Study on the supersonic unsteady aerodynamic force for the morphing airfoil

The two-dimensional small-perturbation equations governing the supersonic flow past the morphing airfoils are calculated using the boundary element method based upon the Green formula.The supersonic unsteady aerodynamic characteristics for morphing airfoil are studied analytically and numerically.The numerical calculations show that the additional unsteady aerodynamic lift caused by the virtual mass force is much more sensitive to the thickness variation than the chord length and chamber variations.When the airfoil performs the deformation only by changing its chord length or chamber,the unsteady aerodynamic lift can be very well approximated by the pseudo-steady aerodynamic lift.For the supersonic morphing airfoil,similar to the incompressible and subsonic cases,the lift of morphing airfoil is approximately equal to the lift of quasi-steady solution adding the corresponding virtual mass force,which is independent of the evolutionary history of deformation.The aerodynamic characteristics of the morphing airfoil during reciprocating deformation are investigated.In sharp contrast to the subsonic cases,it is shown that the energy input to implement the reciprocating deformation for supersonic flow will decrease with increasing the free-stream Mach number and eventually tends to a constant limit.The energy input Ainduced by the virtual mass force is independent of the angle of attack and has a simple mathematical relation with the acceleration rates aof the geometry parameter variations:A ∝a～(1/2).