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

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8402
Author(s):  
Dominik Błoński ◽  
Katarzyna Strzelecka ◽  
Henryk Kudela
Keyword(s):  
Reynolds Number ◽  
Flow Analysis ◽  
Vortex Method ◽  
High Order ◽  
Stream Velocity ◽  
Water Tunnel ◽  
High Order Schemes ◽  
Flow Past ◽  
Moderate Reynolds Number ◽  
Poisson Stream

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.

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

Accelerated flow past a symmetric aerofoil: experiments and computations

2007 ◽  
Vol 591 ◽  
pp. 255-288 ◽  
Author(s):  
T. K. SENGUPTA ◽  
T. T. LIM ◽  
SHARANAPPA V. SAJJAN ◽  
S. GANESH ◽  
J. SORIA
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Angle Of Attack ◽  
Stream Velocity ◽  
Published Data ◽  
Navier Stokes Equation ◽  
Moment Coefficient ◽  
Flow Past ◽  
Naca 0015 ◽  
Accelerated Flow

Accelerated flow past a NACA 0015 aerofoil is investigated experimentally and computationally for Reynolds number Re = 7968 at an angle of attack α = 30°. Experiments are conducted in a specially designed piston-driven water tunnel capable of producing free-stream velocity with different ramp-type accelerations, and the DPIV technique is used to measure the resulting flow field past the aerofoil. Computations are also performed for other published data on flow past an NACA 0015 aerofoil in the range 5200 ≤ Re ≤ 35000, at different angles of attack. One of the motivations is to see if the salient features of the flow captured experimentally can be reproduced numerically. These computations to solve the incompressible Navier–Stokes equation are performed using high-accuracy compact schemes. Load and moment coefficient variations with time are obtained by solving the Poisson equation for the total pressure in the flow field. Results have also been analysed using the proper orthogonal decomposition technique to understand better the evolving vorticity field and its dependence on Reynolds number and angle of attack. An energy-based stability analysis is performed to understand unsteady flow separation.

Vortex Shedding From a Bluff Body Adjacent to a Plane Sliding Wall

1991 ◽  
Vol 113 (3) ◽  
pp. 384-398 ◽  
Author(s):  
M. P. Arnal ◽  
D. J. Goering ◽  
J. A. C. Humphrey
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Solid Wall ◽  
Reynolds Numbers ◽  
Careful Examination ◽  
Recirculation Region ◽  
Stream Velocity ◽  
Flow Past ◽  
Lower Reynolds Number

The characteristics of the flow around a bluff body of square cross-section in contact with a solid-wall boundary are investigated numerically using a finite difference procedure. Previous studies (Taneda, 1965; Kamemoto et al., 1984) have shown qualitatively the strong influence of solid-wall boundaries on the vortex-shedding process and the formation of the vortex street downstream. In the present study three cases are investigated which correspond to flow past a square rib in a freestream, flow past a rib on a fixed wall and flow past a rib on a sliding wall. Values of the Reynolds number studied ranged from 100 to 2000, where the Reynolds number is based on the rib height, H, and bulk stream velocity, Ub. Comparisons between the sliding-wall and fixed-wall cases show that the sliding wall has a significant destabilizing effect on the recirculation region behind the rib. Results show the onset of unsteadiness at a lower Reynolds number for the sliding-wall case (50 ≤ Recrit ≤100) than for the fixed-wall case (Recrit≥100). A careful examination of the vortex-shedding process reveals similarities between the sliding-wall case and both the freestream and fixed-wall cases. At moderate Reynolds numbers (Re≥250) the sliding-wall results show that the rib periodically sheds vortices of alternating circulation in much the same manner as the rib in a freestream; as in, for example, Davis and Moore [1982]. The vortices are distributed asymmetrically downstream of the rib and are not of equal strength as in the freestream case. However, the sliding-wall case shows no tendency to develop cycle-to-cycle variations at higher Reynolds numbers, as observed in the freestream and fixed-wall cases. Thus, while the moving wall causes the flow past the rib to become unsteady at a lower Reynolds number than in the fixed-wall case, it also acts to stabilize or “lock-in” the vortex-shedding frequency. This is attributed to the additional source of positive vorticity immediately downstream of the rib on the sliding wall.

scholarly journals Simulation of flow past two tandem cylinders using deterministic vortex method

2012 ◽  
Vol 16 (5) ◽  
pp. 1460-1464 ◽  
Author(s):  
Guo Huang ◽  
Haiming Huan ◽  
Xiaoliang Xu ◽  
Yu Liu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Sudden Change ◽  
Vortex Method ◽  
Simulation Method ◽  
Critical Distance ◽  
Navier Stokes ◽  
Tandem Cylinders ◽  
Flow Past

The vortex method is a direct numerical simulation method for solving the Navier-Stokes equations. In order to reveal the influence of Reynolds number and distances between the cylinders, the incompressible flow past a pair of tandem cylinders is solved on the base of the vortex method. The results show that for the flow past two tandem cylinders, there is a critical distance of the tandem cylinders. Over the critical distance, the flow field will have a sudden change, and the drag coefficient, lift coefficient and Strouhal number will also change dramatically. The critical distance will diminish as the Reynolds number rises.

Numerical Study on the Flow Past a Twisted Elliptic Cylinder With Subcritical Reynolds Number

2011 ◽  
Author(s):  
Min Ho Kim ◽  
Jin Woog Lee ◽  
Hyun Sik Yoon ◽  
Man Yeong Ha
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Elliptic Cylinder ◽  
Cross Sectional Area ◽  
Stream Velocity ◽  
Spanwise Direction ◽  
Sectional Area ◽  
Cross Sectional ◽  
Flow Past ◽  
Smooth Cylinder

Large eddy simulation of flow past a torsional cylinder has been carried out at a Reynolds number of 3900 based on the cylinder diameter and the free stream velocity using finite volume method. The torsional cylinder has been formed by rotating the elliptic cross sectional area along the spanwise direction. For an ellipse, different eccentricities are considered to observe the effect of eccentricity on the flow fields. The excellent comparisons with previous studies for the cases of a smooth cylinder and a wavy cylinder having sinusoidal variation in cross sectional area along the spanwise direction guarantee the accuracy of present numerical methods. The effect of eccentricity on the drag and lift coefficients representing the fluid flow characteristics has been investigated by comparing with those of the smooth cylinder, resulting in enhancement of drag reduction and suppression of vortex-induced vibration. The isosurface of swirling strength has been adopted to identify the vortical structures in the turbulent wake.

Anisotropy-Invariant Mapping of Turbulence in a Flow Past an Unswept Airfoil at High Angle of Attack

2005 ◽  
Vol 128 (3) ◽  
pp. 559-567 ◽  
Author(s):  
N. Jovičić ◽  
M. Breuer ◽  
J. Jovanović
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Separation Bubble ◽  
Flow Behavior ◽  
Angle Of Attack ◽  
High Angle ◽  
High Angle Of Attack ◽  
Fine Grid ◽  
Flow Past ◽  
Moderate Reynolds Number

Turbulence investigations of the flow past an unswept wing at a high angle of attack are reported. Detailed predictions were carried out using large-eddy simulations (LES) with very fine grids in the vicinity of the wall in order to resolve the near-wall structures. Since only a well-resolved LES ensures reliable results and hence allows a detailed analysis of turbulence, the Reynolds number investigated was restricted to Rec=105 based on the chord length c. Admittedly, under real flight conditions Rec is considerably higher (about (35-40)∙106). However, in combination with the inclination angle of attack α=18 deg this Rec value guarantees a practically relevant flow behavior, i.e., the flow exhibits a trailing-edge separation including some interesting flow phenomena such as a thin separation bubble, transition, separation of the turbulent boundary layer, and large-scale vortical structures in the wake. Due to the fine grid resolution applied, the aforementioned flow features are predicted in detail. Thus, reliable results are obtained which form the basis for advanced turbulence analysis. In order to provide a deeper insight into the nature of turbulence, the flow was analyzed using the invariant theory of turbulence by Lumley and Newman (J. Fluid Mech., 82, 161–178, 1977). Therefore, the anisotropy of various portions of the flow was extracted and displayed in the invariant map. This allowed us to examine the state of turbulence in distinct regions and provided an improved illustration of what happens in the turbulent flow. Thus, turbulence itself and the way in which it develops were extensively investigated, leading to an improved understanding of the physical mechanisms involved, not restricted to a standard test case such as channel flow but for a realistic, practically relevant flow problem at a moderate Reynolds number.

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