General Characteristics of External Flow

External flows are defined as the flows immersed in an unbounded fluid. A body immersed in a fluid experiences a resultant force due to the interaction between the body and fluid surroundings. In some cases, the body moves in stationary fluid medium (e.g. motion of an airplane) while in some instances, the fluid passes over a stationary object (e.g. motion of air over a model in a wind tunnel). In any case, one can fix the coordinate system in the body and treat the situation as the flow past a stationary body at a uniform velocity , known as upstream/free-stream velocity. However, there are unusual instances where the flow is not uniform. Even, the flow in the vicinity of the object can be unsteady in the case of a steady, uniform upstream flow. For instances, when wind blows over a tall building, different velocities are felt at top and bottom part of the building. But, the unsteadiness and non-uniformity are of minor importance rather the flow characteristic on the surface of the body is more important. The shape of the body (e.g. sharp-tip, blunt or streamline) affects structure of an external flow. For analysis point of view, the bodies are often classified as, two-dimensional objects (infinitely long and constant cross-section), axi-symmetric bodies and three-dimensional objects.

There are a number of interesting phenomena that occur in an external viscous flow past an object. For a given shape of the object, the characteristics of the flow depend very strongly on carious parameters such as size, orientation, speed and fluid properties. The most important dimensionless parameter for a typical external incompressible flow is the Reynolds number , which represents the ratio of inertial effects to the viscous effects. In the absence of viscous effects , the Reynolds number is infinite. In other case, when there are no inertia effects, the Reynolds number is zero. However, the nature of flow pattern in an actual scenario depends strongly on Reynolds number and it falls in these two extremes either or . The typical external flows with air/water are associated moderately sized objects with certain characteristics length and free stream velocity that results Reynolds number in the range . So, as a rule of thumb, the flows with , are dominated by viscous effects and inertia effects become predominant when . Hence, the most familiar external flows are dominated by inertia. So, the objective of this section is to quantify the behavior of viscous, incompressible fluids in external flow.