Module 4 - Calculation of Lift and Drag of a Supersonic Wing Flashcards
the simplest theory used to determine aerodynamic characteristics of airfoils in various shapes along a supersonic flow
Ackeret theory
a linearized, first order
theory based on sweeping assumptions which nevertheless give quite good results provided that the Mach number is not too low and the airfoil section is not too thick
Ackeret theory
two conditions of the use of Ackeret theory
- Mach number is not too low
- airfoil section is not too thick
characteristics of supersonic airfoil section
- thinness
- sharp leading edge
- maximum thickness at half chord
- symmetry
why is thinness a characteristic of supersonic airfoil sections?
to minimize flow deviations due to thick airfoil sections which cause shock losses but should still be subject to the structural requirements of the aircraft
why is a sharp leading edge a characteristic of supersonic airfoil sections?
- to keep an attached bow shockwave on the airfoil section and to avoid losses due to a normal, detached shockwave
- to ensure shockwave attachment at low supersonic speeds
how can a sharp leading edge be done?
by employing low thickness to chord ratio to create a small leading edge angle
why is maximum thickness at half chord a characteristic of supersonic airfoil sections?
it ensures expansion behind the maximum thickness point is comparable to the compressions ahead of it which indicates that this is conducive to low values of drag
why is symmetry a characteristic of supersonic airfoil sections?
- a positive camber results in a positive zero lift angle of attack which implies that the lift is reduced by the camber of the airfoil section
- at slow speeds, the effect of camber is to increase the value of drag
what is the best wing section in theory for a supersonic flow?
an infinitely thin, flat plate
why is an infinitely thin, flat plate not achievable in reality?
because the thinness of the airfoil is dependent on the structural integrity of the aircraft
different types of supersonic airfoil sections
- double wedge or diamond
- biconvex
a type of airfoil that achieves the lowest wave drag for a given thickness-to-chord ratio
double wedge or diamond
diamond airfoils generate the ____________ of lift as compared to a flat plate, however _____________ wave drag is generated by this type of airfoil section
same amount, more
which of the two types of supersonic airfoil sections produce more wave drag than the other with the same thickness-to-chord ratio
biconvex
comparison of the lift produced by a biconvex wing to a diamond one
approximately the same
comparison of the leading edge angle and shock attachment Mach number produced by a biconvex wing to a diamond one
- greater leading edge angle
- higher shock attachment Mach number
what is the reason why a biconvex wing produces a higher shock attachment Mach number than a diamond one?
because of greater leading edge angle of the biconvex wing
the Mach number in which the shockwave will attach to the airfoil
shock attachment Mach number
what is more favorable of the two supersonic airfoil sections considering a point of view for structural requirements? why?
biconvex because it contains more space
Consider a flat plate in a supersonic flow, at zero angle of attack there will be ____________________ that will be produced by the plate due to the supersonic flow. Therefore, there is _______________ and ______________ in flow properties.
no lift or wave drag, no flow deviation, no change
what happens when a flat plate in a supersonic flow when the angle of attack is increased to a positive value?
- the airflow approaching the lower surface is compressed at the leading edge corresponding to the value of the angle of attack which causes a shockwave to form
- the airflow approaching the upper surface expands through the same angle of attack which forms an expansion fan in the upper leading edge of the flat plate
- on the trailing edge, the airflow on the lower surface expands and on the leading edge, the airflow is recompressed generating a shockwave
- after the airflow successfully passes the flat plate, the Mach number of the airflow is of the same value as that of the freestream
angle of deflection produced by the expansion fan and the shockwave
airflow deflection angle
The Ackeret linearized theory is used to show that should the assumptions be justified, the pressure coefficient depends only on the _____________.
net angle Θ
what happens to the values of Mach number, pressure, density, and temperature after passing an oblique shockwave
- Mach number decreases
- pressure increases
- density increases
- temperature increases
what happens to the values of Mach number, pressure, density, and temperature after passing an expansion fan
- Mach number increases
- pressure decreases
- density decreases
- temperature decreases
who proposed the Ackeret theory and when?
Jacob Ackeret, 1940
