Understanding Laminar and Turbulent Flow
Hello and Welcome This Blog from The Efficient Engineer is sponsored by Brilliant. One of the very first things you learn in fluid mechanics is the difference between laminar and turbulent flow. And for good reason.
What is turbulent flow?
these two flow regimes behave in very different ways and, as we’ll see in this blog, this has huge implications for fluid flow in the world around us Here we have an example of the laminar flow regime. It's characterized by smooth, even flow. The fluid is moving horizontally in layers, and there is a minimal amount of mixing between layers. As we increase the flow velocity we begin to see some bursts of random motion. This is the start of the transition between the laminar and turbulent regimes. If we continue increasing the velocity went up with the fully turbulent flow. Turbulent flow is characterized by chaotic movement and contains swirling regions called eddies. The chaotic motion and eddies result in significant mixing of the fluid. If we record the velocity at a single point in steady laminar flow, we'll get data that looks like this. There are no random velocity fluctuations, and so in general laminar flow is fairly easy to analyze.
Why is laminar and turbulent flow important?
At what Reynolds number is turbulent flow?
For flow past an airfoil, it will be the chord length. And for flow through a pipe, it will be the pipe diameter. Reynolds number is useful because it tells us the relative importance of the inertial forces and the viscous forces. Inertial forces are related to the momentum of the fluid, and so are essentially the forces that cause the fluid to move. Viscous forces are the frictional shear forces that develop between layers of the fluid due to its viscosity. If viscous forces dominate flow is more likely to be laminar because the frictional forces within the fluid will dampen out any initial turbulent disturbances and random motion. This is why the Reynolds number can be used to predict if the flow will be laminar or turbulent. If inertial forces dominate, flow is more likely to be turbulent. But if viscous forces dominate, it’s more likely to be laminar. And so smaller values of Reynolds number indicate that flow will be laminar. The Reynolds number at which the transition to the turbulent regime occurs will vary depending on the type of flow we are dealing with. These are the ranges usually quoted for flow through a pipe, for example. Under very controlled conditions in a lab, the onset of turbulence can be delayed until much larger Reynolds numbers. Most flows in the world around us are turbulent. The flow of smoke out of a chimney is usually turbulent. And so is the flow of air behind a car travelling at high speed. The flow of blood through vessels on the other hand is mostly laminar because the characteristic length and velocity are small. This is fortunate because if it were turbulent heart would have to work much harder to pump blood around the body. To understand why this is, let's look at how the flow regime affects flow through a circular pipe. The flow velocity right at the pipe wall is always zero. This is called the no-slip condition. For fully developed laminar flow, the velocity then increases to reach the maximum velocity at the center of the pipe. The velocity profile is parabolic. For turbulent flow, the profile is quite different. We still have the no-slip condition, but the average velocity profile is much flatter away from the wall.
Why is turbulent blood flow bad?
This is because turbulence introduces a lot of mixing between the different layers of flow, and this momentum transfer tends to homogenize the flow velocity across the pipe diameter. Note that I have shown the time-averaged velocity here. The instantaneous velocity profile will look something like this. In pipe flow, one thing we are particularly interested in is pressure drop. Across any length of pipe, there will be a drop in pressure due to the frictional shear forces acting within the fluid. The pressure drop in turbulent flow is much larger than in laminar flow, which explains why the heart would have to work harder if blood flow was mostly turbulent! We can calculate Delta-P along the pipe using the Darcy-Weisbach equation. It depends on the average flow velocity, the fluid density, and a friction factor f. For laminar flow, the friction factor can be calculated easily. It is just a function of the Reynolds number. If we combine these two equations we can see that the pressure drop is proportional to the flow velocity. But for turbulent flow calculating f is more complicated. It is defined by the Colebrook equation.
What is laminar flow used for?
appears on both sides of the equation, so it needs to be solved iteratively. Unlike laminar flow, for which the pressure drop is proportional to the flow velocity, it turns out that for turbulent flow it is proportional to the flow velocity squared. And it also depends on the roughness of the pipe surface. Epsilon is the height of the pipe surface roughness, and the term Epsilon/D is called the relative roughness. Surface roughness is important for turbulent flow because it introduces disturbances into the flow, which can be amplified and result in additional turbulence. For laminar flow, it doesn't have a significant effect because these disturbances are dampened out more easily by the viscous forces. Since the Colebrook equation is so difficult to use, engineers usually use its graphical representation, the Moody diagram, to lookup friction factors for different flow conditions. Where flow is laminar the friction factories only a function of Reynolds number, so we get a straight line on the Moody diagram. For turbulent flow, you select the curve corresponding to the relative roughness of your pipe, and you can look up the friction factor for the Reynolds number of interest. So we know that if the Reynolds number is large, inertial forces dominate, and the flow is turbulent.
But even for turbulent flow viscous forces can be significant in the boundary layers that develop at solid walls. Because of the no-slip condition, shear stresses are large close to a wall. This means that in a turbulent boundary layer there remains a very thin area close to the wall where viscous forces dominate and flow is essentially laminar. We call this the laminar, or viscous, sublayer. Its thickness decreases as the Reynolds number increases. Above the laminar sublayer, there is the buffer layer, where both viscous and turbulent effects are significant. And above the buffer layer, turbulent effects are dominant. If the roughness of a surface is contained entirely within the thickness of the laminar sublayer, the surface is said to be hydraulically smooth, because the roughness has no effect on the turbulent flow above the sublayer. This is important in pipe flow because, as can be seen from the Moody diagram, flow in a smooth pipe has a lower friction factor and smaller pressure drop than flow in the rough pipe.