prandtl number model are validated by liquid metal cross flow tube bundle experiments and rectangular groove pulsating flow experimental results. Then the numerical studies were carried out for pulsating velocity amplitude of 0.5, frequency of 10, and Re of 20,000 with transverse and streamwise pitch-to-diameter ratios of 1.5, 1.65, and 1.8. The introduction of pulsating flow effectively improves the turbulence characteristics between the tube bundles, especially at the first three rows, where the velocity fluctuation is enhanced by about 1.5–2 times. The tube heat transfer performances are all improved. The performance evaluation criterion (PEC) variation ranges from 1.04 to 1.32, which signifies that the introduction of pulsating flow can enhance the comprehensive heat transfer performance. The per unit flow rate thermal entropy generation decreased by about 9.7–33.3 %, in addition, a phase difference between the transient thermal entropy production and pulsating velocity was found. The correlation equations about Nu and f factor within the scope of this paper are presented.

Numerical Simulations of Scalar Transport on Rough Surfaces

Numerical simulations provide unfettered access to details of the flow where experimental measurements are difficult to obtain. This paper summarises the progress achieved in the study of passive scalars in flows over rough surfaces thanks to recent numerical simulations. Townsend’s similarity applies to various scalar statistics, implying the differences due to roughness are limited to the roughness sublayer (RSL). The scalar field exhibits a diffusive sublayer that increasingly conforms to the roughness surface as ks+ or Pr increase. The scalar wall flux is enhanced on the windward slopes of the roughness, where the analogy between momentum and scalar holds well; the momentum and scalar fields, however, have very different behaviours downwind of the roughness elements, due to recirculation, which reduces the scalar wall flux. Roughness causes breakdown of the Reynolds analogy: any increase in St is accompanied by a larger increase in cf. A flattening trend for the scalar roughness function, ΔΘ+, is observed as ks+ increases, suggesting the possibility of a scalar fully rough regime, different from the velocity one. The form-induced (FI) production of scalar fluctuations becomes dominant inside the RSL and is significantly different from the FI production of turbulent kinetic energy, resulting in notable differences between the scalar and velocity fluctuations. Several key questions remain open, in particular regarding the existence of a fully rough scalar regime and its characteristics. With the increase in Re and Pr, various quantities such as scalar roughness function, the dispersive fluxes, FI wall flux, etc., appear to trend towards saturation. However, the limited range of Re and Pr achieved by numerical simulations only allows us to speculate regarding such asymptotic behaviour. Beyond extending the range of Re and Pr, systematic coverage of different roughness types and topologies is needed, as the scalar appears to remain sensitive to the geometrical details.

Instability and transition control by steady local blowing/suction in a hypersonic boundary layer

The efficacy of steady large-amplitude blowing/suction on instability and transition control for a hypersonic flat plate boundary layer with Mach number 5.86 is investigated systematically. The influence of the blowing/suction flux and amplitude on instability is examined through direct numerical simulation and resolvent analysis. When a relatively small flux is used, the two-dimensional instability critical frequency that distinguishes the promotion/suppression mode effect closely aligns with the synchronisation frequency. For the oblique wave, as the spanwise wavenumber increases, the suppression effects would become weaker and the mode suppression bandwidth diminishes/increases in general in the blowing/suction control. Increasing the blowing/suction flux can effectively broaden the frequency bandwidth of disturbance suppression. The influence of amplitude on disturbance suppression is weak in a scenario of constant flux. To gain a deeper insight into disturbance suppression mechanism, momentum potential theory (MPT) and kinetic energy budget analysis are further employed in analysing disturbance evolution with and without control. When the disturbance is suppressed, the blowing induces the transport of certain acoustic components along the compression wave out of the boundary layer, whereas the suction does not. The velocity fluctuations are derived from the momentum fluctuations of the MPT. Compared with the momentum fluctuations, the evolutions indicated by each component's velocity fluctuations greatly facilitate the investigations of the acoustic nature of the second mode. The rapid variation of disturbance amplitude near the blowing is caused by the oscillations of the acoustic component and phase speed differences between vortical and thermal components. Kinetic energy budget analysis is performed to address the non-parallel effect of the boundary layer introduced by blowing/suction, which tends to suppress disturbances near the blowing. Moreover, viscous effects leading to energy dissipation are identified to be stronger in regions where the boundary layer is rapidly thickening. Finally, it is demonstrated that a flat plate boundary layer transition triggered by a random disturbance can be delayed by a blowing/suction combination control. The resolvent analysis further demonstrates that disturbances with frequencies that dominate the early transition stage are dampened in the controlled base flow.

Experimental observation of the vortex flow and particle motion in a cyclonic classifier

The complex vortex structure in cyclonic classifiers lacks experimental disclosure. The vortex flow and motion of the particles in the classifier were experimentally investigated by the combination of infrared thermal imaging and particle image velocimetry. The results show that the vortex structure is complex, which is composed of the main vortex and the micro-vortices. The main vortex experiences shedding, growth coalescence. The vortex core oscillation causes the fluctuation of the instantaneous tangential velocity, and the maximum velocity varies between 9 m/s and 18 m/s. When the inlet velocity is 14 m/s, the asymmetry and stability of the vortex improve. Accelerated by the vortex flow, the fine particles (5–10 μm) form large-scale particle agglomerate and the circumferential movement rate of the fine particle reaches a maximum of 2.9 m/s. The research contributes to a profound understanding of the gas-solid flow in the cyclonic classifier.

Turbulence Modulation By Large Heavy Particles In Wall-Bounded Turbulence

"Most studies on particle laden flows have focused either on small heavy particles or large neutrally buoyant particles. We present, for the first time (to the best of our knowledge), results in the regime of large and heavy particles, investigating the particle-turbulence dynamics over a parameter space covering a wide range of particle-volume fractions, Stokes and Froude numbers. We consider a flow in a pipe aligned with the gravitational vector, thus allowing for the investigation of the two-way coupling between particles and carrier phase turbulence, while excluding the effect of gravity on the wall-normal migration of particles. Time-resolved images of both tracers (10 micrometers particles) and the dispersed particles (700 micrometers in diameter) were taken in the streamwise-wall-normal pipe plane using a planar particle image velocimetry (PIV) system consisting of a high speed camera (Phantom VEO 440), and an Nd:YLF Laser as light source. Using Voronoi tessellations to analyze the inertial particle dynamics, we show a strong deviation from Poisson behaviour for cases with and without turbophoresis. From the time-resolved PIV measurements, we also show that the carrier phase turbulence is modulated even at particle concentrations as low as 0.3% indicating that particle-induced stresses due to distortion of fluid streamlines cannot be neglected. An increase or decrease in the peak streamwise velocity fluctuation in the particle laden flow was observed, depending on the Stokes number, while the radial velocity fluctuation was found either to be the same as in the single phase flow case or higher. Furthermore, pressure drop measurements indicate a linear increase in the skin friction coefficient with volume fraction of particles. This was true for all Stokes and Froude numbers considered. The growth rate (β) of the skin friction coefficient was however observed to be only a function of the Froude number. A power-law fit to the data shows that β scales inversely with the Froude number indicating that for Froude numbers less than 1, the influence of gravity cannot be neglected. "

Characterising Horizontal Two-Phase Flows Using Structured-Planar Laser-Induced Fluorescence (S-PLIF) Coupled With Simultaneous Two-Phase PIV (S2P-PIV)

Understanding the physics that underpins the behaviors of two-phase flows is immensely useful for a diverse number of industries, including oil and gas, nuclear, and aerospace. Stratified air-liquid two-phase flows are amenable to the application of two-phase PIV, but this is often only possible if PIV processing parameters can be chosen to match the separate gas and liquid phase image sets. Accurate interface location detection is, therefore, extremely important to facilitate appropriate masking during analysis. This paper examines the effectiveness of using the Structured-Planar Laser Induced Fluorescence (S-PLIF) method to aid in the accurate capture and processing of simultaneous two-phase PIV (S2P-PIV) for a gas-sheared liquid flow. Prior S2P-PIV work made use of direct interface detection, using contrast on images from the air-side camera. However, this method proved limiting in higher gas shear cases when the highly wavy nature of the flow prevented the camera from seeing all of the interface. An alternative prior approach using the liquid-side camera and the planar laser-induced fluorescence (PLIF) technique often led to large errors due to reflections from the free surface. Interface detection using the S-PLIF method facilitates a clearer delineation between the two phases through analysis of the change in the structure of the incident light, significantly reducing errors generated by the traditional PLIF. This then facilitates higher quality PIV analysis, both because interface identification is far more accurate and also because frame specific masking of the individual phases can be more automated. This paper presents air/water data from a rectangular channel with a liquid flowrate of 8 litres per minute and superficial gas velocities in the range 1 - 14 m/s. Data capture of the two phases is concurrent with the developed S-PLIF approach used to locate the interface, enabling separate and more accurate PIV analysis of the two phases over a wider parametric range than was previously possible. The data analysis shows that the transition to the disturbance/roll wave regimes is associated with a change in the liquid’s axial velocity profile and a significant increase in normalized axial velocity root-mean-square velocity fluctuation. Data sets from this work can be used to accurately describe high-speed gas-sheared two-phase flows that will be extremely useful for CFD model development and validation.

Evaluating High-Frequency Fluctuations And Its Effect On Hemodynamics At Varying Heart Rates In Intracranial Aneurysms Via 4D PTV

Hemodynamics have been shown to affect the growth and rupture of intracranial aneurysms (IA). Studies have increasingly reported the presence of high frequency velocity fluctuations in aneurysms. However, it remains undetermined how transient physiological factors like heart rate and inflow blood waveform amplitude affect the hemodynamic parameters and high frequency fluctuations in and around an IA, as well as the risk of IA progression. In this work, we address this question using a volumetric particle tracking velocimetry (PTV) study where a patient-specific right middle cerebral artery (R MCA) aneurysm model was subjected to two heart rate conditions (60 bpm and 137 bpm). The input waveform amplitude for the 137 bpm case was increased by a factor of 1.6 to be physiologically consistent. Captured PTV images were processed using the Shake-the-Box (STB) workflow. Flow parameters including velocity, vorticity, and turbulent kinetic energy (TKE) were evaluated. To evaluate the presence of high frequency fluctuations, a direct numerical simulation (DNS) using the R MCA geometry and same two heart rate cases was conducted and a method for use with STB particle tracks was proposed. As compared to the 60 bpm case, the 137 bpm case had a more concentrated inflow jet that extended further into the aneurysmal sac and a stronger and larger vortical flow structure in the aneurysmal sac. The 60 bpm case maintained a region of slightly elevated TKE at the main junction point where the aneurysmal sac and all vessels merge. In the 137 bpm case, TKE in this region was dramatically higher. Using probe points, the DNS data revealed high frequency velocity fluctuations in an outflow vessel during the deceleration phase of the cycle. Notably, these fluctuations were only observed for the 137 bpm case. For both the DNS and STB data, high frequency components were more prevalent and stronger outside of the aneurysmal sac as opposed to inside the aneurysmal sac. Overall, these results suggest that changes in heart rate induce changes to the flow structure and can induce significant increases in TKE and high frequency fluctuations. Based on our findings, a higher heart rate would be expected to yield a flow field more akin to IA progression. The specific correlation between the high frequency components computed using our proposed STB-based method and the high frequency fluctuations in the flow field could not be well understood. Thus, additional analysis and development of this method is needed.

Experimental Study On Pressure-Velocity Relation Of Near-Field Tip Vortex Using Tomographic PIV

The non-cavitating tip vortex in the near field of an elliptical hydrofoil is studied using tomographic particle image velocimetry (TPIV). By investigating the distributions of the axial velocity difference and streamwise vorticity, the formation and development of the near-field tip vortex are clearly revealed. In the near field, the axial flow within the tip vortex manifests a jet-like profile, and the majority of the vorticity is contained within the vortex core. A special position is identified during the streamwise evolution of the tip vortex, where the vortex core circulation reaches its local maximum for the first time and tip vortex cavitation (TVC) might be more prone to incept. In the vicinity of this crucial position, a concise relation between the static pressure along the tip vortex center line and the local velocity is derived by combining the three-dimensional measured velocity fields with the governing equations. Based on the Reynolds-averaged Navier-Stokes equation, it is revealed that the mean static pressure along the vortex center line is directly related to the local mean axial velocity, whereas the local velocity fluctuation has little impact on the mean static pressure. It is the first attempt to combine the three-dimensional measurement with the governing equations to investigate the near-field tip vortex flow, which might provide valuable insights for understanding and predicting tip vortex cavitation inception.

Estimating Velocity Correlations Using Single Pixel PIV

In this work, we analyze the possibility of determining correlations of turbulent velocity fluctuations from PIV data with improved spatial resolution. The analysis is based on the method presented by Oldenziel et al. (2023), where a joint probability density function of the velocity at two locations is calculated from the single-pixel ensemble correlation for these locations. Synthetic PIV images are used to discuss the occurrence of random and systematic errors and to derive the number of image pairs required for a determination of the correlation coefficient with desired uncertainty, depending on the particle image density. Compared to classical window correlation, the presented method can improve the spatial resolution by about one order of magnitude if a very large number of PIV image pairs are available and/or many statistically independent points with identical flow properties can be used. As an example of application, we show the spatial distribution of a two-point correlation in a compressible turbulent boundary layer flow for a reference point near the wall.

Wall Shear Stress Characteristics Of A Turbulent Boundary Layer Obtained With Multi-Aperture Defocusing Micro-PTV And High-Speed Stereo Profile-PIV

A multi-aperture 3d 3c micro PTV system is presented which relies on single window optical access for both high-speed tracer illumination and image recording. Similar to the “defocusing” concept described by C. Willert &amp; Gharib (1992), the wall distance of individual particles is obtained from the size of projected particle image triplets formed by a triplet of apertures on the entrance pupil of the microscope lens. The present article extends upon previously published material Klinner &amp; Willert (2022) by applying multi-aperture micro particle tracking velocimetry (MA-micro PTV) on a canonical turbulent boundary layer (TBL) to track the near-wall motion of tracer particles with the aim of estimating the unsteady wall-shear stress from particle tracks. The technique is validated with measurements of a TBL inside the closed test section of the 1 m wind tunnel of DLR in Göttingen (1mWK) at free- stream velocities of 5.2 to 20 m/s with corresponding shear Reynolds numbers between 560 and 1630. In the viscous sublayer, the probability density distributions of stream- and span-wise wall shear stress (WSS) components could be reliably captured down to probability densities of 10E−3. As far as we know, this has not been achieved in the past, particularly not for the span-wise component. For the stream-wise component the measured Reynolds-number dependency of the root mean squared fluctuations agrees to correlations by Örlü &amp; Schlatter (2011). Furthermore, the skewness of the stream-wise WSS agrees well to values from DNS. On the other hand, the span-wise WSS fluctuations consistently underestimate the predicted DNS values, for which it is assumed that the deviation can be explained by the rapid decrease of the span-wise velocity fluctuations with increasing wall distance. Wall-normal profiles of 3c velocity statistics were obtained by bin averaging of particle velocities. Up into the buffer layer, these profiles agree well with profiles from stereo PIV as well as from DNS and LES, indicating an accurate determination of both near-wall velocities and inner scaling.