2.4 Subsonic, Transonic, and Supersonic Flow

Flow regimes and Mach number are central concepts in aerospace engineering. They determine how air behaves around an aircraft at different speeds, which directly affects drag, lift, and structural loads. Understanding these principles is essential for designing planes that fly efficiently and safely across a wide range of conditions.

As speed increases, compressibility effects grow more significant. In transonic and supersonic regimes, phenomena like shock waves and drag rise change the game for aerodynamic performance. Engineers have to account for all of this when designing high-speed aircraft and spacecraft.

Flow Regimes and Mach Number

Mach number and flow classification

Before diving into the flow regimes, you need to understand the Mach number, since it's the basis for classifying them.

Mach number ($M$) is the ratio of flow velocity ($v$) to the local speed of sound ($a$):

$M = \frac{v}{a}$

The local speed of sound isn't a fixed value. It depends on the fluid's temperature and properties. For an ideal gas:

$a = \sqrt{\gamma R T}$

where $\gamma$ is the specific heat ratio (1.4 for air), $R$ is the specific gas constant (287 J/kg·K for air), and $T$ is the absolute temperature in Kelvin.

This means the speed of sound is higher in warmer air and lower in colder air. At sea level on a standard day ($T = 288$ K), the speed of sound in air is about 340 m/s (roughly 760 mph). At cruising altitude where temperatures drop to around 220 K, it falls to about 295 m/s.

As Mach number increases, compressibility effects become more significant, changing aerodynamic performance and flow behavior. That's why Mach number, not just speed in mph, is what engineers use to classify flow.

Subsonic, transonic, and supersonic flow regimes

• Subsonic flow ($M < 1$): Flow velocity is below the speed of sound everywhere around the aircraft. Density changes are small enough that they can often be neglected, so the air behaves almost as if it's incompressible. Most commercial passenger jets cruise at about $M = 0.78$ to $M = 0.85$, which is high subsonic.
• Transonic flow (roughly $M \approx 0.8$ to $1.2$): Flow velocity is near the speed of sound. The tricky part here is that even though the aircraft itself may be flying just below $M = 1$, air accelerating over curved surfaces (like the top of a wing) can locally exceed $M = 1$. This creates a mixture of subsonic and supersonic flow regions on the same aircraft, which leads to shock waves and other complex phenomena. Modern fighter jets and commercial airliners at cruise both operate in or near this regime.
• Supersonic flow ($M > 1$): Flow velocity exceeds the speed of sound. Significant compressibility effects and density changes are unavoidable. Shock waves and expansion waves are the dominant flow features. Examples include military jets at full speed, rockets, and missiles.

Flow Phenomena and Compressibility Effects

Flow phenomena in each regime

Subsonic flow is relatively smooth and continuous. Compressibility effects are generally negligible, and the flow behaves predictably. This is the regime you'd see in a low-speed wind tunnel.

Transonic flow is where things get complicated. As local flow over a surface accelerates past $M = 1$, shock waves can form on airfoils and other surfaces. There are two main types:

1. Normal shock waves: Perpendicular to the flow direction. These cause abrupt, sudden changes in pressure, temperature, and density. The flow behind a normal shock is always subsonic.
2. Oblique shock waves: Inclined at an angle to the flow direction. These cause more gradual changes in flow properties, and the flow behind them can remain supersonic (though slower).

Transonic flow also produces shock-induced flow separation, where the sharp pressure rise across a shock wave causes the boundary layer to detach from the surface. This leads to increased drag and buffeting.

Supersonic flow is dominated by shock waves and expansion waves. Two notable phenomena:

• Sonic booms: As shock waves propagate away from a supersonic object, they coalesce into strong pressure disturbances that reach the ground as a boom. The Concorde, for example, was restricted from supersonic flight over land partly because of this.
• Mach cones: A supersonic object creates a conical region of influence bounded by Mach waves (weak shock waves). The half-angle of the cone is given by $\sin(\mu) = \frac{1}{M}$, so the faster the object, the narrower the cone.

Compressibility effects on aerodynamics

How compressibility affects design depends heavily on the flow regime:

Subsonic: Compressibility effects are usually negligible. Aerodynamic performance is primarily influenced by Reynolds number and airfoil shape. Think propeller-driven aircraft and low-speed flight. Standard airfoil theory works well here.

Transonic: Compressibility effects become significant, and several problems emerge:

• Transonic drag rise: As Mach number approaches 1, drag increases rapidly. This is sometimes called the "sound barrier" in popular culture, though it's not a literal barrier. The drag coefficient can increase by a factor of 2 to 3 or more near $M = 1$.
• Shock waves cause flow separation, which reduces lift and increases drag simultaneously.
• Control surfaces lose effectiveness due to shock-induced separation. A classic example is aileron buzz, where shock oscillations cause rapid vibration of control surfaces.

To deal with transonic drag rise, engineers use swept wings. Sweeping the wing back effectively reduces the component of flow velocity perpendicular to the wing's leading edge, delaying the onset of shock formation to a higher flight Mach number.

Supersonic: Compressibility effects dominate all aspects of the flow:

• Wave drag becomes a primary drag component, so thin, highly swept or delta wings are used to minimize it. The SR-71 Blackbird is a classic example, with its slender shape optimized for sustained $M = 3.2$ flight.
• Aerodynamic heating becomes a serious concern because kinetic energy of the high-speed flow converts to thermal energy near surfaces. The Space Shuttle's thermal protection tiles were designed specifically to handle reentry heating at hypersonic speeds.
• Control surfaces must be designed to work in the presence of shock waves and expansion waves. Delta wings are common on supersonic aircraft because they maintain controllability across a wide speed range.