Showing papers on "Starting vortex published in 1981"

Motion of an Elliptic Vortex in a Uniform Shear Flow

Abstract: Motion of an elliptic vortex of uniform vorticity in a uniform straining and vorticity flow is solved exactly. The elliptic shape is preserved and the area of the vortex is conserved but the axis ratio of the ellipse changes in general. Depending on the magnitudes of the vorticity in the vortex and the strain and the vorticity of the shear flow, this vortex exhibits various types of motion such as rotation and nutation around its centre. When the strain is very strong, the vortex is always elongated infinitely in the direction of the strain. A stationary elliptic vortex can exist in a weaker straining flow.

On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6*10^3 to 5*10^6

Abstract: The influence of surface roughness on the vortex-shedding frequency in the wake of a single cylinder has been investigated. The experiments were carried out in an atmospherical and a high-pressure wind tunnel. The tests were started with a smooth cylinder. Then the wake flow of cylinders with relative roughnesses of ks/d = 75 × 10−5, 300 × 10−5, 900 × 10−5, and 3000 × 10−5 was investigated.For all roughness parameters tested the Strouhal number exhibited an increase in the critical flow regime. With growing roughness parameter the step in the curve became smaller. At transcritical flow conditions the Strouhal number was measured to be in the range of Sr = 0·25 ± 0·018 for all surface roughness tested. No regular vortex shedding could be observed in the critical flow range for the smooth cylinder with l/d = 3·38. When prolonging the test body to l/d = 6·75 the wake fluctuations became periodic.

A vortex filament moving without change of form

Abstract: The motion of a very thin vortex filament is investigated using the localized induction equation. A family of vortex filaments which move without change of form are obtained. They are expressed in terms of elliptic integrals of the first, second and third kinds. In general they do not close and have infinite lengths. In some particular cases they take the form of closed coils which wind a doughnut. There exist a family of closed vortex filaments which do not travel in space but only rotate around a fixed axis. Our solutions include various well-known shapes such as the circular vortex ring, the helicoidal filament, the plane sinusoidal filament, Euler's elastica and the solitary-wave-type filament. It is shown that they correspond to the travelling wave solution of a nonlinear Schrodinger equation.

The evolution of an elliptic vortex ring

Abstract: The evolution of a vortex ring in an ideal fluid under self-induction from a flat and elliptic configuration is followed numerically using the cut-off approximation (Crow 1970) for the velocity at the vortex. Calculations are presented for four different axes ratios of the initial ellipse. A particular choice is made for the core size and vorticity distribution in the core of the vortex ring. When the initial axes ratio is close to 1, the vortex ring oscillates periodically. The periodicity is lost as more eccentric cases are considered. For initial axes ratio 0·2, the calculations suggest a break-up of the ring through the core at one portion of the ring touching that at another, initially distant, portion of the ring.Results from quantitative experiments, conducted at moderate Reynolds number with the vortex rings produced by puffing air through elliptic orifices, are compared with the calculations. The agreement is fairly good and it is found that a vortex ring produced from an orifice of axes ratio 0·2 breaks up into two smaller rings. The relevance of the results to the vortex trail of an aircraft is discussed.

A discrete vortex method for the non-steady separated flow over an airfoil

Abstract: A discrete vortex method was used to analyze the separated non-steady flow about a cambered airfoil. The foil flow modelling is based on the thin lifting-surface approach, where the chordwise location of the separation point is assumed to be known from experiments or flow-visualization data. Calculated results provided good agreement when compared with the post-stall aerodynamic data of two airfoils. Those airfoil sections differed in the extent of travel of the separation point with increasing angle of attack. Furthermore, the periodic wake shedding was analyzed and its time-dependent influence on the airfoil was investigated.

The turbulent trailing vortex during roll-up

Abstract: The turbulent trailing vortex forming from a rolling-up vortex sheet is considered. The inviscid, asymptotic roll-up of a vortex sheet is briefly reviewed, as are the effects to the sheet of merging by viscous and turbulent diffusion. The merged region is found to rapidly attain a state of equilibrium and similarity variables are used to describe it. The detailed distributions of circulation and Reynolds stress are seen to depend to some extent upon the initial spanwise distribution of circulation on the wing. However, a tiny region which is independent of the wing circulation distribution is found to exist near the point of peak tangential velocity. It is suggested that this region is described by Hoffmann & Joubert's logarithmic relationship. Assuming this to be the limiting form for the distribution of circulation near r1, the radius where the tangential velocity takes its peak value v1, an approximate form for the distribution of circulation is found and this is used to determine the form of the Reynolds-stress distribution. It is found that two modes for the decay of v1 with time are possible: one when r1 is much less than ½s, the wing semi-span, and v1 decays like t−½n; and the other when r1 = O(½s) and v1 may decay like t½(n-2); 0 < n < 1, for elliptic wing loading n ≃ ½.

Evolution and breakdown of a vortex street in two dimensions

Abstract: The initial-value problem defined by two parallel vortex sheets of opposite sign is studied. Strictly two-dimensional, incompressible, nearly inviscid dynamics is assumed throughout. The roll-up of the sheets into a vortex street is simulated numerically using 4096 point vortices. Much longer runs than in previous work are performed, and it is found that only for a finite range of values of the ratio, h/λ, of sheet separation to perturbation wavelength, does a long-lived vortex street emerge. For h/λ [gsim ] 0·6 a pairing transition within each row intervenes. For h/λ [lsim ] 0·3 we find oscillatory modes.Using up to 16384 point vortices, we also study the breakdown of the metastable street to a two-dimensional, turbulent shear flow. The vortex blobs that made up the street may merge with others of the same sign after the breakdown, but otherwise persist throughout the turbulent regime. Neither their disintegration nor amalgamation with vortices of opposite sign was observed. Using dimensional arguments we derive the relevant scaling theory, and show that it applies to a flow started from two random vortex sheets. The resulting turbulence is not self-similar. For the turbulent flow that follows from the breakdown of a regular vortex street two length scales with different power-law growth in time appear to be necessary. The important differences in the asymptotic structure of flows initialized from random and regular sheets leads us to question the idea of universality. The influence of the symmetry of the initial perturbation on the subsequent development is also considered.

On the Point Vortex Method

Abstract: The discretization of the integrodifferential equation governing the evolution of a vortex sheet leads to a representation of the sheet by point vortices. It is shown, by examination of the special case of a uniform circular vortex sheet, that the chaotic motion which often arises when the point vortex representation is used is due to the amplification of numerically introduced disturbances. The mechanism is a discrete form of Helmholtz instability. The linear smoothing method of Longuet-Higgins and Cokelet (1976) and the repositioning method of Fink and Soh (1978) are shown to reduce the instability.

Vortex-Lattice Method for the Calculation of the Nonsteady Separated Flow over Delta Wings

Abstract: An analysis is made of the wake structure and the forces on a delta wing as it undergoes nonsteady motion, wherein the flow separates at the leading edge. Comparisons of these predictions with existing experimental and theoretical data for the nonsteady linear and nonlinear motions indicate good agreement. It was found that the time-dependent, wake-shedding numerical procedure applied here for the wake rollup and the lift force calculation resulted in considerable saving of computer time over methods using the iterative wake rollup procedure. Calculated results for various motions of the delta wing, including the plunging motion, are presented for both the separated and the attached flow cases.

A higher order panel method applied to Vortex sheet roll-up

Abstract: The paper describes a computational method for two-dimensional vortex sheet motion in incompressible flow. The procedure utilizes a second-order panel method, an adaptive panel scheme, and a concept for treating highly rolled-up portions of the vortex sheet. Results are presented for the roll-up of the wake behind an elliptically loaded wing, a ring wing (nacelle), a fuselage/part-span flap/wing combination, and a delta wing with leadingedge vortex sheets. The examples demonstrate that the method is capable of describing complicated vortex sheet motion in a reliable and stable manner. v \

Properties of a Vortex Street of Finite Vortices

Abstract: Steady solutions of the Euler equations are calculated for an infinite array of vortices, consisting of two staggered parallel rows of identical vortices of finite area and uniform vorticity. These models are similar to the “vortex streets” studied theoretically by von Karman and others, except that here vortices of finite rather than infinitesimal area are employed.

The Coherent Structure of Turbulent Mixing Layers. I. Similarity of the Primary Vortex Structure. II. Secondary Streamwise Vortex Structure

Abstract: The primary spanwise organized vortex structure and the secondary streamwise vortex structure of turbulent mixing layers have been investigated Flow visualization motion pictures of a constant density mixing layer were used to measure the properties of the large scale vortices It was found that after an initial transition region mean properties of the large scale vortices reach the expected linear growth with downstream distance required by similarity In the self-similar region, the vortex core area and visual thickness increase continuously during its life-span A theoretical model of probability distribution function for the large-scale vortex circulation was developed This distribution is found to be lognormal and to have a standard deviation, normalized with the mean of 028 From this model the mean life-span of the vortices could also be obtained and was found to be 067 times the mean life-span position The streamwise streak pattern observed by Konrad (1976) and Breidenthal (1978) in plan-view pictures of the mixing layer was investigated, using flow visualization and spanwise concentration measurements It was confirmed that this pattern is the result of a secondary vortex structure dominated by streamwise, counterrotating vortices A detailed description of its spatial relation to the primary, spanwise vortex structure is presented From time average flow pictures, the onset position and initial scale of the secondary structures were determined From concentration measurements, spanwise variations in mean properties, resulting from the secondary structure, were found This also showed an increase of the spanwise scale with downstream distance and the existence of the streamwise vortices in the fully developed turbulent region In this region the mean spacing is found approximately equal to the vorticity thickness

Utilization of wind energy

Abstract: A wind energy device comprising a first airfoil having a leading edge, a trailing edge and a tip, means supporting the airfoil above a surface, the airfoil being adapted, when traversed by a prevailing wind, to generate a vortex at its tip, an air deflector associated with the airfoil and arranged so as to deflect prevailing wind traversing the deflector into the vortex to augment the energy of the vortex, means to vary the orientation of the airfoil relative to the prevailing wind, and a rotary device located in the path of the vortex and adapted to be driven by the wind in the vortex.

Vortex flow hydraulic shock absorber

Abstract: The shock absorber having a piston reciprocatingly disposed in a cylinder and sized small enough to permit a compact construction. The piston defines therein a vortex chamber with a maximum radius. The vortex chamber communicates with fluid chambers defined in the shock absorber via vortex passages formed in the piston. The vortex passage extends in the ceiling or bottom of the piston and tangentially opens at the upper and lower plane periphery of the vortex chamber. By providing the vortex passages in the above-mentioned manner, the radius of the vortex chamber can be maximized in relation to the radius of the piston thus reducing the size of the piston and, in turn the shock absorber.

Low-Speed Aerodynamic Characteristics of a Small, Fixed-Trailing-Edge Circulation Control Wing Configuration Fitted to a Supercritical Airfoil

Abstract: : Excellent high-lift and cruise performance of a small, round, fixed circulation control wing (CCW) trailing edge fitted to a supercritical airfoil has been confirmed by subsonic wind tunnel investigations. This fixed-trailing- edge blown high-lift airfoil generates a negligible subsonic cruise drag penalty, but can generate a section lift coefficient near 7.0. This configuration is a significant improvement over the flight-proven A-6/CCW airfoil that had similar lift performance, but had a large trailing edge requiring mechanization for transition to cruise flight. Further, the large leading edge radius of the supercritical airfoil allows operating at high lift over a moderate angle-of-attack range. These results imply the feasibility of a mono-element airfoil with no moving components required for high lift; the transition from the cruise to the high-lift configuration is accomplished by blowing from a fixed slot. The favorable characteristics of both the cruise and high-lift airfoils are retained without compromise to either. (Author)

Vortex Instability of Mixed Convection Flow over a Horizontal Flat Plate

Abstract: The vortex instability of laminar, mixed-convection flow over an isothermal, horizontal flat plate is investigated analytically by the linear stability theory. In the analysis, the main flow and thermal fields are treated as non-parallel and the disturbances are assumed to have the form of a stationary longitudinal vortex roll that is periodic in the spanwise direction. Numerical results for the critical Grashof and Reynolds numbers that predict the first occurrence of the vortex rolls are obtained for fluids with Prandtl numbers of 0.7 and 7. It is found that the flow becomes more susceptible to vortex mode of instability as the buoyancy force increases. The present results are compared with available experimental data and also with analytical results from the wave mode of instability.

Airfoil shape for aircraft

Abstract: The invention relates to an airfoil shape for flight at high subsonic speeds, of the type comprising a flat convex upper surface, a thick leading edge and a lower surface convex towards the leading edge and concave towards the trailing, in which airfoil the upper surface comprises a maximum curvature in the vicinity of its rear part, in a zone delimited by points located at distances from the leading edge equal to 65 and 90% of the chord of the airfoil. The invention is applicable to the production of fixed or rotary wings for aircraft, having a high divergence Mach number and a low drag.

Vortex interactions and coherent structures in turbulence

Abstract: This chapter discusses the vortex interactions and coherent structures in turbulence. The study of vortex dynamics is a challenging subject apart from the applications to transition phenomena and turbulent flow. A useful and popular method of analyzing vortex flows, especially for small viscosity and concentrated vorticity, replaces the actual continuous distribution of vorticity by a finite sum over a number of discrete vortices, defined as a volume of rotational fluid surrounded by irrotational fluid. In the atomic representation, the structure of the vortices is supposed given and their motion is described by the Lagrangian evolution equation. In the molecular representation, the deformation and structure of the vortex are at least as important as the motion of the vortex as a whole. The atomic approach is particularly simple for two-dimensional flows when the vortices are usually either points or circles of small radius. The principal method used so far represents the vorticity as a collection of vortex filaments and the velocity is calculated from either the Biot-Savart law of induction with a cut-off proportional to the filament radius to give a finite value to the self-induced velocity, or by redistributing the vorticity on to mesh points of a grid and using a Poisson solver.

Experimental observation of stable arrangement of vortex rings

Abstract: A vortex ring version of the Karman vortex street is observed through flow visualization. A remarkably stable configuration of discrete vortex shedding is recognized with a distinction from the two‐dimensional case that the spacing between the alternating vortices is not equal.

Effect of leading-edge vortex flaps on aerodynamic performance of delta wings

Abstract: The effect of leading-edge vortex flaps on the aerodynamic characteristics of highly swept-back wings is analytically investigated, using the free vortex sheet method. The method, based on a three-dimensional inviscid flow model, is an advanced panel type employing quadratic doublet distributions to represent the wing surface, rolled-up vortex sheet and wake and is capable of computing forces, moments and surface pressures.

Vortex shedding flow measurement

Abstract: An improved vortex shedding flowmeter sensor and method are disclosed. The vortex shedding sensor is a bistable element. The element is constrained to operate in a transition deflection region between two stable stages. The element tends to alternate states at the frequency of vortex shedding, thereby amplifying the input signal at low levels and extending the low range of flow rate measurement.

Effects of vortex flaps on the low-speed aerodynamic characteristics of an arrow wing

Abstract: Tests were conducted in the Langley 12-foot low-speed wind-tunnel to determine the longitudinal and lateral-directional aerodynamic effects of plain and tabbed vortex flaps on a flat-plate, highly swept arrow-wing model. Flow-visualization studies were made using a helium-bubble technique. Static forces and moments were measured over an angle-of-attack range from 0 deg to 50deg for sideslip angles of 0 deg and + or - 4 deg.

The stability of an expanding circular vortex layer

Abstract: The stability of a circular cylindrical vortex layer against small disturbances that do not bend the vortex lines is examined. A short-wave analysis of the equations governing the growth of disturbances for a thin vortex layer reveals the stabilizing influence of the vortex-layer thickness when the layer is undergoing stretching. Also, the onset of amplification of very short waves is found to be delayed. Certain experimental observations due to Crow & Barker (1977) are discussed in view of the results of the analysis.

A Higher-order panel method for the computation of the flow about slender delta wings with leading-edge vortex separation

Abstract: For the limiting cases of conical flow about delta wings and time dependent 2-D development of the wake behind the trailing edge of wings a new second-order panel method is described. It is demonstrated that the panel method is stable for the mixed design/analysis boundary conditions characterizing both problems. The method for following 2-D vortex sheet motion includes an adaptive curvature-dependent panel scheme and a concept for doubly-branched spiralling vortices, which enables the motion of vortex sheets of complicated shape to be followed up to large downstream distances. Conical flow results are presented for different angles of attack and for different cross-sectional shapes. Vortex sheet roll-up results are presented for the wake behind a flat delta wing.

Flow visualization studies of vortices

Abstract: An actual vortex in the Karman vortex street downstream of a circular cylinder has a core of finite dimension which increases downstream. The circulation of the vortex is nearly constant. The ratiob/a which is 0.281 according to the theory of Karman, grows from 0.2 to 0.4 in the near wake.

Experimental investigation of the circulation of large scale vortex rings in HE II

Abstract: The vorticity produced by forcing He II out of a tube 8 mm in diameter was investigated in the region in front of the tube orifice. By a non-disturbing method of measurement based on the flow-induced differences in running times of second-sound shock waves, the formation of large scale vortex rings was observed and measured. The circulation of their normalfluid velocity field was found to be not conserved.