Dissertations / Theses on the topic 'Wings – Mathematical models'

Thesis (M.S.)--Massachusetts Institute of Technology at Woods Hole Oceanographic Institution, 2006.
"September 2006." Description based on title screen as viewed on June 8, 2010. DTIC Descriptor(s): Doppler Radar, Wind Velocity, Sound Ranging, Doppler Sonar, Buoys, Measurement, Motion, Oceanographic Equipment, Theses DTIC Identifier(s): Doppler Sodar, Sodar (Sound Detection and Ranging), ASIS Includes bibliographical references (leaf 75). Also available in print.

The use of an ocean surface velocity dependent wind stress is examined in the context of a 3-layer double-gyre quasigeostrophic wind-driven ocean circulation model. The new wind stress formulation results in a large reduction of the power input by the wind into the oceanic circulation. This wind stress is proportional to a quadratic function of Ua--u o, where Ua is the wind at 10m above the ocean surface and uo is the ocean surface current. Because the winds are typically faster than the ocean currents, the impact of the ocean surface velocity on the wind stress itself is relatively small. However, the power input is found to be greatly reduced with the new formulation. This is shown by simple scaling argument and numerical simulations in a square basin. Our results suggest that the wind power input may be as much as 35% smaller than is typically assumed.
The ocean current signature is clearly visible in the scatterometer-derived wind stress fields. We argue that because the actual ocean velocity differs from the modeled ocean velocities, care must be taken in directly applying scatterometer-derived wind stress products to the ocean circulation models. This is not to say that the scatterometer-derived wind stress is not useful. Clearly the great spatial and temporal coverage make these data sets invaluable. Our point is that it is better to separate the atmospheric and oceanic contribution to the stresses.
Finally, the new wind stress decreases the sensitivity of the solution to the (poorly known) bottom friction coefficient. The dependence of the circulation strength on different values of bottom friction is examined under the standard and the new wind stress forcing for two topographic configurations. A flat bottom and a meridional ridge case are studied. In the flat bottom case, the new wind stress leads to a significant reduction of the sensitivity to the bottom friction parameter, implying that inertial runaway occurs for smaller values of bottom friction coefficient. The ridge case also gives similar results. In the case of the ridge and the new wind stress formulation, no real inertial runaway regime has been found over the range of parameters explored.

Coastal South African cities like Port Elizabeth are said to have a strong potential for wind energy. This study aims to model wind data in order to be able assess the power potential belonging to a given site. The main challenge in modelling wind direction data is that it is categorized as circular data and therefore requires special techniques for handling that are different from usual statistical samples. Statistical tools such as descriptive measures and distribution fitting, were re-invented for directional data by researchers in this field. The von Mises distribution is a predominant distribution in circular statistics and is commonly used to describe wind directions. In this study, the circular principles described by previous researchers were developed by using the statistical software, Mathematica. Graphical methods to present the wind data were developed to give an overview of the behaviour of the winds in any given area. Data collected at Coega, an area near Port Elizabeth, South Africa, was used to illustrate the models which were established in this study. Circular distributions were fit to the directional data in order to make appropriate conclusions about the prevailing wind directions in this area.

Systems biology aims to describe and understand biology at a global scale where biological systems function as a result of complex mechanisms that happen at several scales. Modelling and simulation are computational tools that are invaluable for description, understanding and prediction these mechanisms in a quantitative and integrative way. Thus multi-scale methods that couple the design, simulation and analysis of models spanning several spatial and temporal scales is becoming a new emerging focus of systems biology. This thesis uses an exemplar – Planar cell polarity (PCP) signalling – to illustrate a generic approach to model biological systems at different spatial scales, using the new concept of Hierarchically Coloured Petri Nets (HCPN). PCP signalling refers to the coordinated polarisation of cells within the plane of various epithelial tissues to generate sub-cellular asymmetry along an axis orthogonal to their apical-basal axes. This polarisation is required for many developmental events in both vertebrates and non-vertebrates. Defects in PCP in vertebrates are responsible for developmental abnormalities in multiple tissues including the neural tube, the kidney and the inner ear. In Drosophila wing, PCP is seen in the parallel orientation of hairs that protrude from each of the approximately 30,000 epithelial cells to robustly point toward the wing tip. This work applies HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) in Drosophila wing. HCPN facilitate the construction of mathematically tractable, compact and parameterised large-scale models. Different levels of abstraction that can be used in order to simplify such a complex system are first illustrated. The PCP system is first represented at an abstract level without modelling details of the cell. Each cell is then sub-divided into seven virtual compartments with adjacent cells being coupled via the formation of intercellular complexes. A more detailed model is later developed, describing the intra- and inter-cellular signalling mechanisms involved in PCP signalling. The initial model is for a wild-type organism, and then a family of related models, permitting different hypotheses to be explored regarding the mechanisms underlying PCP, are constructed. Among them, the largest model consists of 800 cells which when unfolded yields 164,000 places (each of which is described by an ordinary differential equation). This thesis illustrates the power and validity of the approach by showing how the models can be easily adapted to describe well-documented genetic mutations in the Drosophila wing using the proposed approach including clustering and model checking over time series of primary and secondary data, which can be employed to analyse and check such multi-scale models similar to the case of PCP. The HCPN models support the interpretation of biological observations reported in literature and are able to make sensible predictions. As HCPN model multi-scale systems in a compact, parameterised and scalable way, this modelling approach can be applied to other large-scale or multi-scale systems.

Cette thèse a pour cadre le développement de méthodes numériques pour la conception optimale de forme de voilure en aérodynamique compressible. Ce travail a donné lieu au développement et à la validation d'un adjoint discret aéro-structure pour l'analyse de sensibilité par rapport aux paramètres de forme et de structure interne de l 'aile dont dépend la fonction d'intérêt, qu' elle soit aérodynamique ou structurale. Les développements logiciels ont été réalisés dans le code de simulation numérique de mécanique des fluides elsA et font suite aux travaux de Marcelet portant sur l'adjoint aéroélastique et dont ils sont une extension. Alors que pour l'adjoint aéro-élastique, on considère une aile flexible, de caractéristiques structurales constantes, pour l'adjoint aérostructure, leur variations sont prises en compte. Pour cela, l'extension de la méthode adjointe s' est accompagnée du développement d' un module de modélisation de la structure interne de l'aile. Ce module est linéarisé et vient donc alimenter le système adjoint. Il a été validé par le dimensionnement de la structure primaire d'une configuration de recherche fournie par l' avionneur Airbus. Dans l'état actuel de développement de la méthode adjointe dans le code elsA, on peut donc désormais calculer les sensibilités d'une fonction aérodynamique ou d'une fonction structure par rapport aux paramètres de forme aérodynamique ou de structure interne de l'aile. Le calcul des gradients ainsi obtenus a été validé par des comparaisons systématiques aux différences finies.

The purpose of this thesis is to develop a vertex model framework that can be used to perform computational experiments related to the dynamics of epithelial tissues in developmental systems. We focus on three example systems: the Drosophila wing imaginal disc, the Drosophila epidermis and the visceral endoderm of the mouse embryo. Within these systems, key questions pertaining to size-control mechanisms and coordination of cell migration remain unanswered and are amenable to computational testing. The vertex model presented here builds upon existing frameworks in three key ways. Firstly, we include novel force terms, representing, for example, the reaction of a cell to being compressed and its shape becoming distorted during a highly dynamic process such as cell migration. Secondly, we incorporate a model of diffusing morphogenetic growth factors within the vertex framework, using an arbitrary Lagrangian-Eulerian formulation of the diffusion equation and solving with the finite-element method (FEM). Finally, we implement the vertex model on the surface of an ellipsoid, in order to simulate cell migration in the mouse embryo. Throughout this thesis, we validate our model by running simple simulations. We demonstrate convergence properties of the FEM scheme and discuss how the time taken to solve the system scales with tissue size. The model is applied to biological systems and its utility demonstrated in several contexts. We show that when growth is dependent on morphogen concentration in the Drosophila wing disc, proliferation occurs preferentially in regions of high concentration. In the Drosophila epidermis, we show that a recently proposed mechanism of compartment size-control, in which a growth-factor is released in limited amounts, is viable. Finally, we examine the phenomenon of rosettes in the mouse embryo, which occur when five or more cells meet at a common vertex. We show, by running simulations both with and without rosettes, that they are crucial facilitators of ordered migration, and are thus critical in the patterning of the early embryo.

This thesis investigates the turbulent flow in the wake of the wing-body junction of the NASA Common Research Model to further reveal its complex vortical structure and to contribute to the reference database used for Computational Fluid Dynamics validation activities. Compressible flows near two wall-boundary layers occurs not only at the wing-body junction but at every control surface of an airplane, therefore increased knowledge about this complex flow structure could potentially improve the estimates of drag performance and control surface efficiency, primarily for minimizing the environmental impact of commercial flight. The airplane model is modified by adding an inboard flap to investigate the influence from the deflection on the vorticity and velocity field. Future flap designs and settings are discussed from a performance improvement point of view, with the investigated flow influence in mind. The experimental measurements for this thesis were collected using a Cobra Probe, a dynamic multi-hole pressure probe, for Reynolds numbers close to one million based on the wing root chord. A pre-programmed three-dimensional grid was used to cover the most interesting parts of the junction flow. The facility used for the tests is a 120 cm by 80 cm indraft, subsonic wind tunnel at NASA Ames Research Center’s Fluid Mechanics Lab, which provides an on-set flow speed of around Mach 0.15, corresponding to approximately 48 m/s.
Den här avhandlingen undersöker det turbulenta flödet runt övergången mellan flygplanskropp och vinge på en NASA Common Research Model för att vidare utforska den komplexa, tredimensionella strukturen av flödet och bidra till NASA’s officiella databas för jämförelser med simulerade flöden. Kompressibla flöden nära tvåväggsgränsskikt uppkommer inte bara vid övergången mellan flygplanskropp och vinge utan även vid varje kontrollyta på ett flygplan. Ökad kunskap om flödets beteende vid sådana områden kan därför bidra till en bättre uppskattning av prestanda och effektivitet av kontrollytorna och flygplanet i sin helhet, vilket kan bidra till minskad miljöpåverkan från kommersiell flygtrafik. Flygplansmodellen är modifierad genom montering av en vingklaff på den inre delen av vingen, detta för att undersöka hur olika vinklar på klaffarnas nedböjning påverkar flödets struktur och hastighetsfält. Framtida klaffdesigner och inställningar för ökad prestanda diskuteras även utifrån denna påverkan. Mätningarna i vindtunneln gjordes med en Cobra Probe, ett dynamisk tryckmätningsinstrument, speciellt designad för turbulenta och instabila flöden. Reynoldsnumren som generades av den subsoniska, indrags-vindtunneln var ungefär en miljon baserad på vingrotens längd, vilket motsvarar knappt en tiondel av normala flygförhållanden för samma flygplansmodell.

Antarctic Wind Engineering deals with the effects of wind on the built environment. The assessment of wind induced forces, wind resource and wind driven snowdrifts are the main tasks for a wind engineer when participating on the design of an Antarctic building. While conventional Wind Engineering techniques are generally applicable to the Antarctic environment, there are some aspects that require further analysis due to the special characteristics of the Antarctic wind climate and its boundary layer meteorology.

The first issue in remote places like Antarctica is the lack of site wind measurements and meteorological information in general. In order to complement this shortage of information various meteorological databases have been surveyed. Global Reanalyses, produced by the European Met Office ECMWF, and RACMO/ANT mesoscale model simulations, produced by the Institute for Marine and Atmospheric Research of Utrecht University (IMAU), have been validated versus independent observations from a network of 115 automatic weather stations. The resolution of these models, of some tens of kilometers, is sufficient to characterize the wind climate in areas of smooth topography like the interior plateaus or the coastal ice shelves. In contrast, in escarpment and coastal areas, where the terrain gets rugged and katabatic winds are further intensified in confluence zones, the models lack resolution and underestimate the wind velocity.

The Antarctic atmospheric boundary layer (ABL) is characterized by the presence of strong katabatic winds that are generated by the presence of surface temperature inversions in sloping terrain. This inversion is persistent in Antarctica due to an almost continuous cooling by longwave radiation, especially during the winter night. As a result, the ABL is stably stratified most of the time and, only when the wind speed is high it becomes near neutrally stratified. This thesis also aims at making a critical review of the hypothesis underlying wind engineering models when extreme boundary layer situations are faced. It will be shown that the classical approach of assuming a neutral log-law in the surface layer can hold for studies of wind loading under strong winds but can be of limited use when detailed assessments are pursued.

The Antarctic landscape, mostly composed of very long fetches of ice covered terrain, makes it an optimum natural laboratory for the development of homogeneous boundary layers, which are a basic need for the formulation of ABL theories. Flux-profile measurements, made at Halley Research Station in the Brunt Ice Shelf by the British Antarctic Survery (BAS), have been used to analyze boundary layer similarity in view of formulating a one-dimensional ABL model. A 1D model of the neutral and stable boundary layer with a transport model for blowing snow has been implemented and verified versus test cases of the literature. A validation of quasi-stationary homogeneous profiles at different levels of stability confirms that such 1D models can be used to classify wind profiles to be used as boundary conditions for detailed 3D computational wind engineering studies.

A summary of the wind engineering activities carried out during the design of the Antarctic Research Station is provided as contextual reference and point of departure of this thesis. An elevated building on top of sloping terrain and connected to an under-snow garage constitutes a challenging environment for building design. Building aerodynamics and snowdrift management were tested in the von Karman Institute L1B wind tunnel for different building geometries and ridge integrations. Not only for safety and cost reduction but also for the integration of renewable energies, important benefits in the design of a building can be achieved if wind engineering is considered since the conceptual phase of the integrated building design process.

Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished

An inverted wing with various endplate configurations was investigated at two different angles of incidence. A moving ground was designed and constructed for use in the UNSW T1 wind tunnel. The test cases were investigated in ground effect using the moving ground. Measurements and observations were obtained using laser sheet flow visualisation and laser doppler anemometry. Computational fluid dynamics models of the test cases were run to gain further understanding of the flow field generated when using inverted wings with endplates. The computational fluid dynamics models correlated well to the experimental results.

M.Ing.
The aim of this dissertation is to apply numerical aerodynamic principles to the characterization of an alternative stepped aerofoil concept. The accurate and efficient determination of the aerodynamic forces caused by the relative fluid motion and the consequent lift and drag coefficients are essential for the characterization of new aerofoils. The numerical method used is in the form of a Computational Fluid Dynamics code, which integrates the Navier-Stokes equations through finite-volume dictretization principals. A two-dimensional approximate analysis procedure is used together with a two-equation turbulence approximation in the form of the "standard" k-c turbulence model. Available software is used and adapted where applicable. A suitable method for comparing wing section characteristics as a function of profile geometry and attitude is developed in this thesis. This is achieved by first refining a numerical test case and quantifying the influences of model parameters such as grid design, boundary conditions and solution variables. Alternative geometrical aerofoil concepts can then be characterized by employing the same principles. This thesis contains selected results of hundreds such numerical simulations, all of which were necessary to refine the test case and eventually characterize the aerofoils. The proposed wing section geometry, incorporating a rearward-facing step shows some improvement in aerodynamic performance over a standard reference case. Geometrical variations of the step concept are also investigated and can later be used in an optimization procedure. A transient simulation approach is employed for unsteady cases and flow visualization is done in order to learn more about the unique aerodynamic action of the proposed concept. Experimental results obtained in a wind tunnel for the pressure around the investigated aerofoils are used to verify numerical results. Further development in the numerical approach may include the use of additional, more advanced turbulence models. This may allow the research of more complex phenomena such as stall and also broader ranges of Reynolds numbers in more detail. To complete the characterization process, the moment coefficients should also be included.

A modeling study is undertaken to better understand the physics of katabatic flows. This study is divided into three topics; a comparison between a large eddy simulation (LES) and a mesoscale model of katabatic flows, a sensitivity study of katabatic flows to various physical parameters, and an investigation into the effect of subgrid scale terrain features on katabatic flow models. In the first topic, a comparison between LES, and a mesoscale model, ARPS, of katabatic flows is made to better quantify the accuracy of subgrid parametenzation in ARPS. It is shown that, although the modeled flows agree on a number of parameters, the LES model produces a lower and faster jet than that of ARPS, and also cools more near the surface. The momentum budgets of the two models agree well with each other. The ARPS model has a higher amount of TKE than the LES model, due to an overproduction by shear in the ARPS subgrid parameterizations. The second portion of this thesis represents a sensitivity study of katabatic flows to various physical parameters. The depth and strength of katabatic flows are shown to vary with surface heat fluxes, slope angle, and ambient stratification. Katabatic flows are shown to grow in depth and magnitude as slope angle increases, due to an increase in entrainment of overlying ambient air. The ratio of advection to mixing is shown to collapse to a near universal value regardless of surface heat fluxes. With increasing ambient stratification, entrainment in katabatic flows becomes small and the momentum equation is reduced to a two-way balance between buoyancy and drag. In this case, the heat flux of entrained air into the katabatic flow approaches that of the surface cooling, and the flow ceases to grow in the down-slope direction. Finally, predictions for bulk velocity and buoyancy strength scales are developed as a function of slope angle and surface heat fluxes. The last portion of this study focuses on the effect of subgrid scale terrain features on katabatic flows. It is shown that in areas of inadequate terrain resolution, the effect of the terrain smoothing routine in ARPS is to increase the slope height in areas of concave mountains. The concept of energy conversion in katabatic flows is introduced, and it is shown that the effect of raising terrain is to assign parcels more buoyant potential energy than they would otherwise have, and thus over-predict the magnitude of katabatic flows. Finally, an investigation into the effect of changing upper slope angle on katabatic flows over combined slopes is made. It is concluded that a combined slope cannot be predicted using a linear combination of simple slopes, since the transition portion of the slope results in a turbulent hydraulic jump with enhanced mixing. The magnitude of mixing in the turbulent hydraulic jump in combined slopes is shown to depend on the difference between upper and lower slope angle.
Graduation date: 2004

A time dependent model of the shallow, tropical convective boundary layer is developed and tested. To simplify the treatment of thermodynamic processes and return to first principles of physics, conserved quantities of entropy and total water density are used as primary model variables. In addition, a new shallow cumulus parameterization scheme is developed and is based on the use of a time dependent cloud kinetic energy equation combining local concepts of cloud processes with the use of a special buoyancy length scale. Two model simulations are performed in an attempt to assess the model's performance and the effectiveness of the parameterization scheme. Results indicate that the model does a reasonable job in both representing the equilibrium structure of a shallow convective boundary layer and in generating a realistic boundary layer structure from an initial state consisting of a shallow moist layer with dry air aloft. The cumulus parameterization scheme appears to adequately represent the transport of thermodynamic quantities associated with convective activity and the use of conserved variables provides an effective way of representing the boundary layer structure and treating the mixing processes associated with cloud processes. This work illustrates the usefulness of generalized conserved variables, particularly entropy and total water density, and indicates that the general approach of using a time dependent cloud kinetic energy equation may be effective for representing thermodynamic processes in the tropical boundary layer.
Graduation date: 1992

The Madden-Julian oscillation (MJO) and the quasi-biennial oscillation (QBO) are two key modes of variability in the tropical atmosphere. The MJO, characterized by propagating, planetary-scale signals in convection and winds, is the main source of subseasonal variability and predictability in the tropics. The QBO is a ~28-month cycle in which the tropical stratospheric zonal winds alternate between easterly and westerly regimes. Via thermal wind balance these winds induce temperature anomalies, and both wind and temperature signals reach the tropopause. Recent observational results show a remarkably strong link between the MJO and the QBO during boreal winter: the MJO is stronger and more predictable when QBO winds in the lower stratosphere are easterly than when winds are westerly. Despite its important implications for MJO theory and prediction, the physical processes driving the MJO-QBO interaction are not well-understood. In this thesis, we use a hierarchy of models – including a cloud-resolving model, a forecast model, and a global climate model – to examine whether models can reproduce the MJO-QBO link, and better understand the possible mechanisms driving the connection. Based in part on our modeling findings, we further explore observed QBO temperature signals thought to be important for the MJO-QBO link. After providing necessary background and context in the first two chapters, the third chapter looks at the MJO-QBO link in a small-domain, cloud-resolving model. The model successfully simulates convection associated with two MJO events that occurred during the DYNAMO field campaign. To examine the effect of QBO, we add various QBO temperature and wind anomalies into the model. We find that QBO temperature anomalies alone, without wind anomalies, qualitatively affect the model MJO similarly to the observed MJO-QBO connection. QBO wind anomalies have no clear effect on the modeled MJO. We note however that the MJO response is quite sensitive to the vertical structure of the QBO temperature anomalies, and for realistic temperature signals the model response is very small. In the fourth chapter, we look at the MJO-QBO link in a state-of-the-art global forecast model with a good representation of the MJO. We conduct 84 hind-cast experiments initialized on dates across winters from 1989-2017. For each of these dates, we artificially impose an easterly and a westerly QBO in the stratospheric initial conditions, and examine the resulting changes to the simulated MJO under different stratospheric states. We find that the effect of the QBO on the model MJO is of the same sign as observations, but is much smaller. A large sample size is required to capture any QBO signal, and tropospheric initial conditions seem more important than the stratosphere in determining the behavior of the simulated MJO. Despite the weak signal, we find that simulations with stronger QBO temperature anomalies have a stronger MJO response. In the fifth chapter, we conduct experiments in recent versions of a NASA general circulation model. We find that a version with a high vertical resolution generates a reasonable QBO and MJO, but has no MJO-QBO link. However, this model has weaker-than-observed QBO temperature anomalies, which may explain the lack of an MJO impact. To explore this potential bias, we impose the QBO by nudging the model stratospheric winds towards reanalysis, leading to more realistic simulation of QBO temperature anomalies. Despite this, the model still fails to show a strong MJO-QBO link across several ensemble experiments and sensitivity tests. We conclude with discussion of possible reasons why the model fails to capture the MJO-QBO connection. The sixth chapter examines QBO temperature signals in a range of observational and reanalysis datasets. In particular, we are motivated by two elements of the MJO-QBO relationship which are especially puzzling: the seasonality (i.e. that the MJO-QBO link is only significant in boreal winter) and long-term trend (i.e. that the MJO-QBO link seems to have only emerged since the 1980s). By examining QBO temperature signals around the tropopause, we highlight changes to the strength and structure of QBO temperature anomalies both in boreal winter and in recent decades. Whether these changes are linked to the MJO-QBO relationship, and what more generally might explain them, is not presently clear. Overall, we demonstrate that capturing the MJO-QBO relationship in a variety of models is a difficult task. The majority of evidence indicates that QBO-induced temperature anomalies are a plausible pathway through which the QBO might modulate the MJO, but the theoretical description of precisely how these temperature anomalies may impact convection is lacking and likely more nuanced than the literature to date suggests. Most models show only a weak modulation of the MJO associated with changes in upper-tropospheric temperatures, and even when those temperature signals are artificially enhanced, comprehensive GCMs still fail to show a significant MJO-QBO connection. Our observational study indicates that temperature anomalies associated with the QBO show striking modulations on various timescales of relevance to the MJO-QBO link, but do not conclusively demonstrate a clear connection to the MJO. This difficulty simulating a strong MJO-QBO connection suggests that models may lack a key process in driving the MJO and coupling the tropical stratosphere and troposphere. It is further possible that the observed link may be in some regards different than is currently theorized -- for example statistically not robust, due to non-stratospheric processes, or driven by some mechanism that has not been suitably explored.

Two micro air vehicles, namely Sapthami and Sapthami-flyer, are developed in this thesis. Their total weight is less than 200grams each. They fit inside a 30cm and 32cm sphere respectively and carry the commercially available Kestrel autopilot hardware. The vehicles have an endurance of around 20-30 minutes. The stall speed of Sapthami is around 7m/s and that of Sapthami-flyer is around 5m/s as found by nonlinear modeling. The low stall speed makes it possible for them to be launched by hand. This enhances their portability as they do not require any launching equipment. The vehicle installed with Kestrel autopilot system is capable of many modes of operations. It is capable of fully autonomous flight with the aid of a variety of sensors like the GPS unit, heading sensor, 2-axis magnetometer, 3-axis accelerometer and 3-axis gyros. The vehicle carrying the Kestrel autopilot hardware is capable of autonomous and semi-autonomous flights after installation and tuning of feedback loops. Sapthami, is a tailless flying wing with an inverse zimmermann profile. A flying wing is a preferred configuration for the MAV as it maximizes the lifting area for a given size constraint. For a maximum size constraint of 30cm and aspect ratio around 1, the vehicle operates at Reynolds number between 100,000 to 250,000, at flight velocity 7 m/s to 15 m/s. The Inverse Zimmerman profile has a higher lift coefficient, CL, in comparison to the other planforms such as rectangular, elliptical and Zimmermann, for aspect ratio 1 to 1.25 and tested at Reynolds number of 100,000. The configuration of Sapthami is clean as there is no fuselage and all the components like autopilot hardware and battery are housed inside the wing. A thick reflex Martin Hepperle (MH) airfoil MH18 is chosen which gives sufficient space to place the components. This airfoil is specially used for tailless configurations due to its negative camber at the trailing edge. This negative camber helps in reducing the negative pitching moment of the wing, since no separate horizontal tail is available on a tailless aircraft to compensate for it. The vehicle is fabricated using the blue foam, having a density of 30kg/m3 . The wing is fabricated by CNC machining after which slots are cut manually to embed the electronics. The vehicle is found to have stable flying characteristics. Limited flight trials are done for Sapthami. It takes large time to fabricate the vehicle due to limited availability of CNC machining facility. Therefore, a new tailless, wing-fuselage configuration, which can be fabricated with balsa wood, is designed. Sapthami-flyer is the second vehicle designed in this thesis. Its wing span is slightly more than Sapthami. Since it is a wing-fuselage configuration, therefore there is no need for a thick airfoil. Mark drela’s AG airfoils are found to have better lift than MH airfoils for the inverse Zimmerman profile. The thickness of the airfoils is reduced to 1% so that the wing can be made by a 1.5mm thick balsa sheet to reduce weight. The inverse Zimmermann profile wing with the AG09 airfoil is found to have best lift-to-drag ratio when compared to AG36, MH45 and MH18. The analysis is done using commercially available AVL software. AG09 with 1% thickness is used in the final configuration. This configuration has better short period damping than Sapthami. It also has slower modes of operation than Sapthami. The operating modes of most of the MAVs, including Sapthami and Sapthami-flyer, are lowly damped but fast. This makes it difficult for the pilot to fly the vehicle. To improve the flying qualities of the vehicle artificial stabilization is required. The feedback is implemented on the Kestrel autopilot hardware. It allows only PID based feedback structures to be implemented, hence gives no choice to the designer to implement higher order control. The digital integrator and differentiator implementation for feedback are non-ideal. This further reduces the effectiveness of control. The problem is dealt with by incorporating the additional dynamics introduced by these implementation while formulating the control problem. Further the modeling of the micro air vehicle is done by using vortex lattice simulation based softwares. The fidelity of the obtained dynamics is low. Therefore, there is high uncertainty in the plant model. The controller also needs to reject the wind gust disturbances which are of the order of the flight speed of the vehicle. All the above stated requirements from the control design can be best addressed by a robust control design. Sapthami-flyer uses aileron and elevator for control. There is no rudder in the configuration in order to reduce weight. In the longitudinal dynamics, pitch rate and pitch error feedback to elevator are used to increase the short period and phugoid damping respectively. In the lateral dynamics, a combination of roll rate, yaw rate and roll error feedback is given to aileron to improve the dutch roll damping and stabilize the spiral mode. The feedback loops for both longitudinal and lateral dynamics are multi-output single input design problems, therefore simultaneous tuning of loops is beneficial. The PID control is designed by first converting the actual plant to a static output feedback equivalent plant. The dynamics introduced by non-ideal differentiator and integrator implementation on the autopilot hardware are incorporated in the open loop static output feedback formulation. The robust pole placement for the SOF plant is done by using the modified iterative matrix inequality algorithm developed in this thesis. It is capable of multi-loop, multi-objective feedback design for SOF plants. The algorithm finds the optimal solution by simultaneously putting constraints on the H2 performance, pole placement, gain and phase margin of the closed loop system. The pole placement is done to minimize the real part of largest eigenvalue. A single controller is designed at a suit-able operating point and constraints are put on the gain and phase margin of the closed loop plant at other operating points. The designed controller is tested in flight on board Sapthami-flyer. The vehicle is also capable of tracking commanded pitch and roll attitude with the help of pitch error, roller or feedbacks. This is shown in the flight when the pilot leaves the RC stick and the vehicle tracks the desired attitude. The vehicle has shown improved flying characteristics in the closed loop mode.

A handling quality investigation was performed on the swept gull-wing configuration. The swept gull-wing configuration is tailless and has a wing with a transition in the sweep and dihedral angle. An example of this type of aircraft is the Exulans. This aircraft is currently under development at the University of Pretoria. The handling quality study was focussed on pitch axis dynamics. The Exulans is a research testbed that will be used to investigate the swept gull-wing configuration and its special controls by means of full-scale flight testing. Variable wing sweep, twisting elevons and winglets will be investigated as means of control. These control devices are configured in such a way as to have minimum impact on the performance of the aircraft. The handling qualities of the swept gull-wing configuration have to be acceptable while using these different control strategies. The study was launched to investigate whether a gull-wing configuration aircraft will have satisfactory handling qualities at CG positions associated with the most favourable aerodynamic performance. There is an aerodynamic performance gain in designing an aircraft so that the CG falls on the so-called `E-point'. The E-point is the centre of pressure for an elliptical circulation distribution. An elliptical circulation distribution is associated with the highest Oswald efficiency for an aircraft. Time domain simulation techniques and frequency domain analysis techniques were used to analyse the handling qualities of the gull-wing configuration. The C-star criterion was used to analyse handling qualities with time domain simulation data as input. Comparative time domain simulations were performed between the Exulans and other aircraft to compare handling qualities. Eigenvalue analysis was used together with the thumbprint criterion to investigate inherent gull-wing airframe dynamics. The Shomber-Gertsen and Military Specification 8785 criteria were also used for the same purpose. The Neal-Smith method was used to investigate the effect of control authority on handling qualities and the effect of a pilot. The Monnich and Dalldorff criterion was used to evaluate gust handling qualities. An analysis chart by Fremaux and Vairo was used to evaluate the tumbling susceptibility of the gull-wing configuration. The pitch handling quality investigation shows sufficient promise that the swept gull-wing configuration will have acceptable handling qualities with the CG placed at positions associated with optimised aerodynamic performance. Analysis showed that the swept gull-wing configuration is potentially prone to tumbling. With low static margins, the configuration should exhibit improved handling qualities in gusty conditions when compared to existing tailless aircraft. It is recommended that a lateral handling quality study be performed before full scale flight testing commences on the Exulans. In addition, the possibility of wingtip stall must be investigated for the case of the swept gull-wing configuration.
Dissertation (MEng)--University of Pretoria, 2008.
Mechanical and Aeronautical Engineering
unrestricted

Indiana University-Purdue University Indianapolis (IUPUI)
Hydraulic wind power transfer systems deliver the captured energy by the blades to the generators differently. In the conventional systems this task is carried out by a gearbox or an intermediate medium. New generation of wind power systems transfer the captured energy by means of high-pressure hydraulic fluids. A hydraulic pump is connected to the blades shaft at a high distance from the ground, in nacelle, to pressurize a hydraulic flow down to ground level equipment through hoses. Multiple wind turbines can also pressurize a flow sending to a single hose toward the generator. The pressurized flow carries a large amount of energy which will be transferred to the mechanical energy by a hydraulic motor. Finally, a generator is connected to the hydraulic motor to generate electrical power. This hydraulic system runs under two main disturbances, wind speed fluctuations and load variations. Intermittent nature of the wind applies a fluctuating torque on the hydraulic pump shaft. Also, variations of the consumed electrical power by the grid cause a considerable load disturbance on the system. This thesis studies the hydraulic wind power transfer systems. To get a better understanding, a mathematical model of the system is developed and studied utilizing the governing equations for every single hydraulic component in the system. The mathematical model embodies nonlinearities which are inherited from the hydraulic components such as check valves, proportional valves, pressure relief valves, etc. An experimental prototype of the hydraulic wind power transfer systems is designed and implemented to study the dynamic behavior and operation of the system. The provided nonlinear mathematical model is then validated by experimental result from the prototype. Moreover, this thesis develops a control system for the hydraulic wind power transfer systems. To maintain a fixed frequency electrical voltage by the system, the generator should remain at a constant rotational speed. The fluctuating wind speed from the upstream, and the load variations from the downstream apply considerable disturbances on the system. A controller is designed and implemented to regulate the flow in the proportional valve and as a consequence the generator maintains its constant speed compensating for load and wind turbine disturbances. The control system is applied to the mathematical model as well as the experimental prototype by utilizing MATLAB/Simulink and dSPACE 1104 fast prototyping hardware and the results are compared.