Cette thèse porte sur l’étude expérimentale de la réduction de traînée par injection de bulles. Le contexte de l’étude est lié à la propulsion navale. Les bulles peuvent, lorsqu’elles sont injectées dans la couche limite en développement le long des carènes de navires, contribuer à réduire significativement la résistance de frottement, en allégeant d’une part le fluide le long de la coque et d’autre part en interagissant avec les structures turbulentes de proche paroi. La configuration expérimentale retenue pour cette étude est l’écoulement de Taylor-Couette, avec cylindre extérieur fixe et injection de bulles calibrées. Nos investigations portent sur les régimes de transition, de turbulence naissante et turbulent avec persistance des cellules de Taylor (Re≤20.104). La taille des bulles varie avec le capillaire et le mélange utilisés, entre 0,05 et 0,12 fois la largeur de l’entrefer. Une méthode originale de suivi de la phase dispersée dans un plan méridien, couplée à des mesures de couple global appliqué au cylindre intérieur ont permis de mettre en évidence deux régimes de réduction de traînée et plusieurs types d’arrangements des bulles, en fonction de leur taille et du nombre de Reynolds. Les bulles peuvent avoir une trajectoire glissante, oscillante, être capturées par les cellules de Taylor ou en proche paroi du cylindre intérieur dans les zones de jets sortants. La caractérisation par PIV des vitesses de la phase liquide en monophasique et diphasique a permis d’étudier les modifications induites par les bulles sur la phase liquide et de discuter des mécanismes impliqués dans la modification du couple global par la présence des bulles. Il ressort de cette étude que pour les nombres de Reynolds en deçà de la capture, les bulles contribuent à stabiliser l’écoulement en accord avec une réduction du couple visqueux pouvant atteindre -30% pour des taux de vide très faible (< 1%). Pour des nombres de Reynolds plus élevés, la capture dans les cellules conduit à une réduction de la longueur d’onde axiale et une augmentation de la vorticité des cellules, associée à une augmentation des vitesses rms. Cette configuration est favorable à une augmentation du couple visqueux. A l’inverse, la capture des bulles dans le jet sortant conduit à une augmentation de la longueur d’onde axiale, associée à une diminution de la vorticité. Cette configuration est favorable à une réduction du couple visqueux, moins marquée qu’en absence de capture. / This work presents experimental study of drag reduction by injection of bubbles. Injection of bubbles into the developing boundary layer along the hulls of ships could help to reduce significantly the frictional resistance by lowering a fluid along the hull and interacting with the near-wall turbulent structures. We investigate the interactions between bubbles, the coherent motion and the viscous torque in a Taylor-Couette flow for outer cylinder at rest, while bubbles are injected constantly through a needle. The Reynolds number ranges up to Re≤20.104, for these values of the Reynolds number, Taylor vortices are persistent leading to an axial periodicity of the flow. Bubbles size varies between 0.05 and 0.12 times the width of the gap, depending on the needle and the liquid used. An original method for tracking bubbles in a meridian plane coupled with measures of overall torque applied to the inner cylinder helped to highlight two regimes of drag reduction and various types of arrangements of bubbles, depending on their size and Reynolds number. Bubbles could have a sliding motion, wavering, be captured by the Taylor cells or in the outflow areas near the inner cylinder. Characterization of the liquid velocity by PIV both in single phase and two-phase flow helped to study the modifications induced by the bubbles on the liquid phase and to discuss about the mechanisms involved in the changes induced by the bubbles in the overall torque. The study show that for the Reynolds number before the capture, bubbles could help to stabilize the flow in agreement to the reduction of the viscous torque up to -30% for lowest void fraction (<1%). For the Reynolds number after the capture, bubbles trapped by the Taylor cells lead to a reduction of the axial wavelength and increasing of the vorticity of the cells, associated to an increasing of the rms. This configuration leads to an increasing of the viscous torque. However, bubbles trapped in the outflow areas near the inner cylinder lead to an increasing of the axial wavelength, associated to a decreasing of the vorticity. The configuration supports a smaller reduction of the viscous torque than in the case without captured.

Im Rahmen des Transferprojektes T01 „Textilbeschichtung mit hochviskosen Massen“ des Sonderforschungsbereiches 532 (SFB 532) wird die Realisierung und Bewertung eines integrierten Beschichtungskonzeptes zur nachhaltigen Verbesserung der Tragfähigkeit von textilbewehrten Betonbauteilen an der RWTH Aachen University untersucht. Dazu wird eine neue Auftragstechnik für hochviskose Beschichtungsmassen entwickelt, die eine vollständige Penetration von Multifilamentgarnen mit großen Garntitern und einer hohen Anzahl an Filamenten in textilen Gelegen erzielt. Des Weiteren werden aktive Beschichtungsmassen auf der Basis von Polyvinylalkohol-Zement-Compositen, die eine homogene Anbindung aller Einzelfilamente an die Zementmatrix ermöglichen, erforscht.

Cette thèse concerne l’aérodynamique de pales d'extrémité transsonique. Ces pales sont conçues pour maximiser le rendement en croisière, tout en générant la traction requise au décollage. Elles ont des profils fins et peu cambrés, travaillant à forte incidence au décollage, ce qui peut entraîner l’apparition d’un tourbillon de bord d’attaque (TBA). Or ce TBA présente des similitudes avec les tourbillons d’apex d’aile Delta, connus pour leur capacité à générer de la portance tourbillonnaire.Cette étude consiste à examiner l’intérêt du TBA pour les performances aérodynamiques.La démarche a consisté dans un premier temps à caractériser la topologie du TBA sur une maquette représentative d’une pale d’ Open Rotor, à l'aide d'essais PIV résolus en temps et de calculs RANS k-omega SST, et à évaluer la capacité de la simulation RANS à reproduire les caractéristiques d’intérêt pour cette étude. Un algorithme a été développé afin d'estimer la contribution de ce TBA à la portance à partir du champ de pression pariétal RANS.Afin d'expliciter l'influence des paramètres géométriques et de fonctionnement de la pale sur la portance tourbillonnaire, un modèle 1D de la portance tourbillonnaire a été développé puis couplé à la méthode de l'élément de pale.Les premières comparaison de géométries à iso-traction ont montré que la portance tourbillonnaire permet de générer la traction requise au décollage avec une surface alaire plus faible. Ces résultats ouvrent de nouvelles perspectives pour la conception de géométries avec un meilleur rendement en croisière. / This thesis deals with the aerodynamic properties of propeller blades. Those blades are designed to maximise cruise efficiency, while achieving the target thrust at take-off. Their thin, low-cambered profiles must work at high incidence at take-off, which may give rise to a leading-edge vortex (LEV).The topology of this LEV looks similar to Delta wing LEVs, which are known to generate vortex lift.the aim of this study is to explore the probable impact of the LEV on lift at take-off in order to reconsider propeller blade designs. The approach first consisted in caracterising the LEV topology on a model blade representative of an Open Rotor front blade, using both Time-Resolved PIV and RANS k-omega SST calculations. The comparison between both methods demonstrated the ability of RANS calculations to reproduce the LEV characteristics of interest to this study.Then, the LEV contribution to lift was evaluated thanks to an algorithm developed to estimate vortex lift contribution from RANS wall pressure fields.In order to explicit the influence of the blade's geometrical and functioning parameters on vortex lift, a 1D vortex lift model was developed and coupled to the Blade Element Momentum Theory.The first blade geometry comparative studies at iso-thrust showed that vortex lift enables to generate target thrust at take-off with a lower blade surface. This opens new perspectives for the design of blade geometries with enhanced cruise efficiency.

Current research within the field of ultrasound contrast agents (UCAs) aims at developing capsules which are not only acoustically active, but also have a chemically modifiable surface. This enables use in new areas, including targeted drug delivery and theranostics. For such purposes, air-filled microbubbles (MBs) with a polyvinyl alcohol (PVA) shell are being studied. Ultrasound imaging velocimetry (UIV) is a technique used to evaluate various types of liquid flows by tracking patterns caused by UCAs across ultrasound images, and has shown great potential for flow measurements in terms of accuracy. The aim of this thesis was to implement a basic UIV program in Matlab to investigate the flow behavior of air-filled PVA MBs being pumped through a phantom, mimicking a blood vessel. The images were acquired using the programmable Verasonics research system by plane wave imaging with coherent compounding, and UIV was implemented as a post-processing technique. Three parameters were varied to study how the UIV performance and flow behavior of the MBs were affected: the concentration of MBs, the flow velocity, and the transducer voltage. The resulting velocity vector fields showed that it is possible to track PVA MBs using the implemented UIV program, and that the concentration 5·106 MBs/ml gave the best results out of the five concentrations tested. The generated velocity vector fields indicated a turbulent and pulsatile flow behavior, which was in line with the predicted flow behavior, although there was a disparity between the measured average flow velocity of the MBs and the predicted flow velocity. It was also observed that the MBs were increasingly pushed in the axial direction with increasing voltage, as according to theory. Even though a more advanced UIV algorithm could improve the accuracy of the velocity measurements, the results show possible use of air-filled PVA MBs in combination with UIV. / Nuvarande forskning inom ultraljudskontrastmedel syftar till att utveckla kapslar som inte bara är akustiskt aktiva, utan som även har en kemiskt modifierbar yta. Detta möjliggör användning inom nya områden, så som målinriktade läkemedel och theanostics. För detta syfte studeras luftfyllda mikrobubblor med ett skal av polyvinylalkohol (PVA). Ultrasound imaging velocimetry (UIV) är en teknik som används för att analysera olika typer av vätskeflöden genom att spåra mönster orsakade av ultraljudskontrastmedel över ett antal ultraljudsbilder. Metoden har visats ha stor potential för flödesmätningar, och hög noggrannhet har uppnåtts. Detta projekt syftade till att implementera ett grundläggande UIV-program i Matlab för att undersöka flödesbeteenden hos luftfyllda PVA-mikrobubblor som pumpas genom en modell av ett blodkärl. Ultraljudsbilderna togs med hjälp av det programmerbara forskningssystemet Verasonics, genom att använda planvågsavbildning och coherent compounding, och UIV implementerades som ett efterbearbetningsprogram. Tre parametrar varierades för att studera hur prestandan av UIV-programmet och flödesbeteendet hos mikrobubblorna påverkades: koncentrationen av mikrobubblor, flödeshastigheten, och spänningsamplituden hos ultraljudsproben. De resulterande hastighetsvektorfälten visade det möjligt att evaluera flödesbeteenden hos PVA-mikrobubblor med hjälp av det implementerade UIV-programmet. Bäst resultat erhölls genom att använda koncentrationen 5·106 mikrobubblor/ml, av de fem testade koncentrationerna. De genererade hastighetsvektorfälten indikerade ett turbulent och pulserande flöde, vilket överensstämde med teorin, trots att det fanns skillnader mellan genomsnittliga uppmätta flödeshastigheter och den beräknade flödeshastigheten. Det kunde också observeras att mikrobubblorna trycktes i den axiella riktningen när spänningsamplituden ökade, vilket överensstämde med teorin. Trots att metodens noggrannhet skulle kunna ökas genom att använda ett mer avancerat UIV-program, visade resultaten på möjligheten att använda luftfyllda PVA-mikrobubblor i kombination med UIV.

Master of Science / Department of Grain Science and Industry / Kingsly Ambrose / Consistent and reliable flow of bulk wheat from hoppers and silos is very significant in wheat handling and processing. Bulk wheat flow challenges such as inconsistent flow, arching, etc., are common during handling. The irregular size and non-uniformity of physical properties, the presence of impurities affects the flow behavior during discharge. Chaff and insects infested kernels are the two most common impurities present in wheat. In this research, the effect of these two impurities on their physical and flow properties of wheat were studied. Physical and flow indicators, such as bulk, tapped, particle densities, angle of repose, Hausner’s ratio, Carr index, and porosity measures the flowability of uncompacted bulk solids. Meanwhile, flow properties tested by shear testing principle based on Jenike’s method, simulated bulk wheat under pressure in bins/hoppers. The dynamic properties tested quantify the energy required to flow, compressibility and permeability at dynamic handling situations. Due to the presence of impurities and moisture content differences, bulk density and angle of repose of wheat varied from 801.54kg/m3 to 718.36kg/m3, and 23.6° to 38.4°, respectively. Angle of internal friction and wall friction angle that reflect interaction between particles and particle with bins/hopper walls, ranged from 23.95° to 43.13° and 15.46° to 20.33°, respectively. In addition to instrumental flow property evaluation, the flow profile, discharge rate, and particle velocity during hopper flow of bulk wheat was studied using Particle Image Velocimetry method. Mass flow and funnel flow hopper dimensions were used for this flow profile analysis. The discharge rate decreased from 1.67 to 1.12 kg/s for mass flow and 1.42 to 0.86 kg/s for funnel flow when the chaff in bulk wheat increased from 0% to 7.5% (weight basis). Analysis of the active flow zone indicated that bulk wheat without chaff had a uniform flow compared to wheat with chaff in the bulk. The findings from this study will be useful for design of hopper bottom bins and handling equipment based on the wheat quality and percent moisture content.

Cardiovascular disease, mostly atherosclerosis, is responsible for one third of all deaths globally, rising to more than 50% in the Western World. Risk factors include smoking, diet, and familial history. Doppler ultrasound can provide estimates of blood velocity and wall shear rate. Clinically, maximum velocity is used to categorise patients for surgery, although Doppler velocity measurement is prone to errors and in need of validation. Wall shear stress—which can be derived from wall shear rate—plays a role in disease initiation and progression, although its clinical utility is unclear due to difficulties associated with its measurement. This thesis investigates the use of Doppler ultrasound as a tool to estimate blood velocity and wall shear rate. A simplified method for estimation of wall shear rate in healthy arteries is developed that uses spectral Doppler ultrasound. This method is based upon the theory of oscillatory flow in rigid pipes, requiring two measurements that are readily available with clinical ultrasound machines. This method is compared to a similar method based on colour flow imaging. The spectral Doppler method underestimated the theoretic value of wall shear rate by between 7 and 22%, with results varying between phantoms. Errors for the colour method were on average 35% greater. Test measurements from one healthy volunteer demonstrated that this method can be applied in-vivo. In more advanced stages of disease, peak velocity distal to a stenosis is of clinical interest and the simplified method for wall shear rate estimation is invalid. Steady flow in a series of simplified stenosis geometries was studied using a dual-beam Doppler system to obtain velocity vectors. These measurements were compared with data from an equivalent system that used particle image velocimetry (PIV) and was considered the gold standard. For Reynolds numbers at the stenosis throat of less than 800, flow remained laminar over the region studied, although distal flow separation did occur. For higher throat Reynolds numbers—corresponding to more severe stenoses or increased flow rates—asymmetric recirculation regions developed; the transition to turbulence occurred more proximally, with a corresponding reduction in stenotic jet and recirculation length. Qualitative agreement was observed in the velocity profile shapes measured using ultrasound and PIV at throat Reynolds numbers less than 800. Above this threshold the qualitative agreement between the velocity profiles became poorer as both downstream distance and the degree of stenosis increased. Peak axial velocity distal to the stenosis was underestimated, on average, by 15% in the ultrasound system. Estimation of shear rate remained difficult with both experimental techniques. Under a Newtonian approximation, the normalised wall shear stresses agree qualitatively. Under pulsatile flow conditions using an idealised flow waveform, superior qualitative agreement was observed in the velocity profiles at diastole than at systole. Similar to the steady flow behaviour, this agreement deteriorated with stenosis severity. The current generation of clinical ultrasound machines are capable of estimating the wall shear rate in healthy arteries. In the presence of significant arterial disease, errors in the peak velocity may result in mis-selection of patients for surgery, while estimation of the wall shear stress remains extremely problematic; particularly with identifying the wall location and measuring velocities close to the wall.

Master of Science / Department of Mechanical and Nuclear Engineering / B. Terry Beck / Mohammad H. Hosni / Cavitation is the change of a liquid to a two-phase mixture of liquid and vapor, similar to boiling. However, boiling generates a vapor by increasing the liquid temperature while cavitation generates vapor through a decrease in pressure. Both processes are endothermic, removing heat from the surroundings. Both the phase change and heat absorption associated with cavitation provide many engineering applications, including contributing to a new type of refrigeration cycle under development. Cavitation can occur at or below the vapor pressure; conditions that delay cavitation and allow for a metastable liquid are not well understood. A converging-diverging nozzle was designed and fabricated to create a low pressure region at the nozzle throat. The converging section of the nozzle increased the water velocity and decreased the pressure, according to Bernoulli’s principle. A cavitation front was formed slightly past the nozzle throat. The cavitation location suggested that the water was metastable near the nozzle throat. Flow through the system was controlled by changing the nozzle inlet and outlet pressures. The flowrate of water was measured while the outlet pressure was lowered. The flowrate increased as the outlet pressure dropped until cavitation occurred. Once cavitation initiated, the flow became choked and remained constant and independent of the nozzle outlet pressure. High-speed imagery was used to visualize the flow throughout the nozzle and the formation and collapse of cavitation in the nozzle’s diverging section. High-speed video taken from 1,000 to 35,000 frames per second captured the formation of the cavitation front and revealed regions of recirculating flow near the nozzle wall in the diverging section. Particle Image Velocimetry (PIV) was used to measure the velocity vector field throughout the nozzle to characterize flow patterns within the nozzle. PIV showed that the velocity profile in the converging section and throat region were nearly uniform at each axial position in the nozzle. In the diverging section, PIV showed a transient, high-velocity central jet surrounded by large areas of recirculation and eddy formation. The single-phase experimental results, prior to cavitation onset, were supplemented by Computational Fluid Dynamics (CFD) simulations of the velocity distribution using Fluent software.

Plasma synthetic jet actuators are investigated experimentally, in which the geometrical design of single dielectric barrier discharge (SDBD) plasma actuators is modified to produce zero-mass flux jets similar to those created by mechanical devices. The SDBD plasma actuator consists of two rectangular electrodes oriented asymmetrically and separated by a layer of dielectric material. Under an input of high voltage, high frequency AC or pulsed DC, a region of plasma is created in the interfacial air gap on account of electrical breakdown of the ambient air. A coupling between the electric field in the plasma and the neutral air near the actuator is introduced, such that the latter experiences a net force which results in a horizontal wall jet. This effect of the actuator has been demonstrated to be useful in mitigating boundary layer separation in aerodynamic flows. To increase the impact that a plasma actuator may have on the flow field, this research investigates the development and characterization of a novel flow control device, the plasma synthetic jet actuator, which tailors the residual air in the form of a vertical jet resembling conventional continuous and synthetic jets. This jet can be either three dimensional using annular electrode arrays, or nearly two dimensional using two rectangular strip exposed electrodes and one embedded electrode. Detailed measurements on the isolated plasma synthetic jet reveal that pulsed operation of the actuator results in the formation of multiple counterrotating vortical structures in the flow field. The output jet velocity and momentum are found to be higher for unsteady pulsing as compared to steady operation. In the case of flow over a flat plate, the actuator is observed to create a localized interaction region within which the baseline flow direction and boundary layer characteristics are modified. The efficiency of the actuator in coupling momentum to the neutral air is found to be related to the plasma morphology, pulsing frequency, actuator dimension, and input power. An analytical scaling model is proposed to describe the effects of varying the above variables on the output jet characteristics and actuator efficiency, and the experimental data is used for model validation.

Atherosclerosis and related cardiovascular diseases (CVDs) are amongst the largest causes of morbidity and mortality in the developed world, causing considerable monetary pressure on public health systems worldwide. Atherosclerosis is characterised by the build up of vascular plaque in medium and large arteries and is a direct precursor to acute vascular syndromes such a myocardial infarction, stroke or peripheral arterial diseases. The causative factors leading to CVD still remain relatively poorly understood, but are becoming increasingly identifiable as a dysfunction of the endothelial cells that line the arterial wall. It is well known that the endothelium responds to the prevailing fluid mechanic (i.e. haemodynamic) environment, which plays a crucial role in the localised occurrence of atherosclerosis near vessel bends and bifurcations. In these areas, disturbed haemodynamics lead to flow separation and very low wall shear stress (WSS), which directly affects the functionality of the endothelium and impedes the transport of important blood borne agonists and antagonists. Detailed full field measurements assessing complex haemodynamics are sparse and consequently this thesis aims to address some of the important questions related to arterial haemodynamics and CVD by performing in-vitro flow measurements in physiologically relevant conditions. In particular, this research develops and uses state-of-the-art Particle Image Velocimetry (PIV) techniques to measure three-dimensional velocity and WSS fields in scaled models of the human carotid artery. For this purpose, the necessary theoretical and experimental concepts are developed and in-depth analyses of the underlying factors affecting the local haemodynamics and their relation to CVD are carried out. In the first part, a methodology for the construct of transparent hydraulic flow phantoms from medical imaging data is developed. The arterial geometries are reproduced in optically clear silicone and the flowing blood is modelled with a refractive index matched blood analogue. Subsequently, planar and Stereo-PIV techniques are developed and verified. A novel interfacial PIV (iPIV) technique is introduced to directly measure WSS by inferring the velocity gradient from the recorded particle images. The new technique offers a maximal achievable resolution of 1 pixel and therefore removes the resolution limit near the wall usually associated with PIV. Furthermore, the iPIV performance is assessed on a number of numerical and experimental test cases and iPIV offers a significantly improved measurement accuracy compared to more traditional techniques. Subsequently, the developed methodologies are applied in three studies to characterise the velocity and WSS fields in the human carotid artery under a number of physiological and experimental conditions. The first study focuses on idealised vessel geometries with and without disease and establishes a general understanding of the haemodynamic environment. Secondly, a physiological accurate vessel geometry under pulsatile flow conditions is investigated to provide a more realistic representation of the true in-vivo flow conditions. The prevailing flow structure in both cases is characterised by flow separation, strong secondary flows and large spatial and temporal variations in WSS. Large spatial and temporal differences exist between the different geometries and flow conditions; spatial variations appear to be more significant than transient events. Thirdly, the three-dimensional flow structure in the physiological carotid artery model is investigated by means of stereoscopic and tomographic PIV, permitting for the first time the measurement of the full 3D-3C velocity field and shear stress tensor in such geometries. The flow field within the model is complex and three-dimensional and inherently determined by the vessel geometry and the build up of an adverse pressure gradient. The main features include strong heliocoidal flow motions and large spatial variations in WSS. Lastly, the physiological implications of the current results are discussed in detail and reference to previous work is given. In summary, the present research develops a novel and versatile PIV methodology for haemodynamic in vitro studies and the functionality and accuracy is demonstrated through a number of physiological relevant flow measurements.

The focus of this thesis is the study of turbulent solid-liquid stirred suspensions, which are involved in many common unit operations in the chemical, pharmaceutical and food industries. The studies of two-phase flows present a big challenge to researchers due to the complexity of experiments; hence there is a lack of quantitative solid and liquid hydrodynamic measurements. Therefore, an investigation of turbulence modulation by dispersed particles on the surrounding fluid in stirred vessels has been carried out, via two-phase fluorescent Particle Image Velocimetry (FPIV) and micromixing experiments. The main property of interest has been the local dissipation rate, as well as root-mean-square (rms) velocities and turbulent kinetic energy (TKE) of the fluid. Initially a single-phase PIV study was conducted to investigate the flow field generated by a sawtooth (EkatoMizer) impeller. The purpose of this study was to gain insight into various PIV techniques before moving on to more complex two-phase flows. Subsequently stereo-, highspeed and angle-resolved measurements were obtained. The EkatoMizer formed a good case study as information regarding its hydrodynamics is not readily available in literature, hence knowledge has been extended in this area. An analysis of the mean flow field elucidated the general structure of fluid drawn into the impeller region axially and discharged radially; the latter characterised the impeller stream. The radial rms velocity was considered to represent best the system turbulence, even though the tangential rms velocity was greater close to the blade; however the radial component was more prevalent in the discharge stream. Due to differences in rms velocities, TKE estimates obtained from two and three velocity components deviated, being greater in the latter case. Integral (1-D and 2-D) length scales were overestimated by the quantity W / 2 in the impeller region. Ratios of longitudinal-to-lateral length scales also indicated flow anisotropy (as they deviated from 2:1). The anisotropy tensor showed that the flow was anisotropic close to the blade, and returned to isotropy further away from the impeller. Instantaneous vector plots revealed vortices in the discharge stream, but these were not associated with flow periodicity. Alternatively, the vortex structures were interpreted as low frequency phenomena between 0-200 Hz; macro-instabilities were found to have a high probability of occurrence in the discharge stream. Dissipation is the turbulent property of most interest as it directly influences micromixing processes, and its calculation is also the most difficult to achieve. Its direct determination from definition requires highly resolved data. Alternative methods have been proposed in the literature, namely dimensional analysis, large eddy simulation (LES) analogy and deduction from the TKE balance. All methods were employed using 2-D and 3-D approximations from stereo-PIV data. The LES analogy was deemed to provide the best estimate, since it accounts for three-dimensionality of the flow and models turbulence at the smallest scales using a subgrid scale model. (Continues...).