Showing papers on "Starting vortex published in 1972"
TL;DR: In this paper, the Kutta-Joukowski lift force, the momentum flux due to the axial motion, and the tension of the vortex lines were used to obtain results for vortices of non-uniform structure and displacements which are not necessarily small compared with the core radius.
Abstract: Infinitesimal waves on a uniform vortex with axial flow are studied The equation for the frequency of helical waves is obtained, and solved for the case of long waves which leave the internal structure almost unaltered A method is developed to obtain results for vortices of non-uniform structure and for displacements which are not necessarily small compared with the core radius The approach consists of balancing the Kutta—Joukowski lift force, the momentum flux due to the axial motion, and the ‘tension’ of the vortex lines A general equation for the motion of a vortex filament is obtained, valid for arbitrary shape and internal structure, and in the presence of an external irrotational velocity field When the axial flow vanishes, the method is equivalent to using the Biot—Savart law for the self-induced velocity, with a suitable cutoff The impulse of a vortex filament is discussed and its rate of change is given
253 citations
TL;DR: The existence theory for steady vortex rings of small cross-section is used to derive asymptotic formulae that describe the shape and overall properties of such rings as discussed by the authors.
Abstract: The existence theory for steady vortex rings of small cross-section is used to derive asymptotic formulae that describe the shape and overall properties of such rings. A certain two-parameter family of rings is studied in detail, to a first approximation; for members of this family, the ratio ω/r (of vorticity to cylindrical radius) falls from a positive maximum at a central point of the core cross-section to a value at the core boundary that can be substantially smaller or even negative. The case of uniform ω/r is considered to a higher order of approximation, and the formulae given for this case appear to be useful for quite substantial cross-sections.
192 citations
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TL;DR: In this paper, a family of exact solutions of the Navier-Stokes equations which applies to the above situation is described. But the results can be used as a basis for numerical calculations of the solutions in question, and several typical flow patterns have been explicitly computed in order to illustrate the theory.
Abstract: We consider an infinite vortex line in a viscous fluid interacting with a plane boundary surface at right angles to the line. If the boundary surface were absent, the vortex would impart to the fluid a circular motion about the vortex line with speed inversely proportional to the distance to the line. The presence of the boundary surface, however, leads to a secondary flow due to the forced adherence of the fluid at the surface. The purpose of the paper is to describe a family of exact solutions of the Navier-Stokes equations which applies to the above situation. Under quite general hypotheses, it is shown that there can exist only three types of motion compatible with the assumed structure. In the first kind, the radial velocity component (using spherical polar coordinates about the point where the vortex meets the plane surface) is directed inward along the plane surface and upward along the axis of the vortex. In the second type of motion the radial velocity component is directed inward along the plane surface and downward on the axis, with a compensating outflow at an intermediate angle. In the third kind the radial velocity is directed outward near the plane and downward on the central axis. The results can also be used as a basis for numerical calculations of the solutions in question, and several typical flow patterns have been explicitly computed in order to illustrate the theory. The paper concludes with a discussion of the relation between the theoretical solutions and observed phenomena near the point of contact of tornadoes with the ground; this requires that the flows under discussion be considered as mean motions in a turbulent flow with constant eddy viscosity. The present work adds theoretical weight to the argument that central downdrafts can occur in tornadoes. Moreover, the model provides an explanation, other than centrifugal action, for the frequent appearance of a cascade effect at the foot of both tornadoes and water-spouts; finally it offers a unified point of view from which to consider the diversity of flow patterns observed when vortex fields interact with a boundary surface.
92 citations
01 Sep 1972
TL;DR: The existence of a steady vortex ring close to Hill's spherical vortex is established in this article, and an approximate description of its boundary is given, where the vorticity in the ring is proportional to the distance from the axis of symmetry.
Abstract: The existence of a steady vortex ring close to Hill's spherical vortex is established, and an approximate description of its boundary is given. The vorticity in the ring is proportional to the distance from the axis of symmetry. The core propagates steadily in an unbounded fluid at rest at infinity. The boundary of the vortex ring is close to an interior stream surface of Hill's vortex.
66 citations
01 Sep 1972
TL;DR: In this paper, an investigation was conducted to determine the flow field and aerodynamic effects of leading edge serrations on a two-dimensional airfoil at a Mach number of 0.13.
Abstract: An investigation was conducted to determine the flow field and aerodynamic effects of leading-edge serrations on a two-dimensional airfoil at a Mach number of 0.13. The model was a NACA 66-012 airfoil section with a 0.76 m (30 in.) chord, 1.02 m (40 in.) span, and floor and end plates. It was mounted in the Ames 7- by 10-Foot Wind Tunnel. Serrated brass strips of various sizes and shapes were attached to the model in the region of the leading edge. Force and moment data, and photographs of tuft patterns and of oil flow patterns are presented. Results indicated that the smaller serrations, when properly placed on the airfoil, created vortices that increased maximum lift and angle of attack for maximum lift. The drag of the airfoil was not increased by these serrations at airfoil angles of attack near zero and was decreased at large angles of attack. Important parameters were serration size, position on the airfoil, and spacing between serrations.
58 citations
TL;DR: In this paper, the movement of a horizontal vortex pair through an inhomogeneous fluid is considered and an approximate solution is obtained, which predicts that the distance between the vortices stays constant and the vortexices accelerate at a constant rate.
Abstract: The movement of a horizontal vortex pair through an inhomogeneous fluid is considered. The problem is formulated first for the case when the ambient fluid is uniform, the fluid moving with the vortex pair has a different density, and the motion is supposed laminar and inviscid. An approximate solution is obtained, which predicts that the distance between the vortices stays constant and the vortices accelerate at a constant rate. This solution is then applied to motion in a stratified atmosphere and it is found that the vortices oscillate vertically with a frequency and amplitude depending on the initial conditions and the stratification. Finally, approximate equations are constructed to describe the effects of turbulent entrainment into the fluid moving with the vortex pair, and an estimate of the damping is obtained.
51 citations
TL;DR: The motion of vortex rings with bilaterally symmetric initial shape is investigated theoretically and experimentally in this paper, where the induced velocity at each point on the vortex ring is computed from the Biot-Savart law.
Abstract: The motion of vortex rings with bilaterally symmetric initial shape is investigated theoretically and experimentally. The induced velocity at each point on the vortex ring is computed from the Biot‐Savart law. The induced velocity is related to the motion of the ring according to two different concepts: (1) Hydrodynamic vortex—the ring moves with the same velocity as the local fluid; (2) Rankine vortex—the local relative velocity produces lift and drag forces on the ring which serve to distort the ring. Observable vortex rings are produced by pulsing dyed fluid through a rectangular orifice and by staining the starting vortex behind ring wings of various shapes. Good qualitative agreement between the analyses and experiments is achieved.
45 citations
TL;DR: In this article, wake patterns of a translatorily oscillating airfoil in a uniform flow were visualized by Schlieren method, and observed wake patterns were classified into three types: straight, shed vorticities move downstream with uniform velocity, and Kutta-Joukowski's condition holds at the trailing edge.
Abstract: For the calculation of unsteady flow around an airfoil, the following assumptions are usually made: 1) Wake is straight, 2) Shed vorticities move downstream with uniform velocity, 3) Kutta-Joukowski's condition holds at the trailing edge. To estimate the validity of these assumptions, wake pattern of a translatorily oscillating airfoil in a uniform flow was visualized by Schlieren method. Instantaneous wake patterns were photographed at reduced frequency between 1 and 19. Observed wake patterns were classified into three types. The range of reduced frequency and oscillation amplitude for each type was given. Kutta-Joukowski's condition was found to be valid at any test condition in the sense that a dividing stream line detached the airfoil at the trailing edge.
39 citations
TL;DR: In this article, a recent numerical integration of the two-dimensional Navier-Stokes equations has tentatively identified an erodic boundary in the space of initial conditions for the turbulent flow.
38 citations
TL;DR: In this paper, the motion of vortex rings ejected from a circular or a lenticular orifice into water was studied, and the diameters and traveling velocities of the vortex rings were determined from these photographs.
Abstract: Experimental studies were made on the motion of vortex rings ejected from a circular or a lenticular orifice into water. The vortex rings were made visible by fine grains of tin made by electrolysis, and photographs were taken. The diameters and the traveling velocities of the vortex rings were determined from these photographs. There is a favorable range of impulse to produce the stable vortex ring. The traveling velocity of the vortex ring is composed of the velocity of the jet flow and the self-induced velocity of the vortex; the former decays rather rapidly and the latter decreases slowly in time as \(\sqrt{
u t}\), where t is the time and ν is the kinematic viscosity of water. The vortex ring ejected from a lenticular orifice changes its shape intermittently, and the period of deformation is prolonged continually, while the traveling distance during one period is nearly constant.
TL;DR: In this paper, the critical energy for the onset of negative temperatures in vortex calculations is determined and the identity of this threshold with other bounds on the initial conditions with respect to initial conditions is noted.
01 Jul 1972
TL;DR: In this paper, an experimental investigation was performed on the effectiveness of circulation control in producing additional lift and preventing separation on a cambered elliptical airfoil section with a rounded trailing edge.
Abstract: : An experimental investigation was performed on the effectiveness of circulation control in producing additional lift and preventing separation on a cambered elliptical airfoil section with a rounded trailing edge Steady blowing and pulsed blowing from a slot near the rear of the airfoil were used for circulation control Downwash studies were conducted for the airfoil using potential flow theory, and Reynolds number effects were studied for the no blowing case Airfoil surface-pressure distributions are presented for the various test conditions (Author)
TL;DR: In this paper, the stability of a rotating axisymmetric jet surrounded by a potential vortex to infinitesimal disturbances in the inviscid incompressible fluid approximation is considered.
Abstract: Stability of a rotating axisymmetric jet surrounded by a potential vortex to infinitesimal disturbances in the inviscid incompressible fluid approximation is considered. The jet and the vortex may have different densities. The dispersion relation for angular frequency covers a wide range of configurations. A rotating or nonrotating jet in a medium at rest is unstable for all density ratios. A vortex enclosing a stagnant core is stable for axisymmetric disturbances for all densities. A vortex with a rotating core without axial velocity is unstable if the jet fluid density is greater than the vortex fluid density. The jet vortex system is destabilized by the slightest amount of axial velocity; increasing jet fluid density has a destabilizing effect. A vortex around a rotating or nonrotating jet of any density suppresses some of the large scale instabilities. In general, axial velocity of the jet, its rotation, and increase in its density have a destabilizing effect. The surface tension between the two fluids has a stabilizing effect for small scale disturbances.
TL;DR: In this paper, the temperature dependence of the vortex core radius in the range 0.35 K ≤T ≤ 0.60 K was determined by means of precise measurements of vortex ring dynamics.
Abstract: Using a newly developed time-of-flight technique, we have determined the temperature dependence of the vortex core radius in the range 0.35 K ≤T ≤ 0.60 K by means of precise measurements of vortex ring dynamics. One of us (W.I.G.) has extended this work to a measurement of the pressure dependence of the vortex core radius. Our results are in agreement with the earlier work of Rayfield and Reif atT=0.28 K and zero pressure 1 and with a model of the vortex core proposed by Glaberson, Strayer, and Donnelly. 2,3 The precision of our measurements enabled us to observe differences in the dynamics of oppositely charged vortex rings in the same electric field configurations. We were able to quantitively account for these differences in a simple way by incorporating the frictional drag associated with the ion bound on the vortex core into the equations of motion. Our results suggest that the negative ion shape is not greatly distorted by its presence on the vortex core, nor is the negative ion strongly shielded by the vortex velocity field. Some of our results have been previously reported. 4–6
TL;DR: In this article, the boundary layer is laminar initially, separates when it encounters the adverse pressure gradient in the vicinity of the airfoil leading edge, becomes turbulent, and reattaches, forming a separation bubble.
Abstract: OME recent research on airfoil dynamic stall by members of the MIT Aeroelastic and Structures Research Laboratory is summarized below. This work tentatively defines the boundary-layer flow processes during dynamic stall. The initial work investigated the forward movement of the laminar separation point of an unsteady laminar boundary layer during rapid changes of angle of attack.1 The separation mechanism considered is shown in Fig. 1. The boundary layer is laminar initially, separates when it encounters the adverse pressure gradient in the vicinity of the airfoil leading edge, becomes turbulent, and reattaches, forming a separation bubble. The analysis included the calculation of the potential flow and the computation of the laminar boundary layer. In the unsteady calculations, a Joukowsky airfoil having the same leading-edge radius as the NACA 0012 airfoil was considered. A plot of the movement of the laminar separation point forward over the airfoil upper surface as angle of attack is increased at various rates is shown in Fig. 2. It is seen that the laminar separation point reached the airfoil leading edge at an angle of attack of about 9° for all rates considered. This result is due to the large adverse pressure gradient near the leading edge at large angles of attack; the boundary layer for either the steady or unsteady case cannot overcome this large gradient and thus separates. Theoretical variation of the airfoil pitching axis location from the airfoil leading edge to the three-quarter chord point had negligible influence on the position of the laminar separation point for the typical rates and pitching axis locations considered, since the effect of pitching-axis location on the potential flow was small. One purpose of these calculations was the prediction of the unusual dynamic stalling behavior of the wing tested by Garelick.2 The wing tested had an NACA 0012 airfoil section, 5-in. chord and 42-in. span between side-walls, with
17 Jan 1972
TL;DR: In this paper, the effects of turbulent mixing and buoyancy on the motion and persistency of a trailing vortex wake behind an aircraft are considered, and a model for the characteristics of a turbulent vortex, based on an analogy to a turbulent boundary layer, is presented.
Abstract: : The effects of turbulent mixing and buoyancy on the motion and persistency of a trailing vortex wake behind an aircraft are considered. A model for the characteristics of a turbulent vortex, based on an analogy to a turbulent boundary layer, is presented. A theory of trailing-vortex characteristics behind an aircraft is presented. A theory of trailing-vortex characteristics behind an aircraft is presented based on considerations of the angular and linear momentum of the vortex and the total pressure variation along the axis. The turbulent shear of the axial flow is analyzed and the model of a buoyant vortex wake is presented.
TL;DR: In this paper, it was shown that axial air injection into a core of a vortex can beneficially spread out the vorticity concentrated in it and prematurely age it, and that the phenomenon is more nearly governed by the momentum flux of injection than by mass flow.
Abstract: It is demonstrated that axial air injection into a core of a vortex can beneficially spread out the vorticity concentrated in it and prematurely age it. It is also shown that the phenomenon is more nearly governed by the momentum flux of injection than by mass flow.
01 Apr 1972
TL;DR: In this article, a yawhead pressure probe was used in a subsonic wind tunnel to obtain detailed mean flow measurements at stations up to 30 chord lengths downstream in an aircraft trailing vortex.
Abstract: Wind tunnel tests to predict the aircraft wake turbulence due to the tip trailing vortex are discussed. A yawhead pressure probe was used in a subsonic wind tunnel to obtain detailed mean flow measurements at stations up to 30 chordlengths downstream in an aircraft trailing vortex. Mass injection at the wingtip was shown to hasten the decay of the trailing vortex. A theoretical method is presented to show the effect which the circulation distribution on the wing has on the structure of the outer portion of the vortex.
23 Dec 1972
TL;DR: In this article, a two dimensional low speed wind-tunnel tests have demonstrated the feasibility of employing trapped vortex diffusion on a high lift airfoil configuration, where trapped vortex cavities, affording boundary layer control with rapid diffusion, are located at each of the flap knees.
Abstract: : Two dimensional low speed wind-tunnel tests have demonstrated the feasibility of employing trapped vortex diffusion on a high lift airfoil configuration. All 11 percent supercritical airfoil was selected as the base contour employing both leading and trailing edge flaps. The leading edge flap was 25 percent chord, drooped 30 degrees with the rear flap, 27 percent chord, deflected 15 degrees and 30 degrees. Trapped vortex cavities, affording boundary layer control with rapid diffusion, are located at each of the flap knees. Because of the high trapped vortex efficiency, blowing requirements are minimal. Section lift coefficients, in excess of 6, were achieved in the test. (Modified author abstract)
TL;DR: In this article, the authors show that vortex dissipation effects similar to those produced by mass injection can be realized without either bleeding power from the engines or using auxiliary power, using the spinning blade concept, which may actually be used to produce power.
Abstract: maximum tangential (swirl) velocities in the flow. Based on their own study of mass injection and the results of other researchers, Mason and Marchman2 concluded that the introduction of turbulence into the vortex by virtually any means is the dominant factor in tangential velocity reduction and the spreading of the core. The present research seems to substantiate this conclusion. These results show that vortex dissipation effects similar to those produced by mass injection can be realized without either bleeding power from the engines or using auxiliary power. In fact, using the spinning blade concept, the vortex dissipator may actually be used to produce power. Of course, such results are never free and the effects of these modifications on the wing aerodynamic characteristics as well as the vortex must be studied. The present study seems to indicate that such modifications can significantly reduce the vortex Lazard to trailing aircraft without the use of auxiliary or other power and with few, if any, detrimental effects on the wing aerodynamics.
01 Jul 1972
TL;DR: In this paper, a method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows.
Abstract: A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.
TL;DR: In this paper, a conformal mapping of the flow region onto the interior of a semicircular region is restricted to flows with at least one stagnation point, and the model of a single vortex with circulation such that the force on the vortex is upward is useful in the description of some of the features of a flow past a submerged lifting body; this flow is adequately described by Gurevich's solution.
Abstract: Recently Gurevich [1] found an exact solution for the problem posed by the plane flow past a vortex of an inviscid, incompressible fluid which is bounded above by a free surface and below by a horizontal wall. This solution, which is found by using a conformal mapping of the flow region onto the interior of a semicircular region, is restricted to flows with at least one stagnation point. The model of a single vortex with circulation such that the force on the vortex is upward is useful in the description of some of the features of the flow past a submerged lifting body; this flow is adequately described by Gurevich's solution. For the case in which the force on the vortex is downward, Gurevich's solution has been extended to include flows without stagnation points but with bifurcation points on the free surface which correspond to singular points of the mapping. This extension describes the flow of a vortex lowered into the fluid from above.
TL;DR: In this article, the evolution of a circular vortex ring with a density 1.5 times of the ambient fluid under gravity was investigated and three distinct patterns, namely, laminar, wavy, and turbulent, were observed.
Abstract: The evolution of a circular vortex ring with a density 1.5 times of the ambient fluid under gravity was investigated. Three distinct patterns, namely, laminar, wavy, and turbulent, were observed. It is found that approximately as Nre > 2000, the vortex becomes turbulent, as Nre < 1500, laminar but to disintegrate into subrings. The stability curve was determined.