Laminar flow exists only at relatively small Reynolds numbers. As the Reynolds number increases, the laminar regime of flow transients in turbulent flow. The laminar flow is well organized so that it looks like thin parallel layers (lamina in Greek means plate or layer) of fluid move unmixed along a pipe or a plate. In contrast to that, the mixing process inside a fluid leading to homogeneous disturbed medium is one of the basic characteristics of turbulent flow. The patterns of these two regimes were first observed by Reynolds in the nineteenth century, who put the dye inside the flow to make it visible. He was also the first to understand that there exists a universal dimensionless number (now known as critical Reynolds number) at which the transition occurs. The critical Reynolds numbers experimentally determined for flows in a circular section pipe and past a plate are: Recr = ûD/v = 2300 and Recr = Ux/v = 3.5 · 105 ÷ 106, where û is an average velocity in a pipe. The value of critical Reynolds number depends on the conditions outside of a pipe or a body and increases as the level of disturbances in the inlet flow decreases. The just indicated critical Reynolds numbers correspond to usually disturbed environment, whereas in the experiments when the disturbance in the inlet flow was reduced, the flow in a pipe remained laminar up to Reynolds number 40000. At the same time at Reynolds numbers less than 2000, the flow in a pipe remains laminar independent of the level of inlet disturbances because these are dissipated by viscosity in flows with smaller than critical Reynolds numbers.
8.1Transition from Laminar to Turbulent Flow
8.2Reynolds Averaged Navier-Stokes Equation (RANS)
8.4One-Equation and Two-Equations Models