The Significance of the Critical Mach Number in Aerodynamics

Key Takeaways

• The Mach number provides a comparison between fluid flow rate and the speed of sound.

• This metric is important in aerodynamics, as certain forces will increase as an aircraft approaches a critical Mach number.

• The critical Mach number can be determined from fluid flow simulation along the body of an aircraft.

Although aircraft and fluid flow with regard to aircraft are complex systems, the primary forces and principles involved in studying aerodynamics are rather simple. We often discuss aerodynamics and aircraft in the context of low relative airspeeds, where the craft is traveling below the speed of sound. The ratio of airflow to the speed of sound is known as the Mach number, and this will define some important characteristics of fluid flow behavior along the body of an aircraft.

During flight, as an aircraft accelerates and eventually reaches the Mach number, an approach to the speed of sound will have important implications on the aircraft’s motion and total energy. It can also affect the ability of an aircraft to maintain its flight trajectory without experiencing stall, excessive drag, or loss of control due to buffeting. In this article, we’ll examine what happens when an aircraft approaches the critical Mach number as well as the resulting effects once the Mach number is exceeded.

What Is the Critical Mach Number?

When airflow occurs across an aircraft during flight, it is not uniform along the airframe. When airflow over any portion of the aircraft approaches the speed of sound, flight characteristics will begin to change, which we will discuss below. We can compare the relative airflow speed at different regions along the craft to the speed of sound using the Mach number (Ma) as described below:

Mach number definition

There is a critical Mach number, which will depend on the slowest part of the local flow velocity across the body of an aircraft. Specifically, the critical Mach number is the slowest free stream Mach number at which the airflow along any other area of the aircraft reaches Ma = 1. In other words, the moment at which the fastest portion of the airflow equals the speed of sound, then the flow and the craft velocity have reached the critical Mach number.

What Happens at the Critical Mach Number?

On the approach to the critical Mach number, the airflow exerts oscillatory (vibration) forces on the structure of the aircraft. This is known as buffeting, which occurs as Ma = 1 is approached, which is felt by the pilot as heavy vibrations. Once the speed of sound is exceeded for the entire flow, flight will feel smooth again. In terms of airflow, a shockwave occurs once the critical Mach number is exceeded, which will be heard by any surrounding observers.

Visually, this is examined by looking at spherical wavefronts produced by the moving aircraft. The aircraft will cause air compression along the leading edge of the airframe, and this air compression will then cause the emission of spherical acoustic waves around the front edge of the aircraft. At the front edge of the craft’s nose cone, these air fronts pile up and eventually produce high compression along the front face of the aircraft when the limit of Ma = 1 in this region.

Wavefronts pile up along the front of the craft when Ma = 1 is approached. When Ma > 1, a shockwave occurs as the aircraft exceeds the speed of sound

This point at which the airflow around the craft approaches the speed of sound, as well as other fluid flow effects that result from such a shockwave event, will depend on the shape and speed of the aircraft. How fluid flow along an aircraft is affected by its shape, and the forces exerted on the aircraft when approaching the critical Mach number, can be examined with CFD simulations. In particular, the critical Mach number can be determined directly from flow simulations, as outlined below.

Determine the Critical Mach Number From CFD Simulations

Aircraft designed for transonic or faster flights are specifically designed to endure the oscillatory shocks that occur when airspeeds approach the speed of sound. The shape of the aircraft will be the biggest influence of its flight characteristics. While we discussed Mach number in terms of airspeed across the airframe during transonic or faster flight, this creates multiple effects that need to be examined in a CFD simulation.

Because the speed of airflow around an aircraft will not be exactly the same as the oncoming airflow rate, the relative speed air across an aircraft needs to be determined to assess the Mach number. Due to this difference between actual aircraft speed and airflow speed, different aircraft will experience different forces when approaching the speed of sound. Some of the points that should be studied at such high airspeeds include:

• Relative airflow speeds across the top and bottom sides of the aircraft body and wings, producing lift.
• Drag at high airspeeds, which will increase during the shockwave produced near the speed of sound.
• The possible transition to turbulent flow across the back edge of the aircraft, which will affect drag.
• Structural forces due to buffeting as the speed of sound is approached, which will affect the ability to control the craft.

Wavefronts due to a shockwave can also be visualized from fluid flow simulations by examining the fluid pressure around the aircraft. An example of this is shown below, where the pressure fronts around a jet aircraft moving above the speed of sound can be clearly seen.

Pressure fronts can be used to identify shockwaves that arise when the critical Mach number is exceeded

Whenever you want to study shockwaves and flight instabilities near the critical Mach number, use the complete set of CFD simulation tools in Omnis from Cadence. Modern numerical approaches used in aerodynamic simulations, turbulent and laminar flow simulations, reduced fluid flow models, and much more can be implemented with these tools.