On the application of isogeometric finite volume method in numerical analysis of wet-steam flow through turbine cascades

The isogeometric finite volume analysis is utilized in this research to numerically simulate the two-dimensional viscous wet-steam flow between stationary cascades of a steam turbine for the first time. In this approach, the analysis-suitable computational mesh with ‘‘curved’’ boundaries is generated for the fluid flow by employing a non- uniform rational B-spline (NURBS) surface that describes the cascade geometry, and the governing equations are then discretized by the NURBS representation. Thanks to smooth and accurate geometry representation of the NURBS formulation, the employed isogeometric framework not only resolves issues concerning the conventional mesh generation techniques of the finite volume method in steam turbine problems, but also, as validated against well-established experiments, significantly improves the accuracy of the numerical solution. In addition, the shock location in the cascade is predicted and tracked with a sufficient accuracy

Isogeometric Shape Optimization in Fluid-Structure Interaction

The objective of this work is to examine the potential of isogeometric methods in the context of multidisciplinary shape optimization. We introduce a shape optimization problem based on a coupled fluid-structure system, whose geometry is defined by NURBS (Non-Uniform Rational B-Spline) curves. This shape optimization problem is then solved by using either an isogeometric approach, or a classical grid-based approach. In spite of the fact that optimization results do not show any major differences, conceptional advantages of the new isogeometric method become apparent. In particular, control points of the spline can be directly handled as design variables without the need of a spline-fit and consequently geometry errors can be excluded at every stages of the optimization loop

Applications of Isogeometric Analysis Coupled with Finite Volume Method

In this thesis, a combination of Isogeometric Analysis (IGA) and Finite Volume Method (FVM) on geometries parameterized by Non-Uniform Rational Basis Splines (NURBS) is explored with applications in fluid flow, heat transfer, and shape optimization. An IGA framework supplemented with FVM is created in MATLAB® to solve problems defined over single patch domains with mesh refinement by node insertion. Additionally, a second-order finite difference method is developed using non-orthogonal curvilinear coordinates and a numerical Jacobian of the NURBS geometry. The examples include fully developed laminar flow through ducts, potential flow around a tilted ellipse, transient heat conduction, linear advection-diffusion, and a basic shape optimization example using a particle swarm technique. The numerical results are compared among the methods and verified with available analytical solutions