Effect of high order interpolation in the stability and efficiency of the time-integration process in vorticity-velocity CFD algorithms

The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

Structural response and dynamics of fluid-structure-control interaction in wind turbine blades

Reducing the uncertainties related to blade dynamics by the improvement of the quality of numerical simulations of the fluid structure interaction process is a key for a breakthrough in wind-turbine technology. A fundamental step in that direction is the implementation of aeroelastic models capable of capturing the complex features of innovative prototype blades, so they can be tested at realistic full-scale conditions with a reasonable computational cost. We make use of a code based on a combination of two advanced numerical models implemented in a parallel HPC supercomputer platform: First, a model of the structural response of heterogeneous composite blades, based on a variation of the dimensional reduction technique proposed by Hodges and Yu. This technique has the capacity of reducing the geometrical complexity of the blade section into a stiffness matrix for an equivalent beam. The reduced 1-D strain energy is equivalent to the actual 3-D strain energy in an asymptotic sense, allowing accurate modeling of the blade structure as a 1-D finite-element problem. This substantially reduces the computational effort required to model the structural dynamics at each time step. Second, a novel aerodynamic model based on an advanced implementation of the BEM(Blade ElementMomentum) Theory; where all velocities and forces are re-projected through orthogonal matrices into the instantaneous deformed configuration to fully include the effects of large displacements and rotation of the airfoil sections into the computation of aerodynamic forces. This allows the aerodynamic model to take into account the effects of the complex flexo-torsional deformation that can be captured by the more sophisticated structural model mentioned above. In this thesis we have successfully developed a powerful computational tool for the aeroelastic analysis of wind-turbine blades. Due to the particular features mentioned above in terms of a full representation of the combined modes of deformation of the blade as a complex structural part and their effects on the aerodynamic loads, it constitutes a substantial advancement ahead the state-of-the-art aeroelastic models currently available, like the FAST-Aerodyn suite. In this thesis, we also include the results of several experiments on the NREL-5MW blade, which is widely accepted today as a benchmark blade, together with some modifications intended to explore the capacities of the new code in terms of capturing features on blade-dynamic behavior, which are normally overlooked by the existing aeroelastic models.

Adaptive sensing for target tracking applications

In a statistical inference scenario, the estimation of target signal or its parameters is done by processing data from informative measurements. The estimation performance can be enhanced if we choose the measurements based on some criteria that help to direct our sensing resources such that the measurements are more informative about the parameter we intend to estimate. While taking multiple measurements, the measurements can be chosen online so that more information could be extracted from the data in each measurement process. This approach fits well in Bayesian inference model often used to produce successive posterior distributions of the associated parameter. We explore the sensor array processing scenario for adaptive sensing of a target parameter. The measurement choice is described by a measurement matrix that multiplies the data vector normally associated with the array signal processing. The adaptive sensing of both static and dynamic system models is done by the online selection of proper measurement matrix over time. For the dynamic system model, the target is assumed to move with some distribution and the prior distribution at each time step is changed. The information gained through adaptive sensing of the moving target is lost due to the relative shift of the target. The adaptive sensing paradigm has many similarities with compressive sensing. We have attempted to reconcile the two approaches by modifying the observation model of adaptive sensing to match the compressive sensing model for the estimation of a sparse vector.

Predicting the Mechanical Properties of Carbon-Based Materials Using Molecular Dynamics

The development of innovative carbon-based materials can be greatly facilitated by molecular modeling techniques. Although molecular modeling has been used extensively to predict elastic properties of materials, modeling of more complex phenomenon such as fracture has only recently been possible with the development of new force fields such as ReaxFF, which is used in this work. It is not fully understood what molecular modeling parameters such as thermostat type, thermostat coupling, time step, system size, and strain rate are required for accurate modeling of fracture. Selection of modeling parameters to model fracture can be difficult and non-intuitive compared to modeling elastic properties using traditional force fields, and the errors generated by incorrect parameters may be non-obvious. These molecular modeling parameters are systematically investigated and their effects on the fracture of well-known carbon materials are analyzed. It is determined that for coupling coefficients of 250 fs and greater do not result in substantial differences in the stress-strain response of the materials using any thermostat type. A time step of 0.5 fs of smaller is required for accurate results. Strain rates greater than 2.2 ns-1 are sufficient to obtain repeatable results with slower strain rates for the materials studied. The results of this study indicate that further refinement of the Chenoweth parameter set is required to accurately predict the mechanical response of carbon-based systems. The ReaxFF has been used extensively to model systems in which bond breaking and formation occur. In particular ReaxFF has been used to model reactions of small molecules. Some elastic and fracture properties have been successfully modeled using ReaxFF in materials such as silicon and some metals. However, it is not clear if current parameterizations for ReaxFF are able to accurately reproduce the elastic and fracture properties of carbon materials. The stress-strain response of a new ReaxFF parameterization is compared to the previous parameterization and density functional theory results for well-known carbon materials. The new ReaxFF parameterization makes xv substantial improvements to the predicted mechanical response of carbon materials, and is found to be suitable for modeling the mechanical response of carbon materials. Finally, a new material composed of carbon nanotubes within an amorphous carbon (AC) matrix is modeled using the ReaxFF. Various parameters that may be experimentally controlled are investigated such as nanotube bundling, comparing multi-walled nanotube with single-walled nanotubes, and degree of functionalization of the nanotubes. Elastic and fracture properties are investigated for the composite systems and compared to results of pure-nanotube and pure-AC models. It is found that the arrangement of the nanotubes and degree of crosslinking may substantially affect the properties of the systems, particularly in the transverse directions.

PARAMETRIC STUDY OF REAXFF SIMULATION PARAMETERS FOR MOLECULAR DYNAMICS MODELING OF REACTIVE CARBON GASES

Abstract The development of innovative carbon-based materials can be greatly facilitated by molecular modeling techniques. Although the Reax Force Field (ReaxFF) can be used to simulate the chemical behavior of carbon-based systems, the simulation settings required for accurate predictions have not been fully explored. Using the ReaxFF, molecular dynamics (MD) simulations are used to simulate the chemical behavior of pure carbon and hydrocarbon reactive gases that are involved in the formation of carbon structures such as graphite, buckyballs, amorphous carbon, and carbon nanotubes. It is determined that the maximum simulation time step that can be used in MD simulations with the ReaxFF is dependent on the simulated temperature and selected parameter set, as are the predicted reaction rates. It is also determined that different carbon-based reactive gases react at different rates, and that the predicted equilibrium structures are generally the same for the different ReaxFF parameter sets, except in the case of the predicted formation of large graphitic structures with the Chenoweth parameter set under specific conditions.

SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

Determing the Effect of Thermal Treatment Timing on Ultra-High Performance Concrete Beams

The loss of prestressing force over time influences the long-term deflection of the prestressed concrete element. Prestress losses are inherently complex due to the interaction of concrete creep, concrete shrinkage, and steel relaxation. Implementing advanced materials such as ultra-high performance concrete (UHPC) further complicates the estimation of prestress losses because of the changes in material models dependent on curing regime. Past research shows compressive creep is "locked in" when UHPC cylinders are subjected to thermal treatment before being loaded in compression. However, the current precasting manufacturing process would typically load the element (through prestressing strand release from the prestressing bed) before the element would be taken to the curing facility. Members of many ages are stored until curing could be applied to all of them at once. This research was conducted to determine the impact of variable curing times for UHPC on the prestress losses, and hence deflections. Three UHPC beams, a rectangular section, a modified bulb tee section, and a pi-girder, were assessed for losses and deflections using an incremental time step approach and material models specific to UHPC based on compressive creep and shrinkage testing. Results show that although it is important for prestressed UHPC beams to be thermally treated, to "lock in" material properties, the timing of thermal treatment leads to negligible differences in long-term deflections. Results also show that for UHPC elements that are thermally treated, changes in deflection are caused only by external loads because prestress losses are "locked-in" following thermal treatment.

ANKLE IMPEDANCE AND ANKLE ANGLES DURING STEP TURN AND STRAIGHT WALK: IMPLICATIONS FOR THE DESIGN OF A STEERABLE ANKLE-FOOT PROSTHETIC ROBOT

During locomotion, turning is a common and recurring event which is largely neglected in the current state-of-the-art ankle-foot prostheses, forcing amputees to use different steering mechanisms for turning, compared to non-amputees. A better understanding of the complexities surrounding lower limb prostheses will lead to increased health and well-being of amputees. The aim of this research is to develop a steerable ankle-foot prosthesis that mimics the human ankle mechanical properties. Experiments were developed to estimate the mechanical impedance of the ankle and the ankles angles during straight walk and step turn. Next, this information was used in the design of a prototype, powered steerable ankle-foot prosthesis with two controllable degrees of freedom. One of the possible approaches in design of the prosthetic robots is to use the human joints’ parameters, especially their impedance. A series of experiments were conducted to estimate the stochastic mechanical impedance of the human ankle when muscles were fully relaxed and co-contracting antagonistically. A rehabilitation robot for the ankle, Anklebot, was employed to provide torque perturbations to the ankle. The experiments were performed in two different configurations, one with relaxed muscles, and one with 10% of maximum voluntary contraction (MVC). Surface electromyography (sEMG) was used to monitor muscle activation levels and these sEMG signals were displayed to subjects who attempted to maintain them constant. Time histories of ankle torques and angles in the lateral/medial (LM) directions, inversion-eversion (IE), and dorsiflexionplantarflexion (DP) were recorded. Linear time-invariant transfer functions between the measured torques and angles were estimated providing an estimate of ankle mechanical impedance. High coherence was observed over a frequency range up to 30 Hz. The main effect of muscle activation was to increase the magnitude of ankle mechanical impedance in all degrees of freedom of the ankle. Another experiment compared the three-dimensional angles of the ankle during step turn and straight walking. These angles were measured to be used for developing the control strategy of the ankle-foot prosthesis. An infrared camera system was used to track the trajectories and angles of the foot and leg. The combined phases of heel strike and loading response, mid stance, and terminal stance and pre-swing were determined and used to measure the average angles at each combined phase. The Range of motion (ROM) in IE increased during turning while ML rotation decreased and DP changed the least. During the turning step, ankle displacement in DP started with similar angles to straight walk and progressively showed less plantarflexion. In IE, the ankle showed increased inversion leaning the body toward the inside of the turn. ML rotation initiated with an increased medial rotation during the step turn relative to the straight walk transitioning to increased lateral rotation at the toe off. A prototype ankle-foot prosthesis capable of controlling both DP and IE using a cable driven mechanism was developed and assessed as part of a feasibility study. The design is capable of reproducing the angles required for straight walk and step turn; generates 712N of lifting force in plantarflexion, and shows passive stiffness comparable to a nonload bearing ankle impedance. To evaluate the performance of the ankle-foot prosthesis, a circular treadmill was developed to mimic human gait during steering. Preliminary results show that the device can appropriately simulate human gait with loading and unloading the ankle joint during the gait in circular paths.

AN ENERGY BASED MINIMUM-TIME OPTIMAL CONTROL OF DC-DC CONVERTERS

Time-optimal response is an important and sometimes necessary characteristic of dynamic systems for specific applications. Power converters are widely used in different electrical systems and their dynamic response will affect the whole system. In many electrical systems like microgrids or voltage regulators which supplies sensitive loads fast dynamic response is a must. Minimum time is the fastest converter to compensate the step output reference or load change. Boost converters as one of the wildly used power converters in the electrical systems are aimed to be controlled in optimal time in this study. Linear controllers are not able to provide the optimal response for a boost converter however they are still useful and functional for other applications like reference tracking or stabilization. To obtain the fastest possible response from boost converters, a nonlinear control approach based on the total energy of the system is studied in this research. Total energy of the system considers as the basis for developing the presented method, since it is easy and accurate to measure besides that the total energy of the system represents the actual operating condition of the boost converter. The detailed model of a boost converter is simulated in MATLAB/Simulink to achieve the time optimal response of the boost converter by applying the developed method. The simulation results confirmed the ability of the presented method to secure the time optimal response of the boost converter under four different scenarios.