An Introduction to Flow Regimes

Inviscid Flows

Inviscid flow is a theoretical type of fluid flow regime having zero internal friction as a result of a fluid having zero viscosity. This type of flow can be approached in the physical world when a fluid has a very low viscosity and viscous-shear and normal stresses are negligible.  Making the further simplification that the fluid is incompressible, in what is called an “ideal” or “perfect” fluid, allows reduction of the Navier-Stokes set of equations to the simpler Euler set of equations which has many more known solutions and deeper mathematical analysis.  Further, Bernoulli’s equation can be derived from the Euler equations via the assumption of steady-state flow, as demonstrated by Leonhard Euler himself in 1752.

In practice, flows with minimal boundary layers are often considered as “inviscid” to simplify their analysis or solution using computational methods. The inviscid approximation implies an infinite  Reynolds’ number. 

What is Reynolds Number and why is it important?   The Reynolds number (Re) is a non-dimensional number representing the ratio of inertial forces to viscous forces in a fluid.  It is a convenient parameter for predicting if a flow will be laminar or turbulent. It can be interpreted that when the viscous forces are dominant (slow flow, low Re) they are sufficient enough to keep all the fluid particles in line and maintain laminar flow.

Real-world flows with very high Reynolds’ numbers where any boundary layers present are very thin compared to the dimension of the solid bodies present are the flows most commonly subject to inviscid analysis. Most of these applications are in high-speed environments such as high-speed jets at cruising speeds and at low angles of attack where the boundary layer never separates from the surfaces of the jet.

An F/A-18 Hornet from Strike Fighter Squadron 137 (VFA-137) files faster than sound, creating a sonic boom and a visual mist during an exercise off the coast of San Diego, California, January 1, 1990.  Courtesy US Navy.

Despite their simplicity, inviscid flows can still be challenging to analyze due to their high-speed nature. Engineers and scientists must carefully consider the fluid's properties and the flow system's geometry to accurately predict and analyze inviscid flows.

Laminar Flows

Laminar flow is a type of fluid flow regime where the fluid motion is smooth and orderly, often in parallel layers (laminae) with little mixing occurring between layers. Laminar flows are inherently stable, i.e., impervious to slight perturbations in their initial states or boundary conditions. Unlike inviscid flows, this type of flow occurs commonly in the physical world and is characteristic of a viscous fluid. Laminar flow typically occurs at relatively slower flow rates or high viscosities, as defined by a low Reynold’s number.  Laminar flows are inefficient at transferring heat or momentum from a boundary to the interior of the flow, due to a lack of perpendicular convective transfer across a boundary layer.  Therefore, they have gently sloping velocity and temperature gradients from boundary to center of flow.

Laminar flows are characterized by the absence of turbulence and are easier to predict and analyze. An example of laminar flow is the flow of syrup from a bottle or the flow of honey on a flat surface.

https://gifer.com/en/IDf5

Laminar flows are used in various engineering applications, such as in the design of heat exchangers and chemical reactors. Understanding laminar flow behavior can help engineers optimize these systems to maximize their efficiency and performance.

Turbulent Flows

Turbulent flows are fluid flow regimes characterized by instability to perturbations where the fluid moves in chaotic motions characterized by vortices, eddies, and fluctuations in pressure and velocity and sensitivity to initial conditions. They are common in fluids with high viscosity and occur at high flow rates. Turbulent flows are generally difficult to predict and understand due to their complex nature.  Contrasts between generalized laminar and turbulent flows are shown in the image below with laminar flow on the top and turbulent flow on the bottom.

Turbulent flows can be found in many natural systems such as rivers and oceans, and they also occur in man-made systems such as pipelines and turbines. Understanding turbulent flow behavior is crucial in many engineering applications, such as in the design of aircraft and automobiles.  Turbulent flows are more efficient conveyors of momentum and heat between boundaries and interior flow regions, leading to steeper velocity gradients across channel flows.  The contrast between laminar and turbulent time-averaged velocity profiles in a pipe are shown in the image below.

From:  https://www.standards.doe.gov/standards-documents/1000/1012-bhdbk-1992-v3/@@images/file

Despite their complexity, turbulent flows can be analyzed using various mathematical models and simulations. These tools allow engineers and scientists to predict and optimize turbulent flow behavior in various systems.

Transitional Flows

Transitional flows are fluid flow regimes somewhere between laminar and turbulent flows. Often turbulent flow will be present near the center of a flow or near an open surface, but laminar flow will be present near boundaries.  In other cases, periodic or aperiodic flow behavior will be demonstrated, violating both the regularity requirement of laminar flow and the highly chaotic behavior of turbulent flows.  The most common example of this type of behavior is the shedding of vortices behind a cylindrical obstruction, known as the von Kármán vortex street, where shedding frequency increases as Reynolds’ number increases and turbulence increases within the vortices and wake. These dynamics are demonstrated in the graphic below. 

Courtesy John Lienhard:

(https://www.uh.edu/engines/vortexcylinders.pdf)

and C.H.K. Williamson:

(https://www.annualreviews.org/doi/pdf/10.1146/annurev.fl.28.010196.002401)

This transition is influenced by factors such as the fluid's properties, the flow rate, and the geometry of the flow system.

Transitional flows are critical because they represent a significant change in the fluid system's behavior and can significantly impact the fluid's overall performance. Detecting when a flow system is transitioning from a laminar to a turbulent flow can help engineers optimize the system's performance. Transitional flows are often studied in various engineering applications, such as in the design of aircraft wings and propellers.

Conclusions

Fluid flow regimes are essential to understanding how fluids behave in different environments. By analyzing the different types of fluid flow regimes, we can better understand fluid behavior and develop more efficient fluid systems. The use of advanced technology such as computational fluid dynamics has revolutionized fluid flow analysis, making it easier to predict and analyze fluid systems' behavior.