In this study, the phenomenon of two-phase flow was investigated in a square channel. The experiment was performed with stagnant liquid conditions. The gas and liquid dynamics of the bubbly flow were observed in two regions far from the inlet. Air was inserted through a porous media at three superficial gas velocities: 4.6 mm/s, 2.5 mm/s, and 1.4 mm/s. Two techniques were applied in the experiment to measure the bubbly flow: an optical probe and an in-house developed tracking algorithm. Measurements of the bubble interface velocity, void fraction, bubble frequency, time of flight, and Sauter mean diameter were obtained by using the optical probe. The duration of the probe measurements for all three flow rates and both regions lasted approximately 33 hours. The tracking algorithm was used to analyze the experimental data for two visual methods: shadowgraphy and Particle Tracking Velocimetry (PTV). Shadowgraphy provided gas-phase measurements of the bubble centroid velocity and its fluctuations, void fraction, bubble size, and Reynolds stresses. Five data sets were acquired for each flow rate, resulting in a total of 327,540 shadowgraphy images. Liquid parameters such as the velocity, fluctuations in the velocity, and the Reynolds stresses were provided by PTV. Only one data set containing 10,918 images was obtained from liquid measurements for each flow rate. One data set was sufficient to provide reliable statistics since tracking two consecutive images lead to approximately 15,000 velocity vectors. The data obtained from this study was an effort to assist in the verification, validation, and improvement of two-phase flow simulations.

abstract: Multi-pulse particle tracking velocimetry (multi-pulse PTV) is a recently proposed flow measurement technique aiming to improve the performance of conventional PTV/ PIV. In this work, multi-pulse PTV is assessed based on PTV simulations in terms of spatial resolution, velocity measurement accuracy and the capability of acceleration measurement. The errors of locating particles, velocity measurement and acceleration measurement are analytically calculated and compared among quadruple-pulse, triple-pulse and dual-pulse PTV. The optimizations of triple-pulse and quadruple-pulse PTV are discussed, and criteria are developed to minimize the combined error in position, velocity and acceleration. Experimentally, the velocity and acceleration fields of a round impinging air jet are measured to test the triple-pulse technique. A high speed beam-splitting camera and a custom 8-pulsed laser system are utilized to achieve good timing flexibility and temporal resolution. A new method to correct the registration error between CCDs is also presented. Consequently, the velocity field shows good consistency between triple-pulse and dual-pulse measurements. The mean acceleration profile along the centerline of the jet is used as the ground truth for the verification of the triple-pulse PIV measurements of the acceleration fields. The instantaneous acceleration field of the jet is directly measured by triple-pulse PIV and presented. Accelerations up to 1,000 g's are measured in these experiments. / Dissertation/Thesis / M.S. Mechanical Engineering 2014

External Beam Radiation Therapy (EBRT) is a common treatment option for patients with prostate cancer. When treating the prostate with EBRT, a geometric volume (PTV margin) is added around the prostate to account for uncertainties in treatment planning and delivery. Current methods for estimating PTV margins rely on the analysis of population-based inter- and intra-fraction motion data. These methods do not consider the patient-to-patient differences in demographic or clinical presentation of patient specific factors (PSFs), such as age, weight, body-mass index, health and performance status, prostate-specific antigen levels, Gleason scores, presence of bowel problems, or other health conditions. The purpose of this thesis is to investigate the feasibility using regression-based predictive algorithms to predict the extent of prostate motion for the purpose of personalizing the PTV margin using PSFs as inputs. Benchmarking simulations of Linear, Ridge, LASSO, SVR, kNN, and MLP algorithms were performed by simulating prostate intra-fraction motion and realistic variations in PSFs. Sample sizes ranged from n=20 to 800, with varying levels of noise into the motion data (0-10mm). Leave-one-out cross validation was used to train and validate algorithm performance. The results suggest that algorithm performance improves significantly within the first 50 – 100 patients, and this rate of improvement is independent of noise in prostate motion. The Ridge regression algorithm predicted intra-fraction motion to the lowest mean absolute error in simulated motion, performing especially well in small datasets. To evaluate the clinical utility of this approach, pre- and post-treatment prostate motion data, treatment time data, and rectal distension data was recorded in 21 patients, along with a variety of PSFs. In the analysis of patient data, the LASSO algorithm out-performed the Ridge algorithm, predicting the mean and standard deviation of an individual prostate cancer patient’s intra-fraction motion to within 0.8mm and 0.4 mm mean absolute error, respectively. However, prostate motion predictions did not correlate with PSFs, possibly due to the small sample size. This work demonstrates the feasibility of using regression-based algorithms for predicting prostate motion, and hence the opportunity to personalize PTV margins in prostate cancer patients. / Graduate / 2018-08-22

The form and dynamics of ocean turbulence are critical to all marine processes; biological, chemical and physical. The three-dimensional turbulence characteristics of the bottom boundary layer of the coastal ocean are examined using a series of 29,991 instantaneous velocity distributions. These data, recorded by a submersible 3D-PTV system at an elevation of 0.64 m above the seabed, represent conditions typical of moderate tidal flows in the coastal ocean. A complexity associated with submersible 3D-PTV in the coastal ocean is that gaps and noise affect the accuracy of the data collected. To accommodate this, a new Physics-Enabled Flow Restoration Algorithm has been tested for the restoration of gappy and noisy velocity measurements where a standard PTV or PIV laboratory set-up (e.g. concentration / size of the particles tracked) is not possible and the boundary and initial conditions are not known a priori. This is able to restore the physical structure of the flow from gappy and noisy data, in accordance with its hydrodynamical basis. In addition to the restoration of the velocity flow field, PEFRA also estimates the maximum possible deviation of the output from the true flow. 3D-PTV measurements show coherent structures, with the hairpin-like vortices highlighted in laboratory measurements and numerical modelling, were frequently present within the logarithmic layer. These exhibit a modal alignment of 8 degrees from the mean flow and a modal elevation of 27 degrees from the seabed, with a mean period of occurrence of 4.3 sec. These appear to straddle sections of zero-mean along-stream velocity, consistent with an interpretation as packets. From these measurements, it is clear that data collected through both laboratory and numerical experiments are directly applicable to geophysical scales – a finding that will enable the fine-scale details of particle transport and pollutant dispersion to be studied in future. Conditional sampling of the Reynolds shear stress (without using Taylor’s hypothesis) reveals that these coherent structures are responsible for the vertical exchange of momentum and, as such, are the key areas where energy is extracted from the mean flow and into turbulence. The present study offers the first assessment of the magnitude of the errors associated with assuming isotropy on shear-based sensors of the TKE dissipation rate and its consequential effect on the Kolmogorov microscale using 3D-PTV data from the bottom boundary layer of the coastal ocean. The results indicate a high degree of spatial variability associated with the low conditions. The averaged data supports the validity of measurements obtained by horizontal and vertical profilers, however along-stream velocity derivatives underestimate the TKE dissipation rate by more than 40% – a factor of two higher than for the equivalent cross-stream and vertical estimates. This has important implications for the deployment of these sensors and the subsequent interpretation of higher-order statistics. Finally, the data have been processed to test four popular sub-grid scale (SGS) stress models and SGS dissipation rate estimates for Large-Eddy Simulations using these in situ experimental data. When the correlation and SGS model coefficients are assessed, the nonlinear model represents the best stress models to use for the present data, consistent with the substantial anisotropy and inhomogeneity associated with these flows. The detailed measurement and analysis of coherent structures in the coastal ocean undertaken therefore supports the development of numerical models and assists with the understanding of all marine processes.

La convection de Marangoni est un phénomène hydrodynamique qui apparaît en présence d'un gradient de tension de surface le long d'une interface entre deux fluides non miscibles. Il est possible de voir apparaître cette convection, dans les échangeurs de chaleur avec changement de phase, autour des bulles de vapeur. Cependant, la convection de Marangoni a longtemps été négligée devant les autres phénomènes intervenant dans le transfert de chaleur. A l'ère de la miniaturisation, il devient impossible de négliger cette micro convection. Le but de la thèse est donc de caractériser la dynamique d'écoulement de la convection de Marangoni autour d'une bulle. La première partie présente la résultats 2D obtenus autour d'une bulle d'air en présence d'un gradient de température. Ce cas est plus simple à mettre en oeuvre et permet ainsi de se familiariser avec la convection de Marangoni. La seconde partie porte cette fois-ci sur l'étude bidimensionnelle de cette convection autour d'une bulle de vapeur. Les résultats ont montré que le phénomène devenait très rapidement tridimensionnel . La dernière partie présente donc une méthode de mesure optique 3D innovatrice qui permet de connaître la dynamique de l'écoulement dans les trois dimensions et les trois composantes. / The Marangoni convection is a phenomenon that appears in the presence of a tension surface gradient along an interface between two immiscible fluids. It is possible to observe that appear convection around vapor bubbles in the heat exchangers with the phase change. However, the Marangoni convection has been neglected to other phenomena involved in the heat transfer. In the age of miniaturization, it becomes impossible to overlook this micro convection. The aim of this thesis si to characterize the dynamics of Marangoni convection around a bubble. The first part deals with the 2D results around an air bubble in the presence of a temperature gradient. This case is easier to implement and allows having a better knowledge with the Marangoni convection. The second part focuses on the two-dimensional study of the convection around a vapor bubble The results showed that the phenomenon quickly became three-dimensional. The last section therefore presents a method for measuring optical innovative 3D3C.

The main goal of my diploma thesis is the design of transport-engineering measures on the Svatoplukova street with the focus on the finalization of the Great Brno ring road and the following changes of traffic intensity. For the implementation and simulation of my designed measures, I used the PTV Vissim modeling software. The simulation outputs were then evaluated and transformed into recommendations to be taken into consideration during the creation of future traffic-engineering measures in the given area.

<p>The impinging jets atomizer is widely used in engineering applications. As two liquid jetsimpinging to each other, a liquid sheet is first formed and then breaks up into small dropletsto comply the atomization. The features such as size, shape, velocity, thickness, etc., of thesheet/droplet are controlled by various impingement parameters such as impinging angle,jet velocity, and physical properties of the liquid. Since the sheet generation is prior to thedroplet, the modeling of the sheet is the premise of the droplet modeling. Therefore, to studythe atomization of the impinging jet atomizer, it is important to pay effort on the research ofimpinging sheet both experimentally and theoretically. In this research, the characterizationof the impinging sheet formed by two jets is given in two specific aspects, the thicknessand the velocity. A non-intrusive measurement technique, partial coherent interferometry(PCI) is developed and applied to measure the thickness of the impinging sheet dynamically.The PCI unitizes the calibrated linear relationship between the optical path difference andthe degree of coherence to measure the impinging sheet thickness. By placing the sheet inone of the two branches of the designed interferometer, the optical path is altered basedon the sheet thickness and shown as the change of the degree of coherence of interferencepattern recorded by the camera. With a calibration process, the thickness of the sheet is thencan be measured via a designed interferometer. The velocity measurement of the impingingsheet is implemented via particle tracking velocimetry (PTV) adopted with the shadowgraphtechnique. To implement the particle tracking velocimetry, seeding particles are added intothe fluid and with the aid of an imaging acquiring system and the post-processing algorithm,the locations of those particles in different frames are identified. Thus, the velocity of the fluidis estimated as the velocity of the particles calculated from the recorded images. However,while applying the PTV to investigate the impinging sheet studied in this research, theparticles can be recorded at a large field of view with insufficient magnification. This is ownedto the so-called "particle induced lens effect" found when applying the small particles to athin liquid sheet. When the seeding particles move to the region where the sheet thicknesshas a similar scale as the particle, the fluid will wrap around the particle and act as a positivelens. For shadowgraph imaging, the collimated light forms an enlarged shadow at the image plane by passing through such lens. Experimentally, the thickness measurements via PCIare implied to the impinging sheet generated under a range of Reynolds number between 269to 370 and velocity measurements via PTV are implied to the ones under Reynolds numberof 362 to 430. The measured results for both thickness and velocity are different from thetheoretical model of the impinging sheet which implies the need for a review of sheet model.Therefore, in this research, the author proposed a revised impinging sheet model considerthe friction effect due to the air over the sheet. A theoretical analysis is made base on theboundary layer equation under the cylindrical coordinate with unique boundary conditionsassumed for the impinging sheet. By introducing the unique similarity variable found byauthor, the equation could be transformed to an ordinary differential equation and solvednumerically. The revised model first predict the air boundary layer profile over the sheet,then, estimate the sheet velocity profile as a function of the distance to the impinging pointand the azimuth angle. As a parameter of the revised sheet model, the jet velocity profilebefore the impingement is also assumed as a free jet gradually developed from a Posieuilleflow and estimated in advance. The revised model is compared with the experimental resultsand some key parameters are identified empirically.</p> <p>Other than the thickness and velocity, this research is also interested in measuring thegeometry of the sheet and the detached droplets. Thus, a multi-view digital inline holography(DIH) technique is developed to capture the three-dimensional shape of the impinging sheetand the locations of the droplets. The DIH determines the shape and location of the targetin a detection volume base on the recorded hologram. The MvDIH, as the name suggested,combines the DIH results from multiple orientations to reconstruct the shape and the locationof the target. Two reconstruction ideologies, cross-section based one and the outline basedone, are proposed. The former estimates the target by finding the intersection of the recordedcross-sections of the target from different views. The latter estimates the target geometryby combining the outlines determined by DIH at different views. To evaluate the feasibilityof such technique, a test model which imitates the droplet and liquid ligament structure isapplied to the measurement in this research. Yet, the application on a real impinging sheetis not implemented.</p>

Ces travaux de thèse s'incrivent dans le cadre du traitement de gaz acides et captage CO2 dans les colonnes à garnissages structurés. Les gaz à traiter réagissent avec un liquide s'écoulant à contre-courant sur des plaques métalliques dont la compléxité géométrique permet d'accroître l'aire d'échange, et donc l'efficacité du procédé. Dans un contexte de modélisation multi-échelles des contacteurs à garnissages structurés, les écoulements gaz-liquide à la plus petite échelle géométrique des plaques de garnissages (de l'ordre de l'épaisseur du film liquide) sont étudiés, pour améliorer la compréhension et la modélisation des écoulements diphasiques et phénomènes de mouillage dans les garnissages. L'objectif final est de développer une méthodologie CFD pour reproduire des écoulements diphasiques 3D sur des géométries complexes telles que les plaques de garnissages. Pour ce faire, il est nécessaire de progresser en méthodes numériques et de proposer des méthodes expérimentales pour observer des écoulements de film liquide sur des géométries complexes. Ces travaux comprennent une partie numérique et une partie expérimentale. Un écoulement sur une plaque de garnissage structuré peut présenter des zones sèches, et donc des lignes de contact (dynamiques), ce qui présente un défi en simulation numérique à cause des différentes échelles de l'écoulement. La méthodologie employée ici en simulation numérique consiste à résoudre l'écoulement jusqu'à une échelle intermédiaire en modélisant les effets des plus petites échelles. Le code de calcul Two-Phase Level-Set a été utilisé et modifié dans ce but. Différentes méthodes level-set ont d'abord été testées de manière à identifier une méthode satisfaisante quant à la réduction des erreurs de conservation de masse, un problème rencontré en level-set. Il est ici montré que certaines combinaisons de schémas de discrétisation spatiale et temporelle permettent de réduire considérablement ces erreurs de conservation de masse. Après avoir réalisé de nombreux tests de validation, une nouvelle méthode numérique est proposée pour simuler les grandes échelles d'écoulements diphasiques 3D avec ligne de contact dynamique en level-set, dans des conditions réalistes. La méthode est ici validée pour des écoulements axisymétriques de gouttes simulés en 3D, en régime visqueux et en régime inertiel, et pour des écoulements de gouttes sur plan incliné. Les résultats sont en très bon accord avec d'autres travaux numériques et expérimentaux. Afin de faciliter l'utilisation de cette méthodologie pour des applications industrielles, un modèle sous-maille similaire a été implémenté dans un code VOF commercial; les résultats sont aussi en très bon accord avec d'autres travaux. En plus de ces développements numériques, une campagne expérimentale est mise en oeuvre pour observer des écoulements de film liquide sur une plaque de garnissage structuré. Les méthodes expérimentales employées sont d'abord testées et validées pour des écoulements de film plat ou ondulé sur plan incliné, et ensuite utilisées pour observer des écoulements de film sur des plaques de garnissage. L'épaisseur de film liquide est mesurée aux creux et aux crêtes des picots des plaques de garnissages, pour différents débits, par imagerie confocale chromatique. Des lois de puissance de l'épaisseur de film en fonction du Reynolds sont proposées; celles-ci sont très différentes suivant la position des relevés de mesure, aux creux ou aux crêtes des picots. La vitesse à l'interface de l'écoulement gaz-liquide est aussi mesurée, par PIV et PTV, en utilisant des particules hydrophobes. Les résultats montrent que le liquide a tendance à dévier du creux des canaux (corrugations), et la norme de la vitesse semblent présenter des extremums correspondant aux creux et crêtes des picots. [...] / The work described in this thesis is motivated by the use of structured packing columns in acid gas treatment and post-combustion CO2 capture. In a counter-current mode, flue gases react with the liquid that flows down over metal sheets, the geometrical complexity of which allows increasing the specific interfacial area, and thereby the overall efficiency of the process. In the context of multiscale modeling of structured-packing contacting devices, the focus in this work is on the gas-liquid flows at the smallest geometrical scale of packing sheets, of the order of the liquid film thickness, aiming to improve understanding and modeling of two-phase flows and wetting phenomena in structured packings. The ultimate objective is to build up a CFD methodology to reproduce 3D two-phase flows over complex surfaces such as structured packing sheets. For this purpose, progress is necessary both in pertinent computational methods and in the adaptation of experimental methods for observing liquid film flows over complex surfaces. This thesis therefore consists of computational and experimental parts. Flows over structured packing sheets may exhibit dry zones, and hence (moving) contact lines, the numerical simulation of which presents a computational challenge due to the disparity in length scales involved. Here, the methodology for large-scale numerical simulations of flows with moving contact lines consists in resolving the flow down to an intermediate scale and modeling effects of smaller ones. The parallelized freeware Two-Phase Level-Set has been extended for this purpose. First though, because some level-set methods have been reproached to yield mass conservation issues, an assessment is made of the mass conservation properties of a range of level-set methods. It is demonstrated that the combined use of some spatial and temporal discretization schemes allows to drastically reduce mass conservation errors in level-set methods. Having thus implemented a level-set method with satisfactory performance at such tests (and others), a novel numerical method is proposed to perform 3D large-scale simulations of flows with moving contact lines in level-set, under realistic conditions. Validation tests of axisymmetric droplet spreading in a viscous, and in an inertial regime, simulated in 3D, and sliding drops are shown to be in excellent agreement with prior experimental and numerical work. The results show that complex contact-line dynamics observed in prior experimental studies on sliding droplets can be simulated using the present large-scale methodology. To facilitate dissemination of this work in industrial applications, a similar subgrid model has been implemented in a commercial volume-of-fluid code; results of validation tests are shown to be in excellent agreement with other work. These computational developments are accompanied by an experimental campaign to observe liquid film flows over structured packing sheets. All experimental methods used herein are tested and validated for flat and wavy films down an inclined plane before being used for observing liquid film flows over packing sheets. The film thickness is measured at local troughs and crests of small-scale corrugations of the structured packing sheet, for different flow rates, by Chromatic Confocal Imaging. Power laws of the Reynolds number for the mean liquid film thickness are suggested, with significant differences for measurements at crests compared to that at troughs. Interface velocity measurements are also performed by PIV and PTV using hydrophobic particles. Results reveal that the liquid tends to deviate from troughs of large-scale corrugations, and seems to exhibit local extrema of the velocity magnitude corresponding to troughs and crests of small-scale corrugations. [...]

The thesis describes state of the art volumetric measurement techniques and applies a 3D measurement technique, 3D Scanning Particle Tracking Velocimetry, to the transitional backward facing step flow. The measurement technique allows the spatial and temporal analysis of coherent structures apparent at the backward facing step. The thesis focusses on the extraction and interaction of coherent flow structures like shear layers or vortical structures.

The knowledge of the behavior of non-spherical particles suspended in turbulent flows covers a wide range of applications in engineering and science. Dispersed two-phase flows and turbulence are the most challenging subjects in engineering, and when combined it gives rise to more complexities as the result of the inherent stochastic nature of the turbulence of the carrier-phase together with the random distribution of the dispersed phase. Moreover, for anisotropic particles the coupling between the translation and rotation of particle increases the complication. Because of the practical importance of prolate particleladen turbulent flows, the plenty of numerical and experimental works have been conducted to study such suspensions. Numerical approaches have given valuable insight of turbulent suspension flows, although the computation has been only carried out at the macro scale and models, not including flow distortion around the particle, comprise the detail of the flow in the order of a particle size. In addition, the model of the forces imposed on the particle by the fluid and mass point treatment are strictly valid for infinitely small particle having size less than all scales of the fluid turbulence. Fully resolved solution at the scale of the dispersed phase in turbulent flows for high Reynolds number has been recently performed but is still a challenge. On the other hand, the presence of particle as the dispersed phase makes experimental measurements much more complicated than those with single phase as a result of particles interference. The area of considerable difficulty with this type of experiments is the measurement of the fluid-phase velocity remarkably close to the particle surface. Generally, experimental researches have been concentrated on measuring the mean velocity and Reynolds stresses of the carrier-phase, and the mean velocity, fluctuations, orientation and accumulation of the non-spherical particles. Higher-order quantities, including Lagrangian particle velocity correlations, the carrier-phase turbulence modulation, and two-particle and particlefluid velocity correlations are also of interest. It has been found that the rotational and translational movements of the fibershaped particle depend on the nature of carrier-phase field and fiber characteristics such as aspect ratio, fiber Stokes number, fiber Reynolds number, and the ratio of fiber to flow length scale. With the development of PIV (Particle Image Velocimetry) and PTV (Particle Tracking Velocimetry) techniques, it has been appeared that combined PIV/PTV will be the best available choice for the experimental study of dispersed two-phase flows. The purpose of combined PIV/PTV measurement of two-phase systems is simultaneous measurements of fluid and suspended objects, where the PIV measurement of the fluid phase are combined with PTV measurement of the dispersed phase. The objective of this doctoral thesis is to study the behavior of rod-like particles suspended in wall-bounded turbulent flow through simultaneous PIV/PTV measurements of the velocity of the flow field and particle motion. As a representative of rod-like particles, I have employed cellulose acetate fibers with the length to diameter ratio (aspect ratio) larger than one. Here, It has been considered only dilute suspensions with no flocculation; thus fiber-fiber interaction is negligible. The measurements have been conducted within the parallel planes (2D view) illuminated by laser in the streamwise direction in thin film suspension flowing on the water table setup at Linné FLOW Centre, KTH Mechanics Lab. It is shown that this setup is a well-behaved experimental model of half channel flows often used in Direct Numerical Simulation (DNS) investigations. Therefore, the experimental results are comparable to their DNS counterpart where it is convenient. A single camera PIV technique has been used to measure flowing suspension. Therefore, it has been needed to preprocess images using a spatial median filter to separate images of two phases, tracer particles as representative of fluid and fibers suspended. The well-known PIV processing algorithms have been applied to the phase of fluid. I have also introduced a novel algorithm to recognize and match fibers in consecutive images to track fibers and estimate their velocity. It is not feasible to study all relevant aspects of particle-laden turbulent flows in a single study. In this study, I present the statistics of the rotational and translational motion of fiber-like particles and the surrounding fluid velocity. To the author’s knowledge, remarkably little experimental work has been published to date on simultaneous measurement of fiber motion and turbulence field in a turbulent fiber suspension flow to reveal dynamics of fibers in this regime. Therefore, the results of this work will be profitable in better understanding of such multiphase flows. The statistical analysis of the translational motion of fibers shows that the size of fiber is a significant factor for the dynamical behavior of the fiber near the wall. It has been observed that, in the region near the wall, the probability of presence of the long fibers is high in both the high-speed and low-speed streaks of flow, and the mean velocity of fibers almost conforms to the mean velocity of flow; whereas the short fibers are mostly present in the low-speed areas, and the fiber mean velocity obey the dominant flow velocity in these areas. In the far-wall regions, the translation of fibers is practically unaffected by the aspect ratio, whereas it depends crucially on the wall-normal distance. Moreover, it was found that in the case of long fibers near the wall, the low speed fibers mostly are orientated in streamwise direction. On the other hand, there is no preferential orientation for fast long fibers. Although wall-normal velocities were not measured in this study, it is hypothesized that this behavior is a result of fibers being affected by the sweep and ejection events known to occur in wall-bounded turbulent flow. The fast fibers are in sweep environment and comes from the upper layer. The low speed fibers are into ejection areas in the vicinity of the wall, and the wall has a stabilizing effect on them. The short fibers are still oriented mostly in streamwise direction for a certain range of low velocity. Furthermore, since a considerable change of the fiber behavior is observed in a certain ratio of the fiber length to the fiber distance from the solid wall, it is supposed that this ratio is also a prominent parameter for the behavior of fiber near the wall. The results presented are in terms of viscous wall units wherever are denoted by superscript “+”.