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P. Liu
than 2%. Generally, this flow can be regarded as incompressible approximately; only when Ma number is greater than 0.3, the compressibility effect
can be considered. Different compressibility has different flow characteristics
and different influences on aerodynamics. For the flow around an aircraft, it is
usually divided by the undisturbed Mach number Ma far ahead. When Ma is
less than 0.3, it is similar to the incompressible flow, which is called low-speed
flow; when Ma is between 0.3 and 0.8, it is subsonic flow, at this time, the
influence of compressibility on aerodynamic characteristics can be corrected
by compressibility on the results of low-speed flow. When Ma is between
0.8 and 1.2, it is a transonic flow. At this time, there will be a local supersonic or local subsonic region in the flow field, and generally shock waves will
appear. In this range, the aerodynamic coefficient will change greatly with the
increase in Ma. When Ma is between 1.2 and 5, it is supersonic flow. When
Ma exceeds 5, the flow is hypersonic flow.
From the analysis of the propagation characteristics of the disturbance
wave in the flow field, it can be seen that for the subsonic flow with Ma
number less than 1, the disturbance propagates throughout the whole flow
field. For the supersonic flow with Ma number greater than 1, the disturbance only propagates to the downstream Mach cone. These characteristics
will affect the properties of control equations and the methods of solving
them.
1. Subsonic flow
When the subsonic flow is an inviscid potential flow, the governing equation is a nonlinear second-order elliptic partial differential equation. The
main approximate method to study this kind of flow is the theory of
small perturbation linearization. Prandtl in 1922 and H. Glauert (British
aerodynamic scientist) in 1928 established, respectively, the compressibility correction rule for the subsonic flow, which is called Prandtl and
Glauert rule. According to this law, the influence of compressibility on
aerodynamic characteristics can be obtained by modifying the compressibility of the results of low-speed flow, and it is not necessary to solve
the compressible flow equation. In 1939, von Karman and Qian Xuesen
further amended the Prandtl–Glauert rule and put forward the famous
Karman Qian rule. This law is better to establish the correction relation of
air compressibility to the surface pressure in subsonic flow, and the range
of application is obviously larger than that of Prandtl–Glauert’s rule, especially the correction of the pressure coefficient on the leeward side of the
airfoil is more reasonable.
P. Liu
than 2%. Generally, this flow can be regarded as incompressible approximately; only when Ma number is greater than 0.3, the compressibility effect
can be considered. Different compressibility has different flow characteristics
and different influences on aerodynamics. For the flow around an aircraft, it is
usually divided by the undisturbed Mach number Ma far ahead. When Ma is
less than 0.3, it is similar to the incompressible flow, which is called low-speed
flow; when Ma is between 0.3 and 0.8, it is subsonic flow, at this time, the
influence of compressibility on aerodynamic characteristics can be corrected
by compressibility on the results of low-speed flow. When Ma is between
0.8 and 1.2, it is a transonic flow. At this time, there will be a local supersonic or local subsonic region in the flow field, and generally shock waves will
appear. In this range, the aerodynamic coefficient will change greatly with the
increase in Ma. When Ma is between 1.2 and 5, it is supersonic flow. When
Ma exceeds 5, the flow is hypersonic flow.
From the analysis of the propagation characteristics of the disturbance
wave in the flow field, it can be seen that for the subsonic flow with Ma
number less than 1, the disturbance propagates throughout the whole flow
field. For the supersonic flow with Ma number greater than 1, the disturbance only propagates to the downstream Mach cone. These characteristics
will affect the properties of control equations and the methods of solving
them.
1. Subsonic flow
When the subsonic flow is an inviscid potential flow, the governing equation is a nonlinear second-order elliptic partial differential equation. The
main approximate method to study this kind of flow is the theory of
small perturbation linearization. Prandtl in 1922 and H. Glauert (British
aerodynamic scientist) in 1928 established, respectively, the compressibility correction rule for the subsonic flow, which is called Prandtl and
Glauert rule. According to this law, the influence of compressibility on
aerodynamic characteristics can be obtained by modifying the compressibility of the results of low-speed flow, and it is not necessary to solve
the compressible flow equation. In 1939, von Karman and Qian Xuesen
further amended the Prandtl–Glauert rule and put forward the famous
Karman Qian rule. This law is better to establish the correction relation of
air compressibility to the surface pressure in subsonic flow, and the range
of application is obviously larger than that of Prandtl–Glauert’s rule, especially the correction of the pressure coefficient on the leeward side of the
airfoil is more reasonable.