Flow Modeling over Airfoils and Vertical Axis Wind Turbines Using Fourier Pseudo-Spectral Method and Coupled Immersed Boundary Method

Abstract

In the present work, verifying the applicability and potentiality of the IMERSPEC methodology for numerical and computational modeling of two-dimensional flows over airfoils and vertical axis wind turbines is proposed. It is a high-order convergence methodology with low computational cost when compared to other high-order methods, resulting from the coupling of the Fourier pseudo-spectral method and the immersed boundary method. To validate the proposed methodology, flow simulations are carried out over an airfoil NACA 0012 for a Reynolds number equal to 1000. From the spatial discretization procedure, there is convergence and good agreement of the lift and drag coefficients and the Strouhal number in relation to reference works. The behavior of the flows over the airfoil, as a function of the angle of attack, is evaluated by pressure and vorticity fields. From the analyzed flows, it is observed that the formation of different wake modes, constituted by swirling structures that vary their characteristic sizes, is influenced by the angle of attack. A case study is proposed based on the analysis of the main fluid dynamic aspects of flows over wind turbines with a vertical axis of three blades for a Reynolds number equal to 100. For this, a mathematical model responsible for the imposition of the rotational movement on the blades is presented in the turbine. Performance parameters, such as the coefficient of tangential force and normal force, and the analysis of velocity fields on the simulated turbine were presented and compared with other numerical methods. The good level of convergence and the accuracy of the obtained results show the promising capacity of the IMERSPEC methodology in solving problems of this nature.

Numerical Simulation of Flows Using the Fourier Pseudospectral Method and the Immersed Boundary Method

“…The combination of these regions generates a periodic domain, which is required by the FPSM, resulting in identical boundary conditions at the domain's exit and entrance. Due to periodicity, physical instabilities exiting the Eulerian domain (fluid recirculations, for example) are reintroduced at its entrance, justifying the presence of the buffer region and the forcing zone [3,15]. In all simulations, the airfoils were centrally positioned within a domain of sufficiently large dimensions to accurately represent the external flow over the profiles.…”

“…where The Lagrangian domain represents the immersed interface in the flow. Being independent of the Eulerian domain, the Lagrangian mesh enables the simulation of flows over complex geometries using a Cartesian domain, eliminating the need for remeshing, even in the case of moving geometries, as only the Lagrangian interface will move [3]. The fundamental characteristic of always working with a fixed Cartesian domain, even for flows over complex, deformable, or moving geometries, is the main reason why researchers opt for the IBM.…”

“…CFD finds widespread use across various fields and applications, including aerodynamics, weather forecasting, heat and mass transfer analysis, chemical engineering processes, metallurgical processes, refrigeration and air conditioning system design, and turbomachinery design [1]. Additionally, CFD is employed in verifying aerodynamic forces on buildings [2], analyzing fluid-structure interactions [3], studying the aerodynamics of land, aquatic, and aerial vehicles [4,5], and determining hydrodynamic forces on submerged structures [6], among other applications.…”

“…This method involves creating two distinct Cartesian grids: the Lagrangian mesh, representing the boundary of the body immersed in the flow, and the Eulerian mesh, where the equations governing fluid flow are solved [20]. The integration of the FPM and IBM resulted in the hybrid methodology known as IMERSPEC [3,15]. With IMERSPEC, the Navier-Stokes equations are solved using the Fourier pseudospectral method, while physical boundary conditions are imposed through the source term of the immersed boundary.…”

Application of the Euler–Lagrange Approach and Immersed Boundary Method to Investigate the Behavior of Rigid Particles in a Confined Flow

“…Successful results can be obtained when the IBM is employed to deal with static geometries [13][14][15][16] and imposed motion geometries with considerable displacements and fluid-structure interaction problems [17][18][19]. The greatest advantage of IBM is that the geometry, particles' motion, or deformation do not imply the need for grid restructuring at every single time step.…”