Critical Mach number

Two different quantities are referred to as the critical Mach number .

Critical Mach number in aviation

On the one hand, the critical Mach number Ma _krit is a term used in aviation . It is to those flight Mach number , in which at a certain point of the aircraft occur for the first time sonic conditions ( sonically denotes the transition from subsonic to supersonic flow , so Mach number = 1). Since the flow velocity at the top of the wing profile is higher than the airspeed , areas with supersonic flow usually occur first at the top of the wing .

In simple terms, even if the aircraft itself is flying at less than the speed of sound , currents at the speed of sound can already occur at individual points in the flow around the aircraft. This airspeed is expressed by the critical Mach number . ${\ displaystyle {\ text {Ma}} _ {krit} \ leq 1}$

With increasing Mach number, the locally sonic area develops into a supersonic area, which is closed with a straight shock wave ; this occurs when the flow crosses from the supersonic to the subsonic range. By exceeding the critical Mach number and the associated emergence of a straight shock wave there may be a separation of the boundary layer are behind the shock wave, the Shock stable (see Coffin Corner ).

The critical Mach number Ma _crit depends on the angle of attack , the wing sweep and the profile thickness .

Critical Mach number, Laval number

The critical Mach number or Laval number M * is also a similarity index in which the flow velocity u is related to the critical sound velocity c * .

The simple Mach number Ma is the ratio of the local flow velocity u to the local speed of sound c , which is determined by the local temperature T :

{\ displaystyle {\ text {Ma}} = {\ frac {u} {c}} = {\ frac {u} {\ sqrt {\ kappa \ cdot R_ {s} \ cdot T}}}}

With

the isentropic exponent ${\ displaystyle \ kappa}$
the specific gas constant ${\ displaystyle R_ {s}.}$

In contrast, the critical Mach number M * is the ratio of the local flow velocity u to the critical sound velocity c * , which is present where the flow velocity is the same as the sound velocity. The critical temperature T * prevails there , which is in a fixed ratio to the rest temperature T _t :

{\ displaystyle M ^ {*} = {\ frac {u} {c ^ {*}}} = {\ frac {u} {\ sqrt {\ kappa \ cdot R_ {s} \ cdot T ^ {*}} }} = {\ frac {u} {\ sqrt {{\ frac {2 \ cdot \ kappa} {\ kappa +1}} \ cdot R_ {s} \ cdot T_ {t}}}}}