Handbook of Compressible Aerodynamics

Chapter 7

Classification of Flows

7.1. Viscous and non-viscous flows: Euler equations

Real fluids are viscous and heat conductors. These properties, known as transport properties, are the result of movement of molecules, which causes a transfer of momentum and heat within the fluid. However, experience shows that in many situations, these transport effects have little influence on the fluid motion. It is said that we then deal with a non-viscous fluid whose motion is governed by equations where the terms involving viscosity and thermal conductivity have been deleted. They are the Euler equations that are written (for an orthonormal coordinate system):

– continuity equation:

– equation of motion:

– energy equation:

These equations play an important role in aerodynamics as they represent the zero-order approximation of the Navier-Stokes equations corresponding to the limit of the infinite Reynolds number (see section 6.1). In fact, in most classic applications of aerodynamics, the Reynolds numbers are very high, Re_∞ being of the order of tens of millions for an airliner (the reference length is the chord of the wing). The transport term of standard equations (see section 6.1), whose ...