Wall Shear Stress Fluctuations Research Articles

Direct numerical simulation of compressible turbulent channel flows over porous boundaries

The impact of porous boundaries on skin friction and heat transfer in compressible turbulent channel flows is explored through direct numerical simulations. Utilizing the volume-averaged Navier–Stokes equations for the porous media, we examine flows at Mach numbers Mb=0.3 and Mb=1.5, with friction Reynolds numbers ranging from 176 to 220, across three permeability levels: 0 (impermeable), 1.6×10−5, and 1.0×10−4. Our findings reveal a dual impact of porous boundaries on skin friction: a direct reduction due to averaged slip velocity at the interface and an indirect increase from amplified Reynolds shear stress due to enhanced wall-normal permeability. This permeability weakens the wall-blocking effect, leading to intensified wall-normal velocity fluctuations and consequently higher Reynolds stress. Additionally, the Mach number significantly influences flow structures, particularly at higher permeabilities, where it disrupts near-wall streaks at Mb=0.3 but has a diminished effect at Mb=1.5. Thermal analysis confirms the validity of the generalized Reynolds analogy for the mean temperature in these flows, with the turbulent Prandtl number approximating 1, in line with the strong Reynolds analogy. Moreover, a strong spatial correlation between heat flux and wall shear stress fluctuations underscores the intertwined dynamics of momentum and thermal transport at the porous–fluid interface.

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.

The statistical characteristics and auto-regeneration of backflow in non-Newtonian turbulent pipe flow

The backflow phenomenon in shear-thinning and shear-thickening fluids is investigated in pipe flows at friction Reynolds number Reτ=180 via direct numerical simulations. Conditional average results show that the extreme fluctuation of wall shear stress around the backflow regions is more abrupt under the shear-thinning effect. The statistical characteristics of the backflow at different flow indices from 0.5 to 1.5 show remarkable differences. The probability of the backflow events at the wall increases in both the shear-thinning and the shear-thickening fluids under different mechanisms. The backflow occurs more frequently and exists further away from the wall in the shear-thinning fluids owing to the suppressed near-wall turbulent structures and the laminarization at low flow indices. The increase in the probability of the backflow events in the shear-thickening fluids is caused by increased Q2 and Q4 events in the near-wall region. The variation in the size and the lifespan of the backflow regions with the flow index is very prominent which both increase with the shear-thinning effect and decrease as the flow becomes dilatant. In the weakly turbulent flow of shear-thinning fluid, large backflow regions appear near the leading edge of the turbulent spots where the off-axial turbulent fluctuations are significantly lowered. Observations show the linked evolution between the hairpin vortices and the backflow regions induced underneath the strong spanwise rotations. The backflow follows the auto-regeneration process of the hairpin vortices in a packet which results in coherent streamwise-aligned backflow regions under the hairpin packets confined closer to the wall.

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.

Stenosis to stented: decrease in flow disturbances following stent implantation of a diseased arteriovenous fistula.

The arteriovenous fistula (AVF) is commonly faced with stenosis at the juxta-anastomotic (JXA) region of the vein. Implantation of a flexible nitinol stent across the stenosed JXA has led to the retention of functioning AVFs leading to the resulting AVF geometry being distinctly altered, thereby affecting the haemodynamic environment within it. In this study, large eddy simulations of the flow field within a patient-specific AVF geometry before and after stent implantation were conducted to detail the change in flow features. Although the diseased AVF had much lower flow rates, adverse flow features, such as recirculation zones and swirling flow at the anastomosis, and jet flow at the stenosis site were present. Larger velocity fluctuations (leading to higher turbulent kinetic energy) stemming from these flow features were apparent in the diseased AVF compared to the stented AVF. The unsteadiness at the stenosis created large regions of wall shear stress (WSS) fluctuations downstream of the stenosis site that were not as apparent in the stented AVF geometry. The larger pressure drop across the diseased vein, compared to the stented vein, was primarily caused by the constriction at the stenosis, potentially causing the lower flow rate. Furthermore, the WSS fluctuations in the diseased AVF could lead to further disease progression downstream of the stenosis. The change in bulk flow unsteadiness, pressure drop, and WSS behaviour confirms that the haemodynamic environment of the diseased AVF has substantially improved following the flexible stent implantation.

Conditional analysis on extreme wall shear stress and heat flux events in compressible turbulent boundary layers

This study presents a comprehensive analysis on the extreme positive and negative events of wall shear stress and heat flux fluctuations in compressible turbulent boundary layers (TBLs) solved by direct numerical simulations. To examine the compressibility effects, we focus on the extreme events in two representative cases, i.e. a supersonic TBL of Mach number $M=2$ and a hypersonic TBL of $M=8$ , by scrutinizing the coherent structures and their correlated dynamics based on conditional analysis. As characterized by the spatial distribution of wall shear stress and heat flux, the extreme events are indicated to be closely related to the structural organization of wall streaks, in addition to the occurrence of the alternating positive and negative structures (APNSs) in the hypersonic TBL. These two types of coherent structures are strikingly different, namely the nature of wall streaks and APNSs are shown to be related to the solenoidal and dilatational fluid motions, respectively. Quantitative analysis using a volumetric conditional average is performed to identify and extract the coherent structures that directly account for the extreme events. It is found that in the supersonic TBL, the essential ingredients of the conditional field are hairpin-like vortices, whose combinations can induce wall streaks, whereas in the hypersonic TBL, the essential ingredients become hairpin-like vortices as well as near-wall APNSs. To quantify the momentum and energy transport mechanisms underlying the extreme events, we proposed a novel decomposition method for extreme skin friction and heat flux, based on the integral identities of conditionally averaged governing equations. Taking advantage of this decomposition method, the dominant transport mechanisms of the hairpin-like vortices and APNSs are revealed. Specifically, the momentum and energy transports undertaken by the hairpin-like vortices are attributed to multiple comparable mechanisms, whereas those by the APNSs are convection dominated. In that, the dominant transport mechanisms in extreme events between the supersonic and hypersonic TBLs are indicated to be totally different.

Simulation of dynamic changes in fluid parameters and flow patterns during condensation

The three-dimensional numerical simulation of the R32 flow condensation is conducted in a circular microchannel with a hydraulic diameter of 1 mm, and the setting of two phase inlets is applied to the transient simulation. The temporal process of flow patterns, velocity contour and temperature contour are obtained for inlet vapor quality of 0.5 and mass flow rate of 100, 150 and 200 kg/(m2·s), respectively. The corresponding relationship between each flow pattern and its internal parameters along the flow direction during condensation are studied in detail. The fluid in the microchannel undergoes annular, slug, bubbly and shrinking bubbly flow in sequence. The fluctuations of wall shear stress (WSS) and turbulent intensity (TI) caused by the oscillation of velocity gradient are the most intense near the transition point of flow regimes. Revealing the relationship between WSS, TI and flow patterns is an excellent supplement to the existing condensation flow. The local heat flux reaches its extreme value at the head of downstream of the annular flow, injection flow and slug flow. Similarly, the fluid temperature fluctuates violently at the same location. The time-average heat transfer coefficient of annular flow is higher than that of other flow patterns, and the peak value of heat transfer coefficient is located at the head of annular flow downstream under different mass flow rates.

Direct numerical simulations of turbulent pipe flow up to

Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10{\rm \pi} R$ at friction Reynolds numbers up to $Re_\tau =5200$ using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor $\lambda$ overshoots by $2\,\%$ and undershoots by $0.6\,\%$ the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $\lambda$ in our results is slightly higher than in Pirozzoli et al. (J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichi et al. (Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to $y^+=250$ , has not yet developed a plateau farther away from the wall in the pipes even for the $Re_\tau =5200$ cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with $Re_\tau$ – are lower in the pipe than in the channel, but the difference decreases with increasing $Re_\tau$ . While the wall value is slightly lower in the channel than in the pipe at the same $Re_\tau$ , the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a $k^{-1}$ dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

Aneurysm Neck Overestimation has a Relatively Modest Impact on Simulated Hemodynamics.

Overestimation of intracranial aneurysm neck width by 3D angiography is a recognized clinical problem, and has long been a concern for image-based computational fluid dynamics (CFD). Recently, it was demonstrated that neck overestimation in 3D rotational angiography (3DRA) could be corrected via segmentation with upsampled resolution and gradient enhancement (SURGE). Our aim was to leverage this approach to determine whether and how neck overestimation actually impacts CFD-derived hemodynamics. A subset of 17 cases having the largest neck errors from a consecutive clinical sample of 60 was segmented from 3DRA using both standard watershed and SURGE methods. High-fidelity, pulsatile CFD was performed, and a variety of scalar hemodynamic parameters that have been associated with aneurysm growth and/or rupture status were derived. With a few exceptions, flow and wall shear stress (WSS) patterns were qualitatively similar between neck-overestimated and corrected models. Sac-averaged WSS values were significantly lower after neck correction (p = 0.0005) but were highly correlated with their neck-overestimated counterparts (R2 = 0.98). Jet impingement was significantly more concentrated in the neck-corrected vs. -uncorrected models (p = 0.0011), and only moderately correlated (R2 = 0.61). Parameters quantifying velocity or WSS fluctuations were not significantly different after neck correction, but this reflected their poorer correlations (R2 < 0.4). Nevertheless, for all hemodynamic parameters, median absolute differences were < 26%, and no parameter had more than 5/17 cases with absolute differences > 50%. Differences in hemodynamicsdue to neck width overestimationwere found to be at most equal to, and often less than, those reported for other sources of error/uncertainty in intracranial aneurysm CFD, such as solver settings or assumed inflow rates.

Numerical study of wall shear stress fluctuations and near-wall structures in a square duct at low Reynolds numbers

Direct numerical simulations (DNS) of turbulent flow through a square duct at two different low Reynolds numbers is performed using OpenFOAM to study the instantaneous wall shear stress fluctuations and near-wall structures. We first benchmarked our simulation results against other DNS studies which used higher-order spectral methods, thereby confirming the accuracy of our results. The mean profile of streamwise wall shear stress is well studied in the literature, however its higher order statistics has not been yet explored. There is also a lack of information on the spanwise component of wall shear stress and its higher-order statistics. Here, we provide an extensive study on streamwise and spanwise wall shear stresses, and their higher-order statistics. The intensities of both components of wall shear stress fluctuations are close to zero near the corner, and monotonically increase while moving towards the duct center. This is in contrast with their mean profiles which do not exhibit similar monotonic trends. However, the third-order moment, i.e. skewness of the streamwise wall shear stress again shows a non-monotonic behavior from the corner to the center. The profiles of the mean as well as the higher-order statistics of wall shear stress follow a better scaling between the two Reynolds number studied, when the spanwise location is normalized using inner scaling. Streamwise velocity correlations near the wall show that the flow structures in a square duct are similar to that of a channel flow near the center, whereas there is a cross-talk of the flow structures between the neighboring walls near the corner. An investigation into the effect of corner on the probability of back flow events is made at a Reynolds number lower than previously reported. The probability follows a non-monotonic behavior as we move from the corner towards the center, where it reaches a minimum at around 50 wall units from the corner. Similar to the wall shear stress profiles, the behavior of the near-wall flow structures as well as the spanwise variation of the probability of backflow events also show a qualitatively similar trend for the two Reynolds numbers, when the spanwise location is normalized using inner scaling.

Appraisal of cavity hot-wire probes for wall-shear-stress measurements

Flush-mounted cavity hot-wire probes have emerged as an alternative to classical hot-wire probes mounted several diameters above the surface for wall-shear stress measurements. They aim at increasing the frequency response and accuracy by circumventing the well-known issue of heat transfer to the substrate that hot-wire and hot-film probes possess. Their use, however, depends on the assumption that the cavity does not influence the flow field. In this study, we show that this assumption does not hold, and that turbulence statistics are modified by the presence of the cavity with sizes that are practically in use. The mean velocity and fluctuations increase near the cavity while the shear stress decreases in its surroundings, all seemingly stemming from the fact that the no-slip condition is not present anymore and that flow reversal occurs. Overall, the energy spectra and the probability density function of the wall shear stress fluctuations indicate a change of nature of turbulence by the presence of the cavity.

Positive and negative pairs of fluctuating wall shear stress and heat flux in supersonic turbulent boundary layers

The negative and positive fluctuations of wall shear stress τ′x and wall heat flux q′w can be related to the wall-attached paired up large-scale velocity and temperature streaks. It is justifiable to infer the spatially paired-up coexistence of those wall flow quantities. The present study aims at testifying this hypothesis. We establish such relations between the negative and positive wall shear stress by exploiting a direct numerical simulation database over heated and cooled walls at the friction Reynolds number of 800 and the Mach number of 2.25. The clustering method is adopted for the search of the in-pair structures. It is found that the τx- and qw-structures are less self-similar for flows over cold walls. As they become wider, the τx-structures are increasingly more streamwise stretched, while the trend is reversed for qw-structures. τx-structures of opposite signs are paired up and aligned in the spanwise directions as the wall-attached streamwise velocity, and are left behind by streamwise rollers. The relative position between qw-structures of opposite signs, on the other hand, is sensitive to the wall temperature. Scrutinizing the statistical structures, we elucidate that such spatial coherence is determined by the meandering of velocity streaks that yields strong streamwise gradients of the streamwise velocity.

Numerical analysis of wall shear stress in a rotating drum based on two fluid model

A better understanding of the interaction between particle and the wall in rotating drums is of great interest. Two Fluid Model (TFM) coupled with kinetic theory of granular flow (KTGF) is used for investigating the wall shear stress of particle phase in a rotating drum. The distribution characteristic of wall shear stress and the effects of operation parameters and contact parameters on wall shear stress are analyzed. The results show that except the fluctuation of wall shear stress with time, its distribution is basically fixed which corresponds to the stable granular flow. The wall shear stress increases with increasing rotational speed and fill level while the degree of increase gradually decreases. With increasing of specularity coefficient which is defined as the average fraction of relative tangential momentum transferred in a particle-boundary collision, the position of shoulder region of granular flow changed a little while the position of toe region is relatively fixed. The distribution of wall shear stress has no essential difference and only a slight increase of its average value with increasing angle of friction with a constant specularity coefficient. Fig. 2. The distribution of wall shear stress of the rotating drum at different times at 65 rpm. • Wall shear stress was studied using TFM coupled with KTGF. • The effect of operation parameters on wall shear stress is analyzed. • The effect of contact parameters on wall shear stress is analyzed.

Wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence, part I: One-point statistics

This two-part study investigates the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. In the first part, we focus on their one-point statistics, including the root mean square (r.m.s.), skewness factor (third-order moment), flatness factor (fourth-order moment), and their correlations. By exploiting the direct numerical simulation databases, we found that the r.m.s. of the streamwise wall shear stress and pressure, the skewness factor of all the flow quantities considered, and the flatness factor of streamwise wall shear stress monotonically vary with the friction Mach number (Mτ), while for the rest, the wall heat flux and global temperature parameters should be taken into account as well for a monotonic trend of variation. The correlation coefficients between wall shear stress, pressure, and heat flux fluctuations increase with the Mach number Mτ, suggesting the underlying interactions between dynamic and thermodynamic processes. The distributions of spectra and probability density functions indicate that the increased correlation is induced by the highly intermittent traveling wave packets among the streaky structures, as reflected by the “double-peak” feature of the spectra that gradually emerges with the increasing compressibility effects. The probability density distribution also manifests the alteration of the occurrence of extreme events caused by these structures. By accordingly decomposing the fluctuations with cutoff filtering, it is found that the root mean squares of streamwise wall shear stress and heat flux fluctuations related to the streaky structures are Mach number-independent, while those related to the traveling wave packets monotonically increase with the friction Mach number.

Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence. II. Spectra, correlation and nonlinear interactions

Wall shear stress, pressure, and heat flux are of significant importance in engineering applications. In this two-part study, we investigate the compressibility effects on wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence by exploiting direct numerical simulation databases. In Paper I, we primarily deal with the one-point statistics, whereas in this second part, we report the effects of compressibility on the frequency spectra, wavenumber-frequency spectra of these flow quantities, and the two-point cross-correlations between them. It is found that the scaling laws of the spectra at low and high frequencies are retained as those of incompressible flows, whereas the spectra intensities at mid frequencies increase with the enhancement of compressibility effects, which is identified to be related to the ever-predominating traveling wave packets. These wave packets are convected downstream at the same velocity of 0.87Ub as that of pressure fluctuations, higher than that of the streaky structures 0.65Ub (Ub the bulk velocity), and enhance the space and time cross correlation between wall shear stress, pressure, and heat flux fluctuations. By extracting the envelopes of the traveling wave packets and inspecting the time and space correlations between the envelopes and the streaky structures, we found that the emergence of traveling wave packets comes later than the streaky structures, both in time and space. Based on these observations, we provide a depiction of the physical processes regarding the formation and evolution of the traveling wave packets.

Effects of wall temperature on two-point statistics of the fluctuating wall shear stress and heat flux in supersonic turbulent boundary layers

In the present study, we investigate two-point statistics of fluctuating streamwise wall shear stress τ′x and wall heat flux q′w by exploiting a direct numerical simulation database of supersonic turbulent boundary layers over a heated wall and a cooled wall at the friction Reynolds number around 800. By separately investigating positive and negative families of τx′ and qw′ with the aid of the conditional correlation analysis, we identify the asymmetrical deformation of τ′x and q′w, reminiscent of and ascribed to the asymmetrical deformations of sweeps and ejections events. The degree of such asymmetry is alleviated by the lower wall temperature. The spatial orientation of τx′ is insensitive to the wall temperature, whereas the spanwise elongated q′w that is closely related to the wall pressure is manifested merely in the cooled-wall case. The cross correlation between τx′ and the fluctuating streamwise velocity u′ reveals that low-speed streaks related to negative τx′ are more inclined to the wall than high-speed ones related to positive τx′ by 4°–5°, and that the phase lag between negative τx′ and u′ is larger than that between positive τx′ and u′ except in the near-wall region. Such a difference is proportional to the wall distance and should be considered for models predicting near-wall and wall quantities using signals in the logarithmic layer.

Consistency between the attached-eddy model and the inner–outer interaction model: a study of streamwise wall-shear stress fluctuations in a turbulent channel flow

The inner–outer interaction model (Marusic et al., Science, vol. 329, 2010, pp. 193–196) and the attached-eddy model (Townsend, Cambridge University Press, 1976) are two fundamental models describing the multiscale turbulence interactions and the organization of energy-containing motions in the logarithmic region of high-Reynolds-number wall-bounded turbulence, respectively. In this paper, by coupling the additive description with the attached-eddy model, the generation process of streamwise wall-shear fluctuations, resulting from wall-attached eddies, is portrayed. Then, by resorting to the inner–outer interaction model, the streamwise wall-shear stress fluctuations generated by attached eddies in a turbulent channel flow are isolated. Direct comparison between the statistics from these two models demonstrates that they are consistent with and complement each other. Meanwhile, we further show that the superpositions of attached eddies follow an additive process strictly by verifying the validity of the strong and extended self-similarity. Moreover, we propose a Gaussian model to characterize the instantaneous distribution of streamwise wall-shear stress, resulting from the attached-eddy superpositions. These findings are important for developing an advanced reduced-order wall model.

Bottom wall shear stress fluctuations in shallow-water Langmuir turbulence

In neutrally stratified shallow water, full-depth Langmuir cells (LCs) can interact with the turbulent benthic boundary layer and, thus, influence bottom wall shear stresses. In this paper the impacts of full-depth LCs on the streamwise and spanwise wall shear stresses are systematically studied using the database obtained from wall-resolved large-eddy simulation of shallow-water Langmuir turbulence. Analyses focus on the instantaneous wall shear stress fluctuations and the joint probability density functions between the stress fluctuations and the LCs parts of the velocity fluctuations, which show that the linear superimposition effect and nonlinear modulation effect of LCs are responsible for the spanwise organized distribution of wall shear stress fluctuations. Compared with the statistics in pure shear-driven turbulence without LCs, the mean square values of wall shear stress fluctuations in shallow-water Langmuir turbulence are enhanced by the strong linear superimposition effect of LCs, while the skewness and kurtosis are reduced by the combination of the linear superimposition effect and nonlinear modulation effect of LCs. Based on the scalings of these effects, a new predictive model of wall shear stress fluctuations is proposed for shallow-water Langmuir turbulence. The proposed model can predict the spatial distribution and statistics of wall shear stress fluctuations using the LCs parts of velocity fluctuations measured above the water bottom. Owing to the persistence of the spanwise inhomogeneity of wall shear stresses induced by full-depth LCs, the new predictive model will be useful for improving the wall-layer modelling for shallow-water Langmuir turbulent flows.

Insights Into the Low Rate of In-Pump Thrombosis With the HeartMate 3: Does the Artificial Pulse Improve Washout?

While earlier studies reported no relevant effect of the HeartMate 3 (HM3) artificial pulse (AP) on bulk pump washout, its effect on regions with prolonged residence times remains unexplored. Using numerical simulations, we compared pump washout in the HM3 with and without AP with a focus on the clearance of the last 5% of the pump volume. Results were examined in terms of flush-volume (Vf, number of times the pump was flushed with new blood) to probe the effect of the AP independent of changing flow rate. Irrespective of the flow condition, the HM3 washout scaled linearly with flush volume up to 70% washout and slowed down for the last 30%. Flush volumes needed to washout 95% of the pump were comparable with and without the AP (1.3–1.4 Vf), while 99% washout required 2.1–2.2 Vf with the AP vs. 2.5 Vf without the AP. The AP enhanced washout of the bend relief and near-wall regions. It also transiently shifted or eliminated stagnation regions and led to rapid wall shear stress fluctuations below the rotor and in the secondary flow path. Our results suggest potential benefits of the AP for clearance of fluid regions that might elicit in-pump thrombosis and provide possible mechanistic rationale behind clinical data showing very low rate of in-pump thrombosis with the HM3. Further optimization of the AP sequence is warranted to balance washout efficacy while limiting blood damage.

Inner-outer decomposition of wall shear stress fluctuations in turbulent channels

Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components. The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions, and the small-scale one is obtained by subtracting the large-scale one from the total, which fully remove the outer influences. We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000, while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000. Therefore, a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000. The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number, and empirical fitting expressions are given in this work.