# The Significance of Reynolds Number in the Aerodynamic Performance of Aerofoils

### Key Takeaways

• In aerodynamic systems, the values of the Reynolds number and Mach number give insight into the flow type.

• The ratio of pressure forces to the viscous shear acting on the aerodynamic body can be described as the Reynolds number.

• The critical Reynolds is the Reynolds number at which laminar flow becomes turbulent. The laminar flow transitions to turbulent flow with an increase in fluid flow velocity

In fluid dynamics, the Reynolds number is used to give a sense of the relationship between the viscous forces and the internal forces acting in a fluid. Reynolds number gives insight into the type of fluid flow.

The fluid flow regimes – laminar and turbulent flows – are of great importance in aerodynamics. For example, in an airplane, the friction drag on the aircraft increases as the fluid flow becomes turbulent. This is an example of the relevance of the Reynolds number in aerodynamics.

## Dimensionless Analysis in Aerodynamics

Identifying the nature of fluid flow is important in the design of aerodynamic systems. The nature of the fluid flow can be identified using dimensional analysis and dimensionless analysis. Dimensionless analysis determines the nature of fluid flow and deals with two main parameters:

1. Reynolds number
2. Mach number

The values of the Reynolds number and Mach number give insight into the flow type.

## The Significance of Reynolds Number in Aerodynamics

The ratio of pressure forces to the viscous shear acting on the aerodynamic body can be described as the Reynolds number. Reynolds number is the measure of the importance of pressure forces relative to shear forces. The comparison between pressure forces and shear forces given by the Reynolds number indicates the decrease in viscous forces for a large value of the Reynolds number.

The Reynolds numbers of common aerodynamic bodies, both living and non-living, are given in the table below. The value of the Reynolds number is large; this way, the flow can be regarded as inviscid. Otherwise, the viscous forces are not that significant in the above-listed air bodies. The only case where the viscous shear becomes significant is the areas near solid surfaces, called boundary layers. At boundary layers, the viscous shear forces are strong and form the wake trailing downstream.

## Reynolds Number and Fluid Flow Type

Reynolds number reveals the effect of fluid viscosity in controlling the flow pattern or velocity of the fluid. Mathematically, the Reynolds number can be given by the following equation, taking into account the flow parameters and fluid properties: Note that p is the density of the fluid, v is the velocity of the fluid, l is the characteristic length of the fluid flow, u is the dynamic viscosity of the fluid, and v is the kinematic viscosity of the fluid.

Generally, the Reynolds number describes the degree of laminar or turbulent fluid flow. The value of the Reynolds number determines whether the flow is laminar or turbulent. When the Reynolds number is between 2300 and 4000, the fluid flow is assumed to be transient. As the Reynolds number increases above 4000, the fluid flow becomes turbulent. Reynolds numbers with a value of less than 2300 indicate a laminar flow of the fluid.

## Critical Reynolds Number

As we have seen the correlation of laminar and turbulent flow with Reynolds number, it is clear that the transition from laminar to turbulent flow brings variations in drag, pressure, and aerodynamic characteristics of an object in the air. The flow transition is influenced by surface geometry, and all these can be characterized using a single dimensionless parameter called the critical Reynolds number.

The critical Reynolds number corresponds to the transition between the laminar and turbulent flow. It is the Reynolds number at which laminar flow becomes turbulent. For example, consider the laminar flow over a smooth flat plate. The transition from laminar to turbulent starts at a Reynolds number of 1×105. However, the full transition to turbulent flow is reached at even higher values. The critical Reynolds number for flows over smooth flat plates is 5×105.

The critical Reynolds number for flows above flat plates is dependent on turbulence level, surface roughness, pressure variations along the surface, etc. The value of the critical Reynolds number decreases as the thickness of the body varies from flat plate to blunt body.

## Aerofoils and Reynolds Number

In aerodynamics, the study of aerofoils is highly significant. Analyzing the aerofoil for decreasing Reynolds number, an increase in drag and a decrease in lift can be observed. This analysis can help identify how strong the influence of the Reynolds number on the aerodynamic performance of the aerofoil is. The effects of various projecting tabs (for example, gurney flaps) on the aerofoil can be predetermined from aerofoil modeling and performance analysis for varying Reynolds numbers.

Aerofoils are used in applications involving wind turbines, aircraft, propellers, and fans. The aerodynamic performance of aerofoils in all these applications is associated with the laminar-turbulent transition. An aerofoil profile tailored to meet its application improves the aerodynamic performance of the air body. Evaluating critical Reynolds numbers in the aerodynamic performance of aerofoils aids in ensuring the aerofoil design matches the requirements of the application.

Cadence can help you model the aerofoils in aircraft such that their aerodynamic performance is enhanced through design revisions. Cadence CFD tools can be utilized to design aerodynamic systems to improve the performance of aircraft, space vehicles, turbines, and propellers.