On the motion of thin airfoils in fluids of finite electrical conductivity

1960 ◽  
Vol 7 (3) ◽  
pp. 449-468 ◽  
Author(s):  
James E. McCune
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Steady Motion ◽  
Magnetic Reynolds Number ◽  
Alfven Wave ◽  
Deep Penetration ◽  
Two Dimensional ◽  
A Value ◽  
Finite Electrical Conductivity ◽  
Field Geometry

A two-dimensional, small-perturbation theory for the steady motion of thin lifting airfoils in an incompressible conducting fluid, with the uniform applied magnetic field perpendicular to (and in the plane of) the undisturbed, uniform flow field, is described. The conductivity of the fluid is assumed to be such that the magnetic Reynolds number,Rm, of the flow is large but finite. Within this assumption, a theory based on superposition of sinusoidal modes is constructed and applied to some simple thin airfoil problems.It is shown that with this particular field geometry the Alfvén wave mechanism is important in making possible very deep penetration into the flow field of currents and their associated vorticity. It is also shown that the current penetration for an airfoil is much larger than for a wavy wall of wavelength equal to the airfoil chord.A value ofRm= 5 is found to be a good approximation to infinity in this study; in fact, use of the present technique for values ofRmof the order of unity is permissible. These results provide an indication of what is meant by ‘large’ magnetic Reynolds number in two-dimensional magneto-aerodynamics.

A physical description of magnetic helicity evolution in the presence of reconnection lines

1991 ◽  
Vol 46 (1) ◽  
pp. 179-199 ◽  
Author(s):  
Andrew N. Wright ◽  
Mitchell A. Berger
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Magnetic Reynolds Number ◽  
Magnetic Helicity ◽  
Two Dimensional ◽  
Flux Tubes ◽  
Physical Description ◽  
Reconnection Region ◽  
Field Geometry ◽  
Field Lines

The dissipation of relative magnetic helicity due to the presence of a resistive reconnection region is considered. We show that when the reconnection region has a vanishing cross-section, helicity is conserved, in agreement with previous studies. It is also shown that in two-dimensional systems reconnection can produce highly twisted reconnected flux tubes. Reconnection at a high magnetic Reynolds number generally conserves helicity to a good approximation. However, reconnection with a small Reynolds number can produce significant dissipation of helicity. We prove that helicity dissipation in two-dimensional configurations is associated with the retention of some of the inflowing magnetic flux by the reconnection region, vr. When the reconnection site is a simple Ohmic conductor, all of the magnetic field parallel to the reconnection line that is swept into vr is retained. (In contrast, the inflowing magnetic field perpendicular to the line is annihilated.) We are able to relate the amount of helicity dissipation to the retained flux. A physical interpretation of helicity dissipation is developed by considering the diffusion of magnetic field lines through vr. When compared with helicity-conserving reconnection, the two halves of a reconnected flux sheet appear to have slipped relative to each other parallel to the reconnection line. This provides a useful method by which the reconnected field geometry can be constructed: the incoming flux sheets are ‘cut’ where they encounter vr, allowed to slip relative to each other, and then ‘pasted’ together to form the reconnected flux sheets. This simple model yields estimates for helicity dissipation and the flux retained by vr in terms of the amount of slippage. These estimates are in agreement with those expected from the governing laws.

scholarly journals Direct Numerical Simulation in Two Dimensional Homogeneous Isotropic Turbulence Using Spectral Method

2013 ◽  
Vol 5 (3) ◽  
pp. 435-445
Author(s):  
M. S. I. Mallik ◽  
M. A. Uddin ◽  
M. A. Rahman
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Flow Field ◽  
Direct Numerical Simulation ◽  
Spectral Method ◽  
Isotropic Turbulence ◽  
Qualitative Behavior ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Decaying Turbulence

Direct numerical simulation (DNS) in two-dimensional homogeneous isotropic turbulence is performed by using the Spectral method at a Reynolds number Re = 1000 on a uniformly distributed grid points. The Reynolds number is low enough that the computational grid is capable of resolving all the possible turbulent scales. The statistical properties in the computed flow field show a good agreement with the qualitative behavior of decaying turbulence. The behavior of the flow structures in the computed flow field also follow the classical idea of the fluid flow in turbulence. Keywords: Direct numerical simulation, Isotropic turbulence, Spectral method. © 2013 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi:http://dx.doi.org/10.3329/jsr.v5i3.12665 J. Sci. Res. 5 (3), 435-445 (2013)  

Multiple bifurcations of the flow over stalled airfoils when changing the Reynolds number

2018 ◽  
Vol 846 ◽  
pp. 356-391 ◽  
Author(s):  
E. Rossi ◽  
A. Colagrossi ◽  
G. Oger ◽  
D. Le Touzé
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Complex Dynamics ◽  
Particle Method ◽  
Micro Air Vehicles ◽  
Suction Side ◽  
Two Dimensional ◽  
Vortex Particle Method ◽  
Critical Configurations ◽  
Lift And Drag

In the present study, the sudden changes of the flow field past stalled airfoils for small variations of the Reynolds number are investigated numerically. A vortex particle method has been used for the simulations in a two-dimensional framework. The most critical configurations found with this solver are verified through the comparison with the solution given by a mesh-based finite volume solver. The airfoils considered are the NACA0010 and a narrow ellipse with the same thickness. The angle of attack is fixed to $\unicode[STIX]{x1D6FC}=30^{\circ }$ for which complex dynamics of the flow can take place in the different viscous regimes inspected. The Reynolds number ranges between $Re=100$ and $Re=3000$ and, within this interval, numerous bifurcations of the solution are observed in terms of mean lift and drag coefficients, Strouhal number and downstream wake. An analysis of these bifurcations is provided and links are made between the wake structures observed. On this base the flow patterns can be classified in different modes similarly to the analysis by Kurtulus (Intl J. Micro Air Vehicles, vol. 7(3), 2015, pp. 301–326; vol. 8(2), 2016, pp. 109–139). A discussion of the vortical evolution of the flow in the vicinity of the suction side of the airfoil is also provided.

Flow Behavior of FENE-P Fluids in Grooved Parallel Plates With Transverse Cavities

2016 ◽  
Author(s):  
Abdelkader Filali ◽  
Lyes Khezzar ◽  
Mohamed Alshehhi
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Parallel Plate ◽  
Flow Behavior ◽  
Rheological Parameters ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Fluid Elasticity ◽  
Newtonian Case ◽  
Plate Channel

Numerical investigation of the flow behavior for Newtonian and viscoelastic FENE-P fluids in a parallel-plate channel with transverse rectangular cavities is carried out using ANSYS-POLYFLOW code. A two-dimensional, laminar and steady flow is considered and the flow behavior influenced by the generated vortices at the transverse rectangular cavities has been studied. The effect of Reynolds number, fluid elasticity and the rheological parameters of the FENE-P model L2, on the flow field is examined. In all non-Newtonian considered cases, different flow field were observed which shows different behavior compared to the Newtonian case.

Stability and Scalar Transport in Laminar Non-Newtonian Flow in a Bifurcating T-Junction

2019 ◽  
Author(s):  
Ajay Chatterjee ◽  
Fatemeh Khalkhal
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Numerical Solutions ◽  
Shear Thinning ◽  
Volume Averaging ◽  
Scalar Transport ◽  
Linear Perturbation ◽  
Perturbation Equation ◽  
Two Dimensional ◽  
Two Dimensional Flow

Abstract We consider the prototype bifurcating T-junction planar flow and compare the stability of the steady two-dimensional flow field for a Newtonian and a shear thinning inelastic fluid. Global stability of the flow to two-dimensional perturbations is analyzed using numerical solutions of the linear perturbation equation. Calculations are performed for two flow ratios between the main channel and the bifurcating channel, and for two different values of the time constant in the non-Newtonian rheological model. The results show that although the steady flow remains stable to two-dimensional perturbations for Newtonian Reynolds number up to ∼ 400, shear thinning is destabilizing in that the decay rate of the perturbation field is slower. The perturbation growth rate curves for all of the different cases may be correlated by volume averaging the local Reynolds number over the flow domain, indicating that the effect of shear thinning on stability may be described using a suitably defined average Reynolds number. These stability results provide some justification for CFD calculations of steady non-Newtonian two-dimensional flows presented in earlier papers. Since scalar transport is of interest in this flow field, we also present some numerical calculations for the Nusselt number profile along the bifurcating channel wall. The results show that for the shear thinning fluid the scalar transport rate is differentially larger by ∼ 75% across one of the bifurcating channel walls, a consequence of fluid rheology enhancing the effect of flow asymmetry in the entrance region of the bifurcation.

Experimental Investigation of Vortex Structure in the Corrugated Channel

2013 ◽  
Author(s):  
Efe Unal ◽  
Hojin Ahn ◽  
Esra Sorguven ◽  
M. Zafer Gul
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Vortex Structure ◽  
Low Reynolds Number ◽  
Bulk Flow ◽  
Two Dimensional ◽  
Mean Flow ◽  
Cross Sectional ◽  
Corrugated Channel ◽  
Low Reynolds

Vortex structure in a corrugated channel has been studied with a PIV system measuring two-dimensional velocity fields at different locations and Reynolds numbers. The geometry of corrugation under investigation is the two-dimensional reflection of the circular cross-sectional stainless-steel flex pipe. The results show that turbulence caused by the corrugated wall affects the whole flow field in the channel even at low Reynolds number. The bulk flow field is rather chaotic in the entire channel. Moreover, the velocity vectors show significant interaction between the flow in the groove and the bulk flow. Vortex generated from the groove is very unstable and intermittent, and the vortex is not confined within the groove even at low Reynolds number. Vortex in the groove either migrates out of the groove without breaking up, or causes bursting flow from the groove to the bulk. In addition, intermittent and time-mean flow reversals are observed near the crest of the corrugation at low Reynolds number. Though the channel design is intended to be two-dimensional, flow structures in the groove appear to be three-dimensional at high Reynolds number while two-dimensional at low Reynolds number.

Two-dimensional incompressible magneto-hydrodynamic flow across an elliptical solenoid

1958 ◽  
Vol 4 (6) ◽  
pp. 553-584 ◽  
Author(s):  
Nelson H. Kemp ◽  
Harry E. Petschek
Keyword(s):  
Magnetic Field ◽  
Flow Field ◽  
Hall Current ◽  
Dynamic Pressure ◽  
Magnetic Reynolds Number ◽  
Two Dimensional ◽  
Zeroth Order ◽  
First Order ◽  
Ion Slip ◽  
The Magnetic Field

An analysis has been made of the two-dimensional flow of an incompressible constant-conductivity fluid through an elliptically shaped solenoid containing a constant magnetic field directed normal to the flow plane. The effect of both Hall current and ion slip has been included in the generalized Ohm's law used for the fluid. The analysis is based on a perturbation procedure in two parameters, one being the magnetic Reynolds number Rm and the other the ratio S of magnetic force per unit area to dynamic pressure. Calculations have been carried to the first order in each parameter, and closed-form analytic expressions have been obtained for the force and moment on the solenoid, the current density, stream function, magnetic field and other pertinent physical quantities.It was found that, to the zeroth order, there is a force but no moment on the solenoid. To the first order in S, where the flow field is modified but the magnetic field is not, there is a moment and a force, the latter being anti-parallel to the zeroth order force. To the first order in Rm, where the magnetic field is modified but the flow field is not, there is a moment but no force. Thus, to the first order the lift to drag ratio is the same as in the zeroth order. Graphs which illustrate some of the effects of angle of attack, fineness ratio of the ellipse, Hall current and ion slip, on the forces and moments are presented.

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