Copyright © A. Filippone (1996-2001). All Rights Reserved.

Atmospheric Flight

In this Chapter

Aerodynamic speeds vary all the way from low subsonic to hypersonic, through a transonic and a supersonic regime. The limits of each regime are summarized on Table 1 in terms of the free stream Mach number. The speed ranges are graphically displayed in Fig. 1 and Fig. 2.

Table 1: speed ranges
Speed Range M
low subsonic < 0.3
high subsonic 0.3-0.6
transonic 0.6-1.1
supersonic 1.0-5.0
hypersonic > 5.

The boundaries are defined by events that change the characteristics of the flow. Most of these changes are gradual, except the M=1 boundary, which is the only case when the flow characteristics change abruptly.

Flow Characteristics

Although the Mach number is used to define the occurrence of some flow features, the basic parameters defining the speed characteristics are three: Reynolds number; Mach number; Knudsen number.

Reynolds Number Effects: Viscosity

The Reynolds number (first introduced by L. Prandtl) dominates the viscous effects by defining the size of the boundary layers.

Almost all aerodynamic flows occur at high Reynolds number, which implies viscous phenomena are limited to narrow boundary layers. The notion high is somewhat arbitrary, although the value of 0.5 × is often the switching boundary.

Flows at Reynolds numbers in the range 0.1 × < Re < 0.5 × are called Low-Reynolds Number Aerodynamics.

Flows at very small Reynolds numbers are dominated by viscosity and are better described with the use of the Stanton number. These flows (sometimes called creeping motions or Stokes flows) are not considered proper domain of aerodynamics.

Fig. 0 below shows the Reynolds number range for some well known cases. The shaded areas denote the very high and very low speeds.

Reynolds number range
Figure 0: Reynolds number range at atmospheric conditions

Mach Number Effects: Compressibility

The Mach number (introduced by J. Ackeret, 1929) defines the appearance of compressibility effects and the changes associated with the shock waves. In the subsonic speed range of Table 1 the compressibility of the flow is negligible.

At transonic speeds there are pockets of flow below and above the speed of sound. The main feature of this speed range is the presence of compression and expansion shock waves.

A supersonic flow is exclusively above the speed of sound. Supersonic aerodynamics differs from aerodynamics at lower speeds because the flow is highly compressible.

The Reynolds and Mach numbers are independent and are both needed to define the characteristics of speeds in the transonic regime. At subsonic speeds the flow is generally treated as a constant-density flow and the Mach number influence is neglected.

Knudsen Number Effects: Molecular Flow

Flows at higher Mach numbers are object of hypersonics (a term due to Tsien, 1946). Other definitions sometimes used for this speed regime is gasdynamics, rarefied gasdynamics and magnetogasdynamics for yet higher speeds.

Two more dimensionless parameters are useful to describe the physics: the Knudsen number and the Damkölher ratio (e.g. the ratio between the ratio between a characteristic time and the molecular relaxation time). The Knudsen number is not quite independent, since it can also be written as a ratio between Mach and Reynolds numbers.

Flows at Knudsen numbers Kn >> 1 are basically collisionless flows (artificial artificial satellites in orbital motion above the Earth); flows at Kn < 1 are in a regime of slight rarefaction, and are called slip flows; flows at intermediate Knudsen numbers are called transitional flows. These flows require some modeling of the molecular gas, and are beyond the domain of validity of the Navier-Stokes equations.

At speeds above M=5 there are changes in the physics of the flow, because of changes in the medium and of the aero- thermodynamic heating. At M > 7 the medium becomes chemically reactive; at M > 12 it is also ionized. The energy produced by the propulsion system is used to overcome the resistance of the flight vehicle (drag), and is converted into compression work on the surrounding medium.

Figure 1: iso-Mach number in atmosphere

Figure 2: iso-Reynolds number in atmosphere

Related Material (in CD-ROM version)

  • Limits of Aeronautic/Aerospace Flight
  • Limits of Aero-Thermodynamic Heating
  • Atmospheric Data

Selected References

  • Shapiro A. The Dynamics and Gas Dynamics of Compressible Fluid Flow; Ronald Press, 1956.

  • Kuethe AM, Chow CY. Foundations of Aerodynamics; McGraw-Hill, 1997 (fifth edition).

  • Ashley H. Engineering Analysis of Flight Vehicles, Addison-Wesley, 1974.

  • Miele A. Flight Mechanics; Addison-Wesley, 1962.

Full Reference List (with book reviews)

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Copyright © A. Filippone (1996-2001). All Rights Reserved.