# What Is Reynolds Number and Why Is It Important?

### Key Takeaways

• Reynolds number is a dimensionless parameter that facilitates the prediction of flow behavior.

• A low Reynolds number indicates laminar flow while a high Reynolds number indicates turbulent flow.

• Identification of flow regime with Reynolds number facilitates the creation of an ideal flow model for efficient fluid system design. The design of aerodynamic or hydraulic systems depends on crucial information about the nature of the fluid flow within the system. This is because the different flow patterns can exert varying forces within the system. Identification of whether the flow is turbulent or laminar allows engineers and system designers to analyze the problems these flow patterns induce and consider these factors in examining system performance.

By using an advanced CFD model for the simulation of flow behavior, it is possible to optimize the design of fluid-dependent systems and ensure efficient performance. The simulation process can be simplified with the help of Reynolds number, which, through flow prediction, can capture all laminar and turbulent motion and boundaries for effective mesh generation. In this article, we will explore what the Reynolds number is and its importance.

## What Is Reynolds Number?

The concept of Reynolds number is named after Osbourne Reynolds, who first studied the relationship between flow velocity and flow behavior through visualization of flow movement using colored dye. A dimensionless parameter was discovered that could easily predict fluid behavior in a wide range of flow conditions. This dimensionless parameter, called Reynolds number, can predict the different flow regimes based on various parameters such as fluid density, flow velocity, and dynamic viscosity.

Numerically, Reynolds number (Re) can be defined as a ratio between inertial force and viscous force. The parameters can be noted as:

ρ: density of the fluid

V: fluid velocity

D: hydraulic diameter (of pipe, tube, or duct).

μ: fluid viscosity

As we discuss what is Reynolds number, it is also important that we understand the different flow regimes that a system may be exposed to. A flow is considered laminar when the fluid moves in a smooth, regular path. In contrast, a turbulent flow has an irregular motion with fluid layers mixing and disrupting each other’s paths. When the prediction is made in terms of Reynolds number, at a value up to 2300, the fluid exhibits laminar properties. As the laminar flow is generally observed when the fluid is flowing at a low-velocity flow or a smaller cross-section and has a smoother flow path, the viscous force is more prominent in comparison to the inertial force. The flow can be considered turbulent when the Reynolds number is 3500 or higher. This is because of the increased inertial force due to the higher flow rate and irregular path. The Reynolds number within 2300 to 3500 is considered to be in the transition phase when the flow has just gained momentum but isn’t erratic enough to be considered a turbulent flow

### Critical Reynolds Number

A critical Reynolds number is associated with the flow as it transitions from laminar to turbulent.  The value may vary depending upon whether the flow is internal or external. Most Reynolds number calculations are based on internal flow, where fluid flows in a confined space, thus, the critical Reynolds number has a similar formula: To accommodate the shape of pipe into numerical consideration, where A = cross-sectional area and P = wetted perimeter:

## D = 4AP

In case the flow is external, (i.e., the flow isn’t constrained) for instance,  when air flows over an aircraft, the critical Reynolds number can vary depending on the body of the flow.

## Re crit = PV x/μ

Note that Vx is the velocity of flow along the x-direction.

Generally:

• ➢ When the fluid flows over a flat plate, the critical Reynolds number is ~ 500,000.
• ➢ For a sphere, laminar flow only exists when the critical Reynolds number is equal to 10.

## Ideal CFD Programs for Flow Prediction and Design

In different flow conditions, the high and low value of Reynolds number points towards a prediction of different flow regimes. This prediction holds significant importance when it comes to choosing strategies for CFD modeling of a fluid system. Some practical applications include:

• Simulation of aircraft or vehicle models in laminar and turbulent flow conditions.
• Developing correlation between the heat transfer and friction factor within the flow system.
• Prediction of the onset of turbulence can help facilitate large-scale prediction of flow behavior.
• Identify pressure requirements with flow rate calculations.

With wide industrial applications involving laminar and turbulent flow regimes, the Reynolds number provides an advantage for engineers during system design. However, specifying what is Reynolds number for complex geometrical designs can be a difficult task compared to the simple calculation of internal flow in cylindrical ducts or pipes.

At a high or low Reynolds number, a solver will allow you to design and display complex systems through automated and accurate mesh generation. The Omnis platform facilitates accurate flow simulation in a single integrated environment with multi-disciplinary analysis ability. And, Pointwise supports auto mesh generation and 3D analysis for a wide range of geometries. With advanced design and simulation capabilities, flow models can be generated and analyzed for relevant time and length scales at the speed and fidelity levels desired.