Optimization of energy extraction in transverse galloping

A numerical method to analyse the stability of transverse galloping based on experimental measurements, as an alternative method to polynomial fitting of the transverse force coefficient Cz, is proposed in this paper. The Glauert–Den Hartog criterion is used to determine the region of angles of attack (pitch angles) prone to present galloping. An analytic solution (based on a polynomial curve of Cz) is used to validate the method and to evaluate the discretization errors. Several bodies (of biconvex, D-shape and rhomboidal cross sections) have been tested in a wind tunnel and the stability of the galloping region has been analysed with the new method. An algorithm to determine the pitch angle of the body that allows the maximum value of the kinetic energy of the flow to be extracted is presented.

Bridge damage identification from moving load induced deflection based on wavelet transform and Lipschitz exponent

The wavelet transform and Lipschitz exponent perform well in detecting signal singularity.With the bridge crack damage modeled as rotational springs based on fracture mechanics, the deflection time history of the beam under the moving load is determined with a numerical method. The continuous wavelet transformation (CWT) is applied to the deflection of the beam to identify the location of the damage, and the Lipschitz exponent is used to evaluate the damage degree. The influence of different damage degrees,multiple damage, different sensor locations, load velocity and load magnitude are studied.Besides, the feasibility of this method is verified by a model experiment.

An efficient nonlinear transformation for the numerical computation of the singular integrals appearing in the 2-D Boundary Element Method

We discuss several methods, based on coordinate transformations, for the evaluation of singular and quasisingular integrals in the direct Boundary Element Method. An intrinsec error of some of these methods is detected. Two new transformations are suggested which improve on those currently available.

Prediction of bendig load capacity of timber beams by finite element method simulation of knots and grain deviation

A finite element model was used to simulate timberbeams with defects and predict their maximum load in bending. Taking into account the elastoplastic constitutive law of timber, the prediction of fracture load gives information about the mechanisms of timber failure, particularly with regard to the influence of knots, and their local graindeviation, on the fracture. A finite element model was constructed using the ANSYS element Plane42 in a plane stress 2D-analysis, which equates thickness to the width of the section to create a mesh which is as uniform as possible. Three sub-models reproduced the bending test according to UNE EN 408: i) timber with holes caused by knots; ii) timber with adherent knots which have structural continuity with the rest of the beam material; iii) timber with knots but with only partial contact between knot and beam which was artificially simulated by means of contact springs between the two materials. The model was validated using ten 45 × 145 × 3000 mm beams of Pinus sylvestris L. which presented knots and graindeviation. The fracture stress data obtained was compared with the results of numerical simulations, resulting in an adjustment error less of than 9.7%

Theoretical analysis and numerical verification of the consistency of viscous smoothed-particle-hydrodynamics formulations in simulating free-surface flows

The theoretical formulation of the smoothed particle hydrodynamics (SPH) method deserves great care because of some inconsistencies occurring when considering free-surface inviscid flows. Actually, in SPH formulations one usually assumes that (i) surface integral terms on the boundary of the interpolation kernel support are neglected, (ii) free-surface conditions are implicitly verified. These assumptions are studied in detail in the present work for free-surface Newtonian viscous flow. The consistency of classical viscous weakly compressible SPH formulations is investigated. In particular, the principle of virtual work is used to study the verification of the free-surface boundary conditions in a weak sense. The latter can be related to the global energy dissipation induced by the viscous term formulations and their consistency. Numerical verification of this theoretical analysis is provided on three free-surface test cases including a standing wave, with the three viscous term formulations investigated.

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Categorical Missing Data Imputation Using Fuzzy Neural Networks with Numerical and Categorical Inputs

There are many situations where input feature vectors are incomplete and methods to tackle the problem have been studied for a long time. A commonly used procedure is to replace each missing value with an imputation. This paper presents a method to perform categorical missing data imputation from numerical and categorical variables. The imputations are based on Simpson’s fuzzy min-max neural networks where the input variables for learning and classification are just numerical. The proposed method extends the input to categorical variables by introducing new fuzzy sets, a new operation and a new architecture. The procedure is tested and compared with others using opinion poll data.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos

Numerical and Experimental Studies of Sail Aerodynamics

The purpose of this investigation was the determination of the aerodynamic performance of sails and gain knowledge of the phenomena involved in order to improve the aerody¬namic characteristics. In this research, the airflow around different sails in four scenarios was studied. The method to analyze these scenarios was the combination of numerical simulations and experimental tests by taking advantage of the best of each tool. Two different Com¬putational Fluid Dynamic codes were utilized: the ANSYS-CFX and the CD-Adapco’s STAR-CCM+. The experimental tests were conducted in the Atmospheric Boundary Layer Wind Tunnel at the Universidad de Granada (Spain), the Twisted Flow Wind Tunnel at the University of Auckland (New Zealand) and the A9 Wind Tunnel at the Universidad Polit´ecnica de Madrid (Spain). Through this research, it was found the three-dimensional effect of the mast on the aerodynamic performance of an IMS Class boat. The pressure distribution on a Transpac 52 Class mainsail was also determined. Moreover, the aerodynamic perfor¬mance of the 43ft and 60ft Dhow Classes was obtained. Finally, a feasibility study was conducted to use a structural wing in combination with conventional propulsions systems. The main conclusion was that this research clarified gaps on the knowledge of the aerodynamic performance of sails. Moreover, since commercial codes were not specifically designed to study sails, a procedure was developed. On the other hand, innovative experimental techniques were used and applied to model-scale sails. The achievements of this thesis are promising and some of the results are already in use by the industry on a daily basis. El propósito de este estudio era determinar el comportamiento aerodinámico de unas velas y mejorar el conocimiento de los fenómenos que suceden para optimizar las características aerodinámicas de dichas velas. En esta investigación se estudió el flujo de aire alrededor de diferentes velas en cuatro escenarios. El método para analizar estos escenarios fue la combinación de simulaciones numéricas y ensayos experimentales mediante el aprovechamiento de las ventajas de cada herramienta. Se utilizaron dos códigos de dinámica de fluidos computacional: el ANSYS-CFX y el STAR-CCM+ de la empresa CD-Adapco. Los ensayos experimentales se desarrollaron en el túnel de viento de capa límite de la Universidad de Granada (España), el túnel de viento de la Universidad de Auckland (Nueva Zelanda) y en el túnel A9 de la Universidad Politécnica de Madrid (España). Mediante esta investigación, se determinó el efecto tridimensional del mástil en un velero de la clase IMS. También se describió la distribución de presiones sobre una mayor de un Transpac 52. Además, se obtuvo el comportamiento aerodinámico de las clases 43ft y 60ft de los veleros Dhows. Finalmente, se llevó a cabo un estudio de viabilidad de la utilización de un ala estructural en combinación con sistemas de propulsión convencionales. La conclusión principal de esta investigación fue la capacidad de explicar ciertas lagunas en el conocimiento del comportamiento aerodinámico de las velas en diferentes escenarios. Además, dado que los códigos comerciales no están específicamente diseñados para el estudio de velas, se desarrolló un procedimiento a tal efecto. Por otro lado, se han utilizado innovadoras técnicas experimentales y se han aplicado a modelos de velas a escala. Los logros de esta investigación son prometedores y algunos de los resultados obtenidos ya están siendo utilizados por la industria en su día a día.

Numerical analysis of axisymmetric shells by one-dimensional continuum elements suitable for high frequency excitations

Axisymmetric shells are analyzed by means of one-dimensional continuum elements by using the analogy between the bending of shells and the bending of beams on elastic foundation. The mathematical model is formulated in the frequency domain. Because the solution of the governing equations of vibration of beams are exact, the spatial discretization only depends on geometrical or material considerations. For some kind of situations, for example, for high frequency excitations, this approach may be more convenient than other conventional ones such as the finite element method.

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model

Preface : (Boundary Element Method) Computers and Structures 83 (2005)

The Boundary Element Method is a powerful numerical technique well rooted in everyday engineering practice. This is shown by boundary element methods included in the most important commercial computer packages and in the continuous publication of books composed to explain the features of the method to beginners or practicing engineers. Our first paper in Computers & Structures on Boundary Elements was published in 1979 (C & S 10, pp. 351–362), so this Special Issue is for us not only the accomplishment of our obligation to show other colleagues the possibilities of a numerical technique in which we believe, but also the celebration of our particular silver jubilee with this Journal.

The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography. The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results.

Simplified computational method for non-linear seismic analysis of bridges

After the experience gained during the past years it seems clear that nonlinear analysis of bridges are very important to compute ductility demands and to localize potential hinges. This is specially true for irregular bridges in which it is not clear weather or not it is possible to use a linear computation followed by a correction using a behaviour factor. To simplify the numerical effort several approximate methods have been proposed. Among them, the so-called Dynamic Plastic Hinge Method in which an evolutionary shape function is used to reduce the structure to a single degree of freedom system seems to mantein a good balance between accuracy and simplicity. This paper presents results obtained in a parametric study conducted under the auspicies of PREC-8 european research program.

A simulation method to estimate closing forces in car-sealing rubber elements

The door-closing process can reinforce the impression of a solid, rock-proof, car body or of a rather cheap, flimsy vehicle. As there are no real prototypes during rubber profile bidding-out stages, engineers need to carry out non-linear numerical simulations that involve complex phenomena as well as static and dynamic loads for several profile candidates. This paper presents a structured virtual design tool based on FEM, including constitutive laws and incompressibility constraints allowing to predict more realistically the final closing forces and even to estimate sealing overpressure as an additional guarantee of noise insulation. Comparisons with results of physical tests are performed.