When placed ih a fluid stream, some bodies generate separated flow over a substantial proportion of their surface and hence can be classified as bluff. On sharp-edged bluff bodies, separation is fixed at the salient edges, whereas on bluff bodies with continuous surface curvature the location of separation depends both on the shape of the body and the state of the boundary layer. At low Reynolds numbers, when separation first occurs, the flow around a bluff body remains stable, but as the Reynolds number is increased a critical value is reached beyond which instabilities develop. These instabilities can lead to organized unsteady wake motion, dis­ organized motion, or a combination of both. Regular vortex shedding, the subject of this article, is a dominant feature of two-dimensional bluff-body wakes and is present irrespective of whether the separating boundary layers are laminar or turbulent. It has been the subject of research for more than a century, and many hundreds of papers have been written. In recent years vortex shedding has been the topic of Euromech meetings reported on by Mair & Maull (1971) and Bearman & Graham (1980), and a comprehensive review has been undertaken by Berger & Wille (1972). Vortex shedding and general wake turbulence induce fluctuating pres­ sures on the surface of the generating bluff body, and if the body is flexible this can cause oscillations. Oscillations excited by vortex shedding are usually in a direction normal to that of the free stream, and amplitudes as large as 1.5 to 2 body diameters may be recorded. In addition to the generating body, any other bodies in its wake may be forced into oscillation. Broad-band force fluctuations, induced by turbulence produced in the flow around a bluff body, rarely lead to oscillations as severe as those caused by vortex shedding. Some form of aerodynamic instability, such that move-

Vortex shedding from oscillating bluff bodies

The time development of the symmetrical standing zone of recirculation, which is formed in the early stage of the flow due to a circular cylinder impulsively set in motion perpendicular to its generators, has been studied using a flow visualization technique. The Reynolds numbers (based upon the diameter) range from 40 to 104. Some new phenomena indicated in the flow patterns are revealed, and several different regimes are differentiated by a detailed analysis of the evolution of the main flow characteristics. A correlation with some theoretical results is established.

The early stage of development of the wake behind an impulsively started cylinder for 40 Re 4

A discrete vortex model based on potential flow and boundary-layer interaction, rediscretization of shear layers, and circulation dissipation is developed to determine the characteristics of an impulsively started flow about a circular cylinder. The evolution of the flow from the start to very large times, lift and drag forces, Strouhal number, oscillations of the separation and stagnation points, and the vortex-street characteristics are calculated and compared with experiments. b CD CL Cpb c D fv h / j m N n q Re St s ds t At U u v w z F 7 6 X v p Nomenclature = longitudinal spacing of vortices = drag coefficient = lift coefficient = base pressure coefficient = radius of the cylinder - diameter of the cylinder ,D = 2c = vortex shedding frequency = transverse spacing of vortices = an index = distance to nascent vortex from cylinder = number of vortices on a sheet = an index = total velocity at a point = Reynolds number, UD/v = Strouhal number, fvD/ U = distance along a sheet = point vortex spacing = time or Ut/c for U= 1 and c = 1 - numerical step size = velocity of the ambient flow = x component of velocity -y component of velocity = complex velocity potential = complex variable = circulation = circulation per unit length = angle measured from ( - c,0) = dissipation parameter = kinematic viscosity of fluid = density of fluid = vorticity

Inviscid Model of Two-Dimensional Vortex Shedding by a Circular Cylinder

body length forebody length forward of rotation center (Fig. 8) nose length = rolling moment, coefficient C, = £/ (p* U^ /2)Sb vortex wake wave length Mach number pitching moment, coefficient Cm=Mp/(PooUl/2)Sc yawing moment, coefficient Cn=n/(p00 U00/2)Sc = normal force, coefficient CN=N/ (p^ C/i/2)S = nose tip roll rate = pitch rate Reynolds number based on dmax and freestream conditions; usually Re = Rd Reynolds number, Rd = U^d/v^ reference area, S = ird /4 reference area ( = projected wing area) time velocity axial body-fixed coordinate (distance from apex) side force, coefficient CY=Y/(PooUx /2)S angle of attack da/df, C^ = d C m / d j > ' l 0 / U ( X ) sideslip angle rotation of plane of symmetry of forebody vortices (Fig. 8) cone half-angle 6A = apex half-angle p = air density = roll angle 5 = three-dimensional separation angle (Fig. 15) a' = total angle of inclination (Fig. 8) v — kinematic viscosity oj = angular rate

Steady and Unsteady Vortex-Induced Asymmetric Loads on Slender Vehicles

A numerical analysis of forced-convection heat transfer from a horizontal stationary circular cylinder dissipating a uniform heat flux in a crossflow of air is conducted by solving the full two-dimensional steady-state Navier-Stokes and energy equations in the range of the Reynolds numbers from 100 to 500 (based on diameter). A numerical study by this author for Reynolds numbers less than 100 was previously conducted and therefore is not repeated here. Dependence on the Reynolds number of the flow and thermal fields, vorticity and pressure distributions, separation angle, drag coefficient, and local and average Nusselt number around the cylinder are shown. Correlations for the separation angle and drag coefficient as functions of Reynolds number are suggested. Quantities such as vorticity, pressure, and Nusselt number at the forward and rear (base) stagnation points are also calculated and correlated as functions of Reynolds number. The local and average values of the Nusselt numbers are shown to be in go...

Steady-State Numerical Solution of the Navier-Stokes and Energy Equations around a Horizontal Cylinder at Moderate Reynolds Numbers from 100 to 500

A method is developed to determine the time-dependent flowfield about an impulsively started circular cylinder. An outer potential flow model is interfaced with an inner viscous flow region. The wake is described by a set of elementary point vortices. The position at which the point vortices are shed from the cylinder is obtained from a solution to the unsteady incompressible laminar boundary-layer equations. A rear shear-layer is postulated to account for backflow induced vorticity. Wake development is detailed from the initial formation of the two symmetric vortices to subsequent asymmetry and eventual alternate shedding. Unsteady pressure distributions, lift and drag forces, and Strouhal number are calculated and compared with experiment.

F. D. Deffenbaugh

Papers

Time development of the flow about an impulsively started cylinder