Modelling of flow around hexagonal and textured cylinders

The flow regime around a hexagonal polygon with low Reynolds numbers Re<200 is numerically investigated in two different orientations namely face-oriented and corner-oriented. The basic flow characteristics, including drag coefficient, lift coefficient, Strouhal number and critical Reynolds number of the hexagonal cylinders, are calculated using 2D transient numerical analysis. Within the studied range of Re, the predicted lift coefficient and Strouhal number of the face-oriented hexagon were higher than those of the corner-oriented hexagon. In contrast, the predicted drag coefficient and critical Reynolds number of the corner-oriented hexagon were greater than those of the face-oriented. Flow characteristics of a novel textured geometry are also studied using 3D transient analysis. The Strouhal number St of the textured geometry was found to be in between the St of both the hexagonal cylinders, and its lift coefficient is lower than that of the hexagonal cylinders

Linear and nonlinear parametric hydrodynamic models for wave energy converters identified from recorded data

Ocean waves represent an important resource of renewable energy, which can provide a significant support to the development of more sustainable energy solutions and to the reduction ofCO2 emissions. The amount of extracted energy from the ocean waves can be increased by optimizing the geometry and the control strategy of the wave energy converter (WEC), which both require mathematical hydrodynamic models, able to correctly describe the WEC-fluid interaction. In general, the construction of a model is based on physical laws describing the system under investigation. The hydrodynamic laws are the foundation for a complete description of the WEC-fluid interaction, but their solution represents a very complex and challenging problem. Different approaches to hydrodynamic WEC-fluid interaction modelling, such as computational fluid dynamics (CFD) and linear potential theory (LPT), lead to different mathematical models, each one characterised by different accuracy and computational speed. Fully nonlinear CFD models are able to describe the full range of hydrodynamic effects, but are very computationally expensive. On the other hand, LPT is based on the strong assumptions of inviscid fluid, irrotational flow, small waves and small body motion, which completely remove the hydrodynamic nonlinearity of the WEC-fluid interaction. Linear models have good computational speed, but are not able to properly describe nonlinear hydrodynamic effects, which are relevant in some WEC power production conditions, since WECs are designed to operate over a wide range of wave amplitudes, experience large motions, and generate viscous drag and vortex shedding. The main objective of this thesis is to propose and investigate an alternative pragmatic framework, for hydrodynamic model construction, based on system identification methodologies. The goal is to obtain models which are between the CFD and LPT extremes, a good compromise able to describe the most important nonlinearities of the physical system, without requiring excessively computational time. The identified models remain sufficiently fast and simple to run in real-time. System identification techniques can ‘inject’ into the model only the information contained in the identification data; therefore, the models obtained from LPT data are not able to describe nonlinear hydrodynamic effects. In this thesis, instead of traditional LPT data, experimental wave tank data (both numerical wave tank (NWT), implemented with a CFD software package, and real wave tank (RWT)) are proposed for hydrodynamic model identification, since CFD-NWT and RWT data can contain the full range of nonlinear hydrodynamic effects. In this thesis, different typologies of wave tank experiments and excitation signals are investigated in order to generate informative data and reduce the experiment duration. Indeed, the reduction of the experiment duration represents an important advantage since, in the case of a CFD-NWT, the amount of computation time can become unsustainable whereas, in the case of a RWT, a set of long tank experiments corresponds to an increase of the facility renting costs

Nonlinear hydrodynamic modelling of wave energy converters under controlled conditions

One of the major challenges facing modern industrialized countries is the provision of energy: traditional sources, mainly based on fossil fuels, are not only growing scarcer and more expensive, but are also irremediably damaging the environment. Renewable and sustainable energy sources are attractive alternatives that can substantially diversify the energy mix, cut down pollution, and reduce the human footprint on the environment. Ocean energy, including energy generated from the motion of wave, is a tremendous untapped energy resource that could make a decisive contribution to the future supply of clean energy. However, numerous obstacles must be overcome for ocean energy to reach economic viability and compete with other energy sources. Energy can be generated from ocean waves by wave energy converters (WECs). The amount of energy extracted from ocean waves, and therefore the profitability of the extraction, can be increased by optimizing the geometry and the control strategy of the wave energy converter, both of which require mathematical hydrodynamic models that are able to correctly describe the WEC- uid interaction. On the one hand, the accuracy and representativeness of such models have a major in uence on the effectiveness of the WEC design. On the other hand, the computational time required by a model limits its applicability, since many iterations or real-time calculations may be required. Critically, computational time and accuracy are often mutually contrasting features of a mathematical model, so an appropriate compromise should be defined in accordance with the purpose of the model, the device type, and the operational conditions. Linear models, often chosen due to their computational convenience, are likely to be imprecise when a control strategy is implemented in a WEC: under controlled conditions, the motion of the device is exaggerated in order to maximize power absorption, which invalidates the assumption of linearity. The inclusion of nonlinearities in a model is likely to improve the model's accuracy, but increases the computational burden. Therefore, the objective is to define a parsimonious model, in which only relevant nonlinearities are modelled in order to obtain an appropriate compromise between accuracy and computational time. In addition to presenting a wider discussion of nonlinear hydrodynamic modelling for WECs, this thesis contributes the development of a computationally efficient nonlinear hydrodynamic model for axisymmetric WEC devices, from one to six degrees of freedom, based on a novel approach to the nonlinear computation of static and dynamic Froude-Krylov forces

Impact of Vibrational Nonequilibrium on the Simulation and Modeling of Dual-Mode Scramjets

The practical realization of supersonic flight relies on the development of a robust propulsion system. These air-breathing scramjet engines process fuel and high-speed air to generate propulsive thrust. Unlike conventional jet engines, scramjets achieve efficient thrust by compressing air through a system of shocks. As a result, the reliability of the engine is highly sensitive to the stability of these shock structures. Physically, these shocks are located in an engine component called the isolator. The shock structures are spatially distributed leading to a region of pressure increase, which is termed the pseudoshock. As vehicle operating conditions change, the length of the pseudoshock will change, reflecting changes to inflow conditions and operation of downstream combustor component. The overall objective of this thesis is to understand the complex flow inside these isolators. Of particular focus is the role of molecular processes in the development of the shocks. At high enthalpy conditions, the internal motions of the molecules are moved out of equilibrium due to compression shocks, which affects not only the thermophysical properties of air, but more critically the fuel-air mixing and chemical reactions. While there exists a vast body of literature on scramjet isolators, almost all of these works focus on low enthalpy conditions due to laboratory experimental limitations, or simply rely on equilibrium thermodynamics. In this work, the effect of nonequilibrium on isolator and scramjet combustors at high-altitude high-enthalpy flight conditions was studied using high-fidelity numerical simulations. Detailed models for the description of molecular nonequilibrium, in the form of multi-temperature model was used. Computational chemistry derived reaction rates were used to describe the combustion processes. These studies revealed the following key features: a) nonequilibrium of vibrational states greatly increases pseudoshock length, b) contrary to external hypersonics, nonequilibrium accelerates chemical reactions in the combustor, reducing the distance from fuel injection to flame ignition and stabilization, c) while multi-temperature models are adequate to express such nonequilibrium effects, more detailed state-specific representations clearly demonstrate that molecular populations do not follow the Boltzmann relation even at subsonic but compressible flow conditions. In a related study but using equilibrium thermal conditions, it was shown that the isolator shock structure can develop a resonance to inflow perturbations that can vastly increase the pseudoshock spatial oscillations. These results verify that isolator flow is a complex nonlinear process and clearly demonstrate that the design of scramjets needs to include the effect of thermal nonequilibrium. To begin addressing this process, reduced-order models in the form of a flux-conserved one-dimensional formulation for estimating pseudoshock length was developed for thermal equilibrium conditions.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143909/1/rfievet_2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/143909/2/rfievet_1.pd

Modelling and control of dynamic platelet aggregation under disturbed blood flow

Diagnosis of platelet function is fundamental for identifying blood disorders of patients, assessing the impact of antiplatelet agents, and enabling the appropriate titration of individual antithrombotic treatments. Following the advancement of new technologies such as microfluidic devices and the use of control engineering methods, new devices have the potential to offer new opportunities in point-of-care diagnosis of platelet function. Such new devices may have significant utility in the development of more tailored antiplatelet therapies. The aim of this thesis is to investigate modelling and control systems which support the study of the dynamic relationship between newly discovered mechanisms of platelet aggregation and disturbed blood flow, using state-of-the-art micro-engineered technologies. In order to observe the dynamics of platelet aggregation under disturbed blood flow, blood perfusion experiments carried out on a device mimicking a scenario of severe vessel narrowing are presented. The resulting biological response, that is the aggregation of platelets, is monitored in real-time and synthesised through novel measures developed using image processing techniques. A mechanistic model identifying four distinct stages observed in the formation of the aggregate is formulated, describing the nonlinear relationship between blood flow dynamics and platelet aggregation. The observed effect of disturbed blood flow on the aggregation of platelets is then modelled mathematically employing System Identification methods. A detailed account of a novel approach for the generation of experimental data is presented, as well as the formulation of tailored mathematical model structures and the calculation of their parameters using collected data. The proposed models replicate experimental results with low variation, and the reduced number of model parameters is suggested as a novel systematic measure of platelet aggregation dynamics in the presence of blood flow disturbances. In order to stabilise, optimise, and automate the measurement of platelet function in response to disturbed blood flow, custom-made control algorithms based on principles of Sliding Mode Control and Pulse-Width Modulation are developed. Moreover, the control algorithms are developed to handle the large variability of the aggregation responses from blood types with platelet hyper- and hypo-function. Simulation results illustrate the robustness of the control algorithms in the presence of time-varying nonlinearities and model uncertainty, and indicate the possibility to regulate the extent of aggregation in the device through modulation of the blood flow rate in the microchannel. The main contribution of this thesis is the development of dynamic models and control systems that allow a systematic measurement of platelet function in response to rapid changes in the blood flow (shear rate micro-gradients), in a microfluidics device containing a scenario of disturbed blood flow. Analysis of the platelet aggregation dynamics revealed that although the aggregate growth appears to be constant at times, measuring its mean fluorescence intensity indicates an increase in the dynamics of platelet density. This densification process appears fundamental for the development of an amplification phase in the aggregation response. The proposed mathematical models and control algorithms facilitate the systematic measurement of platelet function in vitro, pioneering the development of a novel framework for automated blood disorder diagnosis

Automatic Development and Adaptation of Concise Nonlinear Models for System Identification

Mathematical descriptions of natural and man-made processes are the bedrock of science, used by humans to understand, estimate, predict and control the natural and built world around them. The goal of system identification is to enable the inference of mathematical descriptions of the true behavior and dynamics of processes from their measured observations. The crux of this task is the identification of the dynamic model form (topology) in addition to its parameters. Model structures must be concise to offer insight to the user about the process in question. To that end, this dissertation proposes three methods to improve the ability of system identification to identify succinct nonlinear model structures. The first is a model structure adaptation method (MSAM) that modifies first principles models to increase their predictive ability while maintaining intelligibility. Model structure identification is achieved by this method despite the presence of parametric error through a novel means of estimating the gradient of model structure perturbations. I demonstrate MSAM\u27s ability to identify underlying nonlinear dynamic models starting from linear models in the presence of parametric uncertainty. The main contribution of this method is the ability to adapt the structure of existing models of processes such that they more closely match the process observations. The second method, known as epigenetic linear genetic programming (ELGP), conducts symbolic regression without a priori knowledge of the form of the model or its parameters. ELGP incorporates a layer of genetic regulation into genetic programming (GP) and adapts it by local search to tune the resultant model structures for accuracy and conciseness. The introduction of epigenetics is made simple by the use of a stack-based program representation. This method, tested on hundreds of dynamics problems, demonstrates the ability of epigenetic local search to improve GP by producing simpler and more accurate models. The third method relies on a multidimensional GP approach (M4GP) for solving multiclass classification problems. The proposed method uses stack-based GP to conduct nonlinear feature transformations to optimize the clustering of data according to their classes. In comparison to several state-of-the-art methods, M4GP is able to classify test data better on several real-world problems. The main contribution of M4GP is its demonstrated ability to combine the strengths of GP (e.g. nonlinear feature transformations and feature selection) with the strengths of distance-based classification. MSAM, ELGP and M4GP improve the identification of succinct nonlinear model structures for continuous dynamic processes with starting models, continuous dynamic processes without starting models, and multiclass dynamic processes without starting models, respectively. A considerable portion of this dissertation is devoted to the application of these methods to these three classes of real-world dynamic modeling problems. MSAM is applied to the restructuring of controllers to improve the closed-loop system response of nonlinear plants. ELGP is used to identify the closed-loop dynamics of an industrial scale wind turbine and to define a reduced-order model of fluid-structure interaction. Lastly, M4GP is used to identify a dynamic behavioral model of bald eagles from collected data. The methods are analyzed alongside many other state-of-the-art system identification methods in the context of model accuracy and conciseness

Low-Reynolds Number Adaptive Flow Control Using Dielectric Barrier Discharge Actuator.

Active flow control offers insight into fluid physics as well as possible improvements in flight performance for low-Reynolds number flyers – those at the chord-based Reynolds number of 105 or below – whose aerodynamic performance is sensitive to wind gusts, flow separation, and laminar-turbulent transition. Recently, the dielectric barrier discharge (DBD) actuator, characterized by a fast response without moving parts, has emerged as a promising flow control device. Although numerous studies have explored DBD physics and flow generation mechanisms, there is a limited understanding of the performance of the DBD actuator and surrounding flows under different operating and material parameters. Moreover, the disparity of time- and spatial-scales in plasma-dynamics makes direct numerical simulation of the DBD actuator impractical for real-time flow control. In this study aimed at flow control, surrogate modeling techniques are adopted to characterize the impact of the dielectric constant, and the voltage frequency and waveform on the force generation and power requirements of the DBD actuator. Global sensitivity and Pareto front analyses identify parametric dependencies and distinctive regions of interest in the design space. The feedback control is devised by combining surrogate modeling, system estimation and a penalty-based adaptive law. The control algorithm (minimizing a quadratic function of the retrospective performance) requires knowledge of the first nonzero Markov parameter and nonminimum-phase zeros of the linearized flow-actuator model, which are easy to identify. The estimates of these system parameters are analyzed under various flow and actuation conditions using impulse and step response tests. For finite and infinite wings with the SD7003 airfoil geometry with chord-based Reynolds numbers between 300 and 1000, and a 15-degree angle-of-attack, the present control law can stabilize lift under modest free-stream fluctuations. The interaction between control and flow responses indicates that the adjusted pressure and suction regions around the DBD actuator can stabilize lift. Furthermore, by minimizing the lift fluctuation, the drag fluctuation can either increase or decrease depending on flow conditions. The limitations of the linear modeling approach are addressed based on the system’s nonlinear behavior. The present modeling, estimation and control framework offers a new approach for control of low-Reynolds number aerodynamics.Ph.D.Aerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78845/1/yccho_1.pd

Identification of low order models for large scale processes

Many industrial chemical processes are complex, multi-phase and large scale in nature. These processes are characterized by various nonlinear physiochemical effects and fluid flows. Such processes often show coexistence of fast and slow dynamics during their time evolutions. The increasing demand for a flexible operation of a complex process, a pressing need to improve the product quality, an increasing energy cost and tightening environmental regulations make it rewarding to automate a large scale manufacturing process. Mathematical tools used for process modeling, simulation and control are useful to meet these challenges. Towards this purpose, development of process models, either from the first principles (conservation laws) i.e. the rigorous models or the input-output data based models constitute an important step. Both types of models have their own advantages and pitfalls. Rigorous process models can approximate the process behavior reasonably well. The ability to extrapolate the rigorous process models and the physical interpretation of their states make them more attractive for the automation purpose over the input-output data based identified models. Therefore, the use of rigorous process models and rigorous model based predictive control (R-MPC) for the purpose of online control and optimization of a process is very promising. However, due to several limitations e.g. slow computation speed and the high modeling efforts, it becomes difficult to employ the rigorous models in practise. This thesis work aims to develop a methodology which will result in smaller, less complex and computationally efficient process models from the rigorous process models which can be used in real time for online control and dynamic optimization of the industrial processes. Such methodology is commonly referred to as a methodology of Model (order) Reduction. Model order reduction aims at removing the model redundancy from the rigorous process models. The model order reduction methods that are investigated in this thesis, are applied to two benchmark examples, an industrial glass manufacturing process and a tubular reactor. The complex, nonlinear, multi-phase fluid flow that is observed in a glass manufacturing process offers multiple challenges to any model reduction technique. Often, the rigorous first principle models of these benchmark examples are implemented in a discretized form of partial differential equations and their solutions are computed using the Computational Fluid Dynamics (CFD) numerical tools. Although these models are reliable representations of the underlying process, computation of their dynamic solutions require a significant computation efforts in the form of CPU power and simulation time. The glass manufacturing process involves a large furnace whose walls wear out due to the high process temperature and aggressive nature of the molten glass. It is shown here that the wearing of a glass furnace walls result in change of flow patterns of the molten glass inside the furnace. Therefore it is also desired from the reduced order model to approximate the process behavior under the influence of changes in the process parameters. In this thesis the problem of change in flow patterns as result of changes in the geometric parameter is treated as a bifurcation phenomenon. Such bifurcations exhibited by the full order model are detected using a novel framework of reduced order models and hybrid detection mechanisms. The reduced order models are obtained using the methods explained in the subsequent paragraphs. The model reduction techniques investigated in this thesis are based on the concept of Proper Orthogonal Decompositions (POD) of the process measurements or the simulation data. The POD method of model reduction involves spectral decomposition of system solutions and results into arranging the spatio-temporal data in an order of increasing importance. The spectral decomposition results into spatial and temporal patterns. Spatial patterns are often known as POD basis while the temporal patterns are known as the POD modal coefficients. Dominant spatio-temporal patterns are then chosen to construct the most relevant lower dimensional subspace. The subsequent step involves a Galerkin projection of the governing equations of a full order first principle model on the resulting lower dimensional subspace. This thesis can be viewed as a contribution towards developing the databased nonlinear model reduction technique for large scale processes. The major contribution of this thesis is presented in the form of two novel identification based approaches to model order reduction. The methods proposed here are based on the state information of a full order model and result into linear and nonlinear reduced order models. Similar to the POD method explained in the previous paragraph, the first step of the proposed identification based methods involve spectral decomposition. The second step is different and does not involve the Galerkin projection of the equation residuals. Instead, the second step involves identification of reduced order models to approximate the evolution of POD modal coefficients. Towards this purpose, two different methods are presented. The first method involves identification of locally valid linear models to represent the dynamic behavior of the modal coefficients. Global behavior is then represented by ‘blending’ the local models. The second method involves direct identification of the nonlinear models to represent dynamic evolution of the model coefficients. In the first proposed model reduction method, the POD modal coefficients, are treated as outputs of an unknown reduced order model that is to be identified. Using the tools from the field of system identification, a blackbox reduced order model is then identified as a linear map between the plant inputs and the modal coefficients. Using this method, multiple local reduced LTI models corresponding to various working points of the process are identified. The working points cover the nonlinear operation range of the process which describes the global process behavior. These reduced LTI models are then blended into a single Reduced Order-Linear Parameter Varying (ROLPV) model. The weighted blending is based on nonlinear splines whose coefficients are estimated using the state information of the full order model. Along with the process nonlinearity, the nonlinearity arising due to the wear of the furnace wall is also approximated using the RO-LPV modeling framework. The second model reduction method that is proposed in this thesis allows approximation of a full order nonlinear model by various (linear or nonlinear) model structures. It is observed in this thesis, that, for certain class of full order models, the POD modal coefficients can be viewed as the states of the reduced order model. This knowledge is further used to approximate the dynamic behavior of the POD modal coefficients. In particular, reduced order nonlinear models in the form of tensorial (multi-variable polynomial) systems are identified. In the view of these nonlinear tensorial models, the stability and dissipativity of these models is investigated. During the identification of the reduced order models, the physical interpretation of the states of the full order rigorous model is preserved. Due to the smaller dimension and the reduced complexity, the reduced order models are computationally very efficient. The smaller computation time allows them to be used for online control and optimization of the process plant. The possibility of inferring reduced order models from the state information of a full order model alone i.e. the possibility to infer the reduced order models in the absence of access to the governing equations of a full order model (as observed for many commercial software packages) make the methods presented here attractive. The resulting reduced order models need further system theoretic analysis in order to estimate the model quality with respect to their usage in an online controller setting