In this study, which is numerical in nature, direct numerical simulation (DNS) of the pipe flow is performed. For the DNS a solenoidal spectral method is employed, this involves the expansion of the velocity using divergence free functions which also satisfy the prescribed boundary conditions, and a subsequent projection of the N-S equations onto the corresponding dual space. The solenoidal functions are formulated in Legendre polynomial space, which results in more favorable forms for the inner product integrals arising from the Petrov-Galerkin scheme employed. The developed numerical scheme is also used to investigate the effects of spanwise oscillations and phase randomization on turbulence statistics, and drag, in turbulent incompressible pipe flow for low to moderate Reynolds numbers (i.e. $mathrm{Re} sim 5000$) ).

<p>This Master thesis has been performed at CTD- the Centre for Wood Technology and Design at the University of Linköping and has been carried out in Santa Cruz de la Sierra in Bolivia.</p><p>The objective of this thesis is to study the mechanical properties and uses of Guadua chacoensis, a bamboo native to Bolivia. Throughout history, bamboo has been used in many countries for a variety of purposes. In Asia bamboo is an important raw-material for buildings and furniture. It is also used for making paper and for land rehabilitation and fuel. In South America many countries, among them Bolivia, have great potential to use bamboo in the same way. One of the key ideas with this Master thesis is to make a contribution to support the Bolivian economy and welfare by elucidate this, hitherto undeveloped, natural resource.</p><p>This thesis is a Minor field study partly financed by Sida- the Swedish International Development Cooperation Agency. During the field study theoretical studies were made, collecting local and international information about bamboo and Guadua chacoensis in particular. Laboratory tests were prepared and conducted at UPSA- the Private University of Santa Cruz de la Sierra and several localities of the plant were visited.</p><p>Through tensile-, bending- and hardness test it is found that Guadua chacoensis is a flexible, medium soft material and is comparable with European oak when it comes to the tensile strength. This leads to the conclusion that this bamboo species, among other fields of applications, can be used for constructions, like houses and bridges, and furniture manufacturing.</p> / <p>Diese Diplomarbeit wurde durch das CTD- Zentrum für Holztechnik und Design an der Universität Linköping betreut und in Santa Cruz de la Sierra in Bolivien durchgeführt.</p><p>Das Ziel dieser Arbeit ist es die mechanische Beanspruchung und die Anwendungen von Guadua chacoensis , einer bolivischen Bambusart, zu untersuchen. Bambus wurde in der Vergangenheit in vielen Ländern für die unterschiedlichsten Anwendungen wie zum Beispiel Häuser, Werkzeug, Möbel, Lebensmittel, Treibstoff und Papier verwendet.</p><p>In meisten asiatischen Ländern ist Bambus ein wichtiger Rohstoff für kleine und mittlere Unternehmen. Damit werden Arbeitsplätze geschaffen, was der Bevölkerung hilft die Armutsgrenze zu überwinden. Auch in Lateinamerika haben viele Länder, wie zum Beispiel Bolivien, die Chance Bambus in der gleichen Weise zu nutzen. Ein zentraler Gedanke dieser Arbeit ist es daher eine Grundlage für die bolivische Wirtschaft zu schaffen damit dieser bislang kaum entwickelte Rohstoff genutzt werden kann.</p><p>Diese Arbeit wurde von Sida- der Schwedischen Internationalen Entwicklungsorganisation, teilweise finanziell unterstützt. Im Rahmen der durchgeführten Studie wurden sowohl theoretische Aspekte betrachtet, als auch Versuche im Labor der privaten Universität von Santa Cruz de la Sierra durchgeführt. Des Weiteren wurden verschiedene Arten des Bambus in der Natur untersucht.</p><p>Biege- Streck- und Festigkeitsversuche haben gezeigt, dass Guadua chacoensis ein flexibles und weiches Material ist. Von den Streckeigenschaften ist es mit europäischer Eiche zu vergleichen. Diese Ergebnisse führen zu der Schlussfolgerung, dass Guadua chacoensis für die Konstruktion von Häusern und Brücken, für die Herstellung von Möbeln und andere ähnliche Anwendungen eingesetzt werden kann.</p> / <p>Esta tesis ha sido realizada en el Centro de Ciencia de Madera y Diseño- CTD</p><p>de la Universidad de Linköping y ha sido llevada a cabo en la ciudad de Santa Cruz de la Sierra, Bolivia.</p><p>El objetivo de la tesis es estudiar los propiedades mecánicas y usos de la</p><p>Guadua chacoensis, un bambú nativo de Bolivia. A lo largo de la historia, el bambú ha sido utilizado en muchas localidades del mundo en distintas aplicaciones, vale mencionar: viviendas, herramientas, muebles, alimentos, combustible, papel y para rehabilitación de la tierra. En casi todos los países Asiáticos el bambú es un recurso importante para empresas de tamaño pequeño y mediano, proporcionando empleo y contrarrestando la pobreza.</p><p>En América Latina muchos países, incluyendo Bolivia, tienen potencial para aprovechar el bambú del mismo modo. Una de las ideas más importantes de la tesis es hacer una contribución para apoyar a la economía de Bolivia, la cual, hasta ahora, ha desarrollado muy poco este recurso natural.</p><p>La tesis es un Minor field study parcialmente financiado por Asdi- la Agencia Sueca de Cooperación Internacional para el Desarrollo. Durante el Minor field study estudios teóricos fueron realizados, acumulando información nacional e internacional sobre bambú y Guadua chacoensis en particular. Para examinar los propiedades mecánicos de la Guadua chacoensis, pruebas de laboratorio fueron preparadas y efectuadas en la Universidad Privada de Santa Cruz de la Sierra. Asimismo, muchas áreas con bosques naturales donde crece la especie fueron visitadas.</p><p>A través de pruebas de laboratorio de tracción, flexión y dureza ha sido demostrado que la Guadua chacoensis es un material flexible y de dureza media, comparable con el roble europeo cuando se trata de la fuerza de tracción. Eso tiene como resultado que la Guadua chacoensis, entre otros campos de aplicación, puede ser usada para construcciones, como casas y puentes, y para la manufacturación de muebles.</p> / <p>Detta examensarbetete har gjorts vid CTD- Centrum för Träteknik och Design vid Linköpings universitet och har utförts i Santa Cruz de la Sierra i Bolivia.</p><p>Syftet med detta examensarbete är att studera de mekaniska egenskaperna och användningsområden för Guadua chacoensis, en boliviansk bambuart. Genom historien har bambu använts i en mängd olika applikationer såsom hus, verktyg, möbler, mat, bränsle, papper och land-rehabilitering. I de flesta asiatiska länder är bambu en viktig resurs för små- och medelstora företag vilket skapar arbetstillfällen och motverkar fattigdom. I Sydamerika finns många länder, däribland Bolivia, vilka har stora möjligheter att utnyttja bambu på samma sätt. En av huvudidéerna med detta examensarbete är att kunna gynna den bolivianska välfärden genom att belysa denna, hittills outvecklade naturresurs.</p><p>Detta examensarbete är en Minor field study, delvis finansierad av Sida, styrelsen för internationellt utvecklingssamarbete. Under fältarbetet genomfördes teoretiska studier då internationell och inhemsk information om bambu, speciellt om Guadua chacoensis, samlades in. Olika områden där arten växer besöktes och hållfasthetstekniska tester genomfördes vid UPSA- Universidad Privada de Santa Cruz de la Sierra.</p><p>Genom drag-, böj- och hårdhetsprovning har det påvisats att Guadua chacoensis är ett böjligt och medelhårt material med en draghållfasthet som är jämförbar med den för Europeisk ek. Detta gör att denna bambuart lämpar sig bland annat för konstruktioner, såsom hus och broar, samt möbeltillverkning.</p>

No description available.

<p>The project was conducted on a small-scale catchment at Goedertrou in the Riebeek- Kasteel district. The focus of this study was to address some of the hydrological processes active in the research catchment, namely infiltration, run-off and sediment mobilisation on different soil types. It was done to investigate the origin of Berg River pollutants. To answer the overall question about what influence the natural salt load of the Berg River, a number of subprojects have been identified, one of which is to understand the hydrological processes in the soil mantle and vadose zone. Hence, the study aimed to answer the research questions mentioned and discussed in section 1.3 of Chapter 1. Considering the results, it could be suggested that decayed root systems from the rows of plants, soil cracks, small channels and openings created by small animals, as well as slope orientation and, therefore, soil composition, all played a major role in influencing the ability of the soil to absorb the simulated rainfall. In this study, the factors that influenced run-off are micro topography, soil moisture, root system, animal activities in soil profile, soil crack dimensions and the hydraulic conductivity. The main factors that played a major role to influence sediments mobilisation are strongly believed to be the micro topography within the ring, slope gradient and length, vegetation cover and rainfall-simulation intensity. After using different techniques, the results show that farmers must be aware that with storm rainfall, particles smaller than 65 &mu / m are subject to mobilisation. It is important to let land-users know that they need proper and appropriate methods for land-use.</p>

This thesis is an experimental study of turbulent flows over smooth and rough walls in a channel that consists of an upstream parallel section to produce a fully developed channel flow and a diverging section to produce an adverse pressure gradient (APG) flow. The roughness elements used were two-dimensional square ribs of nominal height k = 3 mm. The ribs were secured to the lower wall of the channel and spaced to produce the following three pitches: 2k, 4k and 8k, corresponding to d-type, intermediate and k-type rough walls, respectively. For each rough wall type, the ribs were inclined at 90°, 45° and 30° to the approach flow. The velocity measurements were performed using a particle image velocimetry technique. The results showed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. The level of turbulence production and Reynolds stresses were significantly increased by roughness beyond the roughness sublayer. It was observed that the population, sizes and the level of organization of hairpin vortices varied with roughness and more intense quadrant events were found over the smooth wall than the rough walls. APG reinforced wall roughness in augmenting the equivalent sand grain roughness height, turbulence production and Reynolds stresses. APG also reduced the sizes of the hairpin packets but strengthened the quadrant events in comparison to the results obtained in the parallel section. The secondary flow induced by inclined ribs significantly altered the distributions of the flow characteristics across the span of the channel. Generally, the mean flow was less uniform close to the trailing edge of the ribs compared to the flows at the mid-span and close to the leading edge of the ribs. The Reynolds stresses and hairpin packets were distinctly larger close to the trailing edge of the ribs. Rib inclination also decreased the drag characteristics and significantly modified the distributions of the Reynolds stresses and quadrant events. In the parallel section, the physical sizes of the hairpin packets were larger over 45° ribs whereas in the diverging section, the sizes were larger over perpendicular ribs.

Previous field demonstration projects in metro-Atlanta have shown that seep berms, which are elongated sedimentation basins at the outlet of a disturbed land area, can provide high suspended sediment trap efficiencies with respect to coarse sediments on construction sites having drainage areas greater than five acres. Previous literature has shown that vegetative filter strips are efficient traps for fine suspended sediment in stormwater runoff. A combination of a seep berm and vegetative filter in series was studied in this thesis as an erosion control measure with quantification of its flow resistance and sediment removal efficiency. First, a field demonstration project was implemented to evaluate seep berms as a viable erosion control measure through a side-by-side comparison with the more commonly-used silt fences on construction sites with drainage areas less than five acres in metro Atlanta. High suspended sediment trap efficiencies were recorded for the seep berm on two separate sites, and the seep berm was shown to be superior to silt fences with respect to sediment control in the site runoff. Then a vegetative filter was studied in the laboratory in a specially-built flume for that purpose. The relationship between vegetative drag coefficient and various parameters reflecting flow conditions and vegetation density in steady, uniform open channel flow was studied in the flume. Both rigid, emergent vegetation and submerged, flexible vegetation were studied at two different plant densities. The application of porous media flow concepts to open channel flow through vegetation resulted in a collapse of data for vegetative drag coefficient for the various vegetation types and densities into a single relationship when plotted against vegetative stem Reynolds number. Point velocity and turbulence intensity profiles at different locations in the vegetative filter were recorded with an acoustic Doppler velocimeter to observe the turbulence structure of the flow and its effects on vegetative drag and settling of sediment. A sediment slurry consisting of a suspension of fine sand was fed into the flume, and an automated sampler was used to measure suspended sediment concentrations along the vegetative filter length for a series of discharges from which sediment flux and trap efficiency could be determined. Experimental data for trap efficiency were plotted against a dimensionless settling efficiency for each type of vegetation and density. These relationships, along with the one developed for the coefficient of drag, were applied in a numerical design technique that allows designers to determine the flow depth, velocity and trap efficiency of a vegetative filter of known dimensions for a given flow rate, sediment grain size distribution, slope, and vegetation density. In a typical design example, the combined trap efficiency proved that a seep berm followed by a vegetative filter can be a very effective erosion control measure.

This thesis is an experimental study of turbulent flows over smooth and rough walls in a channel that consists of an upstream parallel section to produce a fully developed channel flow and a diverging section to produce an adverse pressure gradient (APG) flow. The roughness elements used were two-dimensional square ribs of nominal height k = 3 mm. The ribs were secured to the lower wall of the channel and spaced to produce the following three pitches: 2k, 4k and 8k, corresponding to d-type, intermediate and k-type rough walls, respectively. For each rough wall type, the ribs were inclined at 90°, 45° and 30° to the approach flow. The velocity measurements were performed using a particle image velocimetry technique. The results showed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. The level of turbulence production and Reynolds stresses were significantly increased by roughness beyond the roughness sublayer. It was observed that the population, sizes and the level of organization of hairpin vortices varied with roughness and more intense quadrant events were found over the smooth wall than the rough walls. APG reinforced wall roughness in augmenting the equivalent sand grain roughness height, turbulence production and Reynolds stresses. APG also reduced the sizes of the hairpin packets but strengthened the quadrant events in comparison to the results obtained in the parallel section. The secondary flow induced by inclined ribs significantly altered the distributions of the flow characteristics across the span of the channel. Generally, the mean flow was less uniform close to the trailing edge of the ribs compared to the flows at the mid-span and close to the leading edge of the ribs. The Reynolds stresses and hairpin packets were distinctly larger close to the trailing edge of the ribs. Rib inclination also decreased the drag characteristics and significantly modified the distributions of the Reynolds stresses and quadrant events. In the parallel section, the physical sizes of the hairpin packets were larger over 45° ribs whereas in the diverging section, the sizes were larger over perpendicular ribs.

There is currently a great deal of interest within the aviation community in the design of small, slow-flying but manoeuvrable uninhabited vehicles for reconnaissance, surveillance, and search and rescue operations in urban environments. Inspired by observation of birds, insects, fish and cetaceans, flapping wings are being actively studied in the hope that they may provide greater propulsive efficiencies than propellers and rotors at low Reynolds numbers for such Micro-Air Vehicles (MAVs). Researchers have posited the Strouhal number (combining flapping frequency, amplitude and forward speed) as the parameter controlling flapping wing aerodynamics in cruising flight, although there is conflicting evidence. This thesis explores the effect of flapping frequency and amplitude on forces and wake structures, as well as physical mechanisms leading to optimum propulsive efficiency. Two-dimensional rigid airfoils are considered at Reynolds number 2,000 ??? 40,000. A compressible Navier-Stokes simulation is combined with numerical and analytical potential flow techniques to isolate and evaluate the effect of viscosity, leading and trailing edge vortex separation, and wake vortex dynamics. The wake structures of a plunging airfoil are shown to be sensitive to the flapping frequency independent of the Strouhal number. For a given frequency, the wake of the airfoil exhibits ???vortex lock-in??? as the amplitude of motion is increased, in a manner analogous to an oscillating circular cylinder. This is caused by interaction between the flapping frequency and the ???bluff-body??? vortex shedding frequency apparent even for streamlined airfoils at low Reynolds number. The thrust and propulsive efficiency of a plunging airfoil are also shown to be sensitive to the flapping frequency independent of Strouhal number. This dependence is the result of vortex shedding from the leading edge, and an interaction between the flapping frequency and the time for vortex formation, separation and convection over the airfoil surface. The observed propulsive efficiency peak for a pitching and plunging airfoil is shown to be the result of leading edge vortex shedding at low flapping frequencies (low Strouhal numbers), and high power requirements at large flapping amplitudes (high Strouhal numbers). The efficiency peak is governed by flapping frequency and amplitude separately, rather than the Strouhal number directly.

The interaction of a shock wave with a boundary layer is a classic viscous/inviscid interaction problem that occurs over a wide range of high speed aerodynamic flows. For example, on transonic wings, in supersonic air intakes, in propelling nozzles at offdesign conditions and on deflected controls at supersonic/transonic speeds, to name a few. The transonic interaction takes place at Mach numbers typically between 1.1 and 1.5. On an aerofoil, its existence can cause problems that range from a mild increase in section drag to flow separation and buffeting. In the absence of separation the drag increase is predominantly due to wave drag, caused by a rise in entropy through the interaction. The control of the turbulent interaction as applied to a transonic aerofoil is addressed in this thesis. However, the work can equally be applied to the control of interaction for numerous other occurrences where a shock meets a turbulent boundary layer. It is assumed that, for both swept normal shock and unswept normal shock interactions, as long as the Mach number normal to the shock is the same, then the interaction, and therefore its control, should be the same. Numerous schemes have been suggested to control such interaction. However, they have generally been marred by the drag reduction obtained being negated by the additional drag due to the power requirements, for example the pumping power in the case of mass transfer and the drag of the devices in the case of vortex generators. A system of piezoelectrically controlled flaps is presented for the control of the interaction. The flaps would aeroelastically deflect due to the pressure difference created by the pressure rise across the shock and by piezoelectrically induced strains. The amount of deflection, and hence the mass flow through the plenum chamber, would control the interaction. It is proposed that the flaps will delay separation of the boundary layer whilst reducing wave drag and overcome the disadvantages of previous control methods. Active control can be utilised to optimise the effects of the boundary layer shock wave interaction as it would allow the ability to control the position of the control region around the original shock position, mass transfer rate and distribution. A number of design options were considered for the integration of the piezoelectric ceramic into the flap structure. These included the use of unimorphs, bimorphs and polymorphs, with the latter capable of being directly employed as the flap. Unimorphs, with an aluminium substrate, produce less deflection than bimorphs and multimorphs. However, they can withstand and overcome the pressure loads associated with SBLI control. For the current experiments, it was found that near optimal control of the swept and unswept shock wave boundary layer interactions was attained with flap deflections between 1mm and 3mm. However, to obtain the deflection required for optimal performance in a full scale situation, a more powerful piezoelectric actuator material is required than currently available. A theoretical model is developed to predict the effect of unimorph flap deflection on the displacement thickness growth angles, the leading shock angle and the triple point height. It is shown that optimal deflection for SBLI control is a trade-off between reducing the total pressure losses, which is implied with increasing the triple point height, and minimising the frictional losses.

The scope of this work is the theoretical and computational modeling of the interaction between a Newtonian fluid and a cellular biological medium attached on the surface of a vessel. First and foremost, an extensive and comprehensive review is presented with regard to the available approaches for modeling momentum transfer within cellular biological media, including single-scale-single-phase approaches, Biot's poroelasticity, mixture theory, upscaling methods and multiscale computational equation free methods. Thereafter, at the cellular biological medium level, a theoretical model is developed for the description of momentum transfer within a poroelastic biomaterial, taking into account the interaction between the extracellular fluid and the solid skeleton that consists of cells and extracellular matrix (ECM). A continuum based formulation of momentum transport in a fluid-solid system at the finer spatial scale is used as starting point, and then the method of local spatial averaging with a weight function is implemented in order to establish the partial differential equations that describe the dynamics of fluid flow and matrix deformation at the coarser (macroscopic) spatial scale. In the special case of a homogeneous medium and under certain other conditions, the derived equations become similar to those which are postulated in the theory of interacting continua (mixture theory) and Biot's theory of poroelasticity. At the vessel level, the contribution of this work is twofold. First, a benchmark problem is developed for the validation of numerical methods used to solve problems that involve interactions between a fluid and a poroelastic material. Specifically, an analytical solution is developed for the problem of plane Couette-Poiseuille flow past a poroelastic layer. Second, a computational study is performed for plane Poiseuille flow past and through a semi-elliptical poroelastic biomaterial, which is attached to the surface of a straight vessel. Fluid flow in the clear fluid region is described by the Navier-Stokes equations, and momentum transfer within the biomaterial is described by the upscaled biphasic equations established in this work. The effect of the Reynolds and Darcy number that characterize the flow past and through the biomaterial, respectively, is investigated for obstacles with different configuration with respect to flow (semicircle, oblate semi-ellipse, prolate semi-ellipse). The distribution of the von Mises stress within the biomaterial is determined and, also, the drag and lift forces exerted by the fluid on the biomaterial are calculated. / Στόχος της παρούσας εργασίας είναι η θεωρητική και υπολογιστική μοντελοποίηση της αλληλεπίδρασης μεταξύ ενός Νευτώνειου ρευστού και ενός κυτταρικού βιολογικού υλικού το οποίο βρίσκεται προσκολημμένο στην επιφάνεια ενός αγγείου. Αρχικά παρουσιάζεται μια εκτεταμένη και περιεκτική ανασκόπηση των διαθέσιμων προσεγγίσεων για τη μοντελοποίηση της μεταφοράς ορμής σε κυτταρικά βιολογικά υλικά, συμπεριλαμβανομένων των προσεγγίσεων μιας κλίμακας και μιας φάσης, της θεωρίας ποροελαστικότητας του Biot, της θεωρίας αλληλεπιδρώντων συνεχών, των τεχνικών αλλαγής κλίμακας προς τα άνω, και τέλος, των υπολογιστικών τεχνικών πολλαπλών κλιμάκων χωρις τον ορισμό καταστατικών εξισώσεων. Στην συνέχεια, στο επίπεδο του κυτταρικού βιολογικού υλικού, αναπτύσεται ένα θεωρητικό μοντέλο για την περιγραφή της μεταφοράς ορμής εντός ενός ποροελαστικού υλικού, λαμβάνοντας υπόψη την αλληλεπίδραση μεταξύ του εξωκυτταρικού ρευστού και της στερεής μήτρας που αποτελείται από τα κύτταρα και το δίκτυο εξωκυτταρικών πολυμερών. Ως σημείο εκκίνησης στην μικρότερη κλίμακα παρατήρησης, χρησιμοποιείται μια περιγραφή της μεταφοράς ορμής που βασίζεται σε ένα συνεχές μοντέλο και έπειτα εφαρμόζεται η μέθοδος χωρικής στάθμισης μέσω συνάρτησης βάρους προκειμένου να εξαχθούν οι μερικές διαφορικές εξισώσεις που περιγράφουν την δυναμική της ροής του εξωκυτταρικού ρευστού και της παραμόρφωσης της στερεής μήτρας στην μακροσκοπική κλίμακα. Για την ειδική περίπτωση ενός ομογενούς μέσου και υπό την ισχύ ορισμένων πρόσθετων συνθηκών, οι εξαχθείσες εξισώσεις λαμβάνουν μορφή παρόμοια με αυτή των αντίστοιχων εξισώσεων οι οποίες ισχύουν στην θεωρία αλληλεπιδρώντων συνεχών καθώς και στην θεωρία ποροελαστικότητας του Biot. Στο επίπεδο του αγγείου, η συνεισφορά της παρούσας εργασίας λαμβάνει χώρα σε δύο άξονες. Κατά πρώτον, αναπτύσσεται ένα πρότυπο πρόβλημα το οποίο μπορεί να χρησιμεύσει για την επαλήθευση αριθμητικών μεθόδων που χρησιμοποιούνται για την επίλυση προβλημάτων στα οποία ενέχεται η αλληλεπίδραση ενός ρευστού με ένα ποροελαστικό υλικό. Συγκεκριμένα, εξάγεται μια αναλυτική λύση σε κλειστή μορφή για το πρόβλημα της επίπεδης ροής Couette-Poiseuille μέσα και γύρω από ένα ποροελαστικό στρώμα. Κατά δεύτερον, διεξάγεται μια υπολογιστική μελέτη της επίπεδης ροής Poiseuille μέσα και γύρω από ένα ημιελλειπτικό ποροελαστικό βιολογικό υλικό, το οποίο βρίσκεται προσκολημμένο στην επιφάνεια ενός ευθύγραμμου αγγείου. Στην περιοχή καθαρού ρευστού, η ροή περιγράφεται από τις εξισώσεις Navier-Stokes , ενώ η μεταφορά ορμής εντός του βιολογικού υλικού περιγράφεται με τις εξισώσεις που εξήχθησαν σε αυτή την εργασία μέσω της μεθόδου χωρικής στάθμισης. Η επίδραση των αριθμών Reynolds και Darcy, οι οποίοι χαρακτηρίζουν τη ροή γύρω και μέσα από το βιολογικό υλικό αντίστοιχα, διερευνάται για εμπόδια με διάφορες γωμετρικές διαμορφώσεις (ημικύκλιο, και ημιέλλειψη). Προσδιορίζεται η χωρική κατανομή της τάσης von Mises εντός του βιολογικού υλικού και, επιπρόσθετα, υπολογίζονται η οπισθέλκουσα και η ανυψωτική δύναμη που ασκούνται από το ρευστό στο υλικό.