# Examining Reynolds Number For Turbulent Flow

### Key Takeaways

• The high value of the Reynolds number predicts the turbulent nature of flow while the low value indicates laminar flow.

• Reynolds number for turbulent flow is >3500.

• An understanding of the turbulent regime prominent in most industrial applications facilitates the development of turbulent flow models that can be utilized for system design and optimization.

Developing a complete CFD (computational fluid dynamics) model requires analysts to break down the nature of flow and its ultimate effect on a fluid system. While a laminar flow can be observed when air flows over an aircraft or when viscous fluid flows through a pipe or tube, it is the turbulent flow that is most prominently observed in nature and can be seen in effect, for instance, in systems such as turbine blades and heat exchangers. A high or low value of the Reynolds number is one way engineers and system designers can accurately predict if the flow experienced by the system is turbulent or laminar.

With computational modeling of the appropriate flow regime, it is possible to capture the challenges of flow dynamics and develop solutions to address the variables. For complex commercial systems, the logistics of flow modeling, such as the calculation of Reynolds number for turbulent flow, can be made easier with the help of CFD analysis software.

## Reynolds Number for Turbulent Flow

Reynolds number is one of the governing factors in the prediction of the fluid flow regime. It is a dimensionless parameter that is defined as the ratio between inertial force and viscous force during fluid flow. Numerically, Reynolds number (Re) for turbulent flow can be expressed as:

Considering this formula, it is clear that when fluid is flowing through an enclosed system—in this instance, a pipe, tube, or duct of hydraulic diameter (D)—Reynolds number is dependent on the density of the fluid (ρ), the velocity of the flow (V), and the viscosity of the flowing fluid (μ).

When the inertial force is greater than the viscous force (i.e., Reynolds number is higher) the flow tends to be turbulent. When the viscous force comes into play and is greater than the inertial force (i.e., Reynolds number is low) the flow tends to be laminar.

### Turbulent Flow Criteria

Calculating Reynolds number for turbulent flow is important for engineers, as most flow observed in industrial applications tends to be turbulent flow. A flow is considered to be turbulent when the fluid layers move in an irregular pattern, exhibiting a change in velocity and flow direction. Unlike in laminar flow, where the fluid layers move in a smooth, parallel path, turbulent flow can be characterized by the eddies and swirls and mixing of the flow paths with each other. In terms of Reynolds number, the flow is considered to be turbulent when Re > 3500. It is considered fully turbulent when Re > 4000. The following are some key attributes of turbulent flow:

• Usually occurs at high velocity and low dynamic viscosity.
• The average motion of the fluid particles is in the direction of flow.
• Characterized by non-zero vorticity and a three-dimensional vortex stretching mechanism.
• Has high diffusivity that causes rapid mixing and energy transfer.

It is possible for a system to exhibit both laminar and turbulent flow patterns. But, given the constant variations in the flow parameters, turbulence analysis becomes challenging. With the examination of high and low Reynolds numbers, the development of an appropriate turbulence model can be made easier. The accurate simulation of turbulent flow dynamics on a small scale can be used to develop a large-scale solution.

## Understanding Turbulent Flow Is Important for Industrial Applications

Turbulent flow plays a major role in most industrial applications. Thus, turbulence modeling is an important part of fluid flow analysis in industries including:

• Oil and gas: Helps predict energy loss and pressure drop during oil and gas transport over a long distance.
• Aerospace: Helps optimize the lift-drag ratio during the design of aircraft wings.
• Pharmaceuticals: Aids in the design of mixing equipment.
• Wind turbines: Aids in calculating the wake-effect to optimize turbine performance.
• Automotive: Helps predict drag to deliver aerodynamic design.

Ensuring the design and optimization of fluid-dependent systems can be a challenge. However, through accurate computation and simulation facilitated by a CFD solver, it is possible to resolve turbulent flow problems and deliver excellent product performance.

## Turbulence Modeling With a CFD Solver

Given the complex nature of turbulence analysis, CFD modeling can be challenging for system designers. Advanced CFD platforms allow designers to optimize their designs for complex systems for a range of Reynolds numbers for turbulent flow. These platforms are especially beneficial when it comes to the design of complex geometrical systems where analyzing pressure or flow rate requirements manually can be difficult.

CFD tools such as  Omnis can help you run accurate simulations, and Pointwise can help with precise mesh generation and 3D analysis for a range of complex geometrical designs. Through integrated analysis abilities, CFD models can be analyzed and optimized to deliver high-performance yet cost-efficient designs.