Combining simultaneous density and velocity measurements of rotor blade tip vortices under cyclic pitch conditions

An investigation into blade tip vortices of a sub-scale rotor under cyclic pitch conditions is carried out. Background oriented schlieren (BOS), particle image velocimetry (PIV), and computational fluid dynamics (CFD) are applied to the same test cases. This approach allows to combine the velocity data from PIV in a measurement plane, the density related data from BOS in a measurement volume, and the comprehensive set of flow variables provided by unsteady detached eddy simulations. Vortices up to an age of $$\varPsi _{{\text {v}}}= {70}^\circ$$ Ψ v = 70 ∘ in case of PIV and CFD, and up to $$\varPsi _{{\text {v}}}= {200}^\circ$$ Ψ v = 200 ∘ in case of BOS are considered. The vortex locations are obtained through all three techniques. The unsteadiness of the vortices was obtained by the experimental results, whereas CFD provides an average solution. An increased position scatter was observed during the downstroke of the pitch cycle with both experimental methods and was found to be in good agreement. In the second part, the PIV velocity data are compared to common vortex models. An approach to link the density distribution and the swirl velocity is applied to the measured data. Based on the CFD results, it is shown that the assumption of isothermal flow yields better agreement between velocity and density than isentropic flow. Graphic abstract

An improved de Laval nozzle experiment

Exposing students to hands-on experiments has been a common approach to illustrating complex physical phenomena that have been otherwise modelled solely mathematically. Compressible, isentropic flow in a duct is an example of such a phenomenon, and it is often demonstrated via a de Laval nozzle experiment. We have improved an existing converging/diverging nozzle experiment so that students can modify the location of the normal shock that develops in the diverging portion to better understand the relationship between the shock and the pressure. We have also improved the data acquisition system for this experiment and explained how visualisation of the standing shock is now possible. The results of the updated system demonstrate that the accuracy of the isentropic flow characteristics has not been lost. Through pre- and post-laboratory quizzes, we show the impact on student learning as well.

MASK GENERATOR FOR ORTHOGONAL REGULAR MESH

Existing mesh generators are focused mainly on obtaining non-orthogonal irregular grids designed to describe the curved boundaries of streamlined bodies. However, the thickening of the grid leads to an increase in the calculation time, and the non-conformity of the grid leads to unphysical effects. The software package (SP) developed by the authors for the simulation of gas-thermodynamic processes is oriented toward a much simpler description of the geometry, i. e., uses a different principle of increasing the smoothness of the solution in places with a complex surface structure. This principle consists in superimposing on the flow such sources of momentum and energy, which are equivalent in their effect on the flow to the interaction with the solid wall. SP contains a mask generator of an orthogonal regular grid. The initial data for building the mask is a 3D model created in any CAD application, which is saved in the STL format and placed in the project directory. Each cell contains information about the presence of a three-dimensional solid, the permeability of each face of the hexahedron, and the direction of the normal vector to the streamlined surface. In this regard, the generator creates three types of masks: volumetric, surface full and incomplete permeability, as well as a mask of guiding cosines. To obtain a volume (solid) mask from the center of each cell along the axes, a straight line is drawn and its intersection is checked with each triangle approximating the surface of the body under study. An odd number of intersections of triangles and a straight line indicates the presence of a volume mask in the cells. A surface impermeable mask is formed in three directions at the free cell section and the occupied volume mask. If it is necessary to introduce a semipermeable mask, its localization and measure are assigned by the user. The mask of the guiding cosines is assigned in the cell, which is adjacent to the surface impermeable mask. The values of the guiding cosines are assigned equal to the corresponding values of the nearby triangle approximating the surface of the 3D model. The generated masks are formed as separate files. A SolidWorks application has been developed that allows for volumetric visualization. In the decisive program, the information about the presence of the volume mask is used as follows: the volume mask is excluded from the solution area, self-similar problems are solved near the surface, and if there are guiding properties, an isentropic flow rotation is performed.

A Coupled Overset Mesh and Hybridizable Discontinuous Galerkin Algorithm for Pseudo-Compressible Flow

A previously presented overset mesh enabled hybridizable discontinuous Galerkin (HDG) finite element method is extended in this work to an isentropic compressible (pseudo-compressible) fluid. This formulation is a first-principles approach and is complementary to the augmented Lagrangian approach that was utilized in the previous HDG incompressible Navier–Stokes formulations which eliminate the global pressure field. This is the first original presentation combining overset meshes, HDG, and fluid flow, specifically isentropic flow for low Mach number applications. Verification of the code implementation of the proposed overset-HDG formulation is performed via the method of manufactured solutions (MMS) on a successively refined overset mesh configuration containing five meshes, and for order k=1,…,4, Lagrange polynomial elements in both two and three dimensions. Optimal order convergence, k + 1, can be observed in all fields for both the two- and three-dimensional simulations, for each mesh. A two-dimensional benchmark problem is also presented to enable code-to-code comparison as a preliminary validation exercise.