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Correlating Laminar and Turbulent Types of Flow With Reynolds Number

Key Takeaways

  • Fluid flow is characterized by different parameters such as velocity, density, pressure, and viscosity. 

  • Reynolds number gives the ratio of inertial forces to viscous forces in a fluid.

  • When Reynolds number is less than 2300, fluid flow is laminar.

Illustration of laminar and turbulent flows

The range of Reynold numbers indicates whether the flow is laminar or turbulent

In fluid flow, parameters such as velocity, pressure, and density change in different patterns,  affecting fluid behavior. Fluid flow can be classified into different types based on the conditional variance of flow parameters over space and time. Laminar and turbulent flow come under one such classification of fluid flow. There is a correlation between laminar and turbulent types of flow and Reynolds number, which is a dimensionless parameter. In this article, we will discuss various types of flows and how Reynolds number differentiates laminar and turbulent flow.

Classifications of Fluid Flow 

Fluid flow is characterized by different parameters such as velocity, density, pressure, and viscosity. When any of these parameters change, the flow pattern changes. Considering the fluid flow parameter variation, there are six classifications of fluid flow:

  1. Steady Flow or Unsteady Flow

When flow characteristics remain constant over time, fluid is in a steady flow. In unsteady fluid flow, the parameters change with respect to time. 

  1. Uniform or Non-Uniform Flow

When the velocity of the flow remains the same over the length of direction of the flow, flow is considered to be uniform flow. In non-uniform flow, the velocity of flow changes with respect to time. 

  1. Compressible or Incompressible Flow

A compressible flow is a flow in which the density of the fluid changes with respect to time. In incompressible flow, the density of the fluid remains constant. 

  1. 1-Dimensional, 2-Dimensional, or 3-Dimensional Fluid Flow

The type of flow in which the velocity is a function of time and one space coordinate is called 1-D flow. There is only one velocity component in 1-D flow. In 2-D flow, the velocity has two components in directions perpendicular to each other, say x- and y-direction, and can be expressed as a function of time and two rectangular space coordinates. When the velocity is a function of time and 3 space coordinates, the flow is 3-dimensional. 

  1. Rotational or Irrotational Flow

In rotational fluid flow, fluid particles rotate on their own axis while flowing along the streamline. When the fluid flows along the streamline and there is no rotation of the particle on its own axis, the flow is irrotational. 

  1. Laminar or Turbulent Flow

In laminar flow, fluid particles move along streamlines that are straight and parallel. Laminar flow moves along well-defined paths in fluid layers that are laid one over the other. Laminar flow is also called streamlined or viscous flow. When the fluid particles move in an agitated way and form eddies (which lead to high energy loss), then the flow is turbulent. 

Let’s see how laminar and turbulent flow can be determined from Reynolds number

Defining Reynolds Number

Aerodynamics engineers determine flow type using a dimensional quantity called Reynolds number. Fluid can be gas or liquid, and the value of the Reynolds number can be used to classify the flow type. Reynolds number gives the ratio of inertial forces to viscous forces in a fluid. In small dimensional objects with considerably less inertia, where fluid flow is mainly driven by viscous forces, Reynolds number is small. As the dimension of the object increases, so does Reynolds number. With the increase in dimension, inertial forces dominate over viscous forces and Reynolds number attains a higher value.

Reynolds number is significant in categorizing fluid systems where the viscosity of the fluid influences its flow velocity and flow pattern. Reynolds number of flow can be given by the equation:

 Reynolds number equation

V is the velocity, ρ is the density, D is the diameter, and μ is the viscosity. 

Correlating Laminar and Turbulent Types of Flow and Reynolds Number

Depending on Reynolds number, the type of flow can be categorized into either laminar, turbulent, or transient (critical) flow. The range of Reynolds numbers indicates whether the flow is laminar, turbulent, or in transition between the two flow types. The table below gives the limits of Reynolds number and the corresponding flow type. 

Table showing the limits of Reynolds number and type of fluid flow

Correlating the types of flow and Reynolds number provides a better picture of the transport properties of fluid particles in a fluid. Understanding the relationship between Reynolds number and flow types helps engineers solve complex fluid flow problems. 

You can characterize the flow regime in fluid problems using Cadence’s suite of CFD software. This software makes it easy to run CFD simulations in complex fluid-dependent systems to facilitate fluid flow modeling.

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About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

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