Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation

Abstract

This paper presents a two-dimensional implementation of the high-order penalized vortex in cell method applied to solve the flow past an airfoil with a vortex trapping cavity operating under moderate Reynolds number. The purpose of this article is to investigate the fundamentals of the vortex trapping cavity. The first part of the paper treats with the numerical implementation of the method and high-order schemes incorporated into the algorithm. Poisson, stream-velocity, advection, and diffusion equations were solved. The derivation, finite difference formulation, Lagrangian particle remeshing procedure, and accuracy tests were shown. Flow past complex geometries was possible through the penalization method. A procedure description for preparing geometry data was included. The entire methodology was tested with flow past impulsively started cylinder for three Reynolds numbers: 550, 3000, 9500. Drag coefficient, streamlines, and vorticity contours were checked against results obtained by other authors. Afterwards, simulations and experimental results are presented for a standard airfoil and those equipped with a trapping vortex cavity. Airfoil with an optimized cavity shape was tested under three angles of attack: 3°, 6°, 9°. The Reynolds number is equal to Re = 2 × 104. Apart from performing flow analysis, drag and lift coefficients for different shapes were measured to assess the effect of vortex trapping cavity on aerodynamic performance. Flow patterns were compared against ultraviolet dye visualizations obtained from the water tunnel experiment.

Turbulence and Fluid Mechanics

“…The article [10] entitled "Vortex Trapping Cavity on Airfoil: High-Order Penalized Vortex Method Numerical Simulation and Water Tunnel Experimental Investigation" presents new possibilities of using the vortex-in-cell (VIC) method to model geometrically complicated flows. The authors use their method to model aerodynamic profiles with various vortex trapping cavities.…”

Numerical Methodology to Reduce the Drag and Control Flow around a Cam-Shaped Cylinder Integrated with Backward Splitter Plate

“…Moreover, the efficacy of a splitter plate on flow separation control significantly differs for unlike-shaped bluff bodies such as circular and square cylinders, which was also previously reported [29][30][31][32]. In addition, the aspect of boundary layer separation around the bluff bodies is explored in [33][34][35]. The goal of the current study is to amalgamate both aspects, i.e., bluff body shape modification and attaching a splitter plate behind the bluff body, for significant drag reduction.…”

High-precision numerical investigation of a VAWT starting process

“…Multiple solutions have been analysed regarding active [37,38]and passive flow control [39], either by creating cavities inside the blades [40], much like the novel VAWT geometry studied in this paper, or by mounting vortex generators on the extrados [41].The trapped vortex cavity offers the advantage of flow separation occurring inside of the cavity and reattach towards the end of the cavity. This leads to significantly diminish the wake area and constraining the vorticity region to the cavity, resulting in higher lift-todrag ratio [42,43]. To further analyse the effect of vortices and flow separation on the Cp, the authors 3 in [44] have introduced a new parameter, the Vorticity Index (VI), calculated by dividing the vorticity in the Leading Edge (LE) by the vorticity in the Trailing Edge (TE) which can help detect a possible vortex separation, either from the LE to the TE, when this index approaches a value of 1, or from the TE to the LE, when the index approaches a value around 0.2.…”