Studio della fluidodinamica e della reazione chimica in un reattore agitato tramite modellazione cfd

L’attività di tesi è stata rivolta a realizzare l’accoppiamento tra modelli di reazione chimica e modelli di fluidodinamica per una reazione eterogenea solido-liquido in un reattore agitato, in ambito di un codice commerciale di fluidodinamica numerica. Lo studio ha avuto come punto di partenza la definizione e la discretizzazione del dominio di calcolo tramite un apposito programma. Per una trattazione completa, si sono svolti studi preliminari volti ad identificare le incertezze dovute ai metodi numerici e i limiti dovuti alla formulazione dei modelli per la descrizione del sistema. Lo studio si è svolto considerando sistemi di complessità crescente, partendo da simulazioni monofase fino ad arrivare allo studio di diverse soluzioni per sistemi reagenti con reazioni eterogenee solido-liquido. Questi ultimi esempi applicativi sono serviti come verifica del modello sviluppato (dove con modello si è indicato l’insieme dei modelli relativi alla fluidodinamica accoppiati al modello di reazione). Questa attività ha contribuito ad affrontare un problema di simulazione completa e completamente predittiva dei reattori chimici, essendo la letteratura a riguardo limitata, a differenza di quella relativa alle simulazioni puramente fluidodinamiche.

Analisi cfd in un motore pfi del moto di tumble a carico parzializzato al variare dell'angolo di rotazione della valvola a farfalla

Studio del moto di tumble e della generazione di turbolenza tramite simulazioni CFD tridimensionali al variare del grado di parzializzazione e del verso di rotazione della valvola a farfalla

Effect of mesh distortion on the accuracy of high order vorticity-velocity CFD approaches

The numerical solution of the incompressible Navier-Stokes equations offers an alternative to experimental analysis of fluid-structure interaction (FSI). We would save a lot of time and effort and help cut back on costs, if we are able to accurately model systems by these numerical solutions. 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 Kinematic Laplacian Equation (KLE) to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ordinary differential equations (ODE) time integration schemes, allowing us to tackle each problem as a separate module. The current algortihm for the KLE uses an unstructured quadrilateral mesh, formed by dividing each triangle of an unstructured triangular mesh into three quadrilaterals for spatial discretization. This research deals with determining a suitable measure of mesh quality based on the physics of the problems being tackled. This is followed by exploring methods to improve the quality of quadrilateral elements obtained from the triangles and thereby improving the overall mesh quality. A series of numerical experiments were designed and conducted for this purpose and the results obtained were tested on different geometries with varying degrees of mesh density.

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.

Analysis of internal helically finned tubes for parabolic trough design by CFD tools

This paper has analysed the effect of the utilization of internal finned tubes for the design of parabolic trough collectors with computational fluid dynamics tools. Our numerical approach has been qualified with the computational estimation of reported experimental data regarding phenomena involved in finned tube applications and solar irradiation of parabolic trough collector. The application of finned tubes to the design of parabolic trough collectors must take into account features as the pressure losses, thermal losses and thermo-mechanical stress and thermal fatigue. Our analysis shows an improvement potential in parabolic trough solar plants efficiency by the application of internal finned tubes.

Accelerating CFD via local POD plus Galerkin projections

Se desarrollan varias técnicas basadas en descomposición ortogonal propia (DOP) local y proyección de tipo Galerkin para acelerar la integración numérica de problemas de evolución, de tipo parabólico, no lineales. Las ideas y métodos que se presentan conllevan un nuevo enfoque para la modelización de tipo DOP, que combina intervalos temporales cortos en que se usa un esquema numérico estándard con otros intervalos temporales en que se utilizan los sistemas de tipo Galerkin que resultan de proyectar las ecuaciones de evolución sobre la variedad lineal generada por los modos DOP, obtenidos a partir de instantáneas calculadas en los intervalos donde actúa el código numérico. La variedad DOP se construye completamente en el primer intervalo, pero solamente se actualiza en los demás intervalos según las dinámicas de la solución, aumentando de este modo la eficiencia del modelo de orden reducido resultante. Además, se aprovechan algunas propiedades asociadas a la dependencia débil de los modos DOP tanto en la variable temporal como en los posibles parámetros de que pueda depender el problema. De esta forma, se aumentan la flexibilidad y la eficiencia computacional del proceso. La aplicación de los métodos resultantes es muy prometedora, tanto en la simulación de transitorios en flujos laminares como en la construcción de diagramas de bifurcación en sistemas dependientes de parámetros. Las ideas y los algoritmos desarrollados en la tesis se ilustran en dos problemas test, la ecuación unidimensional compleja de Ginzburg-Landau y el problema bidimensional no estacionario de la cavidad. Abstract Various ideas and methods involving local proper orthogonal decomposition (POD) and Galerkin projection are presented aiming at accelerating the numerical integration of nonlinear time dependent parabolic problems. The proposed methods come from a new approach to the POD-based model reduction procedures, which combines short runs with a given numerical solver and a reduced order model constructed by expanding the solution of the problem into appropriate POD modes, which span a POD manifold, and Galerkin projecting some evolution equations onto that linear manifold. The POD manifold is completely constructed from the outset, but only updated as time proceeds according to the dynamics, which yields an adaptive and flexible procedure. In addition, some properties concerning the weak dependence of the POD modes on time and possible parameters in the problem are exploited in order to increase the flexibility and efficiency of the low dimensional model computation. Application of the developed techniques to the approximation of transients in laminar fluid flows and the simulation of attractors in bifurcation problems shows very promising results. The test problems considered to illustrate the various ideas and check the performance of the algorithms are the onedimensional complex Ginzburg-Landau equation and the two-dimensional unsteady liddriven cavity problem.

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 CFD modelling of non-neutral atmospheric boundary layers for offshore wind resource assessment based on Monin-Obukhov theory

The presented works aim at proposing a methodology for the simulation of offshore wind conditions using CFD. The main objective is the development of a numerical model for the characterization of atmospheric boundary layers of different stability levels, as the most important issue in offshore wind resource assessment. Based on Monin-Obukhov theory, the steady k-ε Standard turbulence model is modified to take into account thermal stratification in the surface layer. The validity of Monin-Obukhov theory in offshore conditions is discussed with an analysis of a three day episode at FINO-1 platform.

Modelling wake effects using two CFD techniques

Comparativa de dos técnica de simulación de rotor: BEM (Blade Element Momentum) y MRF (Moving Reference Frame) para el perfil S809 de NREL

Simulation of wind farms in flat and complex terrain using CFD

Use of computational fluid dynamic (CFD) methods to predict the power production from wind entire wind farms in flat and complex terrain is presented in this paper. Two full 3D Navier–Stokes solvers for incompressible flow are employed that incorporate the k–ε and k–ω turbulence models respectively. The wind turbines (W/Ts) are modelled as momentum absorbers by means of their thrust coefficient using the actuator disk approach. The WT thrust is estimated using the wind speed one diameter upstream of the rotor at hub height. An alternative method that employs an induction-factor based concept is also tested. This method features the advantage of not utilizing the wind speed at a specific distance from the rotor disk, which is a doubtful approximation when a W/T is located in the wake of another and/or the terrain is complex. To account for the underestimation of the near wake deficit, a correction is introduced to the turbulence model. The turbulence time scale is bounded using the general “realizability” constraint for the turbulent velocities. Application is made on two wind farms, a five-machine one located in flat terrain and another 43-machine one located in complex terrain. In the flat terrain case, the combination of the induction factor method along with the turbulence correction provides satisfactory results. In the complex terrain case, there are some significant discrepancies with the measurements, which are discussed. In this case, the induction factor method does not provide satisfactory results.

CFD modelling of wind farms in complex terrain

Modelling of entire wind farms in flat and complex terrain using a full 3D Navier–Stokes solver for incompressible flow is presented in this paper. Numerical integration of the governing equations is performed using an implicit pressure correction scheme, where the wind turbines (W/Ts) are modelled as momentum absorbers through their thrust coefficient. The k–ω turbulence model, suitably modified for atmospheric flows, is employed for closure. A correction is introduced to account for the underestimation of the near wake deficit, in which the turbulence time scale is bounded using a general “realizability” constraint for the fluctuating velocities. The second modelling issue that is discussed in this paper is related to the determination of the reference wind speed for the thrust calculation of the machines. Dealing with large wind farms and wind farms in complex terrain, determining the reference wind speed is not obvious when a W/T operates in the wake of another WT and/or in complex terrain. Two alternatives are compared: using the wind speed value at hub height one diameter upstream of the W/T and adopting an induction factor-based concept to overcome the utilization of a wind speed at a certain distance upwind of the rotor. Application is made in two wind farms, a five-machine one located in flat terrain and a 43-machine one located in complex terrain.

Analysis and validation of CFD wind farm models in complex terrain. Effects induced by topography and wind turbines

Wind farms have been extensively simulated through engineering models for the estimation of wind speed and power deficits inside wind farms. These models were designed initially for a few wind turbines located in flat terrain. Other models based on the parabolic approximation of Navier Stokes equations were developed, making more realistic and feasible the operational resolution of big wind farms in flat terrain and offshore sites. These models have demonstrated to be accurate enough when solving wake effects for this type of environments. Nevertheless, few analyses exist on how complex terrain can affect the behaviour of wind farm wake flow. Recent numerical studies have demonstrated that topographical wakes induce a significant effect on wind turbines wakes, compared to that on flat terrain. This circumstance has recommended the development of elliptic CFD models which allow global simulation of wind turbine wakes in complex terrain. An accurate simplification for the analysis of wind turbine wakes is the actuator disk technique. Coupling this technique with CFD wind models enables the estimation of wind farm wakes preserving the extraction of axial momentum present inside wind farms. This paper describes the analysis and validation of the elliptical wake model CFDWake 1.0 against experimental data from an operating wind farm located in complex terrain. The analysis also reports whether it is possible or not to superimpose linearly the effect of terrain and wind turbine wakes. It also represents one of the first attempts to observe the performance of engineering models compares in large complex terrain wind farms.

CFD modelling of the interaction between the Surface Boundary Layer and rotor wake. Comparison of results obtained with different turbulence models and mesh strategies

A simplified CFD wake model based on the actuator disk concept is used to simulate the wind turbine, represented by a disk upon which a distribution of forces, defined as axial momentum sources, are applied on the incoming non-uniform flow. The rotor is supposed to be uniformly loaded, with the exerted forces function of the incident wind speed, the thrust coefficient and the rotor diameter. The model is tested under different parameterizations of turbulence models and validated through experimental measurements downwind of a wind turbine in terms of wind speed deficit and turbulence intensity.

Validation of a CFD wake model based on the actuator disk technique and the thrust coefficient. Preliminary results

A simplified CFD wake model based on the actuator-disk concept is used to simulate the wind turbine, represented by an actuator disk upon which a distribution of forces, defined as axial momentum sources, are applied on the incoming flow. The rotor is supposed to be uniformly loaded, with the exerted forces as a function of the incident wind speed, the thrust coefficient and the rotor diameter. The model is validated through experimental measurements downwind of a wind turbine in terms of wind speed deficit. Validation on turbulence intensity will also be made in the near future.