scholarly journals Coriolis effect and the attachment of the leading edge vortex

2017 ◽  
Vol 820 ◽  
pp. 312-340 ◽  
Author(s):  
T. Jardin
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Coriolis Effect ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Leading Edge Vortex ◽  
Edge Vortex ◽  
Vorticity Transport ◽  
Rotating Wing

The role of the Coriolis effect on the attachment of the leading edge vortex (LEV) is investigated. Toward that end, the Navier–Stokes equations are solved in the non-inertial reference frame of a high angle of attack $\unicode[STIX]{x1D6FC}$ rotating wing with the Coriolis term being artificially tuned. Reynolds numbers in the range $Re\in [100;750]$ are considered to identify the interplay between Coriolis and viscous effects. Similarly, artificial tuning of the centrifugal term is achieved to identify the interplay between Coriolis and centrifugal effects. It is shown that (i) the Coriolis effect is the key element in LEV stability for $Re>200$, (ii) viscous effects are the key element for $Re<200$ and (iii) centrifugal effects have a marginal role. The Coriolis effect is found to promote spanwise flow in the core and behind the LEV, which is known to promote outboard vorticity transport and presumably contributes to stabilizing the aft boundary layer. These mechanisms of LEV stabilization have increased authority as $\unicode[STIX]{x1D6FC}$ decreases.

Leading Edge Vortex Development on a Pitch-Up Airfoil

2013 ◽  
Author(s):  
Kyle Hord ◽  
Yongsheng Lian
Keyword(s):  
Stokes Equations ◽  
Leading Edge ◽  
Navier Stokes ◽  
Vortex Generation ◽  
Navier Stokes Equations ◽  
Leading Edge Vortex ◽  
Overlapping Grids ◽  
Wing Motion ◽  
Circulatory Effects ◽  
Edge Vortex

The dynamics of leading edge vortex (LEV) on an airfoil due to pitch-up motion is investigated using computational fluid dynamics techniques to solve the Navier-Stokes equations on composite overlapping grids. The objectives are to (1) quantify the contribution of circulatory effects caused by vortex development, and non-circulatory effects due to rotational acceleration of the pitch up, and (2) measure the growth rate of the LEV. The pitch-up angle is from 0 to 45 degrees, an approximation of the wing motion of a perching flyer, and the Reynolds number is approximately 500. Previous studies have investigated vortex development on pitch-up airfoils, and found the development of the LEV varies with pitch rate; however this phenomenon has never been quantified. In this study we will look at how vortex generation and diffusion at lower Reynolds numbers affect circulatory forces on the wing. The Q-criterion method is used to identify and isolate vortex structures from shear vorticity in order to numerically calculate the circulation in the computation domain caused by the LEV. The calculated circulation due to vortices will then be compared to the lift force by the pitch-up motion to obtain a better understanding of the contribution to lift exclusively by vortex generation. Previous studies involving pitch-up maneuvers have hypothesized that the increase of lift with pitch rate may be due to virtual mass effects, also known as noncirculatory forces. However this increase in lift has not been quantified. Using the noncirculatory component of Theodorsen’s theory, the lift forces can be broken into parts caused by the rotation of the wing, and the aerodynamic effects. Results have shown that noncirculatory forces only contribute 10–20% of the lifting force and the remaining is due to the LEV. It was also found that the LEV growth is time dependent and not angle dependent; however the circulation strength of the LEV is a function of pitch rate. Thus the higher pitch rates have smaller, yet stronger LEVs.

Computational analysis of unsteady supersonic cavity flows driven by thick shear layers

1988 ◽  
Vol 92 (919) ◽  
pp. 365-374 ◽  
Author(s):  
X. Zhang ◽  
J. A. Edwards
Keyword(s):  
Stokes Equations ◽  
Fluid Dynamic ◽  
Leading Edge ◽  
Navier Stokes ◽  
Cavity Flows ◽  
Navier Stokes Equations ◽  
Continuous Formation ◽  
Depth Ratio ◽  
Edge Vortex ◽  
Supersonic Cavity

Abstract Supersonic cavity flows driven by a thick shear layer at Mach 1·5 and 2·5 are studied by solving the two-dimensional unsteady compressible Navier-Stokes equations in terms of mass-averaged variables. The length to depth ratio of the rectangular cavity is three. The numerical scheme used is the finite-difference algorithm by Brailovskaya. A two-layer eddy-viscosity turbulence model is used. The results are compared with experimental data. The computations show the self-sustained oscillations at Mach 1·5 and 2·5. The continuous formation and downstream shedding of leading edge vortices is demonstrated. The oscillatory modes are correctly predicted. The first mode is attributed to a large unsteady trailing edge vortex moving in the transverse direction. Based on the analysis, it is considered that the oscillation in the length to depth ratio three cavity is a longitudinal one and is controlled by a fluid dynamic mechanism rather than a purely acoustic one.

Vorticity transport in the leading-edge vortex on a rotating blade

2014 ◽  
Vol 743 ◽  
pp. 249-261 ◽  
Author(s):  
Craig J. Wojcik ◽  
James H. J. Buchholz
Keyword(s):  
Leading Edge ◽  
Quasi Equilibrium ◽  
Transport Mechanisms ◽  
Leading Edge Vortex ◽  
Rotating Blade ◽  
Edge Vortex ◽  
Rotation Motion ◽  
Vorticity Transport ◽  
Control Volumes ◽  
Quiescent Fluid

AbstractVorticity transport is analysed within the leading-edge vortex generated on a rectangular flat plate of aspect ratio 4 undergoing a starting rotation motion in a quiescent fluid. Two analyses are conducted on the inboard half of the blade to better understand the vorticity transport mechanisms responsible for maintaining the quasi-equilibrium state of the leading-edge vortex. An initial global analysis between the $25$ and $50\, \%$ spanwise positions suggests that, although spanwise velocity is significant, spanwise convection of vorticity is insufficient to balance the flux of vorticity from the leading-edge shear layer. Subsequent detailed analyses of vorticity transport in planar control volumes at the $25$ and $50\, \%$ spanwise positions verify this conclusion and demonstrate that vorticity annihilation due to interaction between the leading-edge vortex and the opposite-sign layer on the plate surface is an important, often dominant, mechanism for regulation of leading-edge-vortex circulation. Thus, it provides an important condition for maintenance of an attached leading-edge vortex on the inboard portion of the blade.

Fully Nonlinear Potential/RANSE Simulation of Wave Interaction With Ships and Marine Structures

2008 ◽  
Author(s):  
Pierre Ferrant ◽  
Lionel Gentaz ◽  
Bertrand Alessandrini ◽  
Romain Luquet ◽  
Charles Monroy ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Fully Nonlinear ◽  
Nonlinear Potential ◽  
6 Degrees Of Freedom

This paper documents recent advances of the SWENSE (Spectral Wave Explicit Navier-Stokes Equations) approach, a method for simulating fully nonlinear wave-body interactions including viscous effects. The methods efficiently combines a fully nonlinear potential flow description of undisturbed wave systems with a modified set of RANS with free surface equations accounting for the interaction with a ship or marine structure. Arbitrary incident wave systems may be described, including regular, irregular waves, multidirectional waves, focused wave events, etc. The model may be fixed or moving with arbitrary speed and 6 degrees of freedom motion. The extension of the SWENSE method to 6 DOF simulations in irregular waves as well as to manoeuvring simulations in waves are discussed in this paper. Different illlustative simulations are presented and discussed. Results of the present approach compare favorably with available reference results.

Numerical Simulation of Clocking Effect on Wake Transportation and Interaction in a 1.5-Stage Axial Turbine

2010 ◽  
Author(s):  
Wei Li ◽  
Hua Ouyang ◽  
Zhao-hui Du
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Maximum Efficiency ◽  
Suction Surface ◽  
Navier Stokes Equations ◽  
Pressure Surface ◽  
Turbine Efficiency ◽  
Small Influence

To give insight into the clocking effect and its influence on the wake transportation and its interaction, the unsteady three-dimensional flow through a 1.5-stage axial low pressure turbine is simulated numerically using a density-correction based, Reynolds-Averaged Navier-Stokes equations commercial CFD code. The 2nd stator clocking is applied over ten equal tangential positions. The results show that the harmonic blade number ratio is an important factor affecting the clocking effect. The clocking effect has a very small influence on the turbine efficiency in this investigation. The efficiency difference between the maximum and minimum configuration is nearly 0.1%. The maximum efficiency can be achieved when the 1st stator wake enters the 2nd stator passage near blade suction surface and its adjacent wake passes through the 2nd stator passage close to blade pressure surface. The minimum efficiency appears if the 1st stator wake impinges upon the leading edge of the 2nd stator and its adjacent wake of the 1st stator passed through the mid-channel in the 2nd stator.

A Cartesian Explicit Solver for Complex Hydrodynamic Applications

2014 ◽  
Author(s):  
P. Bigay ◽  
A. Bardin ◽  
G. Oger ◽  
D. Le Touzé
Keyword(s):  
Level Set ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Navier Stokes ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Flow Past A Cylinder ◽  
Explicit Solver

In order to efficiently address complex problems in hydrodynamics, the advances in the development of a new method are presented here. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with a ghost-cell method for geometry handling and a Level-set method for the treatment of biphase-flows. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used. The treatment of arbitrary geometries is addressed in the hyperbolic and viscous framework. Viscous effects are computed via a finite difference computation of viscous fluxes and turbulent effects are addressed via a Large-Eddy Simulation method (LES). The Level-Set solver used to handle biphase flows is also presented. The solver is validated on 2-D test cases (flow past a cylinder, 2-D dam break) and future improvements are discussed.

Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements

1985 ◽  
Vol 160 ◽  
pp. 93-117 ◽  
Author(s):  
Ta Phuoc Loc ◽  
R. Bouard
Keyword(s):  
Circular Cylinder ◽  
Flow Structure ◽  
Stokes Equations ◽  
Early Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Unsteady Viscous Flow ◽  
Vorticity Transport ◽  
New Phenomena

Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analysed numerically by direct integration of the Navier–Stokes equations – a fourth-order finite-difference scheme is used for the resolution of the stream-function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments.The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is reported. The computed results are compared qualitatively and quantitatively with experimental visualization and measurements. The comparison is found to be satisfactory.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

Effects of Non-Dimensional Parameters on Formation and Break Up of Cylindrical Droplets

2004 ◽  
Author(s):  
Mohammad Taeibi-Rahni ◽  
Shervin Sharafatmand
Keyword(s):  
Stokes Equations ◽  
Fluid Model ◽  
Time Dependent ◽  
Navier Stokes ◽  
Ohnesorge Number ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Dimensional Parameters ◽  
Break Up ◽  
Eotvos Number

The consistent behavior of non-dimensional parameters on the formation and break up of large cylindrical droplets has been studied by direct numerical simulations (DNS). A one-fluid model with a finite difference method and an advanced front tracking scheme was employed to solve unsteady, incompressible, viscous, immiscible, multi-fluid, two-dimensional Navier-Stokes equations. This time dependent study allows investigation of evolution of the droplets in different cases. For moderate values of Atwood number (AT), increasing Eotvos number (Eo) explicitly increases the deformation rate in both phenomena. Otherwise, raising the Ohnesorge number (Oh) basically amplifies the viscous effects.

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