Wall Shear Stress Measurements Research Articles

Theory for electrodiffusional wall shear stress measurement by directionally sensitive twin semicircular probe

This study investigates the theoretical aspects of mass transport at the surface of a twin semicircular electrodiffusion probe tailored to measure the magnitude and direction of near-wall fluid flows. A critical aspect of this research is the development of a theoretical framework that facilitates experimental measurements by analytically relating measured electric currents to the wall shear stress vector. Central to the study is the derivation of analytical expressions for the mass transfer coefficients of the front and rear segments of the probe, which are essential for quantifying near-wall hydrodynamics. Validation of these analytical relations is achieved through numerical solutions of the convection–diffusion equation, providing a robust confirmation of the underlying theory. A comprehensive procedure for experimental data processing is proposed, taking into account both frontal and reverse flow conditions across the probe. In addition, a sensitivity analysis of the twin semicircular probe is performed. This analysis focuses on the response of current ratios to changes in the flow direction, an aspect critical to understanding the operational performance of the probe. The results of this analysis are compared to the characteristics of two-segment strip probes, highlighting the distinct sensitivity nuances of the twin semicircular probe. Our findings provide insight into the optimal application of this probe in various fluid dynamics scenarios.

Non-invasive measurement of wall shear stress in microfluidic chip for osteoblast cell culture using improved depth estimation of defocus particle tracking method.

The development of a non-invasive method for measuring the internal fluid behavior and dynamics of microchannels in microfluidics poses critical challenges to biological research, such as understanding the impact of wall shear stress (WSS) in the growth of a bone-forming osteoblast. This study used the General Defocus Particle Tracking (GDPT) technique to develop a non-invasive method for quantifying the fluid velocity profile and calculated the WSS within a microfluidic chip. The GDPT estimates particle motion in a three-dimensional space by analyzing two-dimensional images and video captured using a single camera. However, without a lens to introduce aberration, GDPT is prone to error in estimating the displacement direction for out-of-focus particles, and without knowing the exact refractive indices, the scaling from estimated values to physical units is inaccurate. The proposed approach addresses both challenges by using theoretical knowledge on laminar flow and integrating results obtained from multiple analyses. The proposed approach was validated using computational fluid dynamics (CFD) simulations and experimental video of a microfluidic chip that can generate different WSS levels under steady-state flow conditions. By comparing the CFD and GDPT velocity profiles, it was found that the Mean Pearson Correlation Coefficient is 0.77 (max = 0.90) and the Mean Intraclass Correlation Coefficient is 0.66 (max = 0.82). The densitometry analysis of osteoblast cells cultured on the designed microfluidic chip for four days revealed that the cell proliferation rate correlates positively with the measured WSS values. The proposed analysis can be applied to quantify the laminar flow in microfluidic chip experiments without specialized equipment.

Age-related wall shear stress changes assessed by vascular vector flow mapping in the carotid arteries of healthy adults: a cross-sectional study.

Wall shear stress (WSS) is related to the pathogenesis of atherosclerosis. WSS is affected by a variety of hemodynamic factors, and there is still a lack of accurate and objective methods for measuring it. This study sought to evaluate hemodynamic changes in WSSmaximum (max), WSSmean, WSSminimum (min) in the common carotid artery of healthy adults of different ages using vascular vector flow mapping (VFM). A retrospective analysis was conducted on 70 healthy volunteers aged 20-89 years who were recruited from our Ultrasound Department between February 2021 and June 2021. An ultrasound system with a 3-15 MHz probe was used to determine regions of interest (ROIs) of the common carotid artery. VFM-based WSS measurements were obtained by selecting ROIs with optimal image quality from three full cardiac cycles. The participants were divided into the following seven age groups: the 20s group, the 30s group, the 40s group, the 50s group, the 60s group, the 70s group, and the 80s group. The WSS parameters were compared among the age groups. An analysis of variance or a Kruskal-Wallis test was used to evaluate the difference among the groups, and a Pearson analysis and linear regression were used for the correlation and trend analysis. The WSS parameters were quantified using vascular VFM software. The WSSmax, WSSmean, WSSmin differed among the age groups and gradually decreased with age, the elderly were significantly lower than the young. The Pearson correlation coefficient of the WSSmax and age was -0.556 (P<0.001), that of the WSSmean and age was -0.461 (P<0.001), and that of the WSSmin and age was -0.308 (P<0.001). The WSS parameters with age are negatively correlated the carotid intima-media thickness differed between the groups. The carotid WSSmax, WSSmean, WSSmin can be quantitatively and visually analyzed using the vascular VFM technique. In healthy adults of different ages, the carotid WSSmax, WSSmean, WSSmin decreased with age. Our findings about the normal values of carotid WSS maybe have clinical reference value for future studies.

Rapid prediction of wall shear stress in stenosed coronary arteries based on deep learning.

There is increasing evidence that coronary artery wall shear stress (WSS) measurement provides useful prognostic information that allows prediction of adverse cardiovascular events. Computational Fluid Dynamics (CFD) has been extensively used in research to measure vessel physiology and examine the role of the local haemodynamic forces on the evolution of atherosclerosis. Nonetheless, CFD modelling remains computationally expensive and time-consuming, making its direct use in clinical practice inconvenient. A number of studies have investigated the use of deep learning (DL) approaches for fast WSS prediction. However, in these reports, patient data were limited and most of them used synthetic data generation methods for developing the training set. In this paper, we implement 2 approaches for synthetic data generation and combine their output with real patient data in order to train a DL model with a U-net architecture for prediction of WSS in the coronary arteries. The model achieved 6.03% Normalised Mean Absolute Error (NMAE) with inference taking only 0.35s; making this solution time-efficient and clinically relevant.

Opposition flow control for reducing skin-friction drag of a turbulent boundary layer

This work explores the dynamic response of a turbulent boundary layer to large-scale reactive opposition control, at a friction Reynolds number of Reτ≈2240. A surface-mounted hot-film is employed as the input sensor, capturing large-scale fluctuations in the wall-shear stress, and actuation is performed with a single on/off wall-normal blowing jet positioned 2.4δ downstream of the input sensor, operating with an exit velocity of vj=0.4U∞. Our study builds upon the work of Abbassi [] and includes a control-calibration experiment and a performance assessment using PIV- and PTV-based flow field analyses. With the control-off calibration-experiment conducted , a transfer kernel is identified so that the velocity fluctuations that are to-be-controlled can be estimated. The controller targets large-scale high-speed zones in an “opposing” mode and low-speed zones in a “reinforcing” mode. A desynchronized mode was tested for reference and consisted of a statistically similar control mode, but without synchronization to the incoming velocity fluctuations. An energy-attenuation of about 40 % is observed for the opposing control mode in the frequency band corresponding to the passage of large-scale motions. This proves the effectiveness of the control in targeting large-scale motions: an energy-intensification of roughly 45% occurs for the reinforcing control mode instead, while no change in energy, within the wall-normal range targeted, appears with the desynchronized control mode. Moreover, direct measures of the skin-friction drag are inferred from PTV data. Results indicate that the opposing control logic yields the lowest wall-shear stress (3% lower than the desynchronized control, and 10% lower than the uncontrolled flow). Finally, a FIK-decomposition of the skin-friction coefficient revealed that the off-the-wall turbulence follows a consistent trend with the PTV-based wall-shear stress measurements, although biased by an increased shear in the wake of the boundary layer given the formation of a plume due to the jet-in-crossflow actuation. Published by the American Physical Society 2024

Clinical implications of haemodynamics in symptomatic intracranial atherosclerotic stenosis by computational fluid dynamics modelling: a systematic review

BackgroundRecently, computational fluid dynamics (CFD) has been used to simulate blood flow of symptomatic intracranial atherosclerotic stenosis (sICAS) and investigate the clinical implications of its haemodynamic features, which were systematically...

Temperature dependence of constant current hot-film sensors: Investigation with application to temperature correction for wall-shear stress measurements

Hot-film sensors measure wall-shear stress based on the forced convective heat transfer. Variations of ambient temperatures lead to significant measurement errors for such thermal sensors and must be corrected for sometimes. Although methods for correcting the temperature shifts of hot-film sensors driven in constant temperature or constant voltage mode have been suggested over the years, the temperature dependence and relevant correction schemes of constant current mode of operation are still open questions. In this study, temperature dependence characteristics of constant current hot-film sensors are investigated within relatively large temperature changes in air and water channel flows (28 °C and 16 °C, respectively). The specific property of constant overheat ratios under varying temperatures for constant current driving mode is found and a quite simple temperature correction function is derived on that basis to eliminate the temperature dependence without any assumed heat transfer correlation. With the correction function, the data at different ambient temperatures are collapsed to single curves with high R2 factors over 0.99, typically. Furthermore, after correction, the relative errors of the measured wall-shear stress are reduced to within ±6 % of the true values. It will then enable the constant current hot-film sensors to calibrate at only one ambient temperature instead of a multiple range of temperatures as with many other schemes, which is more practical and convenient.

Calorimetric wall-shear-stress microsensors for low-speed aerodynamics

This article describes the design, calibration, and testing of new calorimetric microsensors for the measurement of wall shear stress in low-speed aerodynamic flows. The sensors are made of three beams of platinum-plated silicon nitride suspended over a small cavity. Their range of operation and their bandwidth are of the order of ±10\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm 10$$\\end{document} Pa and 1 kHz, respectively. Results from experimental campaigns in a laminar separation bubble, a turbulent separation bubble, and on a NACA 0015 airfoil at low Reynolds number indicate a high sensitivity and an inherent capacity to measure instantaneous backflow. This demonstrates the capability of the new sensors to accurately determine the mean and fluctuating wall shear stress in laminar, transitional, and turbulent separating and reattaching flows.

Wall shear stress measurement using a zero-displacement floating-element balance

The floating-element (FE) principle, introduced nearly a century ago, remains one of the most versatile direct wall shear stress measurement methods. Yet, its intrinsic sources of systematic error, associated with the flow-exposed gap, off-axis load sensitivity, and calibration, have thus far limited its widespread application. In combination with the lack of standard designs and testing procedures, measurement reliability still hinges heavily on individual judgement and expertise. This paper presents a framework to curb these limitations, whereby the design and operation of a FE balance are leveraged by an analytical model that attempts to capture the behaviour and predict the relative contribution of the systematic sources of error. The design is based on a parallel-shift linkage and a zero-displacement force-feedback system. The FE has a surface area of 200×200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$200\ imes 200\\,$$\\end{document} mm, and measurement sensitivity is adjustable depending on the surface condition and the Reynolds number. It is thus suitable for application in a wide range of low-speed, boundary-layer wind tunnels, small or large scale. Measurements of the skin friction coefficient over a smooth wall show a remarkable agreement with oil-film interferometry, especially for Reθ>1.3×104\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\rm Re}_{\ heta } > 1.3 \ imes 10^4$$\\end{document}. The discrepancy relative to the empirical Coles–Fernholz relation (κ=0.39\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa = 0.39$$\\end{document} and C=4.352\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C = 4.352$$\\end{document}) is within 0.5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.5\\,$$\\end{document}%, and the level of uncertainty is below 1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1\\,$$\\end{document}% for a confidence interval of 95\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$95\\,$$\\end{document}%.

Blood flow effects in a patient with a thoracic aortic endovascular prosthesis

This work analyzes hemodynamic phenomena within the aorta of two elderly patients and their impact on blood flow behavior, particularly affected by an endovascular prosthesis in one of them (Patient II). Computational Fluid Dynamics (CFD) was utilized for this study, involving measurements of velocity, pressure, and wall shear stress (WSS) at various time points during the third cardiac cycle, at specific positions within two cross sections of the thoracic aorta. The first cross-section (Cross-Section 1, CS1) is located before the initial fluid bifurcation, just before the right subclavian artery. The second cross-section (Cross-Section 2, CS2) is situated immediately after the left subclavian artery. The results reveal that, under regular aortic geometries, velocity and pressure magnitudes follow the principles of fluid dynamics, displaying variations. However, in Patient II, an endoprosthesis near the CS2 and the proximal border of the endoprosthesis significantly disrupts fluid behavior owing to the pulsatile flow. The cross-sectional areas of Patient I are smaller than those of Patient II, leading to higher flow magnitudes. Although in CS1 of Patient I, there is considerable variability in velocity magnitudes, they exhibit a more uniform and predictable transition. In contrast, CS2 of Patient II, where magnitude variation is also high, displays irregular fluid behavior due to the endoprosthesis presence. This cross-section coincides with the border of the fluid bifurcation. Additionally, the irregular geometry caused by endovascular aneurysm repair contributes to flow disruption as the endoprosthesis adjusts to the endothelium, reshaping itself to conform with the vessel wall. In this context, significant alterations in velocity values, pressure differentials fluctuating by up to 10%, and low wall shear stress indicate the pronounced influence of the endovascular prosthesis on blood flow behavior. These flow disturbances, when compounded by the heart rate, can potentially lead to changes in vascular anatomy and displacement, resulting in a disruption of the prosthesis-endothelium continuity and thereby causing clinical complications in the patient.

Wall shear stress measurement of turbulent bubbly flows using laser Doppler displacement sensor

A novel wall shear stress meter is developed to promote studies of frictional drag reduction by injecting air bubbles into a turbulent boundary layer. Such studies require a tool having a time resolution sufficiently high to capture the unsteady effect of turbulent characteristics due to various bubble passage patterns. The present study adopts the principle of the heterodyne interferometer to capture of time variation of wall shear stress in turbulent flow up to 500 Hz in sampling frequency. We demonstrate the performance of the tool by applying it to bubbly flows beneath a flat-bottom model ship running at 3 m/s in a towing water reservoir, where bubbles experience wavy passage around a few Hz in frequency. The data obtained by the proposed shear stress meter agree well with Dean's formula for single-phase turbulent channel flow. The scattering of the data across three trials is sufficiently small, at approximately 3 %. This high reproducibility is a great advantage over conventional direct measurements, which have low reproducibility and a large scatter of the data of approximately 15 %. The obtained results represent reasonable drag reductions by injecting bubbles with different void fractions. We also evaluate histogram of the wall shear stress fluctuation to characterize the effect of drag reduction by unsteady passage of bubbles.

Experimental verification of wall shear stress measurement with MEMS sensors array for underwater applications with flat plate benchmark tests

Underwater wall shear stress measurement based on a newly developed MEMS sensors array is experimentally verified utilizing a set of flat plate benchmark tests conducted in a precision water flume. The array is firstly calibrated in a well-defined 2D flow and then flush embedded on the plate surface to measure WSS directly. The local freestream velocities ranging from 0.1 m/s to 0.7 m/s are adopted for the test cases of naturally developing flow and deliberately stimulated turbulence. The boundary layer profiles of interests are correspondingly detected with LDV, and mean WSS values are extrapolated from suitable fits to known profile shapes for flat plate with a zero pressure gradient. The results from the MEMS sensors match well with those from the LDV velocity profile fits and are in good agreement with empirical estimations with an overall bias of less than 5%. Also, the direct simultaneous measurements from multiple sensors on the MEMS array favorably exhibit the streamwise variation of the wall-bounded flow. Generally, the MEMS sensors array-based underwater wall shear stress measurement is characterized by desirable accuracy and spatial resolution for further practical applications.

Improvement of extraction method of the Fizeau fringes spacing in the oil film interferometry and measurement of wall shear stress on an airfoil surface

Improvement of extraction method of the Fizeau fringes spacing in the oil film interferometry and measurement of wall shear stress on an airfoil surface

Assessment of aerodynamic roughness parameters of turbulent boundary layers over barnacle-covered surfaces

Full-scale drag penalty predictions of flows over rough walls require surface roughness characterisation from laboratory experiments or numerical simulations. In either approach, it is necessary to determine the so-called equivalent sand-grain roughness height (k_s). There are several steps involved in determining this aerodynamic roughness lengthscale, but its procedure typically includes a combination of measurement of wall-shear stress (tau _w) using direct or indirect methods as well as analysis of velocity profiles. Indirect methods usually rely on assumptions made about flow and its scaling including the validity of universal outer-layer similarity. However, the implications of the underlying assumptions involved in full-scale drag prediction are unclear. In this work, we carry out wind tunnel measurements over a realistic rough surface (from a fouled ship-hull) to evaluate the impact of different methods with an emphasis on using the outer-layer similarity hypothesis for full-scale drag predictions. Wall-shear stress is measured using an in-house floating-element drag balance (DB), and velocity profiles are obtained using particle image velocimetry (PIV), allowing the evaluation of k_s, and the associated wake parameters through several methods. The aerodynamic roughness parameters hence obtained are used for full-scale drag penalty calculations. It is observed that the predicted drag penalty can vary by over 15% among the different methods highlighting the care that should be taken when employing such methods.

Effect of Particle Migration on the Stress Field in Microfluidic Flows of Blood Analog Fluids at High Reynolds Numbers.

In the present paper, we investigate how the reductions in shear stresses and pressure losses in microfluidic gaps are directly linked to the local characteristics of cell-free layers (CFLs) at channel Reynolds numbers relevant to ventricular assist device (VAD) applications. For this, detailed studies of local particle distributions of a particulate blood analog fluid are combined with wall shear stress and pressure loss measurements in two complementary set-ups with identical flow geometry, bulk Reynolds numbers and particle Reynolds numbers. For all investigated particle volume fractions of up to 5%, reductions in the stress and pressure loss were measured in comparison to a flow of an equivalent homogeneous fluid (without particles). We could explain this due to the formation of a CFL ranging from 10 to 20 μm. Variations in the channel Reynolds number between Re = 50 and 150 did not lead to measurable changes in CFL heights or stress reductions for all investigated particle volume fractions. These measurements were used to describe the complete chain of how CFL formation leads to a stress reduction, which reduces the apparent viscosity of the suspension and results in the Fåhræus-Lindqvist effect. This chain of causes was investigated for the first time for flows with high Reynolds numbers (Re∼100), representing a flow regime which can be found in the narrow gaps of a VAD.

Development and Evaluation of a Multifrequency Ultrafast Doppler Spectral Analysis (MFUDSA) Algorithm for Wall Shear Stress Measurement: A Simulation and In Vitro Study.

Cardiovascular pathology is the leading cause of death and disability in the Western world, and current diagnostic testing usually evaluates the anatomy of the vessel to determine if the vessel contains blockages and plaques. However, there is a growing school of thought that other measures, such as wall shear stress, provide more useful information for earlier diagnosis and prediction of atherosclerotic related disease compared to pulsed-wave Doppler ultrasound, magnetic resonance angiography, or computed tomography angiography. A novel algorithm for quantifying wall shear stress (WSS) in atherosclerotic plaque using diagnostic ultrasound imaging, called Multifrequency ultrafast Doppler spectral analysis (MFUDSA), is presented. The development of this algorithm is presented, in addition to its optimisation using simulation studies and in-vitro experiments with flow phantoms approximating the early stages of cardiovascular disease. The presented algorithm is compared with commonly used WSS assessment methods, such as standard PW Doppler, Ultrafast Doppler, and Parabolic Doppler, as well as plane-wave Doppler. Compared to an equivalent processing architecture with one-dimensional Fourier analysis, the MFUDSA algorithm provided an increase in signal-to-noise ratio (SNR) by a factor of 4-8 and an increase in velocity resolution by a factor of 1.10-1.35. The results indicated that MFUDSA outperformed the others, with significant differences detected between the typical WSS values of moderate disease progression (p = 0.003) and severe disease progression (p = 0.001). The algorithm demonstrated an improved performance for the assessment of WSS and has potential to provide an earlier diagnosis of cardiovascular disease than current techniques allow.

The electrodiffusional theory for the wall shear stress measurement by two-strip probe

This article deals with the derivation of the fundamental theory describing the mass transport on the active surface of a two-strip mass transfer probe for an arbitrary direction of fluid flow. The existence of such a general theory is a critical point for the application of the electrodiffusion method using a two-strip probe. Considering the different possible sizes of the probe segments, the analytical formulas for the average mass transfer coefficients are derived and presented in dimensionless forms for both segments. The correctness of the derived analytical expressions is verified by numerical solution of the convection-diffusion transport equation. A methodology for possible experimental data treatment is also proposed. It is based on the evaluation of two current signals collected from the segments of a two-strip probe. From the derived equations, it is possible to determine the magnitude and direction of the wall shear rate vector for both frontal and reverse flow regimes. From the analysis of the current ratio predictions for different probe geometries, an optimal probe configuration is found with respect to the sensitivity of the flow direction measurement.

Preliminary study on modeling blood flow velocity profile for ultrasonic measurement of wall shear stress

The wall shear stress (WSS) contains useful information for the diagnosis of vascular diseases. To improve the accuracy of WSS measurements by ultrasound, some studies have attempted to correct the underestimation of the WSS by approximating a blood flow velocity profile measured by ultrasound to a velocity distribution model such as laminar flow. In this study, a blood flow velocity profile measured by ultrasound was modeled by the Womersley flow model, in order to correct underestimation of WSS in cases of measurements of vessels with complex geometries such as stenotic vessels. The simulation results showed that the rms error of the estimated WSSs was 45.8% from the stenotic vessel with a stenotic ratio of 40% when the spatial gradient was estimated by fitting a linear model to the measured flow profile. Such an error was improved from 45.8% to 25.3% by fitting a Womersley flow model to the measured blood velocity profile.

Measurement of Skin Friction in the University of Texas at Arlington Arcjet

Arcjet flows are known to have significant uncertainties associated with the fundamental flow quantities. A detailed characterization is critical to augment the current understanding of these complex flows as well as developing, screening, and qualifying thermal protection systems. Classically, estimations of skin friction have been made indirectly using heat flux analogies. These techniques, however, are marred by high levels of measurement uncertainty and require a priori assumptions about the flowfield. Directly measuring the wall shear stress removes the demand for these assumptions. A direct measurement of shear stress in supersonic high-enthalpy flow at the Office of Naval Research/University of Texas at Arlington arcjet facility has been conducted. The measured wall shear stress was (average combined calibration uncertainty), which matches well with estimations for laminar flow. Two shear stress sensors separated by a distance of 1.905 cm (0.75 in.) were integrated into a 20 deg half-angle shear-wedge platform. The two sensors tracked together within 10% of each other, implying a uniform flowfield over the region studied. Approximately 1.5 s into the test window, a steady increase in skin friction was observed. The cause of this nonphysically accurate increase in the shear stress measurement is discussed.

Downstream persistence of frictional drag reduction with repetitive bubble injection

Frictional drag reduction using repetitive bubble injection is investigated in a turbulent boundary layer beneath a 36-m-long flat-bottom model ship towed at 8.0 m/s. Bubbles are injected with air flow rates periodically fluctuating at a repetition frequency of 0.5–2.0 Hz. The drag-reduction ratio reaches 24%, which is a 5% improvement relative to the conventional method of continuous bubble injection. Measurement of the local wall shear stress acting on the bottom plate and optical visualization of bubbly flow reveal that the transition of the status of bubble dispersion causes the streamwise decay of local drag reduction. The downstream persistence of the drag-reduction effect can be improved by a factor of 15 through the use of repetitive bubble injection. The estimation of the full-scale performance indicates that repetitive bubble injection provides approximately 7 times the frictional drag reduction provided by continuous bubble injection for long ship hulls exceeding 130 m.