Significant progress has been made towards developing an effective solution method for predicting low-speed flows through vertical-axis wind turbines. A Godunov-type finite-volume scheme has been developed for the solution of the Euler equations in two-dimensions on a multi-block mesh. The proposed algorithm features a parallel block-based adaptive mesh refinement scheme and a mesh adjustment procedure to enable straightforward meshing of irregular solid boundaries. A low-Mach-Number preconditioner is used in conjunction with a dual timestepping scheme to reduce the computational costs of simulating low-speed unsteady flows. A second-order backwards differencing time-marching scheme is used for the outer physicaltime discretization, and an explicit optimally-smoothing multi-stage time-stepping scheme with multigrid acceleration is used for the inner pseudo-time loop. Results are presented for various low-speed flows that demonstrate the suitability of the algorithms for wind turbine flows. Additional theory and discussion are also presented for extension of the schemes to the full Navier-Stokes equations.

Significant progress has been made towards developing an effective solution method for predicting low-speed flows through vertical-axis wind turbines. A Godunov-type finite-volume scheme has been developed for the solution of the Euler equations in two-dimensions on a multi-block mesh. The proposed algorithm features a parallel block-based adaptive mesh refinement scheme and a mesh adjustment procedure to enable straightforward meshing of irregular solid boundaries. A low-Mach-Number preconditioner is used in conjunction with a dual timestepping scheme to reduce the computational costs of simulating low-speed unsteady flows. A second-order backwards differencing time-marching scheme is used for the outer physicaltime discretization, and an explicit optimally-smoothing multi-stage time-stepping scheme with multigrid acceleration is used for the inner pseudo-time loop. Results are presented for various low-speed flows that demonstrate the suitability of the algorithms for wind turbine flows. Additional theory and discussion are also presented for extension of the schemes to the full Navier-Stokes equations.

La descripción del flujo de fluidos involucra la solución de las ecuaciones de Navier-Stokes compresible, un problema muy complejo cuya estructura matemática no es del todo comprendida. Por lo tanto, mediante análisis asintótico, se pueden derivar modelos simplificados bajo ciertas hipótesis sobre el problema hechas en términos de parámetros adimensionales que miden la importancia relativa de los diferentes procesos físicos. Los flujos a baja velocidad se pueden describir por diferentes modelos que incluyen las ecuaciones de Navier Stokes incompresible cuya matemática es mucho mas conocida. Sin embargo, algunos flujos importantes no se pueden considerar incompresibles debido a la presencia de efectos térmicos. En esta clase de problemas se pueden derivar otra clase de ecuaciones simplificadas: las ecuaciones de Boussinesq y las ecuaciones de bajo numero de Mach.La complejidad de estos problemas matemáticos hace que su solución numérica sea muy difícil. En estos problemas el método de los elementos finitos es inestable, lo que en la práctica implica soluciones numéricas que presentan oscilaciones nodo a nodo de naturaleza no física. En las ecuaciones de Navier Stokes incompresible, dos fuentes bien conocidas de inestabilidad son la condición de incompresibilidad y la presencia del término convectivo. Muchas técnicas de estabilización utilizadas hoy en día se basan en la separación de escalas, descomponiendo la incógnita en una parte gruesa inducida por la discretización del domino y una parte fina de subescala. Modelar la subescala y su influencia conduce a un problema modificado para la escala gruesa que resulta estable.Aunque las técnicas de estabilización son ampliamente utilizadas hoy en día, importantes problemas permanecen abiertos. Contribuyendo a su comprensión, en este trabajo se analizan varios aspectos del modelado de las subescalas. Para problemas escalares de segundo orden, se encuentra la dependencia de la subescala con el tamaño de la malla en el caso general de mallas anisótropas. Estas ideas son extendidas a sistemas de ecuaciones para considerar el problema de Oseen. También se analiza el modelado de las subescalas en problemas transitorios, obteniendo un mejor esquema de integración temporal para el problema de escala gruesa. Para considerar flujos a baja velocidad, se presenta la extensión de estas técnicas a problemas no lineales acoplados, lo que esta íntimamente relacionado con el problema del modelado de la turbulencia, que es un tema en si mismo.Los flujos acoplados térmicamente, aparte del interés intrínseco que merecen, son importantes desde un punto de vista ingenieril. Una solución precisa del problema de flujo es necesaria para definir las cargas térmicas sobre las estructuras, que en muchos casos responden fuertemente, haciendo el problema acoplado. Esta clase de problemas, que motivaron este trabajo, incluyen la respuesta estructural en el caso de un incendio. / A general description of a fluid flow involves the solution of the compressible Navier-Stokes equations, a very complex problem whose mathematical structure is not well understood. Therefore, simplified models can be derived by asymptotic analysis under some assumptions on the problem, made in terms of dimensionless parameters that measure the relative importance of different physical processes. Low speed flows can be described by several models including the incompressible Navier Stokes equations whose mathematical structure is much better understood. However many important flows cannot be considered as incompressible, even at low speed, due to the presence of thermal effects. In such kind of problems another class of simplified equations can be derived: the Boussinesq equations and the Low Mach number equations.The complexity of these mathematical problems makes their numerical solution very difficult. For these problems the standard finite element method is unstable, what in practice means that node to node oscillations of non physical nature may appear in the numerical solution. In the incompressible Navier Stokes equations, two well known sources of numerical instabilities are the incompressibility constraint and the presence of the convective terms. Many stabilization techniques used nowadays are based on scale separation, splitting the unknown into a coarse part induced by the discretization of the domain and a fine subgrid part. The modelling of the subgrid scale and its influence leads to a modified coarse scale problem that now can be shown to be stable. Although stabilization techniques are nowadays widely used, important problems remain open. Contributing to their understanding, several aspects of the subgrid scale modelling are analyzed in this work. For second order scalar problems, the dependence of the subgrid scale on the mesh size, in the general anisotropic case, is clarified. These ideas are extended to systems of equations to consider the Oseen problem. The modelling of the subgrid scales in transient problems is also analyzed, leading to an improved time discretization scheme for the coarse scale problem. To consider low speed flow models, the extension of these techniques to nonlinear and coupled problems is presented, something that is intimately related to the problem of turbulence modelling, which a entire subject on its own right. Thermally coupled flow problems, despite the intrinsic interest they deserve, are important from an engineering point of view. An accurate solution of a flow problem is needed to define thermal loads on structures which, in many cases have a strong response, making the problem coupled. This kind of problems, that motivated this work, include the problem of a structural response in the case of fires.

The aerodynamic sound generated by wind turbines was identified as a growing concern within the industry. Prior to performing wind turbine aeroacoustic research, however, a technique suitable for studying low speed airfoils needed to be designed, serving as the primary research objective. A review of aeroacoustic theory and literature indicated that low speed flows are best studied using experimental methods, leading to the design of a near field pressure measurement technique. To facilitate the near field pressure measurements, a custom piezoelectric sensor was developed, exhibiting a pressure and frequency range of approximately 67 to 140[dB], and 100 to 10000[Hz], respectively. As a secondary research objective, a series of experiments were performed to validate the designed technique. The experiments were performed in a non-anechoic wind tunnel using a cylindrical test specimen. Using the near field pressure measurements, as well as a simple far field measurement, the sources of aerodynamic sound were effectively resolved. The Strouhal numbers corresponding to the contributing flow structures were generally within 1.5[%] of correlation based predictions. The near field pressures were consistently 10 to 15[dB] higher than the far field, quantifying the benefit of the near field technique. The method was also effective in detecting the decreasing coherence of the aeroacoustic sources with increasing Reynolds number. A minor deficiency was observed in which the ability to localize aeroacoustic sources was impeded, however, the cylinder experiments were particularly vulnerable to such a deficiency. Although the near field pressure measurements were shown to be effective in characterizing the aeroacoustic sources, a number of recommendations are presented to further improve the flexibility and measurement uncertainty of the experimental technique.

The aerodynamic sound generated by wind turbines was identified as a growing concern within the industry. Prior to performing wind turbine aeroacoustic research, however, a technique suitable for studying low speed airfoils needed to be designed, serving as the primary research objective. A review of aeroacoustic theory and literature indicated that low speed flows are best studied using experimental methods, leading to the design of a near field pressure measurement technique. To facilitate the near field pressure measurements, a custom piezoelectric sensor was developed, exhibiting a pressure and frequency range of approximately 67 to 140[dB], and 100 to 10000[Hz], respectively. As a secondary research objective, a series of experiments were performed to validate the designed technique. The experiments were performed in a non-anechoic wind tunnel using a cylindrical test specimen. Using the near field pressure measurements, as well as a simple far field measurement, the sources of aerodynamic sound were effectively resolved. The Strouhal numbers corresponding to the contributing flow structures were generally within 1.5[%] of correlation based predictions. The near field pressures were consistently 10 to 15[dB] higher than the far field, quantifying the benefit of the near field technique. The method was also effective in detecting the decreasing coherence of the aeroacoustic sources with increasing Reynolds number. A minor deficiency was observed in which the ability to localize aeroacoustic sources was impeded, however, the cylinder experiments were particularly vulnerable to such a deficiency. Although the near field pressure measurements were shown to be effective in characterizing the aeroacoustic sources, a number of recommendations are presented to further improve the flexibility and measurement uncertainty of the experimental technique.