Turbulent Flow Verses Laminar Flow

Figure 1 shows two different flow patterns in pipes for laminar flow and turbulent flow. It is evident in the image that turbulent flow undergoes irregular flow patterns while laminar flow moves in smooth layers while maintaining a constant flow direction. The turbulent flows happen at a high Reynolds number where inertial forces are higher than viscous forces and perturbations can become amplified, whereas the laminar flows occur at a low Reynolds number in which any induced perturbations are damped out due to relatively strong viscous forces.

Figure 1. Flow Patterns

Figure 2 shows the time history of local velocity variations for laminar flows and turbulent flows, respectively. These patterns can be obtained from hot wire anemometer measurements or CFD simulations. For the pipe flow cases, laminar flows have nearly constant velocity, while turbulent flows have random or chaotic velocity fluctuation patterns. For a cylinder in cross flow, laminar flows produce a sine wave velocity pattern at a downstream location of the cylinder, while the turbulent flows have similar wave patterns but with embedded fluctuations.

Figure 2. Time History of Instantaneous Velocity at a Local Point

If you consider a flat plate immersed in a flow field with finite viscosity, a thin boundary layer will begin to develop as a function of the distance traveled along the plate (x). The image below shows a comparison of time-averaged velocity profiles for laminar flow and turbulent flow over a flat plate. The time-averaged velocity profile in a turbulent flow appears more uniform than in a laminar flow because the eddy motions in turbulent flow transport momentum more actively from one place to another. This process results in a more uniform profile outside the boundary layer. The velocity gradient near the wall is higher than the one seen in a laminar flow resulting in a larger skin friction coefficient ( $C_f$ ) than the laminar flow. The skin friction coefficient can be defined as (1)

$$C_f=\frac{{\tau }_w}{\frac{1}{2}\rho U^2}$$

where ${\tau }_w=\mu \frac{\partial U}{\partial y}$ is the wall shear stress, $\mu$ is the dynamic viscosity, $\rho$ is the density and $U$ is the mean velocity. The local Reynolds number ( $R{e}_x$ ) is calculated by using the distance from the leading edge of the flat plate as the length scale. $R{e}_x$ measures the local ratio of inertial to viscous forcing and provides an indication of the state of the flow regime as it moves from laminar to turbulent.

Figure 3. Time Averaged Velocity Profiles for Laminar and Turbulent Flows

Figure 4. Time Averaged Skin Friction Coefficient for Laminar Flow and Turbulent Flow

The information below includes equations of boundary layer thickness and skin friction coefficient for turbulent flow and laminar flow. These equations where developed through empirical relationships between local Reynolds number and boundary layer characteristics. The information below also provides a summary of general characteristics that are present in turbulent flow and laminar flow.