Characteristics of Unsteady Separated Laminar Boundary Layer Flows over Spinning Bodies (original) (raw)

Dzet Ani olarak harekete gef{irilmi~, donen, eksenel simetrik, izotermal ve gef{irgen yuzeyli bir cisim uzerinden "aminer Slnlr tabaka akl~lnln geli~imi kan~lk ve dogal konveksiyon durumlan if{in incelendi. Aklm fonksiyonu, ~evresel hrz ve slcaklrk zaman cinsinden kuvvet serileri Be ifade edildi. Genel sonuf{lar, karr~lk konveksiyon durumunda yuzey gef{irgenligi ve kaldlrma kuvvetinin hlz ve slcakllk alanl Ozerine etkisini belirlemek; dogal konveksiyon durumunda slnlr tabaka akl~ rejimlerini ortaya f{lkarmak if{in d6nen bir kGreye uygulandl. Anahtar Kelirneler : D6nen cisimler, daimi olmayan rejim, Slnlr tabaka, laminer ve aynlml~ akl~ CHARACTERISTICS OF UNSTEADY SEPARATED LAMINAR BOUNDARY LAYER FLOWS OVER SPINNING BODIES Abstract Initial development of the laminar boundary-layer flow over an impulsively started spinning isothermal permeable body of revolution in mixed and free convection is investigated. Stream function, swirl velocity and temperature were expanded in series of time. The general results were applied to a spinning sphere to determine the effects of surface transpiration and buoyancy on the velocity and temperature fields in the case of forced convection and to investigate the type of boundary layer flow regimes in the case of free convection. Keywords: Spinning bodies, unsteady, boundary layer, laminar and separated flow 1. Introduction Boundary-layer flow over spinning bodies of revolution has important engineering applications involving projectile motion, reentry missile behaviour and rotary machine design. The flow field is greatly affected by the rotation of the body. In the case of a bluff body, the boundary layer separates and the flow field becomes more complex. The centrifugal force caused by the rotation of the body is known to facilitate and speed up the flow separation. Surface blowing and suction also influence the onset of separation providing a boundary-layer control mechanism. Furthermore when the temperature difference between the surface and the fluid is large and the velocity is small, the buoyancy force due to the density variation interacts with the centrifugal force altering the velocity field. In the case of free convection from a heated vertical body spinning in an otherwise quiescent fluid, interaction between the buoyancy and the centrifugal forces determines the boundary layer flow regimes. The number of solutions of the boundary-layer flows including the swirl velocity is very few. Flow about a spinning body of revolution has been investigated by Illingworth (1), Chu and Tifford (2). Schlichting (3) and Hoskin (4). These are all momentum-integral approximations and of uncertain accuracy. Measurements of Luthander and Rydberg (5) and the study of Hoskin (4) show that there is a marked influence of rotation on drag and separation on a spinning sphere in an axial stream. The problem of mixed convection about a rotating sphere in a stream has been investigated by Rajasekaran and Palekar (6). Tile results show that velocity profiles affected by buoyancy display an overshoot beyond a local free stream velocity for aiding flow. Le Palec and Daguenet (7) have used power series expansions for the stream function and temperature to study the laminar mixed convection about an isothermal rotating sphere in a stream of arbitrary direction with respect to the axis of rotation and solved the boundary layer equations numerically. Mixed convection over a spinning sphere with blowing and suction has been investigated numerically by Lien et al (8) and Wang and KleinstrelJer (9) to show that the wall suction and body rotation enhances heat transfer for aiding flow.