Laminar and Turbulent Flows

LAMINAR AND TURBULENT FLOWS

The translation of the energy of flow from one form to another has been described with little reference to the actual nature of flow. Flow of fluids can be laminar (and may be depicted by streamlines) or turbulent, terms that are best introduced by describing a series of simple experiments performed in 1883 by Osborne Reynolds. The apparatus, shown in Figure 2.8, consisted of a straight glass tube through which the fluid was allowed to flow. The nature of flow may be examined by introducing a dye into the axis of the tube. At low speeds, the dye forms a coherent thread, which grows very little in thickness with distance down the tube. 

FIGURE 2.8 The Reynold’s experiment (A) Laminar; (B) Turbulent and; (C) illustration of the use of a mean velocity for turbulent flow.

However, with progressive increase in speed, the line of dye first began to waver and then break up. Secondary motions, crossing and recrossing the general flow direction, occur. Finally, at very high speeds, no filament of dye could be detected and mixing to a dilute color was almost instantaneous. In this experiment, flow changes from laminar to turbulent, the change occurring at a critical speed. Generalizing, in laminar flow, the instantaneous velocity at a point is always the same as the mean velocity in both magnitude and direction. In turbulent flow, order is lost and irregular motions are imposed on the main steady motion of the fluid. At any instant of time, the fluid velocity at a point varies both in magnitude and direction, having components perpendicular as well as parallel to the direction of net flow. Over a period of time, these fluc-tuations even out to give the net velocity in the direction of flow.

In turbulent flow, rapidly fluctuating velocities produce high-velocity gradients within the fluid. Proportionately large shear stresses are developed, and to overcome them, mechanical energy is degraded and dissipated in the form of heat. The degradation of energy in laminar flow is much smaller.

The random motions of turbulent flow provide a mechanism of momen-tum transfer not present in laminar flow. If a variation in velocity occurs across a fluid stream, as in a pipe, a quantity of fast-moving fluid can move across the flow direction to a slower-moving region, increasing the momentum of the latter. A corresponding movement must take place in the reverse direction elsewhere, and a complementary set of rotational movements, called an eddy, is imposed on the main flow. This is a powerful mechanism for equalizing momentum. By the same mechanism, any variation in the concentration of a component is quickly eliminated. Admitting dye to the fluid stream in Reynolds’ original experiment showed this. Similarly, the gross mixing of turbulent flow quickly erases variations in temperature.

The turbulent mechanism that carries motion, heat, or matter from one part of the fluid to another is absent in laminar flow. The agency of momentum transfer is the shear stress arising from the variations in velocity, that is, the viscosity. Similarly, heat and matter can only be transferred across streamlines on a molecular scale, heat by conduction and matter by diffusion. These mechanisms, which are present but less important in turbulent flow, are com-paratively slow. Velocity, temperature, and concentration gradients are, there-fore, much higher than that in turbulent flow.