This paper is devoted to application of the Reduced-Order Model (ROM) based on Volterra series to prediction of lift and drag forces due to airfoil periodic translation in transonic flow region. When there is large amplitude oscillation of the relative Mach number, as appeared in helicopter rotor movement in forward flight, the conventional Volterra ROM is found to be unsatisfactory. To cover such applications, a matched Volterra ROM, inspired from previous multistep nonlinear indicial response method based on Duhamel integration, is thus considered, in which the step motions are defined inside a number of equal intervals with both positive and negative step motions to match the airfoil forward and backward movement, and the kernel functions are constructed independently at each interval. It shows that, at least for the translation movement considered, this matched Volterra ROM greatly improves the accuracy of prediction. Moreover, the matched Volterra ROM, with the total number of step motions and thus the computational cost close to those of the conventional Volterra ROM method, has the additional advantage that the same set of kernels can match various translation motions with different starting conditions so the kernels can be predesigned without knowing the specific motion of airfoil.

Symmetric Mach reflection in steady supersonic flow has been usually studied by solving a half-plane problem with the symmetric line treated as reflecting surface, thus losing the opportunity to discover antisymmetric flow structures. Here in this paper we treat this problem as an entire-plane problem. Using an unsteady numerical approach, we find that the two sliplines exhibit antisymmetric unsteadiness if the Mach stem height is small while the flow remains symmetric if the Mach stem height is large. The mechanism by which disturbance, generated in the downstream of the flow duct between the two sliplines, propagates upstream is identified and it is also shown that the interaction between the transmitted expansion waves and the sliplines increases the amplitude of the unstable modes. The present study suggests a new type of compressible jet that deserves further studies.

The transit time difference of fluid particles moving along the upper and lower surfaces of a lift-producing airfoil is studied here both theoretically and numerically. We show that, under thin airfoil assumption and for potential flow, the transit time difference is equal to the circulation divided by the square of the inflow velocity and the lift coefficient is equal to half of the number of chords travelled by the airfoil during the transit time difference. An analysis of transit time difference for very thick airfoil (c.f. very large angle of attack) suggests the transit time may change sign beyond thin airfoil assumption, a conclusion supported by an example of flow with an attached vortex. Thus, fluid particles may transit the upper surface with less, equal and more time than those transiting the lower surface for lift producing airfoils, depending on the configuration of flow structure and geometry.