Pressure distribution around a cylinder

Abstract

Pressure distribution near the edge of a cylinder and on its end face is very little dealt with as one can see from books on fluid dynamics and aerodynamics which one commonly meets with. Therefore it is the aim of this project to investigate the motion of air past a circular cylinder, particularly near the edge and on its end face. The streaming motion of air past a cylinder closes a region of recirculating air for which the theory fails to provide satisfactorily description of the hydrodynamic conditions at the interface making impossible the evaluation of pressure in the area confined by the wake. In consequence, knowledge of flow past a cylinder is drawn mostly from experimentation and observation. Determination of high Reynolds number flow produced by a body moving steadily through a fluid at rest at infinity or, equivalently, the flow past a fixed body in a stream which is steady and uniform at infinity is a basic problem in fluid dynamics of great practical importance in several engineering fields. The feature of the motion of a fluid at infinity round a cylinder which is of most practical significance is the total force exerted on the body by the fluid. Contribution to this total force are made by the tangential stress at the body surface, integrated over that surface, and by the normal stress. The former is termed the friction drag since it is wholly and directly a consequence of viscosity of the fluid. The total force due to the normal stress at the surface of the body is due to the pressure distribution around it. The pressure distribution is affected by the existence of vortices which trail downstream from the body. In classical hydrodynamics the motion of an inviscid fluid past a body is irrotational. The perfect fluid theory leads to the conclusion that a solid body moves through an infinitely extended fluid at rest or vice versa, experiences no force, i.e. its drag is zero. This is referred to as D'Alembert's paradox. The arrangement of the stream lines for a perfect fluid past a cylinder is symmetrical in the direction of the flow and it can be concluded that the drag in this direction is zero. This result is in glaring contradiction to the observed fact as drag is measured on all bodies. The flow at the rear of a cylinder is far from having the assumed irrotational form. Measurements have been made of the mean and fluctuating pressure distribution on long circular cylinder (which exclude the effect of finite length cylinder) at various Reynolds numbers in both uniform and turbulent streams. The presence of stream turbulence at Reynolds number ranging from 2.10 4 to 2.0x10 s was found to suppress vortex shedding on smooth cylinders and gave rise to a complex pressure filed in which the mean pressure distribution was almost independent of Reynolds numbers over this range. This pressure distribution on rough cylinders was found to be completely different in uniform and turbulent streams. The presence of turbulence gave rise to an increase in the level of vortex shedding, and produced mean pressure distributions similar to those obtained on smooth cylinders at Reynolds numbers of the order 10 7. The flow covering a circular cylinder in the Reynolds number range of 2x10 5 to 10 7 is a strong function of Reynolds number. Measurements indicate that the pressure distribution changes considerably over this range. For values of Reynolds number below the critical the pressure minimum occurs already at 0=70° and the pressure minimum shifts to 0=90° approximately in agreement with the potential flow theory, and on the whole pressure distribution diviates less from that given by the potential flow theory than in the previous case. Between these values, i.e. [...] a critical Reynolds number of approximately [...] the drag coefficient of the circular cylinder decrease abruptly and this phenomenon indicates that the boundary layer has become turbulent. In this experiment investigations were carried out on a smooth cylinder and Reynolds numbers below the critical Reynolds number.